Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 69.9% → 99.5%

Time: 1.2min

Alternatives: 26

Speedup: 6.0×

• 46.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 69.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	t_3 = Float64(fma(x1, Float64(x1 * 3.0), Float64(Float64(2.0 * x2) - x1)) / fma(x1, x1, 1.0))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)))) + Float64(t_0 * t_2)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1)))) <= Inf)
		tmp = Float64(x1 + fma(3.0, Float64(Float64(t_0 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), Float64(x1 + fma(fma(x1, x1, 1.0), fma(x1, Float64(x1 * fma(t_3, 4.0, -6.0)), Float64(t_3 * Float64(Float64(x1 * 2.0) * Float64(t_3 + -3.0)))), fma(t_0, t_3, (x1 ^ 3.0))))));
	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[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision] + N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(3.0 * N[(N[(t$95$0 - N[(2.0 * x2 + x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * x1 + 1.0), $MachinePrecision] * N[(x1 * N[(x1 * N[(t$95$3 * 4.0 + -6.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 * N[(N[(x1 * 2.0), $MachinePrecision] * N[(t$95$3 + -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$3 + N[Power[x1, 3.0], $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 99.7%

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

   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 10.1%

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

      1. *-commutative 10.1%

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

   4. Simplified 10.1%

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

   5. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.8%

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

Alternative 2: 99.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_2)
	t_4 = Float64(Float64(fma(Float64(x1 * 3.0), x1, Float64(2.0 * x2)) - x1) / fma(x1, x1, 1.0))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_2 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(t_3 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0)))) + Float64(t_1 * t_3)) + t_0)) + Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2)))) <= Inf)
		tmp = Float64(x1 + Float64(Float64(t_0 + fma(fma(Float64(Float64(x1 * 2.0) * t_4), Float64(-3.0 + t_4), Float64(Float64(x1 * x1) * fma(4.0, t_4, -6.0))), fma(x1, x1, 1.0), Float64(t_1 * t_4))) + Float64(x1 + Float64(3.0 * Float64(Float64(Float64(t_1 + Float64(x2 * -2.0)) - x1) / fma(x1, x1, 1.0))))));
	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[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(N[(x1 * 3.0), $MachinePrecision] * x1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$2 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * t$95$3), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(N[(t$95$0 + N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(-3.0 + t$95$4), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(4.0 * t$95$4 + -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x1 * x1 + 1.0), $MachinePrecision] + N[(t$95$1 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(3.0 * N[(N[(N[(t$95$1 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $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 99.4%

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

   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 10.1%

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

      1. *-commutative 10.1%

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

   4. Simplified 10.1%

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

   5. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.6%

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

Alternative 3: 99.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_2}\\ t_4 := t_1 \cdot t_3\\ t_5 := \left(\left(x1 \cdot 2\right) \cdot t_3\right) \cdot \left(t_3 - 3\right)\\ t_6 := 3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_2}\\ \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(t_2 \cdot \left(t_5 + \left(x1 \cdot x1\right) \cdot \left(t_3 \cdot 4 - 6\right)\right) + t_4\right) + t_0\right)\right) + t_6\right) \leq \infty:\\ \;\;\;\;x1 + \left(t_6 + \left(x1 + \left(t_0 + \left(t_4 + t_2 \cdot \left(t_5 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(\frac{\mathsf{fma}\left(x1 \cdot 3, x1, x2 + x2\right)}{\mathsf{fma}\left(x1, x1, 1\right)} - \frac{x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \end{array} \end{array} \]

FPCore

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

C

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

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_2)
	t_4 = Float64(t_1 * t_3)
	t_5 = Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(t_3 - 3.0))
	t_6 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_2 * Float64(t_5 + Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0)))) + t_4) + t_0)) + t_6)) <= Inf)
		tmp = Float64(x1 + Float64(t_6 + Float64(x1 + Float64(t_0 + Float64(t_4 + Float64(t_2 * Float64(t_5 + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(Float64(fma(Float64(x1 * 3.0), x1, Float64(x2 + x2)) / fma(x1, x1, 1.0)) - Float64(x1 / fma(x1, x1, 1.0)))) - 6.0)))))))));
	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[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$1 * t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$2 * N[(t$95$5 + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(t$95$6 + N[(x1 + N[(t$95$0 + N[(t$95$4 + N[(t$95$2 * N[(t$95$5 + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(N[(N[(N[(x1 * 3.0), $MachinePrecision] * x1 + N[(x2 + x2), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] - N[(x1 / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $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%

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

      1. fma-def 99.4%

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

      2. div-sub 99.4%

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

      3. fma-def 99.4%

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

      4. count-2 99.4%

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

   3. Applied egg-rr 99.4%

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

   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 10.1%

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

      1. *-commutative 10.1%

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

   4. Simplified 10.1%

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

   5. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.5%

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

Alternative 4: 99.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_2}\\ t_4 := t_1 \cdot t_3\\ t_5 := \left(\left(x1 \cdot 2\right) \cdot t_3\right) \cdot \left(t_3 - 3\right)\\ t_6 := 3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_2}\\ \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(t_2 \cdot \left(t_5 + \left(x1 \cdot x1\right) \cdot \left(t_3 \cdot 4 - 6\right)\right) + t_4\right) + t_0\right)\right) + t_6\right) \leq \infty:\\ \;\;\;\;x1 + \left(t_6 + \left(x1 + \left(t_0 + \left(t_4 + t_2 \cdot \left(t_5 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\mathsf{fma}\left(x1 \cdot 3, x1, x2 + x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \end{array} \end{array} \]

FPCore

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

C

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

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_2)
	t_4 = Float64(t_1 * t_3)
	t_5 = Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(t_3 - 3.0))
	t_6 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_2 * Float64(t_5 + Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0)))) + t_4) + t_0)) + t_6)) <= Inf)
		tmp = Float64(x1 + Float64(t_6 + Float64(x1 + Float64(t_0 + Float64(t_4 + Float64(t_2 * Float64(t_5 + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(Float64(fma(Float64(x1 * 3.0), x1, Float64(x2 + x2)) - x1) / fma(x1, x1, 1.0))) - 6.0)))))))));
	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[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$1 * t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$2 * N[(t$95$5 + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(t$95$6 + N[(x1 + N[(t$95$0 + N[(t$95$4 + N[(t$95$2 * N[(t$95$5 + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(N[(N[(N[(x1 * 3.0), $MachinePrecision] * x1 + N[(x2 + x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $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%

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

      1. fma-def 99.4%

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

      2. div-sub 99.4%

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

      3. fma-def 99.4%

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

      4. count-2 99.4%

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

   3. Applied egg-rr 99.4%

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

      1. div-sub 99.4%

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

   5. Simplified 99.4%

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

   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 10.1%

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

      1. *-commutative 10.1%

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

   4. Simplified 10.1%

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

   5. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.5%

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

Alternative 5: 99.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   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 10.1%

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

      1. *-commutative 10.1%

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

   4. Simplified 10.1%

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

   5. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.5%

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

Alternative 6: 94.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 9\right) - x1\\ t_2 := x1 \cdot \left(x1 \cdot x1\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := \frac{\left(t_3 + 2 \cdot x2\right) - x1}{t_0}\\ t_5 := \left(x1 \cdot x1\right) \cdot \left(t_4 \cdot 4 - 6\right)\\ t_6 := \left(x1 \cdot 2\right) \cdot t_4\\ t_7 := x1 + \left(\left(x1 + \left(\left(t_0 \cdot \left(t_6 \cdot \left(t_4 - 3\right) + t_5\right) + t_3 \cdot t_4\right) + t_2\right)\right) + 9\right)\\ \mathbf{if}\;x1 \leq -6.5 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq -0.0035:\\ \;\;\;\;t_7\\ \mathbf{elif}\;x1 \leq 1.15:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_3 - 2 \cdot x2\right) - x1}{t_0} + \left(x1 + \left(t_2 + \left(t_0 \cdot \left(t_5 + t_6 \cdot \left(\left(x2 + x2\right) - 3\right)\right) + t_3 \cdot \left(x2 + x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{+153}:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (- (* x1 (* x1 9.0)) x1))
        (t_2 (* x1 (* x1 x1)))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (/ (- (+ t_3 (* 2.0 x2)) x1) t_0))
        (t_5 (* (* x1 x1) (- (* t_4 4.0) 6.0)))
        (t_6 (* (* x1 2.0) t_4))
        (t_7
         (+
          x1
          (+
           (+ x1 (+ (+ (* t_0 (+ (* t_6 (- t_4 3.0)) t_5)) (* t_3 t_4)) t_2))
           9.0))))
   (if (<= x1 -6.5e+104)
     t_1
     (if (<= x1 -0.0035)
       t_7
       (if (<= x1 1.15)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_3 (* 2.0 x2)) x1) t_0))
           (+
            x1
            (+
             t_2
             (+
              (* t_0 (+ t_5 (* t_6 (- (+ x2 x2) 3.0))))
              (* t_3 (+ x2 x2)))))))
         (if (<= x1 1e+153) t_7 t_1))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = (x1 * (x1 * 9.0)) - x1;
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	double t_5 = (x1 * x1) * ((t_4 * 4.0) - 6.0);
	double t_6 = (x1 * 2.0) * t_4;
	double t_7 = x1 + ((x1 + (((t_0 * ((t_6 * (t_4 - 3.0)) + t_5)) + (t_3 * t_4)) + t_2)) + 9.0);
	double tmp;
	if (x1 <= -6.5e+104) {
		tmp = t_1;
	} else if (x1 <= -0.0035) {
		tmp = t_7;
	} else if (x1 <= 1.15) {
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0)) + (x1 + (t_2 + ((t_0 * (t_5 + (t_6 * ((x2 + x2) - 3.0)))) + (t_3 * (x2 + x2))))));
	} else if (x1 <= 1e+153) {
		tmp = t_7;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = (x1 * (x1 * 9.0d0)) - x1
    t_2 = x1 * (x1 * x1)
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = ((t_3 + (2.0d0 * x2)) - x1) / t_0
    t_5 = (x1 * x1) * ((t_4 * 4.0d0) - 6.0d0)
    t_6 = (x1 * 2.0d0) * t_4
    t_7 = x1 + ((x1 + (((t_0 * ((t_6 * (t_4 - 3.0d0)) + t_5)) + (t_3 * t_4)) + t_2)) + 9.0d0)
    if (x1 <= (-6.5d+104)) then
        tmp = t_1
    else if (x1 <= (-0.0035d0)) then
        tmp = t_7
    else if (x1 <= 1.15d0) then
        tmp = x1 + ((3.0d0 * (((t_3 - (2.0d0 * x2)) - x1) / t_0)) + (x1 + (t_2 + ((t_0 * (t_5 + (t_6 * ((x2 + x2) - 3.0d0)))) + (t_3 * (x2 + x2))))))
    else if (x1 <= 1d+153) then
        tmp = t_7
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = (x1 * (x1 * 9.0)) - x1;
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	double t_5 = (x1 * x1) * ((t_4 * 4.0) - 6.0);
	double t_6 = (x1 * 2.0) * t_4;
	double t_7 = x1 + ((x1 + (((t_0 * ((t_6 * (t_4 - 3.0)) + t_5)) + (t_3 * t_4)) + t_2)) + 9.0);
	double tmp;
	if (x1 <= -6.5e+104) {
		tmp = t_1;
	} else if (x1 <= -0.0035) {
		tmp = t_7;
	} else if (x1 <= 1.15) {
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0)) + (x1 + (t_2 + ((t_0 * (t_5 + (t_6 * ((x2 + x2) - 3.0)))) + (t_3 * (x2 + x2))))));
	} else if (x1 <= 1e+153) {
		tmp = t_7;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = (x1 * (x1 * 9.0)) - x1
	t_2 = x1 * (x1 * x1)
	t_3 = x1 * (x1 * 3.0)
	t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0
	t_5 = (x1 * x1) * ((t_4 * 4.0) - 6.0)
	t_6 = (x1 * 2.0) * t_4
	t_7 = x1 + ((x1 + (((t_0 * ((t_6 * (t_4 - 3.0)) + t_5)) + (t_3 * t_4)) + t_2)) + 9.0)
	tmp = 0
	if x1 <= -6.5e+104:
		tmp = t_1
	elif x1 <= -0.0035:
		tmp = t_7
	elif x1 <= 1.15:
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0)) + (x1 + (t_2 + ((t_0 * (t_5 + (t_6 * ((x2 + x2) - 3.0)))) + (t_3 * (x2 + x2))))))
	elif x1 <= 1e+153:
		tmp = t_7
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(Float64(x1 * Float64(x1 * 9.0)) - x1)
	t_2 = Float64(x1 * Float64(x1 * x1))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(Float64(Float64(t_3 + Float64(2.0 * x2)) - x1) / t_0)
	t_5 = Float64(Float64(x1 * x1) * Float64(Float64(t_4 * 4.0) - 6.0))
	t_6 = Float64(Float64(x1 * 2.0) * t_4)
	t_7 = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_0 * Float64(Float64(t_6 * Float64(t_4 - 3.0)) + t_5)) + Float64(t_3 * t_4)) + t_2)) + 9.0))
	tmp = 0.0
	if (x1 <= -6.5e+104)
		tmp = t_1;
	elseif (x1 <= -0.0035)
		tmp = t_7;
	elseif (x1 <= 1.15)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_3 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 + Float64(t_2 + Float64(Float64(t_0 * Float64(t_5 + Float64(t_6 * Float64(Float64(x2 + x2) - 3.0)))) + Float64(t_3 * Float64(x2 + x2)))))));
	elseif (x1 <= 1e+153)
		tmp = t_7;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = (x1 * (x1 * 9.0)) - x1;
	t_2 = x1 * (x1 * x1);
	t_3 = x1 * (x1 * 3.0);
	t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	t_5 = (x1 * x1) * ((t_4 * 4.0) - 6.0);
	t_6 = (x1 * 2.0) * t_4;
	t_7 = x1 + ((x1 + (((t_0 * ((t_6 * (t_4 - 3.0)) + t_5)) + (t_3 * t_4)) + t_2)) + 9.0);
	tmp = 0.0;
	if (x1 <= -6.5e+104)
		tmp = t_1;
	elseif (x1 <= -0.0035)
		tmp = t_7;
	elseif (x1 <= 1.15)
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0)) + (x1 + (t_2 + ((t_0 * (t_5 + (t_6 * ((x2 + x2) - 3.0)))) + (t_3 * (x2 + x2))))));
	elseif (x1 <= 1e+153)
		tmp = t_7;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$4 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision]}, Block[{t$95$7 = N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$0 * N[(N[(t$95$6 * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 * t$95$4), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -6.5e+104], t$95$1, If[LessEqual[x1, -0.0035], t$95$7, If[LessEqual[x1, 1.15], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$3 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$2 + N[(N[(t$95$0 * N[(t$95$5 + N[(t$95$6 * N[(N[(x2 + x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 * N[(x2 + x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1e+153], t$95$7, t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -6.5000000000000005e104 or 1e153 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x2 around inf 0.0%

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

      1. associate-*r/ 0.0%

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

      2. unpow2 0.0%

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

      3. +-commutative 0.0%

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

      4. unpow2 0.0%

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

      5. fma-udef 0.0%

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

   4. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 67.2%

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

      1. *-commutative 67.2%

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

      2. fma-def 67.2%

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

      3. +-commutative 67.2%

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

      4. fma-def 75.9%

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

      5. *-commutative 75.9%

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

      6. fma-neg 75.9%

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

      7. metadata-eval 75.9%

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

      8. unpow2 75.9%

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

      9. associate-*r* 75.9%

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

      10. *-commutative 75.9%

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

      11. associate-*l* 75.9%

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

      12. unpow2 75.9%

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

      13. cancel-sign-sub-inv 75.9%

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

      14. metadata-eval 75.9%

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

      15. +-commutative 75.9%

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

      16. count-2 75.9%

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

   7. Simplified 75.9%

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

   8. Taylor expanded in x2 around 0 90.6%

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

      1. associate-+r+ 90.6%

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

      2. distribute-rgt1-in 90.6%

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

      3. metadata-eval 90.6%

         \[\leadsto \color{blue}{-1} \cdot x1 + 9 \cdot {x1}^{2} \]

      4. neg-mul-1 90.6%

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

      5. +-commutative 90.6%

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

      6. unsub-neg 90.6%

         \[\leadsto \color{blue}{9 \cdot {x1}^{2} - x1} \]

      7. *-commutative 90.6%

         \[\leadsto \color{blue}{{x1}^{2} \cdot 9} - x1 \]

      8. unpow2 90.6%

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

      9. associate-*l* 90.6%

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

   10. Simplified 90.6%

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

   if -6.5000000000000005e104 < x1 < -0.00350000000000000007 or 1.1499999999999999 < x1 < 1e153

   1. Initial program 99.5%

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

   2. Taylor expanded in x1 around inf 97.2%

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

   if -0.00350000000000000007 < x1 < 1.1499999999999999

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 98.8%

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

      1. count-2 98.8%

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

   4. Simplified 98.8%

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

   5. Taylor expanded in x1 around 0 98.8%

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

      1. count-2 98.8%

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

   7. Simplified 98.8%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6.5 \cdot 10^{+104}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \mathbf{elif}\;x1 \leq -0.0035:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 9\right)\\ \mathbf{elif}\;x1 \leq 1.15:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\left(x2 + x2\right) - 3\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \end{array} \]

Alternative 7: 94.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+97} \lor \neg \left(x1 \leq 4 \cdot 10^{+76}\right):\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_0 \cdot t_2 + t_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t_2 \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(\left(x2 + x2\right) - 3\right)\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (if (or (<= x1 -1e+97) (not (<= x1 4e+76)))
     (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) 9.0))
     (+
      x1
      (+
       (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (* t_0 t_2)
          (*
           t_1
           (+
            (* (* x1 x1) (- (* t_2 4.0) 6.0))
            (* (* (* x1 2.0) t_2) (- (+ x2 x2) 3.0))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -1e+97) || !(x1 <= 4e+76)) {
		tmp = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + 9.0);
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((x1 * x1) * ((t_2 * 4.0) - 6.0)) + (((x1 * 2.0) * t_2) * ((x2 + x2) - 3.0))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    if ((x1 <= (-1d+97)) .or. (.not. (x1 <= 4d+76))) then
        tmp = x1 + ((x1 + (6.0d0 * (x1 ** 4.0d0))) + 9.0d0)
    else
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((x1 * x1) * ((t_2 * 4.0d0) - 6.0d0)) + (((x1 * 2.0d0) * t_2) * ((x2 + x2) - 3.0d0))))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -1e+97) || !(x1 <= 4e+76)) {
		tmp = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + 9.0);
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((x1 * x1) * ((t_2 * 4.0) - 6.0)) + (((x1 * 2.0) * t_2) * ((x2 + x2) - 3.0))))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1
	tmp = 0
	if (x1 <= -1e+97) or not (x1 <= 4e+76):
		tmp = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + 9.0)
	else:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((x1 * x1) * ((t_2 * 4.0) - 6.0)) + (((x1 * 2.0) * t_2) * ((x2 + x2) - 3.0))))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if ((x1 <= -1e+97) || !(x1 <= 4e+76))
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + 9.0));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * t_2) + Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)) + Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(Float64(x2 + x2) - 3.0)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	tmp = 0.0;
	if ((x1 <= -1e+97) || ~((x1 <= 4e+76)))
		tmp = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + 9.0);
	else
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((x1 * x1) * ((t_2 * 4.0) - 6.0)) + (((x1 * 2.0) * t_2) * ((x2 + x2) - 3.0))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[x1, -1e+97], N[Not[LessEqual[x1, 4e+76]], $MachinePrecision]], N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * t$95$2), $MachinePrecision] + N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(N[(x2 + x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.0000000000000001e97 or 4.0000000000000002e76 < x1

   1. Initial program 16.9%

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

   2. Taylor expanded in x1 around inf 25.3%

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

      1. *-commutative 25.3%

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

   4. Simplified 25.3%

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

   5. Taylor expanded in x1 around inf 100.0%

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

   if -1.0000000000000001e97 < x1 < 4.0000000000000002e76

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 95.3%

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

      1. count-2 95.0%

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

   4. Simplified 95.3%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+97} \lor \neg \left(x1 \leq 4 \cdot 10^{+76}\right):\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\left(x2 + x2\right) - 3\right)\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 8: 96.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_2}\\ t_4 := \left(x1 \cdot x1\right) \cdot \left(t_3 \cdot 4 - 6\right)\\ t_5 := \left(x1 \cdot 2\right) \cdot t_3\\ t_6 := x1 \cdot \left(x1 \cdot x1\right)\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq -0.034:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t_2 \cdot \left(t_5 \cdot \left(t_3 - 3\right) + t_4\right) + t_0 \cdot t_3\right) + t_6\right)\right) + 9\right)\\ \mathbf{elif}\;x1 \leq 3.5 \cdot 10^{+48}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_2} + \left(x1 + \left(t_6 + \left(t_2 \cdot \left(t_4 + t_5 \cdot \left(\left(x2 + x2\right) - 3\right)\right) + t_0 \cdot \left(x2 + x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) 9.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (/ (- (+ t_0 (* 2.0 x2)) x1) t_2))
        (t_4 (* (* x1 x1) (- (* t_3 4.0) 6.0)))
        (t_5 (* (* x1 2.0) t_3))
        (t_6 (* x1 (* x1 x1))))
   (if (<= x1 -5e+102)
     t_1
     (if (<= x1 -0.034)
       (+
        x1
        (+
         (+ x1 (+ (+ (* t_2 (+ (* t_5 (- t_3 3.0)) t_4)) (* t_0 t_3)) t_6))
         9.0))
       (if (<= x1 3.5e+48)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_2))
           (+
            x1
            (+
             t_6
             (+
              (* t_2 (+ t_4 (* t_5 (- (+ x2 x2) 3.0))))
              (* t_0 (+ x2 x2)))))))
         t_1)))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + 9.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	double t_4 = (x1 * x1) * ((t_3 * 4.0) - 6.0);
	double t_5 = (x1 * 2.0) * t_3;
	double t_6 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -5e+102) {
		tmp = t_1;
	} else if (x1 <= -0.034) {
		tmp = x1 + ((x1 + (((t_2 * ((t_5 * (t_3 - 3.0)) + t_4)) + (t_0 * t_3)) + t_6)) + 9.0);
	} else if (x1 <= 3.5e+48) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) + (x1 + (t_6 + ((t_2 * (t_4 + (t_5 * ((x2 + x2) - 3.0)))) + (t_0 * (x2 + x2))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = x1 + ((x1 + (6.0d0 * (x1 ** 4.0d0))) + 9.0d0)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = ((t_0 + (2.0d0 * x2)) - x1) / t_2
    t_4 = (x1 * x1) * ((t_3 * 4.0d0) - 6.0d0)
    t_5 = (x1 * 2.0d0) * t_3
    t_6 = x1 * (x1 * x1)
    if (x1 <= (-5d+102)) then
        tmp = t_1
    else if (x1 <= (-0.034d0)) then
        tmp = x1 + ((x1 + (((t_2 * ((t_5 * (t_3 - 3.0d0)) + t_4)) + (t_0 * t_3)) + t_6)) + 9.0d0)
    else if (x1 <= 3.5d+48) then
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_2)) + (x1 + (t_6 + ((t_2 * (t_4 + (t_5 * ((x2 + x2) - 3.0d0)))) + (t_0 * (x2 + x2))))))
    else
        tmp = t_1
    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 + (6.0 * Math.pow(x1, 4.0))) + 9.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	double t_4 = (x1 * x1) * ((t_3 * 4.0) - 6.0);
	double t_5 = (x1 * 2.0) * t_3;
	double t_6 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -5e+102) {
		tmp = t_1;
	} else if (x1 <= -0.034) {
		tmp = x1 + ((x1 + (((t_2 * ((t_5 * (t_3 - 3.0)) + t_4)) + (t_0 * t_3)) + t_6)) + 9.0);
	} else if (x1 <= 3.5e+48) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) + (x1 + (t_6 + ((t_2 * (t_4 + (t_5 * ((x2 + x2) - 3.0)))) + (t_0 * (x2 + x2))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + 9.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2
	t_4 = (x1 * x1) * ((t_3 * 4.0) - 6.0)
	t_5 = (x1 * 2.0) * t_3
	t_6 = x1 * (x1 * x1)
	tmp = 0
	if x1 <= -5e+102:
		tmp = t_1
	elif x1 <= -0.034:
		tmp = x1 + ((x1 + (((t_2 * ((t_5 * (t_3 - 3.0)) + t_4)) + (t_0 * t_3)) + t_6)) + 9.0)
	elif x1 <= 3.5e+48:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) + (x1 + (t_6 + ((t_2 * (t_4 + (t_5 * ((x2 + x2) - 3.0)))) + (t_0 * (x2 + x2))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + 9.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_2)
	t_4 = Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0))
	t_5 = Float64(Float64(x1 * 2.0) * t_3)
	t_6 = Float64(x1 * Float64(x1 * x1))
	tmp = 0.0
	if (x1 <= -5e+102)
		tmp = t_1;
	elseif (x1 <= -0.034)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_2 * Float64(Float64(t_5 * Float64(t_3 - 3.0)) + t_4)) + Float64(t_0 * t_3)) + t_6)) + 9.0));
	elseif (x1 <= 3.5e+48)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_2)) + Float64(x1 + Float64(t_6 + Float64(Float64(t_2 * Float64(t_4 + Float64(t_5 * Float64(Float64(x2 + x2) - 3.0)))) + Float64(t_0 * Float64(x2 + x2)))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + 9.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	t_4 = (x1 * x1) * ((t_3 * 4.0) - 6.0);
	t_5 = (x1 * 2.0) * t_3;
	t_6 = x1 * (x1 * x1);
	tmp = 0.0;
	if (x1 <= -5e+102)
		tmp = t_1;
	elseif (x1 <= -0.034)
		tmp = x1 + ((x1 + (((t_2 * ((t_5 * (t_3 - 3.0)) + t_4)) + (t_0 * t_3)) + t_6)) + 9.0);
	elseif (x1 <= 3.5e+48)
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) + (x1 + (t_6 + ((t_2 * (t_4 + (t_5 * ((x2 + x2) - 3.0)))) + (t_0 * (x2 + x2))))));
	else
		tmp = t_1;
	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[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision]}, Block[{t$95$6 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5e+102], t$95$1, If[LessEqual[x1, -0.034], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$2 * N[(N[(t$95$5 * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$3), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.5e+48], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$6 + N[(N[(t$95$2 * N[(t$95$4 + N[(t$95$5 * N[(N[(x2 + x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(x2 + x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5e102 or 3.4999999999999997e48 < x1

   1. Initial program 19.7%

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

   2. Taylor expanded in x1 around inf 26.0%

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

      1. *-commutative 26.0%

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

   4. Simplified 26.0%

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

   5. Taylor expanded in x1 around inf 98.1%

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

   if -5e102 < x1 < -0.034000000000000002

   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 95.8%

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

   if -0.034000000000000002 < x1 < 3.4999999999999997e48

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 98.2%

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

      1. count-2 98.2%

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

   4. Simplified 98.2%

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

   5. Taylor expanded in x1 around 0 97.1%

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

      1. count-2 98.2%

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

   7. Simplified 97.1%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{elif}\;x1 \leq -0.034:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 9\right)\\ \mathbf{elif}\;x1 \leq 3.5 \cdot 10^{+48}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\left(x2 + x2\right) - 3\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \end{array} \]

Alternative 9: 89.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -2.9 \cdot 10^{+103} \lor \neg \left(x1 \leq 4.5 \cdot 10^{+153}\right):\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_0 \cdot \left(x2 + x2\right) + t_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t_2 \cdot 4 - 6\right) + \left(t_2 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right)\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (if (or (<= x1 -2.9e+103) (not (<= x1 4.5e+153)))
     (- (* x1 (* x1 9.0)) x1)
     (+
      x1
      (+
       (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (* t_0 (+ x2 x2))
          (*
           t_1
           (+
            (* (* x1 x1) (- (* t_2 4.0) 6.0))
            (* (- t_2 3.0) (* (* x1 2.0) (- (* 2.0 x2) x1)))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -2.9e+103) || !(x1 <= 4.5e+153)) {
		tmp = (x1 * (x1 * 9.0)) - x1;
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (x2 + x2)) + (t_1 * (((x1 * x1) * ((t_2 * 4.0) - 6.0)) + ((t_2 - 3.0) * ((x1 * 2.0) * ((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) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    if ((x1 <= (-2.9d+103)) .or. (.not. (x1 <= 4.5d+153))) then
        tmp = (x1 * (x1 * 9.0d0)) - x1
    else
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (x2 + x2)) + (t_1 * (((x1 * x1) * ((t_2 * 4.0d0) - 6.0d0)) + ((t_2 - 3.0d0) * ((x1 * 2.0d0) * ((2.0d0 * x2) - 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) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -2.9e+103) || !(x1 <= 4.5e+153)) {
		tmp = (x1 * (x1 * 9.0)) - x1;
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (x2 + x2)) + (t_1 * (((x1 * x1) * ((t_2 * 4.0) - 6.0)) + ((t_2 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - x1)))))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1
	tmp = 0
	if (x1 <= -2.9e+103) or not (x1 <= 4.5e+153):
		tmp = (x1 * (x1 * 9.0)) - x1
	else:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (x2 + x2)) + (t_1 * (((x1 * x1) * ((t_2 * 4.0) - 6.0)) + ((t_2 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - x1)))))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if ((x1 <= -2.9e+103) || !(x1 <= 4.5e+153))
		tmp = Float64(Float64(x1 * Float64(x1 * 9.0)) - x1);
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * Float64(x2 + x2)) + Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)) + Float64(Float64(t_2 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(Float64(2.0 * x2) - x1))))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	tmp = 0.0;
	if ((x1 <= -2.9e+103) || ~((x1 <= 4.5e+153)))
		tmp = (x1 * (x1 * 9.0)) - x1;
	else
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (x2 + x2)) + (t_1 * (((x1 * x1) * ((t_2 * 4.0) - 6.0)) + ((t_2 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - 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[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[x1, -2.9e+103], N[Not[LessEqual[x1, 4.5e+153]], $MachinePrecision]], N[(N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * N[(x2 + x2), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -2.8999999999999998e103 or 4.5000000000000001e153 < 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 x2 around inf 0.0%

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

      1. associate-*r/ 0.0%

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

      2. unpow2 0.0%

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

      3. +-commutative 0.0%

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

      4. unpow2 0.0%

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

      5. fma-udef 0.0%

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

   4. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 67.2%

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

      1. *-commutative 67.2%

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

      2. fma-def 67.2%

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

      3. +-commutative 67.2%

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

      4. fma-def 75.9%

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

      5. *-commutative 75.9%

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

      6. fma-neg 75.9%

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

      7. metadata-eval 75.9%

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

      8. unpow2 75.9%

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

      9. associate-*r* 75.9%

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

      10. *-commutative 75.9%

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

      11. associate-*l* 75.9%

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

      12. unpow2 75.9%

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

      13. cancel-sign-sub-inv 75.9%

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

      14. metadata-eval 75.9%

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

      15. +-commutative 75.9%

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

      16. count-2 75.9%

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

   7. Simplified 75.9%

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

   8. Taylor expanded in x2 around 0 90.6%

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

      1. associate-+r+ 90.6%

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

      2. distribute-rgt1-in 90.6%

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

      3. metadata-eval 90.6%

         \[\leadsto \color{blue}{-1} \cdot x1 + 9 \cdot {x1}^{2} \]

      4. neg-mul-1 90.6%

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

      5. +-commutative 90.6%

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

      6. unsub-neg 90.6%

         \[\leadsto \color{blue}{9 \cdot {x1}^{2} - x1} \]

      7. *-commutative 90.6%

         \[\leadsto \color{blue}{{x1}^{2} \cdot 9} - x1 \]

      8. unpow2 90.6%

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

      9. associate-*l* 90.6%

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

   10. Simplified 90.6%

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

   if -2.8999999999999998e103 < x1 < 4.5000000000000001e153

   1. Initial program 99.4%

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

   2. Taylor expanded in x1 around 0 95.4%

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

      1. count-2 95.4%

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

   4. Simplified 95.4%

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

   5. Taylor expanded in x1 around 0 94.0%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.9 \cdot 10^{+103} \lor \neg \left(x1 \leq 4.5 \cdot 10^{+153}\right):\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + x2\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right)\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 10: 92.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 \cdot \left(x1 \cdot 9\right) - x1\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := t_3 \cdot \left(x2 + x2\right)\\ t_5 := \frac{\left(t_3 + 2 \cdot x2\right) - x1}{t_1}\\ t_6 := \left(x1 \cdot 2\right) \cdot t_5\\ t_7 := x1 + \left(9 + \left(x1 + \left(t_0 + \left(t_1 \cdot \left(t_6 \cdot \left(t_5 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t_5 \cdot 4 - 6\right)\right) + t_4\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -7.5 \cdot 10^{+105}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x1 \leq -0.0115:\\ \;\;\;\;t_7\\ \mathbf{elif}\;x1 \leq 0.65:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_3 - 2 \cdot x2\right) - x1}{t_1} + \left(x1 + \left(t_0 + \left(t_4 + t_1 \cdot \left(t_6 \cdot \left(\left(x2 + x2\right) - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(x2 + x2\right) - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (- (* x1 (* x1 9.0)) x1))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (* t_3 (+ x2 x2)))
        (t_5 (/ (- (+ t_3 (* 2.0 x2)) x1) t_1))
        (t_6 (* (* x1 2.0) t_5))
        (t_7
         (+
          x1
          (+
           9.0
           (+
            x1
            (+
             t_0
             (+
              (* t_1 (+ (* t_6 (- t_5 3.0)) (* (* x1 x1) (- (* t_5 4.0) 6.0))))
              t_4)))))))
   (if (<= x1 -7.5e+105)
     t_2
     (if (<= x1 -0.0115)
       t_7
       (if (<= x1 0.65)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_3 (* 2.0 x2)) x1) t_1))
           (+
            x1
            (+
             t_0
             (+
              t_4
              (*
               t_1
               (+
                (* t_6 (- (+ x2 x2) 3.0))
                (* (* x1 x1) (- (* 4.0 (+ x2 x2)) 6.0)))))))))
         (if (<= x1 4.5e+153) t_7 t_2))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = (x1 * (x1 * 9.0)) - x1;
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = t_3 * (x2 + x2);
	double t_5 = ((t_3 + (2.0 * x2)) - x1) / t_1;
	double t_6 = (x1 * 2.0) * t_5;
	double t_7 = x1 + (9.0 + (x1 + (t_0 + ((t_1 * ((t_6 * (t_5 - 3.0)) + ((x1 * x1) * ((t_5 * 4.0) - 6.0)))) + t_4))));
	double tmp;
	if (x1 <= -7.5e+105) {
		tmp = t_2;
	} else if (x1 <= -0.0115) {
		tmp = t_7;
	} else if (x1 <= 0.65) {
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_1)) + (x1 + (t_0 + (t_4 + (t_1 * ((t_6 * ((x2 + x2) - 3.0)) + ((x1 * x1) * ((4.0 * (x2 + x2)) - 6.0))))))));
	} else if (x1 <= 4.5e+153) {
		tmp = t_7;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = x1 * (x1 * x1)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = (x1 * (x1 * 9.0d0)) - x1
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = t_3 * (x2 + x2)
    t_5 = ((t_3 + (2.0d0 * x2)) - x1) / t_1
    t_6 = (x1 * 2.0d0) * t_5
    t_7 = x1 + (9.0d0 + (x1 + (t_0 + ((t_1 * ((t_6 * (t_5 - 3.0d0)) + ((x1 * x1) * ((t_5 * 4.0d0) - 6.0d0)))) + t_4))))
    if (x1 <= (-7.5d+105)) then
        tmp = t_2
    else if (x1 <= (-0.0115d0)) then
        tmp = t_7
    else if (x1 <= 0.65d0) then
        tmp = x1 + ((3.0d0 * (((t_3 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + (t_0 + (t_4 + (t_1 * ((t_6 * ((x2 + x2) - 3.0d0)) + ((x1 * x1) * ((4.0d0 * (x2 + x2)) - 6.0d0))))))))
    else if (x1 <= 4.5d+153) then
        tmp = t_7
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = (x1 * (x1 * 9.0)) - x1;
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = t_3 * (x2 + x2);
	double t_5 = ((t_3 + (2.0 * x2)) - x1) / t_1;
	double t_6 = (x1 * 2.0) * t_5;
	double t_7 = x1 + (9.0 + (x1 + (t_0 + ((t_1 * ((t_6 * (t_5 - 3.0)) + ((x1 * x1) * ((t_5 * 4.0) - 6.0)))) + t_4))));
	double tmp;
	if (x1 <= -7.5e+105) {
		tmp = t_2;
	} else if (x1 <= -0.0115) {
		tmp = t_7;
	} else if (x1 <= 0.65) {
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_1)) + (x1 + (t_0 + (t_4 + (t_1 * ((t_6 * ((x2 + x2) - 3.0)) + ((x1 * x1) * ((4.0 * (x2 + x2)) - 6.0))))))));
	} else if (x1 <= 4.5e+153) {
		tmp = t_7;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = (x1 * x1) + 1.0
	t_2 = (x1 * (x1 * 9.0)) - x1
	t_3 = x1 * (x1 * 3.0)
	t_4 = t_3 * (x2 + x2)
	t_5 = ((t_3 + (2.0 * x2)) - x1) / t_1
	t_6 = (x1 * 2.0) * t_5
	t_7 = x1 + (9.0 + (x1 + (t_0 + ((t_1 * ((t_6 * (t_5 - 3.0)) + ((x1 * x1) * ((t_5 * 4.0) - 6.0)))) + t_4))))
	tmp = 0
	if x1 <= -7.5e+105:
		tmp = t_2
	elif x1 <= -0.0115:
		tmp = t_7
	elif x1 <= 0.65:
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_1)) + (x1 + (t_0 + (t_4 + (t_1 * ((t_6 * ((x2 + x2) - 3.0)) + ((x1 * x1) * ((4.0 * (x2 + x2)) - 6.0))))))))
	elif x1 <= 4.5e+153:
		tmp = t_7
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(x1 * Float64(x1 * 9.0)) - x1)
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(t_3 * Float64(x2 + x2))
	t_5 = Float64(Float64(Float64(t_3 + Float64(2.0 * x2)) - x1) / t_1)
	t_6 = Float64(Float64(x1 * 2.0) * t_5)
	t_7 = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_0 + Float64(Float64(t_1 * Float64(Float64(t_6 * Float64(t_5 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_5 * 4.0) - 6.0)))) + t_4)))))
	tmp = 0.0
	if (x1 <= -7.5e+105)
		tmp = t_2;
	elseif (x1 <= -0.0115)
		tmp = t_7;
	elseif (x1 <= 0.65)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_3 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(t_0 + Float64(t_4 + Float64(t_1 * Float64(Float64(t_6 * Float64(Float64(x2 + x2) - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(x2 + x2)) - 6.0)))))))));
	elseif (x1 <= 4.5e+153)
		tmp = t_7;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = (x1 * x1) + 1.0;
	t_2 = (x1 * (x1 * 9.0)) - x1;
	t_3 = x1 * (x1 * 3.0);
	t_4 = t_3 * (x2 + x2);
	t_5 = ((t_3 + (2.0 * x2)) - x1) / t_1;
	t_6 = (x1 * 2.0) * t_5;
	t_7 = x1 + (9.0 + (x1 + (t_0 + ((t_1 * ((t_6 * (t_5 - 3.0)) + ((x1 * x1) * ((t_5 * 4.0) - 6.0)))) + t_4))));
	tmp = 0.0;
	if (x1 <= -7.5e+105)
		tmp = t_2;
	elseif (x1 <= -0.0115)
		tmp = t_7;
	elseif (x1 <= 0.65)
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_1)) + (x1 + (t_0 + (t_4 + (t_1 * ((t_6 * ((x2 + x2) - 3.0)) + ((x1 * x1) * ((4.0 * (x2 + x2)) - 6.0))))))));
	elseif (x1 <= 4.5e+153)
		tmp = t_7;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 * N[(x2 + x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 * 2.0), $MachinePrecision] * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(x1 + N[(9.0 + N[(x1 + N[(t$95$0 + N[(N[(t$95$1 * N[(N[(t$95$6 * N[(t$95$5 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$5 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -7.5e+105], t$95$2, If[LessEqual[x1, -0.0115], t$95$7, If[LessEqual[x1, 0.65], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$3 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$0 + N[(t$95$4 + N[(t$95$1 * N[(N[(t$95$6 * N[(N[(x2 + x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(x2 + x2), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.5e+153], t$95$7, t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -7.5000000000000002e105 or 4.5000000000000001e153 < 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 x2 around inf 0.0%

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

      1. associate-*r/ 0.0%

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

      2. unpow2 0.0%

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

      3. +-commutative 0.0%

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

      4. unpow2 0.0%

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

      5. fma-udef 0.0%

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

   4. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 67.2%

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

      1. *-commutative 67.2%

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

      2. fma-def 67.2%

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

      3. +-commutative 67.2%

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

      4. fma-def 75.9%

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

      5. *-commutative 75.9%

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

      6. fma-neg 75.9%

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

      7. metadata-eval 75.9%

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

      8. unpow2 75.9%

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

      9. associate-*r* 75.9%

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

      10. *-commutative 75.9%

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

      11. associate-*l* 75.9%

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

      12. unpow2 75.9%

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

      13. cancel-sign-sub-inv 75.9%

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

      14. metadata-eval 75.9%

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

      15. +-commutative 75.9%

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

      16. count-2 75.9%

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

   7. Simplified 75.9%

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

   8. Taylor expanded in x2 around 0 90.6%

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

      1. associate-+r+ 90.6%

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

      2. distribute-rgt1-in 90.6%

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

      3. metadata-eval 90.6%

         \[\leadsto \color{blue}{-1} \cdot x1 + 9 \cdot {x1}^{2} \]

      4. neg-mul-1 90.6%

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

      5. +-commutative 90.6%

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

      6. unsub-neg 90.6%

         \[\leadsto \color{blue}{9 \cdot {x1}^{2} - x1} \]

      7. *-commutative 90.6%

         \[\leadsto \color{blue}{{x1}^{2} \cdot 9} - x1 \]

      8. unpow2 90.6%

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

      9. associate-*l* 90.6%

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

   10. Simplified 90.6%

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

   if -7.5000000000000002e105 < x1 < -0.0115 or 0.650000000000000022 < x1 < 4.5000000000000001e153

   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 84.1%

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

      1. count-2 84.1%

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

   4. Simplified 84.1%

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

   5. Taylor expanded in x1 around inf 84.1%

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

   if -0.0115 < x1 < 0.650000000000000022

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 98.8%

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

      1. count-2 98.8%

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

   4. Simplified 98.8%

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

   5. Taylor expanded in x1 around 0 98.7%

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

      1. count-2 98.8%

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

   7. Simplified 98.7%

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

   8. Taylor expanded in x1 around 0 98.8%

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

      1. count-2 98.8%

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

   10. Simplified 98.8%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.5 \cdot 10^{+105}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \mathbf{elif}\;x1 \leq -0.0115:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.65:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + x2\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\left(x2 + x2\right) - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(x2 + x2\right) - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \end{array} \]

Alternative 11: 89.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -1.45 \cdot 10^{+107} \lor \neg \left(x1 \leq 5 \cdot 10^{+153}\right):\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_0 \cdot \left(x2 + x2\right) + t_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t_2 \cdot 4 - 6\right) + \left(t_2 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 + x2\right)\right)\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (if (or (<= x1 -1.45e+107) (not (<= x1 5e+153)))
     (- (* x1 (* x1 9.0)) x1)
     (+
      x1
      (+
       (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (* t_0 (+ x2 x2))
          (*
           t_1
           (+
            (* (* x1 x1) (- (* t_2 4.0) 6.0))
            (* (- t_2 3.0) (* (* x1 2.0) (+ x2 x2)))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -1.45e+107) || !(x1 <= 5e+153)) {
		tmp = (x1 * (x1 * 9.0)) - x1;
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (x2 + x2)) + (t_1 * (((x1 * x1) * ((t_2 * 4.0) - 6.0)) + ((t_2 - 3.0) * ((x1 * 2.0) * (x2 + x2)))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    if ((x1 <= (-1.45d+107)) .or. (.not. (x1 <= 5d+153))) then
        tmp = (x1 * (x1 * 9.0d0)) - x1
    else
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (x2 + x2)) + (t_1 * (((x1 * x1) * ((t_2 * 4.0d0) - 6.0d0)) + ((t_2 - 3.0d0) * ((x1 * 2.0d0) * (x2 + x2)))))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -1.45e+107) || !(x1 <= 5e+153)) {
		tmp = (x1 * (x1 * 9.0)) - x1;
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (x2 + x2)) + (t_1 * (((x1 * x1) * ((t_2 * 4.0) - 6.0)) + ((t_2 - 3.0) * ((x1 * 2.0) * (x2 + x2)))))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1
	tmp = 0
	if (x1 <= -1.45e+107) or not (x1 <= 5e+153):
		tmp = (x1 * (x1 * 9.0)) - x1
	else:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (x2 + x2)) + (t_1 * (((x1 * x1) * ((t_2 * 4.0) - 6.0)) + ((t_2 - 3.0) * ((x1 * 2.0) * (x2 + x2)))))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if ((x1 <= -1.45e+107) || !(x1 <= 5e+153))
		tmp = Float64(Float64(x1 * Float64(x1 * 9.0)) - x1);
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * Float64(x2 + x2)) + Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)) + Float64(Float64(t_2 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(x2 + x2))))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	tmp = 0.0;
	if ((x1 <= -1.45e+107) || ~((x1 <= 5e+153)))
		tmp = (x1 * (x1 * 9.0)) - x1;
	else
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (x2 + x2)) + (t_1 * (((x1 * x1) * ((t_2 * 4.0) - 6.0)) + ((t_2 - 3.0) * ((x1 * 2.0) * (x2 + x2)))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[x1, -1.45e+107], N[Not[LessEqual[x1, 5e+153]], $MachinePrecision]], N[(N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * N[(x2 + x2), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(x2 + x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.44999999999999994e107 or 5.00000000000000018e153 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x2 around inf 0.0%

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

      1. associate-*r/ 0.0%

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

      2. unpow2 0.0%

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

      3. +-commutative 0.0%

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

      4. unpow2 0.0%

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

      5. fma-udef 0.0%

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

   4. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 67.2%

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

      1. *-commutative 67.2%

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

      2. fma-def 67.2%

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

      3. +-commutative 67.2%

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

      4. fma-def 75.9%

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

      5. *-commutative 75.9%

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

      6. fma-neg 75.9%

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

      7. metadata-eval 75.9%

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

      8. unpow2 75.9%

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

      9. associate-*r* 75.9%

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

      10. *-commutative 75.9%

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

      11. associate-*l* 75.9%

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

      12. unpow2 75.9%

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

      13. cancel-sign-sub-inv 75.9%

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

      14. metadata-eval 75.9%

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

      15. +-commutative 75.9%

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

      16. count-2 75.9%

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

   7. Simplified 75.9%

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

   8. Taylor expanded in x2 around 0 90.6%

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

      1. associate-+r+ 90.6%

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

      2. distribute-rgt1-in 90.6%

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

      3. metadata-eval 90.6%

         \[\leadsto \color{blue}{-1} \cdot x1 + 9 \cdot {x1}^{2} \]

      4. neg-mul-1 90.6%

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

      5. +-commutative 90.6%

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

      6. unsub-neg 90.6%

         \[\leadsto \color{blue}{9 \cdot {x1}^{2} - x1} \]

      7. *-commutative 90.6%

         \[\leadsto \color{blue}{{x1}^{2} \cdot 9} - x1 \]

      8. unpow2 90.6%

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

      9. associate-*l* 90.6%

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

   10. Simplified 90.6%

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

   if -1.44999999999999994e107 < x1 < 5.00000000000000018e153

   1. Initial program 99.4%

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

   2. Taylor expanded in x1 around 0 95.4%

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

      1. count-2 95.4%

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

   4. Simplified 95.4%

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

   5. Taylor expanded in x1 around 0 93.6%

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

      1. count-2 95.4%

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

   7. Simplified 93.6%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.45 \cdot 10^{+107} \lor \neg \left(x1 \leq 5 \cdot 10^{+153}\right):\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + x2\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 + x2\right)\right)\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 12: 89.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot \left(x1 \cdot 9\right) - x1\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_2}\\ t_4 := x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_0 \cdot \left(x2 + x2\right) + t_2 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t_3 \cdot 4 - 6\right) + \left(t_3 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 + x2\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -4.3 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq -0.45:\\ \;\;\;\;x1 + \left(9 + t_4\right)\\ \mathbf{elif}\;x1 \leq 0.004:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_2} + \left(x1 + 4 \cdot \left(2 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(t_4 + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (- (* x1 (* x1 9.0)) x1))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (/ (- (+ t_0 (* 2.0 x2)) x1) t_2))
        (t_4
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* t_0 (+ x2 x2))
            (*
             t_2
             (+
              (* (* x1 x1) (- (* t_3 4.0) 6.0))
              (* (- t_3 3.0) (* (* x1 2.0) (+ x2 x2))))))))))
   (if (<= x1 -4.3e+104)
     t_1
     (if (<= x1 -0.45)
       (+ x1 (+ 9.0 t_4))
       (if (<= x1 0.004)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_2))
           (+ x1 (* 4.0 (* 2.0 (* x2 (* x1 x2)))))))
         (if (<= x1 4.5e+153) (+ x1 (+ t_4 (* 3.0 (* x2 -2.0)))) t_1))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * (x1 * 9.0)) - x1;
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	double t_4 = x1 + ((x1 * (x1 * x1)) + ((t_0 * (x2 + x2)) + (t_2 * (((x1 * x1) * ((t_3 * 4.0) - 6.0)) + ((t_3 - 3.0) * ((x1 * 2.0) * (x2 + x2)))))));
	double tmp;
	if (x1 <= -4.3e+104) {
		tmp = t_1;
	} else if (x1 <= -0.45) {
		tmp = x1 + (9.0 + t_4);
	} else if (x1 <= 0.004) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) + (x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))));
	} else if (x1 <= 4.5e+153) {
		tmp = x1 + (t_4 + (3.0 * (x2 * -2.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * (x1 * 9.0d0)) - x1
    t_2 = (x1 * x1) + 1.0d0
    t_3 = ((t_0 + (2.0d0 * x2)) - x1) / t_2
    t_4 = x1 + ((x1 * (x1 * x1)) + ((t_0 * (x2 + x2)) + (t_2 * (((x1 * x1) * ((t_3 * 4.0d0) - 6.0d0)) + ((t_3 - 3.0d0) * ((x1 * 2.0d0) * (x2 + x2)))))))
    if (x1 <= (-4.3d+104)) then
        tmp = t_1
    else if (x1 <= (-0.45d0)) then
        tmp = x1 + (9.0d0 + t_4)
    else if (x1 <= 0.004d0) then
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_2)) + (x1 + (4.0d0 * (2.0d0 * (x2 * (x1 * x2))))))
    else if (x1 <= 4.5d+153) then
        tmp = x1 + (t_4 + (3.0d0 * (x2 * (-2.0d0))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * (x1 * 9.0)) - x1;
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	double t_4 = x1 + ((x1 * (x1 * x1)) + ((t_0 * (x2 + x2)) + (t_2 * (((x1 * x1) * ((t_3 * 4.0) - 6.0)) + ((t_3 - 3.0) * ((x1 * 2.0) * (x2 + x2)))))));
	double tmp;
	if (x1 <= -4.3e+104) {
		tmp = t_1;
	} else if (x1 <= -0.45) {
		tmp = x1 + (9.0 + t_4);
	} else if (x1 <= 0.004) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) + (x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))));
	} else if (x1 <= 4.5e+153) {
		tmp = x1 + (t_4 + (3.0 * (x2 * -2.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * (x1 * 9.0)) - x1
	t_2 = (x1 * x1) + 1.0
	t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2
	t_4 = x1 + ((x1 * (x1 * x1)) + ((t_0 * (x2 + x2)) + (t_2 * (((x1 * x1) * ((t_3 * 4.0) - 6.0)) + ((t_3 - 3.0) * ((x1 * 2.0) * (x2 + x2)))))))
	tmp = 0
	if x1 <= -4.3e+104:
		tmp = t_1
	elif x1 <= -0.45:
		tmp = x1 + (9.0 + t_4)
	elif x1 <= 0.004:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) + (x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))))
	elif x1 <= 4.5e+153:
		tmp = x1 + (t_4 + (3.0 * (x2 * -2.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * Float64(x1 * 9.0)) - x1)
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_2)
	t_4 = Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * Float64(x2 + x2)) + Float64(t_2 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0)) + Float64(Float64(t_3 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(x2 + x2))))))))
	tmp = 0.0
	if (x1 <= -4.3e+104)
		tmp = t_1;
	elseif (x1 <= -0.45)
		tmp = Float64(x1 + Float64(9.0 + t_4));
	elseif (x1 <= 0.004)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_2)) + Float64(x1 + Float64(4.0 * Float64(2.0 * Float64(x2 * Float64(x1 * x2)))))));
	elseif (x1 <= 4.5e+153)
		tmp = Float64(x1 + Float64(t_4 + Float64(3.0 * Float64(x2 * -2.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * (x1 * 9.0)) - x1;
	t_2 = (x1 * x1) + 1.0;
	t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	t_4 = x1 + ((x1 * (x1 * x1)) + ((t_0 * (x2 + x2)) + (t_2 * (((x1 * x1) * ((t_3 * 4.0) - 6.0)) + ((t_3 - 3.0) * ((x1 * 2.0) * (x2 + x2)))))));
	tmp = 0.0;
	if (x1 <= -4.3e+104)
		tmp = t_1;
	elseif (x1 <= -0.45)
		tmp = x1 + (9.0 + t_4);
	elseif (x1 <= 0.004)
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) + (x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))));
	elseif (x1 <= 4.5e+153)
		tmp = x1 + (t_4 + (3.0 * (x2 * -2.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * N[(x2 + x2), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$3 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(x2 + x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.3e+104], t$95$1, If[LessEqual[x1, -0.45], N[(x1 + N[(9.0 + t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.004], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(2.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.5e+153], N[(x1 + N[(t$95$4 + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.3000000000000002e104 or 4.5000000000000001e153 < 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 x2 around inf 0.0%

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

      1. associate-*r/ 0.0%

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

      2. unpow2 0.0%

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

      3. +-commutative 0.0%

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

      4. unpow2 0.0%

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

      5. fma-udef 0.0%

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

   4. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 67.2%

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

      1. *-commutative 67.2%

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

      2. fma-def 67.2%

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

      3. +-commutative 67.2%

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

      4. fma-def 75.9%

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

      5. *-commutative 75.9%

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

      6. fma-neg 75.9%

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

      7. metadata-eval 75.9%

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

      8. unpow2 75.9%

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

      9. associate-*r* 75.9%

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

      10. *-commutative 75.9%

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

      11. associate-*l* 75.9%

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

      12. unpow2 75.9%

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

      13. cancel-sign-sub-inv 75.9%

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

      14. metadata-eval 75.9%

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

      15. +-commutative 75.9%

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

      16. count-2 75.9%

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

   7. Simplified 75.9%

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

   8. Taylor expanded in x2 around 0 90.6%

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

      1. associate-+r+ 90.6%

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

      2. distribute-rgt1-in 90.6%

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

      3. metadata-eval 90.6%

         \[\leadsto \color{blue}{-1} \cdot x1 + 9 \cdot {x1}^{2} \]

      4. neg-mul-1 90.6%

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

      5. +-commutative 90.6%

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

      6. unsub-neg 90.6%

         \[\leadsto \color{blue}{9 \cdot {x1}^{2} - x1} \]

      7. *-commutative 90.6%

         \[\leadsto \color{blue}{{x1}^{2} \cdot 9} - x1 \]

      8. unpow2 90.6%

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

      9. associate-*l* 90.6%

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

   10. Simplified 90.6%

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

   if -4.3000000000000002e104 < x1 < -0.450000000000000011

   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 77.3%

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

      1. count-2 77.3%

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

   4. Simplified 77.3%

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

   5. Taylor expanded in x1 around 0 73.5%

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

      1. count-2 77.3%

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

   7. Simplified 73.5%

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

   8. Taylor expanded in x1 around inf 73.5%

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

   if -0.450000000000000011 < x1 < 0.0040000000000000001

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 88.7%

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

   3. Taylor expanded in x2 around inf 88.7%

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

      1. unpow2 88.1%

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

      2. associate-*r* 98.7%

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

      3. *-commutative 98.7%

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

   5. Simplified 99.3%

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

   if 0.0040000000000000001 < x1 < 4.5000000000000001e153

   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 86.9%

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

      1. count-2 86.9%

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

   4. Simplified 86.9%

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

   5. Taylor expanded in x1 around 0 79.9%

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

      1. count-2 86.9%

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

   7. Simplified 79.9%

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

   8. Taylor expanded in x1 around 0 80.7%

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

      1. *-commutative 80.7%

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

   10. Simplified 80.7%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.3 \cdot 10^{+104}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \mathbf{elif}\;x1 \leq -0.45:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + x2\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 + x2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.004:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(2 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + x2\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 + x2\right)\right)\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \end{array} \]

Alternative 13: 89.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := t_0 \cdot \left(x2 + x2\right)\\ t_2 := x1 \cdot \left(x1 \cdot 9\right) - x1\\ t_3 := x1 \cdot x1 + 1\\ t_4 := x1 \cdot \left(x1 \cdot x1\right)\\ t_5 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_3}\\ t_6 := x1 + \left(t_4 + \left(t_1 + t_3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t_5 \cdot 4 - 6\right) + \left(t_5 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 + x2\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -3.3 \cdot 10^{+107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x1 \leq -1.45:\\ \;\;\;\;x1 + \left(9 + t_6\right)\\ \mathbf{elif}\;x1 \leq 0.004:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_3} + \left(x1 + \left(t_4 + \left(t_1 + t_3 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_5\right) \cdot \left(\left(x2 + x2\right) - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(x2 + x2\right) - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(t_6 + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (* t_0 (+ x2 x2)))
        (t_2 (- (* x1 (* x1 9.0)) x1))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (* x1 (* x1 x1)))
        (t_5 (/ (- (+ t_0 (* 2.0 x2)) x1) t_3))
        (t_6
         (+
          x1
          (+
           t_4
           (+
            t_1
            (*
             t_3
             (+
              (* (* x1 x1) (- (* t_5 4.0) 6.0))
              (* (- t_5 3.0) (* (* x1 2.0) (+ x2 x2))))))))))
   (if (<= x1 -3.3e+107)
     t_2
     (if (<= x1 -1.45)
       (+ x1 (+ 9.0 t_6))
       (if (<= x1 0.004)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_3))
           (+
            x1
            (+
             t_4
             (+
              t_1
              (*
               t_3
               (+
                (* (* (* x1 2.0) t_5) (- (+ x2 x2) 3.0))
                (* (* x1 x1) (- (* 4.0 (+ x2 x2)) 6.0)))))))))
         (if (<= x1 4.5e+153) (+ x1 (+ t_6 (* 3.0 (* x2 -2.0)))) t_2))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = t_0 * (x2 + x2);
	double t_2 = (x1 * (x1 * 9.0)) - x1;
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = x1 * (x1 * x1);
	double t_5 = ((t_0 + (2.0 * x2)) - x1) / t_3;
	double t_6 = x1 + (t_4 + (t_1 + (t_3 * (((x1 * x1) * ((t_5 * 4.0) - 6.0)) + ((t_5 - 3.0) * ((x1 * 2.0) * (x2 + x2)))))));
	double tmp;
	if (x1 <= -3.3e+107) {
		tmp = t_2;
	} else if (x1 <= -1.45) {
		tmp = x1 + (9.0 + t_6);
	} else if (x1 <= 0.004) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3)) + (x1 + (t_4 + (t_1 + (t_3 * ((((x1 * 2.0) * t_5) * ((x2 + x2) - 3.0)) + ((x1 * x1) * ((4.0 * (x2 + x2)) - 6.0))))))));
	} else if (x1 <= 4.5e+153) {
		tmp = x1 + (t_6 + (3.0 * (x2 * -2.0)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = t_0 * (x2 + x2)
    t_2 = (x1 * (x1 * 9.0d0)) - x1
    t_3 = (x1 * x1) + 1.0d0
    t_4 = x1 * (x1 * x1)
    t_5 = ((t_0 + (2.0d0 * x2)) - x1) / t_3
    t_6 = x1 + (t_4 + (t_1 + (t_3 * (((x1 * x1) * ((t_5 * 4.0d0) - 6.0d0)) + ((t_5 - 3.0d0) * ((x1 * 2.0d0) * (x2 + x2)))))))
    if (x1 <= (-3.3d+107)) then
        tmp = t_2
    else if (x1 <= (-1.45d0)) then
        tmp = x1 + (9.0d0 + t_6)
    else if (x1 <= 0.004d0) then
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_3)) + (x1 + (t_4 + (t_1 + (t_3 * ((((x1 * 2.0d0) * t_5) * ((x2 + x2) - 3.0d0)) + ((x1 * x1) * ((4.0d0 * (x2 + x2)) - 6.0d0))))))))
    else if (x1 <= 4.5d+153) then
        tmp = x1 + (t_6 + (3.0d0 * (x2 * (-2.0d0))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = t_0 * (x2 + x2);
	double t_2 = (x1 * (x1 * 9.0)) - x1;
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = x1 * (x1 * x1);
	double t_5 = ((t_0 + (2.0 * x2)) - x1) / t_3;
	double t_6 = x1 + (t_4 + (t_1 + (t_3 * (((x1 * x1) * ((t_5 * 4.0) - 6.0)) + ((t_5 - 3.0) * ((x1 * 2.0) * (x2 + x2)))))));
	double tmp;
	if (x1 <= -3.3e+107) {
		tmp = t_2;
	} else if (x1 <= -1.45) {
		tmp = x1 + (9.0 + t_6);
	} else if (x1 <= 0.004) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3)) + (x1 + (t_4 + (t_1 + (t_3 * ((((x1 * 2.0) * t_5) * ((x2 + x2) - 3.0)) + ((x1 * x1) * ((4.0 * (x2 + x2)) - 6.0))))))));
	} else if (x1 <= 4.5e+153) {
		tmp = x1 + (t_6 + (3.0 * (x2 * -2.0)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = t_0 * (x2 + x2)
	t_2 = (x1 * (x1 * 9.0)) - x1
	t_3 = (x1 * x1) + 1.0
	t_4 = x1 * (x1 * x1)
	t_5 = ((t_0 + (2.0 * x2)) - x1) / t_3
	t_6 = x1 + (t_4 + (t_1 + (t_3 * (((x1 * x1) * ((t_5 * 4.0) - 6.0)) + ((t_5 - 3.0) * ((x1 * 2.0) * (x2 + x2)))))))
	tmp = 0
	if x1 <= -3.3e+107:
		tmp = t_2
	elif x1 <= -1.45:
		tmp = x1 + (9.0 + t_6)
	elif x1 <= 0.004:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3)) + (x1 + (t_4 + (t_1 + (t_3 * ((((x1 * 2.0) * t_5) * ((x2 + x2) - 3.0)) + ((x1 * x1) * ((4.0 * (x2 + x2)) - 6.0))))))))
	elif x1 <= 4.5e+153:
		tmp = x1 + (t_6 + (3.0 * (x2 * -2.0)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(t_0 * Float64(x2 + x2))
	t_2 = Float64(Float64(x1 * Float64(x1 * 9.0)) - x1)
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(x1 * Float64(x1 * x1))
	t_5 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_3)
	t_6 = Float64(x1 + Float64(t_4 + Float64(t_1 + Float64(t_3 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_5 * 4.0) - 6.0)) + Float64(Float64(t_5 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(x2 + x2))))))))
	tmp = 0.0
	if (x1 <= -3.3e+107)
		tmp = t_2;
	elseif (x1 <= -1.45)
		tmp = Float64(x1 + Float64(9.0 + t_6));
	elseif (x1 <= 0.004)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_3)) + Float64(x1 + Float64(t_4 + Float64(t_1 + Float64(t_3 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_5) * Float64(Float64(x2 + x2) - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(x2 + x2)) - 6.0)))))))));
	elseif (x1 <= 4.5e+153)
		tmp = Float64(x1 + Float64(t_6 + Float64(3.0 * Float64(x2 * -2.0))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = t_0 * (x2 + x2);
	t_2 = (x1 * (x1 * 9.0)) - x1;
	t_3 = (x1 * x1) + 1.0;
	t_4 = x1 * (x1 * x1);
	t_5 = ((t_0 + (2.0 * x2)) - x1) / t_3;
	t_6 = x1 + (t_4 + (t_1 + (t_3 * (((x1 * x1) * ((t_5 * 4.0) - 6.0)) + ((t_5 - 3.0) * ((x1 * 2.0) * (x2 + x2)))))));
	tmp = 0.0;
	if (x1 <= -3.3e+107)
		tmp = t_2;
	elseif (x1 <= -1.45)
		tmp = x1 + (9.0 + t_6);
	elseif (x1 <= 0.004)
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3)) + (x1 + (t_4 + (t_1 + (t_3 * ((((x1 * 2.0) * t_5) * ((x2 + x2) - 3.0)) + ((x1 * x1) * ((4.0 * (x2 + x2)) - 6.0))))))));
	elseif (x1 <= 4.5e+153)
		tmp = x1 + (t_6 + (3.0 * (x2 * -2.0)));
	else
		tmp = t_2;
	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[(x2 + x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$6 = N[(x1 + N[(t$95$4 + N[(t$95$1 + N[(t$95$3 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$5 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$5 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(x2 + x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3.3e+107], t$95$2, If[LessEqual[x1, -1.45], N[(x1 + N[(9.0 + t$95$6), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.004], 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[(x1 + N[(t$95$4 + N[(t$95$1 + N[(t$95$3 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$5), $MachinePrecision] * N[(N[(x2 + x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(x2 + x2), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.5e+153], N[(x1 + N[(t$95$6 + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -3.30000000000000032e107 or 4.5000000000000001e153 < 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 x2 around inf 0.0%

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

      1. associate-*r/ 0.0%

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

      2. unpow2 0.0%

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

      3. +-commutative 0.0%

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

      4. unpow2 0.0%

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

      5. fma-udef 0.0%

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

   4. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 67.2%

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

      1. *-commutative 67.2%

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

      2. fma-def 67.2%

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

      3. +-commutative 67.2%

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

      4. fma-def 75.9%

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

      5. *-commutative 75.9%

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

      6. fma-neg 75.9%

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

      7. metadata-eval 75.9%

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

      8. unpow2 75.9%

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

      9. associate-*r* 75.9%

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

      10. *-commutative 75.9%

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

      11. associate-*l* 75.9%

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

      12. unpow2 75.9%

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

      13. cancel-sign-sub-inv 75.9%

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

      14. metadata-eval 75.9%

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

      15. +-commutative 75.9%

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

      16. count-2 75.9%

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

   7. Simplified 75.9%

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

   8. Taylor expanded in x2 around 0 90.6%

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

      1. associate-+r+ 90.6%

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

      2. distribute-rgt1-in 90.6%

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

      3. metadata-eval 90.6%

         \[\leadsto \color{blue}{-1} \cdot x1 + 9 \cdot {x1}^{2} \]

      4. neg-mul-1 90.6%

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

      5. +-commutative 90.6%

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

      6. unsub-neg 90.6%

         \[\leadsto \color{blue}{9 \cdot {x1}^{2} - x1} \]

      7. *-commutative 90.6%

         \[\leadsto \color{blue}{{x1}^{2} \cdot 9} - x1 \]

      8. unpow2 90.6%

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

      9. associate-*l* 90.6%

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

   10. Simplified 90.6%

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

   if -3.30000000000000032e107 < x1 < -1.44999999999999996

   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 77.3%

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

      1. count-2 77.3%

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

   4. Simplified 77.3%

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

   5. Taylor expanded in x1 around 0 73.5%

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

      1. count-2 77.3%

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

   7. Simplified 73.5%

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

   8. Taylor expanded in x1 around inf 73.5%

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

   if -1.44999999999999996 < x1 < 0.0040000000000000001

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 99.3%

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

      1. count-2 99.3%

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

   4. Simplified 99.3%

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

   5. Taylor expanded in x1 around 0 99.3%

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

      1. count-2 99.3%

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

   7. Simplified 99.3%

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

   8. Taylor expanded in x1 around 0 99.3%

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

      1. count-2 99.3%

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

   10. Simplified 99.3%

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

   if 0.0040000000000000001 < x1 < 4.5000000000000001e153

   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 86.9%

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

      1. count-2 86.9%

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

   4. Simplified 86.9%

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

   5. Taylor expanded in x1 around 0 79.9%

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

      1. count-2 86.9%

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

   7. Simplified 79.9%

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

   8. Taylor expanded in x1 around 0 80.7%

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

      1. *-commutative 80.7%

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

   10. Simplified 80.7%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.3 \cdot 10^{+107}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \mathbf{elif}\;x1 \leq -1.45:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + x2\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 + x2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.004:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + x2\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\left(x2 + x2\right) - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(x2 + x2\right) - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + x2\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 + x2\right)\right)\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \end{array} \]

Alternative 14: 89.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := t_0 \cdot \left(x2 + x2\right)\\ t_2 := x1 \cdot \left(x1 \cdot 9\right) - x1\\ t_3 := x1 \cdot x1 + 1\\ t_4 := x1 \cdot \left(x1 \cdot x1\right)\\ t_5 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_3}\\ t_6 := x1 + \left(t_4 + \left(t_1 + t_3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t_5 \cdot 4 - 6\right) + \left(t_5 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 + x2\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -2.85 \cdot 10^{+103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x1 \leq -0.66:\\ \;\;\;\;x1 + \left(t_6 + 3 \cdot \left(3 + \frac{-1}{x1}\right)\right)\\ \mathbf{elif}\;x1 \leq 0.004:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_3} + \left(x1 + \left(t_4 + \left(t_1 + t_3 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_5\right) \cdot \left(\left(x2 + x2\right) - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(x2 + x2\right) - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(t_6 + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (* t_0 (+ x2 x2)))
        (t_2 (- (* x1 (* x1 9.0)) x1))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (* x1 (* x1 x1)))
        (t_5 (/ (- (+ t_0 (* 2.0 x2)) x1) t_3))
        (t_6
         (+
          x1
          (+
           t_4
           (+
            t_1
            (*
             t_3
             (+
              (* (* x1 x1) (- (* t_5 4.0) 6.0))
              (* (- t_5 3.0) (* (* x1 2.0) (+ x2 x2))))))))))
   (if (<= x1 -2.85e+103)
     t_2
     (if (<= x1 -0.66)
       (+ x1 (+ t_6 (* 3.0 (+ 3.0 (/ -1.0 x1)))))
       (if (<= x1 0.004)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_3))
           (+
            x1
            (+
             t_4
             (+
              t_1
              (*
               t_3
               (+
                (* (* (* x1 2.0) t_5) (- (+ x2 x2) 3.0))
                (* (* x1 x1) (- (* 4.0 (+ x2 x2)) 6.0)))))))))
         (if (<= x1 4.5e+153) (+ x1 (+ t_6 (* 3.0 (* x2 -2.0)))) t_2))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = t_0 * (x2 + x2);
	double t_2 = (x1 * (x1 * 9.0)) - x1;
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = x1 * (x1 * x1);
	double t_5 = ((t_0 + (2.0 * x2)) - x1) / t_3;
	double t_6 = x1 + (t_4 + (t_1 + (t_3 * (((x1 * x1) * ((t_5 * 4.0) - 6.0)) + ((t_5 - 3.0) * ((x1 * 2.0) * (x2 + x2)))))));
	double tmp;
	if (x1 <= -2.85e+103) {
		tmp = t_2;
	} else if (x1 <= -0.66) {
		tmp = x1 + (t_6 + (3.0 * (3.0 + (-1.0 / x1))));
	} else if (x1 <= 0.004) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3)) + (x1 + (t_4 + (t_1 + (t_3 * ((((x1 * 2.0) * t_5) * ((x2 + x2) - 3.0)) + ((x1 * x1) * ((4.0 * (x2 + x2)) - 6.0))))))));
	} else if (x1 <= 4.5e+153) {
		tmp = x1 + (t_6 + (3.0 * (x2 * -2.0)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = t_0 * (x2 + x2)
    t_2 = (x1 * (x1 * 9.0d0)) - x1
    t_3 = (x1 * x1) + 1.0d0
    t_4 = x1 * (x1 * x1)
    t_5 = ((t_0 + (2.0d0 * x2)) - x1) / t_3
    t_6 = x1 + (t_4 + (t_1 + (t_3 * (((x1 * x1) * ((t_5 * 4.0d0) - 6.0d0)) + ((t_5 - 3.0d0) * ((x1 * 2.0d0) * (x2 + x2)))))))
    if (x1 <= (-2.85d+103)) then
        tmp = t_2
    else if (x1 <= (-0.66d0)) then
        tmp = x1 + (t_6 + (3.0d0 * (3.0d0 + ((-1.0d0) / x1))))
    else if (x1 <= 0.004d0) then
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_3)) + (x1 + (t_4 + (t_1 + (t_3 * ((((x1 * 2.0d0) * t_5) * ((x2 + x2) - 3.0d0)) + ((x1 * x1) * ((4.0d0 * (x2 + x2)) - 6.0d0))))))))
    else if (x1 <= 4.5d+153) then
        tmp = x1 + (t_6 + (3.0d0 * (x2 * (-2.0d0))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = t_0 * (x2 + x2);
	double t_2 = (x1 * (x1 * 9.0)) - x1;
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = x1 * (x1 * x1);
	double t_5 = ((t_0 + (2.0 * x2)) - x1) / t_3;
	double t_6 = x1 + (t_4 + (t_1 + (t_3 * (((x1 * x1) * ((t_5 * 4.0) - 6.0)) + ((t_5 - 3.0) * ((x1 * 2.0) * (x2 + x2)))))));
	double tmp;
	if (x1 <= -2.85e+103) {
		tmp = t_2;
	} else if (x1 <= -0.66) {
		tmp = x1 + (t_6 + (3.0 * (3.0 + (-1.0 / x1))));
	} else if (x1 <= 0.004) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3)) + (x1 + (t_4 + (t_1 + (t_3 * ((((x1 * 2.0) * t_5) * ((x2 + x2) - 3.0)) + ((x1 * x1) * ((4.0 * (x2 + x2)) - 6.0))))))));
	} else if (x1 <= 4.5e+153) {
		tmp = x1 + (t_6 + (3.0 * (x2 * -2.0)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = t_0 * (x2 + x2)
	t_2 = (x1 * (x1 * 9.0)) - x1
	t_3 = (x1 * x1) + 1.0
	t_4 = x1 * (x1 * x1)
	t_5 = ((t_0 + (2.0 * x2)) - x1) / t_3
	t_6 = x1 + (t_4 + (t_1 + (t_3 * (((x1 * x1) * ((t_5 * 4.0) - 6.0)) + ((t_5 - 3.0) * ((x1 * 2.0) * (x2 + x2)))))))
	tmp = 0
	if x1 <= -2.85e+103:
		tmp = t_2
	elif x1 <= -0.66:
		tmp = x1 + (t_6 + (3.0 * (3.0 + (-1.0 / x1))))
	elif x1 <= 0.004:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3)) + (x1 + (t_4 + (t_1 + (t_3 * ((((x1 * 2.0) * t_5) * ((x2 + x2) - 3.0)) + ((x1 * x1) * ((4.0 * (x2 + x2)) - 6.0))))))))
	elif x1 <= 4.5e+153:
		tmp = x1 + (t_6 + (3.0 * (x2 * -2.0)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(t_0 * Float64(x2 + x2))
	t_2 = Float64(Float64(x1 * Float64(x1 * 9.0)) - x1)
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(x1 * Float64(x1 * x1))
	t_5 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_3)
	t_6 = Float64(x1 + Float64(t_4 + Float64(t_1 + Float64(t_3 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_5 * 4.0) - 6.0)) + Float64(Float64(t_5 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(x2 + x2))))))))
	tmp = 0.0
	if (x1 <= -2.85e+103)
		tmp = t_2;
	elseif (x1 <= -0.66)
		tmp = Float64(x1 + Float64(t_6 + Float64(3.0 * Float64(3.0 + Float64(-1.0 / x1)))));
	elseif (x1 <= 0.004)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_3)) + Float64(x1 + Float64(t_4 + Float64(t_1 + Float64(t_3 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_5) * Float64(Float64(x2 + x2) - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(x2 + x2)) - 6.0)))))))));
	elseif (x1 <= 4.5e+153)
		tmp = Float64(x1 + Float64(t_6 + Float64(3.0 * Float64(x2 * -2.0))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = t_0 * (x2 + x2);
	t_2 = (x1 * (x1 * 9.0)) - x1;
	t_3 = (x1 * x1) + 1.0;
	t_4 = x1 * (x1 * x1);
	t_5 = ((t_0 + (2.0 * x2)) - x1) / t_3;
	t_6 = x1 + (t_4 + (t_1 + (t_3 * (((x1 * x1) * ((t_5 * 4.0) - 6.0)) + ((t_5 - 3.0) * ((x1 * 2.0) * (x2 + x2)))))));
	tmp = 0.0;
	if (x1 <= -2.85e+103)
		tmp = t_2;
	elseif (x1 <= -0.66)
		tmp = x1 + (t_6 + (3.0 * (3.0 + (-1.0 / x1))));
	elseif (x1 <= 0.004)
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3)) + (x1 + (t_4 + (t_1 + (t_3 * ((((x1 * 2.0) * t_5) * ((x2 + x2) - 3.0)) + ((x1 * x1) * ((4.0 * (x2 + x2)) - 6.0))))))));
	elseif (x1 <= 4.5e+153)
		tmp = x1 + (t_6 + (3.0 * (x2 * -2.0)));
	else
		tmp = t_2;
	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[(x2 + x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$6 = N[(x1 + N[(t$95$4 + N[(t$95$1 + N[(t$95$3 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$5 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$5 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(x2 + x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.85e+103], t$95$2, If[LessEqual[x1, -0.66], N[(x1 + N[(t$95$6 + N[(3.0 * N[(3.0 + N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.004], 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[(x1 + N[(t$95$4 + N[(t$95$1 + N[(t$95$3 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$5), $MachinePrecision] * N[(N[(x2 + x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(x2 + x2), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.5e+153], N[(x1 + N[(t$95$6 + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.85000000000000016e103 or 4.5000000000000001e153 < 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 x2 around inf 0.0%

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

      1. associate-*r/ 0.0%

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

      2. unpow2 0.0%

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

      3. +-commutative 0.0%

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

      4. unpow2 0.0%

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

      5. fma-udef 0.0%

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

   4. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 67.2%

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

      1. *-commutative 67.2%

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

      2. fma-def 67.2%

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

      3. +-commutative 67.2%

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

      4. fma-def 75.9%

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

      5. *-commutative 75.9%

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

      6. fma-neg 75.9%

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

      7. metadata-eval 75.9%

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

      8. unpow2 75.9%

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

      9. associate-*r* 75.9%

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

      10. *-commutative 75.9%

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

      11. associate-*l* 75.9%

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

      12. unpow2 75.9%

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

      13. cancel-sign-sub-inv 75.9%

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

      14. metadata-eval 75.9%

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

      15. +-commutative 75.9%

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

      16. count-2 75.9%

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

   7. Simplified 75.9%

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

   8. Taylor expanded in x2 around 0 90.6%

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

      1. associate-+r+ 90.6%

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

      2. distribute-rgt1-in 90.6%

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

      3. metadata-eval 90.6%

         \[\leadsto \color{blue}{-1} \cdot x1 + 9 \cdot {x1}^{2} \]

      4. neg-mul-1 90.6%

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

      5. +-commutative 90.6%

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

      6. unsub-neg 90.6%

         \[\leadsto \color{blue}{9 \cdot {x1}^{2} - x1} \]

      7. *-commutative 90.6%

         \[\leadsto \color{blue}{{x1}^{2} \cdot 9} - x1 \]

      8. unpow2 90.6%

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

      9. associate-*l* 90.6%

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

   10. Simplified 90.6%

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

   if -2.85000000000000016e103 < x1 < -0.660000000000000031

   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 77.3%

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

      1. count-2 77.3%

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

   4. Simplified 77.3%

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

   5. Taylor expanded in x1 around 0 73.5%

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

      1. count-2 77.3%

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

   7. Simplified 73.5%

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

   8. Taylor expanded in x1 around inf 73.5%

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

   if -0.660000000000000031 < x1 < 0.0040000000000000001

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 99.3%

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

      1. count-2 99.3%

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

   4. Simplified 99.3%

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

   5. Taylor expanded in x1 around 0 99.3%

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

      1. count-2 99.3%

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

   7. Simplified 99.3%

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

   8. Taylor expanded in x1 around 0 99.3%

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

      1. count-2 99.3%

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

   10. Simplified 99.3%

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

   if 0.0040000000000000001 < x1 < 4.5000000000000001e153

   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 86.9%

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

      1. count-2 86.9%

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

   4. Simplified 86.9%

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

   5. Taylor expanded in x1 around 0 79.9%

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

      1. count-2 86.9%

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

   7. Simplified 79.9%

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

   8. Taylor expanded in x1 around 0 80.7%

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

      1. *-commutative 80.7%

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

   10. Simplified 80.7%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.85 \cdot 10^{+103}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \mathbf{elif}\;x1 \leq -0.66:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + x2\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 + x2\right)\right)\right)\right)\right)\right) + 3 \cdot \left(3 + \frac{-1}{x1}\right)\right)\\ \mathbf{elif}\;x1 \leq 0.004:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + x2\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\left(x2 + x2\right) - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(x2 + x2\right) - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + x2\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 + x2\right)\right)\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \end{array} \]

Alternative 15: 89.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot \left(x1 \cdot 9\right) - x1\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_2}\\ t_4 := x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_0 \cdot \left(x2 + x2\right) + t_2 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t_3 \cdot 4 - 6\right) + \left(t_3 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 + x2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -3.8 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq -0.45:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x1 \leq 1.75:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_2} + \left(x1 + 4 \cdot \left(2 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (- (* x1 (* x1 9.0)) x1))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (/ (- (+ t_0 (* 2.0 x2)) x1) t_2))
        (t_4
         (+
          x1
          (+
           9.0
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* t_0 (+ x2 x2))
              (*
               t_2
               (+
                (* (* x1 x1) (- (* t_3 4.0) 6.0))
                (* (- t_3 3.0) (* (* x1 2.0) (+ x2 x2))))))))))))
   (if (<= x1 -3.8e+103)
     t_1
     (if (<= x1 -0.45)
       t_4
       (if (<= x1 1.75)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_2))
           (+ x1 (* 4.0 (* 2.0 (* x2 (* x1 x2)))))))
         (if (<= x1 5e+153) t_4 t_1))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * (x1 * 9.0)) - x1;
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	double t_4 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (x2 + x2)) + (t_2 * (((x1 * x1) * ((t_3 * 4.0) - 6.0)) + ((t_3 - 3.0) * ((x1 * 2.0) * (x2 + x2)))))))));
	double tmp;
	if (x1 <= -3.8e+103) {
		tmp = t_1;
	} else if (x1 <= -0.45) {
		tmp = t_4;
	} else if (x1 <= 1.75) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) + (x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))));
	} else if (x1 <= 5e+153) {
		tmp = t_4;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * (x1 * 9.0d0)) - x1
    t_2 = (x1 * x1) + 1.0d0
    t_3 = ((t_0 + (2.0d0 * x2)) - x1) / t_2
    t_4 = x1 + (9.0d0 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (x2 + x2)) + (t_2 * (((x1 * x1) * ((t_3 * 4.0d0) - 6.0d0)) + ((t_3 - 3.0d0) * ((x1 * 2.0d0) * (x2 + x2)))))))))
    if (x1 <= (-3.8d+103)) then
        tmp = t_1
    else if (x1 <= (-0.45d0)) then
        tmp = t_4
    else if (x1 <= 1.75d0) then
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_2)) + (x1 + (4.0d0 * (2.0d0 * (x2 * (x1 * x2))))))
    else if (x1 <= 5d+153) then
        tmp = t_4
    else
        tmp = t_1
    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 * 9.0)) - x1;
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	double t_4 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (x2 + x2)) + (t_2 * (((x1 * x1) * ((t_3 * 4.0) - 6.0)) + ((t_3 - 3.0) * ((x1 * 2.0) * (x2 + x2)))))))));
	double tmp;
	if (x1 <= -3.8e+103) {
		tmp = t_1;
	} else if (x1 <= -0.45) {
		tmp = t_4;
	} else if (x1 <= 1.75) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) + (x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))));
	} else if (x1 <= 5e+153) {
		tmp = t_4;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * (x1 * 9.0)) - x1
	t_2 = (x1 * x1) + 1.0
	t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2
	t_4 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (x2 + x2)) + (t_2 * (((x1 * x1) * ((t_3 * 4.0) - 6.0)) + ((t_3 - 3.0) * ((x1 * 2.0) * (x2 + x2)))))))))
	tmp = 0
	if x1 <= -3.8e+103:
		tmp = t_1
	elif x1 <= -0.45:
		tmp = t_4
	elif x1 <= 1.75:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) + (x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))))
	elif x1 <= 5e+153:
		tmp = t_4
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * Float64(x1 * 9.0)) - x1)
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_2)
	t_4 = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * Float64(x2 + x2)) + Float64(t_2 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0)) + Float64(Float64(t_3 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(x2 + x2))))))))))
	tmp = 0.0
	if (x1 <= -3.8e+103)
		tmp = t_1;
	elseif (x1 <= -0.45)
		tmp = t_4;
	elseif (x1 <= 1.75)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_2)) + Float64(x1 + Float64(4.0 * Float64(2.0 * Float64(x2 * Float64(x1 * x2)))))));
	elseif (x1 <= 5e+153)
		tmp = t_4;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * (x1 * 9.0)) - x1;
	t_2 = (x1 * x1) + 1.0;
	t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	t_4 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (x2 + x2)) + (t_2 * (((x1 * x1) * ((t_3 * 4.0) - 6.0)) + ((t_3 - 3.0) * ((x1 * 2.0) * (x2 + x2)))))))));
	tmp = 0.0;
	if (x1 <= -3.8e+103)
		tmp = t_1;
	elseif (x1 <= -0.45)
		tmp = t_4;
	elseif (x1 <= 1.75)
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) + (x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))));
	elseif (x1 <= 5e+153)
		tmp = t_4;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(9.0 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * N[(x2 + x2), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$3 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(x2 + x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3.8e+103], t$95$1, If[LessEqual[x1, -0.45], t$95$4, If[LessEqual[x1, 1.75], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(2.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], t$95$4, t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.7999999999999997e103 or 5.00000000000000018e153 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x2 around inf 0.0%

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

      1. associate-*r/ 0.0%

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

      2. unpow2 0.0%

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

      3. +-commutative 0.0%

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

      4. unpow2 0.0%

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

      5. fma-udef 0.0%

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

   4. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 67.2%

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

      1. *-commutative 67.2%

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

      2. fma-def 67.2%

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

      3. +-commutative 67.2%

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

      4. fma-def 75.9%

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

      5. *-commutative 75.9%

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

      6. fma-neg 75.9%

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

      7. metadata-eval 75.9%

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

      8. unpow2 75.9%

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

      9. associate-*r* 75.9%

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

      10. *-commutative 75.9%

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

      11. associate-*l* 75.9%

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

      12. unpow2 75.9%

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

      13. cancel-sign-sub-inv 75.9%

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

      14. metadata-eval 75.9%

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

      15. +-commutative 75.9%

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

      16. count-2 75.9%

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

   7. Simplified 75.9%

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

   8. Taylor expanded in x2 around 0 90.6%

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

      1. associate-+r+ 90.6%

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

      2. distribute-rgt1-in 90.6%

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

      3. metadata-eval 90.6%

         \[\leadsto \color{blue}{-1} \cdot x1 + 9 \cdot {x1}^{2} \]

      4. neg-mul-1 90.6%

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

      5. +-commutative 90.6%

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

      6. unsub-neg 90.6%

         \[\leadsto \color{blue}{9 \cdot {x1}^{2} - x1} \]

      7. *-commutative 90.6%

         \[\leadsto \color{blue}{{x1}^{2} \cdot 9} - x1 \]

      8. unpow2 90.6%

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

      9. associate-*l* 90.6%

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

   10. Simplified 90.6%

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

   if -3.7999999999999997e103 < x1 < -0.450000000000000011 or 1.75 < x1 < 5.00000000000000018e153

   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 84.1%

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

      1. count-2 84.1%

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

   4. Simplified 84.1%

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

   5. Taylor expanded in x1 around 0 78.6%

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

      1. count-2 84.1%

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

   7. Simplified 78.6%

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

   8. Taylor expanded in x1 around inf 78.6%

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

   if -0.450000000000000011 < x1 < 1.75

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 88.2%

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

   3. Taylor expanded in x2 around inf 88.2%

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

      1. unpow2 87.7%

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

      2. associate-*r* 98.2%

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

      3. *-commutative 98.2%

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

   5. Simplified 98.6%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.8 \cdot 10^{+103}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \mathbf{elif}\;x1 \leq -0.45:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + x2\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 + x2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.75:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(2 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + x2\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 + x2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \end{array} \]

Alternative 16: 78.9% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+91} \lor \neg \left(x1 \leq 4.1 \cdot 10^{+130}\right):\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(2 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -4.5e+91) (not (<= x1 4.1e+130)))
   (- (* x1 (* x1 9.0)) x1)
   (+
    x1
    (+
     (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
     (+ x1 (* 4.0 (* 2.0 (* x2 (* x1 x2)))))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -4.5e+91) || !(x1 <= 4.1e+130)) {
		tmp = (x1 * (x1 * 9.0)) - x1;
	} else {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-4.5d+91)) .or. (.not. (x1 <= 4.1d+130))) then
        tmp = (x1 * (x1 * 9.0d0)) - x1
    else
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0))) + (x1 + (4.0d0 * (2.0d0 * (x2 * (x1 * x2))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -4.5e+91) || !(x1 <= 4.1e+130)) {
		tmp = (x1 * (x1 * 9.0)) - x1;
	} else {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -4.5e+91) or not (x1 <= 4.1e+130):
		tmp = (x1 * (x1 * 9.0)) - x1
	else:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -4.5e+91) || !(x1 <= 4.1e+130))
		tmp = Float64(Float64(x1 * Float64(x1 * 9.0)) - 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(x1 + Float64(4.0 * Float64(2.0 * Float64(x2 * Float64(x1 * x2)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -4.5e+91) || ~((x1 <= 4.1e+130)))
		tmp = (x1 * (x1 * 9.0)) - x1;
	else
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -4.5e+91], N[Not[LessEqual[x1, 4.1e+130]], $MachinePrecision]], N[(N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] - x1), $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[(x1 + N[(4.0 * N[(2.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -4.5e91 or 4.09999999999999978e130 < x1

   1. Initial program 8.0%

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

   2. Taylor expanded in x2 around inf 0.2%

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

      1. associate-*r/ 0.2%

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

      2. unpow2 0.2%

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

      3. +-commutative 0.2%

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

      4. unpow2 0.2%

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

      5. fma-udef 0.2%

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

   4. Simplified 0.2%

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

   5. Taylor expanded in x1 around 0 62.0%

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

      1. *-commutative 62.0%

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

      2. fma-def 62.0%

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

      3. +-commutative 62.0%

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

      4. fma-def 71.3%

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

      5. *-commutative 71.3%

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

      6. fma-neg 71.3%

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

      7. metadata-eval 71.3%

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

      8. unpow2 71.3%

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

      9. associate-*r* 71.3%

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

      10. *-commutative 71.3%

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

      11. associate-*l* 71.3%

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

      12. unpow2 71.3%

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

      13. cancel-sign-sub-inv 71.3%

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

      14. metadata-eval 71.3%

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

      15. +-commutative 71.3%

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

      16. count-2 71.3%

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

   7. Simplified 71.3%

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

   8. Taylor expanded in x2 around 0 83.9%

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

      1. associate-+r+ 83.9%

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

      2. distribute-rgt1-in 83.9%

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

      3. metadata-eval 83.9%

         \[\leadsto \color{blue}{-1} \cdot x1 + 9 \cdot {x1}^{2} \]

      4. neg-mul-1 83.9%

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

      5. +-commutative 83.9%

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

      6. unsub-neg 83.9%

         \[\leadsto \color{blue}{9 \cdot {x1}^{2} - x1} \]

      7. *-commutative 83.9%

         \[\leadsto \color{blue}{{x1}^{2} \cdot 9} - x1 \]

      8. unpow2 83.9%

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

      9. associate-*l* 83.9%

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

   10. Simplified 83.9%

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

   if -4.5e91 < x1 < 4.09999999999999978e130

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 75.8%

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

   3. Taylor expanded in x2 around inf 75.8%

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

      1. unpow2 75.3%

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

      2. associate-*r* 83.6%

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

      3. *-commutative 83.6%

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

   5. Simplified 84.1%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+91} \lor \neg \left(x1 \leq 4.1 \cdot 10^{+130}\right):\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(2 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 17: 74.0% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 9\right) - x1\\ \mathbf{if}\;x1 \leq -3.7 \cdot 10^{+91}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq -5 \cdot 10^{-114}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot \left(x2 \cdot 8\right)\right) + x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 5.4 \cdot 10^{-235}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 4.1 \cdot 10^{+130}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* x1 (* x1 9.0)) x1)))
   (if (<= x1 -3.7e+91)
     t_0
     (if (<= x1 -5e-114)
       (+ (* x1 (+ -1.0 (* x2 (* x2 8.0)))) (* x2 -6.0))
       (if (<= x1 5.4e-235)
         (- (* x2 -6.0) x1)
         (if (<= x1 4.1e+130)
           (+
            x1
            (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0))))
           t_0))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * (x1 * 9.0)) - x1;
	double tmp;
	if (x1 <= -3.7e+91) {
		tmp = t_0;
	} else if (x1 <= -5e-114) {
		tmp = (x1 * (-1.0 + (x2 * (x2 * 8.0)))) + (x2 * -6.0);
	} else if (x1 <= 5.4e-235) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 4.1e+130) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x1 * (x1 * 9.0d0)) - x1
    if (x1 <= (-3.7d+91)) then
        tmp = t_0
    else if (x1 <= (-5d-114)) then
        tmp = (x1 * ((-1.0d0) + (x2 * (x2 * 8.0d0)))) + (x2 * (-6.0d0))
    else if (x1 <= 5.4d-235) then
        tmp = (x2 * (-6.0d0)) - x1
    else if (x1 <= 4.1d+130) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * (x1 * 9.0)) - x1;
	double tmp;
	if (x1 <= -3.7e+91) {
		tmp = t_0;
	} else if (x1 <= -5e-114) {
		tmp = (x1 * (-1.0 + (x2 * (x2 * 8.0)))) + (x2 * -6.0);
	} else if (x1 <= 5.4e-235) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 4.1e+130) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * (x1 * 9.0)) - x1
	tmp = 0
	if x1 <= -3.7e+91:
		tmp = t_0
	elif x1 <= -5e-114:
		tmp = (x1 * (-1.0 + (x2 * (x2 * 8.0)))) + (x2 * -6.0)
	elif x1 <= 5.4e-235:
		tmp = (x2 * -6.0) - x1
	elif x1 <= 4.1e+130:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * Float64(x1 * 9.0)) - x1)
	tmp = 0.0
	if (x1 <= -3.7e+91)
		tmp = t_0;
	elseif (x1 <= -5e-114)
		tmp = Float64(Float64(x1 * Float64(-1.0 + Float64(x2 * Float64(x2 * 8.0)))) + Float64(x2 * -6.0));
	elseif (x1 <= 5.4e-235)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	elseif (x1 <= 4.1e+130)
		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 = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * (x1 * 9.0)) - x1;
	tmp = 0.0;
	if (x1 <= -3.7e+91)
		tmp = t_0;
	elseif (x1 <= -5e-114)
		tmp = (x1 * (-1.0 + (x2 * (x2 * 8.0)))) + (x2 * -6.0);
	elseif (x1 <= 5.4e-235)
		tmp = (x2 * -6.0) - x1;
	elseif (x1 <= 4.1e+130)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, If[LessEqual[x1, -3.7e+91], t$95$0, If[LessEqual[x1, -5e-114], N[(N[(x1 * N[(-1.0 + N[(x2 * N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.4e-235], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 4.1e+130], 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], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -3.69999999999999984e91 or 4.09999999999999978e130 < x1

   1. Initial program 8.0%

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

   2. Taylor expanded in x2 around inf 0.2%

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

      1. associate-*r/ 0.2%

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

      2. unpow2 0.2%

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

      3. +-commutative 0.2%

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

      4. unpow2 0.2%

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

      5. fma-udef 0.2%

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

   4. Simplified 0.2%

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

   5. Taylor expanded in x1 around 0 62.0%

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

      1. *-commutative 62.0%

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

      2. fma-def 62.0%

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

      3. +-commutative 62.0%

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

      4. fma-def 71.3%

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

      5. *-commutative 71.3%

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

      6. fma-neg 71.3%

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

      7. metadata-eval 71.3%

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

      8. unpow2 71.3%

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

      9. associate-*r* 71.3%

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

      10. *-commutative 71.3%

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

      11. associate-*l* 71.3%

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

      12. unpow2 71.3%

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

      13. cancel-sign-sub-inv 71.3%

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

      14. metadata-eval 71.3%

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

      15. +-commutative 71.3%

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

      16. count-2 71.3%

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

   7. Simplified 71.3%

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

   8. Taylor expanded in x2 around 0 83.9%

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

      1. associate-+r+ 83.9%

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

      2. distribute-rgt1-in 83.9%

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

      3. metadata-eval 83.9%

         \[\leadsto \color{blue}{-1} \cdot x1 + 9 \cdot {x1}^{2} \]

      4. neg-mul-1 83.9%

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

      5. +-commutative 83.9%

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

      6. unsub-neg 83.9%

         \[\leadsto \color{blue}{9 \cdot {x1}^{2} - x1} \]

      7. *-commutative 83.9%

         \[\leadsto \color{blue}{{x1}^{2} \cdot 9} - x1 \]

      8. unpow2 83.9%

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

      9. associate-*l* 83.9%

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

   10. Simplified 83.9%

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

   if -3.69999999999999984e91 < x1 < -4.99999999999999989e-114

   1. Initial program 99.2%

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

   2. Taylor expanded in x2 around inf 72.4%

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

      1. associate-*r/ 72.4%

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

      2. unpow2 72.4%

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

      3. +-commutative 72.4%

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

      4. unpow2 72.4%

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

      5. fma-udef 72.4%

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

   4. Simplified 72.4%

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

   5. Taylor expanded in x1 around 0 68.9%

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

      1. *-commutative 68.9%

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

      2. fma-def 69.0%

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

      3. +-commutative 69.0%

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

      4. fma-def 69.0%

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

      5. *-commutative 69.0%

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

      6. fma-neg 69.0%

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

      7. metadata-eval 69.0%

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

      8. unpow2 69.0%

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

      9. associate-*r* 69.0%

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

      10. *-commutative 69.0%

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

      11. associate-*l* 69.0%

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

      12. unpow2 69.0%

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

      13. cancel-sign-sub-inv 69.0%

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

      14. metadata-eval 69.0%

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

      15. +-commutative 69.0%

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

      16. count-2 69.0%

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

   7. Simplified 69.0%

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

   8. Taylor expanded in x1 around 0 72.3%

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

      1. pow1 72.3%

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

      2. pow2 72.3%

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

      3. *-commutative 72.3%

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

   10. Applied egg-rr 72.3%

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

       1. unpow1 72.3%

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

       2. associate-*l* 72.3%

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

   12. Simplified 72.3%

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

   if -4.99999999999999989e-114 < x1 < 5.4000000000000003e-235

   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 x2 around inf 87.4%

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

      1. associate-*r/ 87.4%

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

      2. unpow2 87.4%

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

      3. +-commutative 87.4%

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

      4. unpow2 87.4%

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

      5. fma-udef 87.4%

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

   4. Simplified 87.4%

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

   5. Taylor expanded in x1 around 0 87.6%

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

      1. *-commutative 87.6%

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

      2. fma-def 87.8%

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

      3. +-commutative 87.8%

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

      4. fma-def 87.8%

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

      5. *-commutative 87.8%

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

      6. fma-neg 87.8%

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

      7. metadata-eval 87.8%

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

      8. unpow2 87.8%

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

      9. associate-*r* 87.8%

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

      10. *-commutative 87.8%

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

      11. associate-*l* 87.8%

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

      12. unpow2 87.8%

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

      13. cancel-sign-sub-inv 87.8%

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

      14. metadata-eval 87.8%

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

      15. +-commutative 87.8%

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

      16. count-2 87.8%

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

   7. Simplified 87.8%

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

   8. Taylor expanded in x1 around 0 87.7%

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

   9. Taylor expanded in x2 around 0 99.7%

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

       1. *-commutative 99.7%

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

       2. mul-1-neg 99.7%

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

       3. unsub-neg 99.7%

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

   11. Simplified 99.7%

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

   if 5.4000000000000003e-235 < x1 < 4.09999999999999978e130

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 67.8%

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

   3. Taylor expanded in x1 around 0 67.1%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.7 \cdot 10^{+91}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \mathbf{elif}\;x1 \leq -5 \cdot 10^{-114}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot \left(x2 \cdot 8\right)\right) + x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 5.4 \cdot 10^{-235}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 4.1 \cdot 10^{+130}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \end{array} \]

Alternative 18: 78.6% accurate, 5.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -5.3 \cdot 10^{+91} \lor \neg \left(x1 \leq 4.1 \cdot 10^{+130}\right):\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(2 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -5.3e+91) (not (<= x1 4.1e+130)))
   (- (* x1 (* x1 9.0)) x1)
   (+
    x1
    (+ (+ x1 (* 4.0 (* 2.0 (* x2 (* x1 x2))))) (* 3.0 (- (* x2 -2.0) x1))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -5.3e+91) || !(x1 <= 4.1e+130)) {
		tmp = (x1 * (x1 * 9.0)) - x1;
	} else {
		tmp = x1 + ((x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))) + (3.0 * ((x2 * -2.0) - x1)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-5.3d+91)) .or. (.not. (x1 <= 4.1d+130))) then
        tmp = (x1 * (x1 * 9.0d0)) - x1
    else
        tmp = x1 + ((x1 + (4.0d0 * (2.0d0 * (x2 * (x1 * x2))))) + (3.0d0 * ((x2 * (-2.0d0)) - x1)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -5.3e+91) || !(x1 <= 4.1e+130)) {
		tmp = (x1 * (x1 * 9.0)) - x1;
	} else {
		tmp = x1 + ((x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))) + (3.0 * ((x2 * -2.0) - x1)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -5.3e+91) or not (x1 <= 4.1e+130):
		tmp = (x1 * (x1 * 9.0)) - x1
	else:
		tmp = x1 + ((x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))) + (3.0 * ((x2 * -2.0) - x1)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -5.3e+91) || !(x1 <= 4.1e+130))
		tmp = Float64(Float64(x1 * Float64(x1 * 9.0)) - x1);
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(2.0 * Float64(x2 * Float64(x1 * x2))))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -5.3e+91) || ~((x1 <= 4.1e+130)))
		tmp = (x1 * (x1 * 9.0)) - x1;
	else
		tmp = x1 + ((x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))) + (3.0 * ((x2 * -2.0) - x1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -5.3e+91], N[Not[LessEqual[x1, 4.1e+130]], $MachinePrecision]], N[(N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(4.0 * N[(2.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -5.29999999999999997e91 or 4.09999999999999978e130 < x1

   1. Initial program 8.0%

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

   2. Taylor expanded in x2 around inf 0.2%

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

      1. associate-*r/ 0.2%

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

      2. unpow2 0.2%

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

      3. +-commutative 0.2%

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

      4. unpow2 0.2%

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

      5. fma-udef 0.2%

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

   4. Simplified 0.2%

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

   5. Taylor expanded in x1 around 0 62.0%

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

      1. *-commutative 62.0%

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

      2. fma-def 62.0%

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

      3. +-commutative 62.0%

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

      4. fma-def 71.3%

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

      5. *-commutative 71.3%

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

      6. fma-neg 71.3%

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

      7. metadata-eval 71.3%

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

      8. unpow2 71.3%

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

      9. associate-*r* 71.3%

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

      10. *-commutative 71.3%

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

      11. associate-*l* 71.3%

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

      12. unpow2 71.3%

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

      13. cancel-sign-sub-inv 71.3%

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

      14. metadata-eval 71.3%

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

      15. +-commutative 71.3%

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

      16. count-2 71.3%

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

   7. Simplified 71.3%

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

   8. Taylor expanded in x2 around 0 83.9%

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

      1. associate-+r+ 83.9%

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

      2. distribute-rgt1-in 83.9%

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

      3. metadata-eval 83.9%

         \[\leadsto \color{blue}{-1} \cdot x1 + 9 \cdot {x1}^{2} \]

      4. neg-mul-1 83.9%

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

      5. +-commutative 83.9%

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

      6. unsub-neg 83.9%

         \[\leadsto \color{blue}{9 \cdot {x1}^{2} - x1} \]

      7. *-commutative 83.9%

         \[\leadsto \color{blue}{{x1}^{2} \cdot 9} - x1 \]

      8. unpow2 83.9%

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

      9. associate-*l* 83.9%

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

   10. Simplified 83.9%

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

   if -5.29999999999999997e91 < x1 < 4.09999999999999978e130

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 75.8%

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

   3. Taylor expanded in x1 around 0 75.3%

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

      1. mul-1-neg 75.3%

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

      2. unsub-neg 75.3%

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

      3. *-commutative 75.3%

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

   5. Simplified 75.3%

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

   6. Taylor expanded in x2 around inf 75.3%

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

      1. unpow2 75.3%

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

      2. associate-*r* 83.6%

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

      3. *-commutative 83.6%

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

   8. Simplified 83.6%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.3 \cdot 10^{+91} \lor \neg \left(x1 \leq 4.1 \cdot 10^{+130}\right):\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(2 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \end{array} \]

Alternative 19: 64.8% accurate, 5.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 9\right) - x1\\ t_1 := x2 \cdot -6 - x1\\ t_2 := x1 + \left(x1 \cdot x2\right) \cdot \left(x2 \cdot 8\right)\\ \mathbf{if}\;x1 \leq -1.12 \cdot 10^{+89}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq -6.8 \cdot 10^{+40}:\\ \;\;\;\;\frac{x2 \cdot x2}{\frac{x1}{8}}\\ \mathbf{elif}\;x1 \leq -4.2 \cdot 10^{-25}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 2.25 \cdot 10^{-154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq 1.1 \cdot 10^{-105}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x1 \leq 2.6 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq 4.1 \cdot 10^{+130}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* x1 (* x1 9.0)) x1))
        (t_1 (- (* x2 -6.0) x1))
        (t_2 (+ x1 (* (* x1 x2) (* x2 8.0)))))
   (if (<= x1 -1.12e+89)
     t_0
     (if (<= x1 -6.8e+40)
       (/ (* x2 x2) (/ x1 8.0))
       (if (<= x1 -4.2e-25)
         t_0
         (if (<= x1 2.25e-154)
           t_1
           (if (<= x1 1.1e-105)
             t_2
             (if (<= x1 2.6e-28) t_1 (if (<= x1 4.1e+130) t_2 t_0)))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * (x1 * 9.0)) - x1;
	double t_1 = (x2 * -6.0) - x1;
	double t_2 = x1 + ((x1 * x2) * (x2 * 8.0));
	double tmp;
	if (x1 <= -1.12e+89) {
		tmp = t_0;
	} else if (x1 <= -6.8e+40) {
		tmp = (x2 * x2) / (x1 / 8.0);
	} else if (x1 <= -4.2e-25) {
		tmp = t_0;
	} else if (x1 <= 2.25e-154) {
		tmp = t_1;
	} else if (x1 <= 1.1e-105) {
		tmp = t_2;
	} else if (x1 <= 2.6e-28) {
		tmp = t_1;
	} else if (x1 <= 4.1e+130) {
		tmp = t_2;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (x1 * (x1 * 9.0d0)) - x1
    t_1 = (x2 * (-6.0d0)) - x1
    t_2 = x1 + ((x1 * x2) * (x2 * 8.0d0))
    if (x1 <= (-1.12d+89)) then
        tmp = t_0
    else if (x1 <= (-6.8d+40)) then
        tmp = (x2 * x2) / (x1 / 8.0d0)
    else if (x1 <= (-4.2d-25)) then
        tmp = t_0
    else if (x1 <= 2.25d-154) then
        tmp = t_1
    else if (x1 <= 1.1d-105) then
        tmp = t_2
    else if (x1 <= 2.6d-28) then
        tmp = t_1
    else if (x1 <= 4.1d+130) then
        tmp = t_2
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * (x1 * 9.0)) - x1;
	double t_1 = (x2 * -6.0) - x1;
	double t_2 = x1 + ((x1 * x2) * (x2 * 8.0));
	double tmp;
	if (x1 <= -1.12e+89) {
		tmp = t_0;
	} else if (x1 <= -6.8e+40) {
		tmp = (x2 * x2) / (x1 / 8.0);
	} else if (x1 <= -4.2e-25) {
		tmp = t_0;
	} else if (x1 <= 2.25e-154) {
		tmp = t_1;
	} else if (x1 <= 1.1e-105) {
		tmp = t_2;
	} else if (x1 <= 2.6e-28) {
		tmp = t_1;
	} else if (x1 <= 4.1e+130) {
		tmp = t_2;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * (x1 * 9.0)) - x1
	t_1 = (x2 * -6.0) - x1
	t_2 = x1 + ((x1 * x2) * (x2 * 8.0))
	tmp = 0
	if x1 <= -1.12e+89:
		tmp = t_0
	elif x1 <= -6.8e+40:
		tmp = (x2 * x2) / (x1 / 8.0)
	elif x1 <= -4.2e-25:
		tmp = t_0
	elif x1 <= 2.25e-154:
		tmp = t_1
	elif x1 <= 1.1e-105:
		tmp = t_2
	elif x1 <= 2.6e-28:
		tmp = t_1
	elif x1 <= 4.1e+130:
		tmp = t_2
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * Float64(x1 * 9.0)) - x1)
	t_1 = Float64(Float64(x2 * -6.0) - x1)
	t_2 = Float64(x1 + Float64(Float64(x1 * x2) * Float64(x2 * 8.0)))
	tmp = 0.0
	if (x1 <= -1.12e+89)
		tmp = t_0;
	elseif (x1 <= -6.8e+40)
		tmp = Float64(Float64(x2 * x2) / Float64(x1 / 8.0));
	elseif (x1 <= -4.2e-25)
		tmp = t_0;
	elseif (x1 <= 2.25e-154)
		tmp = t_1;
	elseif (x1 <= 1.1e-105)
		tmp = t_2;
	elseif (x1 <= 2.6e-28)
		tmp = t_1;
	elseif (x1 <= 4.1e+130)
		tmp = t_2;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * (x1 * 9.0)) - x1;
	t_1 = (x2 * -6.0) - x1;
	t_2 = x1 + ((x1 * x2) * (x2 * 8.0));
	tmp = 0.0;
	if (x1 <= -1.12e+89)
		tmp = t_0;
	elseif (x1 <= -6.8e+40)
		tmp = (x2 * x2) / (x1 / 8.0);
	elseif (x1 <= -4.2e-25)
		tmp = t_0;
	elseif (x1 <= 2.25e-154)
		tmp = t_1;
	elseif (x1 <= 1.1e-105)
		tmp = t_2;
	elseif (x1 <= 2.6e-28)
		tmp = t_1;
	elseif (x1 <= 4.1e+130)
		tmp = t_2;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(N[(x1 * x2), $MachinePrecision] * N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.12e+89], t$95$0, If[LessEqual[x1, -6.8e+40], N[(N[(x2 * x2), $MachinePrecision] / N[(x1 / 8.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -4.2e-25], t$95$0, If[LessEqual[x1, 2.25e-154], t$95$1, If[LessEqual[x1, 1.1e-105], t$95$2, If[LessEqual[x1, 2.6e-28], t$95$1, If[LessEqual[x1, 4.1e+130], t$95$2, t$95$0]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.11999999999999995e89 or -6.79999999999999977e40 < x1 < -4.20000000000000005e-25 or 4.09999999999999978e130 < x1

   1. Initial program 17.8%

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

   2. Taylor expanded in x2 around inf 6.2%

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

      1. associate-*r/ 6.2%

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

      2. unpow2 6.2%

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

      3. +-commutative 6.2%

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

      4. unpow2 6.2%

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

      5. fma-udef 6.2%

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

   4. Simplified 6.2%

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

   5. Taylor expanded in x1 around 0 61.6%

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

      1. *-commutative 61.6%

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

      2. fma-def 61.6%

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

      3. +-commutative 61.6%

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

      4. fma-def 69.9%

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

      5. *-commutative 69.9%

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

      6. fma-neg 69.9%

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

      7. metadata-eval 69.9%

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

      8. unpow2 69.9%

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

      9. associate-*r* 69.9%

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

      10. *-commutative 69.9%

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

      11. associate-*l* 69.9%

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

      12. unpow2 69.9%

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

      13. cancel-sign-sub-inv 69.9%

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

      14. metadata-eval 69.9%

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

      15. +-commutative 69.9%

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

      16. count-2 69.9%

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

   7. Simplified 69.9%

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

   8. Taylor expanded in x2 around 0 78.8%

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

      1. associate-+r+ 78.8%

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

      2. distribute-rgt1-in 78.8%

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

      3. metadata-eval 78.8%

         \[\leadsto \color{blue}{-1} \cdot x1 + 9 \cdot {x1}^{2} \]

      4. neg-mul-1 78.8%

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

      5. +-commutative 78.8%

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

      6. unsub-neg 78.8%

         \[\leadsto \color{blue}{9 \cdot {x1}^{2} - x1} \]

      7. *-commutative 78.8%

         \[\leadsto \color{blue}{{x1}^{2} \cdot 9} - x1 \]

      8. unpow2 78.8%

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

      9. associate-*l* 78.8%

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

   10. Simplified 78.8%

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

   if -1.11999999999999995e89 < x1 < -6.79999999999999977e40

   1. Initial program 99.3%

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

   2. Taylor expanded in x2 around inf 37.4%

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

      1. associate-*r/ 37.4%

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

      2. unpow2 37.4%

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

      3. +-commutative 37.4%

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

      4. unpow2 37.4%

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

      5. fma-udef 37.4%

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

   4. Simplified 37.4%

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

   5. Taylor expanded in x1 around -inf 41.5%

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

      1. associate-+r+ 41.5%

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

      2. +-commutative 41.5%

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

      3. mul-1-neg 41.5%

         \[\leadsto x1 + \left(\left(x1 + 9\right) + \color{blue}{\left(-\frac{3 + -8 \cdot {x2}^{2}}{x1}\right)}\right) \]

      4. *-commutative 41.5%

         \[\leadsto x1 + \left(\left(x1 + 9\right) + \left(-\frac{3 + \color{blue}{{x2}^{2} \cdot -8}}{x1}\right)\right) \]

      5. unpow2 41.5%

         \[\leadsto x1 + \left(\left(x1 + 9\right) + \left(-\frac{3 + \color{blue}{\left(x2 \cdot x2\right)} \cdot -8}{x1}\right)\right) \]

   7. Simplified 41.5%

      \[\leadsto x1 + \color{blue}{\left(\left(x1 + 9\right) + \left(-\frac{3 + \left(x2 \cdot x2\right) \cdot -8}{x1}\right)\right)} \]

   8. Taylor expanded in x2 around inf 41.9%

      \[\leadsto \color{blue}{8 \cdot \frac{{x2}^{2}}{x1}} \]
   9. Step-by-step derivation

      1. associate-*r/ 41.9%

         \[\leadsto \color{blue}{\frac{8 \cdot {x2}^{2}}{x1}} \]

      2. *-commutative 41.9%

         \[\leadsto \frac{\color{blue}{{x2}^{2} \cdot 8}}{x1} \]

      3. associate-/l* 41.9%

         \[\leadsto \color{blue}{\frac{{x2}^{2}}{\frac{x1}{8}}} \]

      4. unpow2 41.9%

         \[\leadsto \frac{\color{blue}{x2 \cdot x2}}{\frac{x1}{8}} \]

   10. Simplified 41.9%

       \[\leadsto \color{blue}{\frac{x2 \cdot x2}{\frac{x1}{8}}} \]

   if -4.20000000000000005e-25 < x1 < 2.2499999999999999e-154 or 1.10000000000000002e-105 < x1 < 2.6e-28

   1. Initial program 99.3%

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

   2. Taylor expanded in x2 around inf 92.1%

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

      1. associate-*r/ 92.1%

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

      2. unpow2 92.1%

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

      3. +-commutative 92.1%

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

      4. unpow2 92.1%

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

      5. fma-udef 92.1%

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

   4. Simplified 92.1%

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

   5. Taylor expanded in x1 around 0 92.5%

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

      1. *-commutative 92.5%

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

      2. fma-def 92.7%

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

      3. +-commutative 92.7%

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

      4. fma-def 92.7%

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

      5. *-commutative 92.7%

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

      6. fma-neg 92.7%

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

      7. metadata-eval 92.7%

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

      8. unpow2 92.7%

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

      9. associate-*r* 92.7%

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

      10. *-commutative 92.7%

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

      11. associate-*l* 92.7%

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

      12. unpow2 92.7%

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

      13. cancel-sign-sub-inv 92.7%

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

      14. metadata-eval 92.7%

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

      15. +-commutative 92.7%

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

      16. count-2 92.7%

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

   7. Simplified 92.7%

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

   8. Taylor expanded in x1 around 0 92.6%

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

   9. Taylor expanded in x2 around 0 85.9%

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

       1. *-commutative 85.9%

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

       2. mul-1-neg 85.9%

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

       3. unsub-neg 85.9%

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

   11. Simplified 85.9%

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

   if 2.2499999999999999e-154 < x1 < 1.10000000000000002e-105 or 2.6e-28 < x1 < 4.09999999999999978e130

   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 42.6%

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

   3. Taylor expanded in x2 around inf 33.2%

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

      1. *-commutative 33.2%

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

      2. unpow2 33.2%

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

      3. associate-*r* 48.7%

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

      4. associate-*l* 48.7%

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

      5. *-commutative 48.7%

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

   5. Simplified 48.7%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot x1\right) \cdot \left(x2 \cdot 8\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.12 \cdot 10^{+89}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \mathbf{elif}\;x1 \leq -6.8 \cdot 10^{+40}:\\ \;\;\;\;\frac{x2 \cdot x2}{\frac{x1}{8}}\\ \mathbf{elif}\;x1 \leq -4.2 \cdot 10^{-25}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \mathbf{elif}\;x1 \leq 2.25 \cdot 10^{-154}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 1.1 \cdot 10^{-105}:\\ \;\;\;\;x1 + \left(x1 \cdot x2\right) \cdot \left(x2 \cdot 8\right)\\ \mathbf{elif}\;x1 \leq 2.6 \cdot 10^{-28}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 4.1 \cdot 10^{+130}:\\ \;\;\;\;x1 + \left(x1 \cdot x2\right) \cdot \left(x2 \cdot 8\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \end{array} \]

Alternative 20: 74.0% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 9\right) - x1\\ t_1 := x1 \cdot \left(-1 + x2 \cdot \left(x2 \cdot 8\right)\right) + x2 \cdot -6\\ \mathbf{if}\;x1 \leq -7.9 \cdot 10^{+90}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq -5 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq 7.8 \cdot 10^{-235}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 4.1 \cdot 10^{+130}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* x1 (* x1 9.0)) x1))
        (t_1 (+ (* x1 (+ -1.0 (* x2 (* x2 8.0)))) (* x2 -6.0))))
   (if (<= x1 -7.9e+90)
     t_0
     (if (<= x1 -5e-114)
       t_1
       (if (<= x1 7.8e-235)
         (- (* x2 -6.0) x1)
         (if (<= x1 4.1e+130) t_1 t_0))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * (x1 * 9.0)) - x1;
	double t_1 = (x1 * (-1.0 + (x2 * (x2 * 8.0)))) + (x2 * -6.0);
	double tmp;
	if (x1 <= -7.9e+90) {
		tmp = t_0;
	} else if (x1 <= -5e-114) {
		tmp = t_1;
	} else if (x1 <= 7.8e-235) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 4.1e+130) {
		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 * 9.0d0)) - x1
    t_1 = (x1 * ((-1.0d0) + (x2 * (x2 * 8.0d0)))) + (x2 * (-6.0d0))
    if (x1 <= (-7.9d+90)) then
        tmp = t_0
    else if (x1 <= (-5d-114)) then
        tmp = t_1
    else if (x1 <= 7.8d-235) then
        tmp = (x2 * (-6.0d0)) - x1
    else if (x1 <= 4.1d+130) 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 * 9.0)) - x1;
	double t_1 = (x1 * (-1.0 + (x2 * (x2 * 8.0)))) + (x2 * -6.0);
	double tmp;
	if (x1 <= -7.9e+90) {
		tmp = t_0;
	} else if (x1 <= -5e-114) {
		tmp = t_1;
	} else if (x1 <= 7.8e-235) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 4.1e+130) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * (x1 * 9.0)) - x1
	t_1 = (x1 * (-1.0 + (x2 * (x2 * 8.0)))) + (x2 * -6.0)
	tmp = 0
	if x1 <= -7.9e+90:
		tmp = t_0
	elif x1 <= -5e-114:
		tmp = t_1
	elif x1 <= 7.8e-235:
		tmp = (x2 * -6.0) - x1
	elif x1 <= 4.1e+130:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * Float64(x1 * 9.0)) - x1)
	t_1 = Float64(Float64(x1 * Float64(-1.0 + Float64(x2 * Float64(x2 * 8.0)))) + Float64(x2 * -6.0))
	tmp = 0.0
	if (x1 <= -7.9e+90)
		tmp = t_0;
	elseif (x1 <= -5e-114)
		tmp = t_1;
	elseif (x1 <= 7.8e-235)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	elseif (x1 <= 4.1e+130)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * (x1 * 9.0)) - x1;
	t_1 = (x1 * (-1.0 + (x2 * (x2 * 8.0)))) + (x2 * -6.0);
	tmp = 0.0;
	if (x1 <= -7.9e+90)
		tmp = t_0;
	elseif (x1 <= -5e-114)
		tmp = t_1;
	elseif (x1 <= 7.8e-235)
		tmp = (x2 * -6.0) - x1;
	elseif (x1 <= 4.1e+130)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * N[(-1.0 + N[(x2 * N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -7.9e+90], t$95$0, If[LessEqual[x1, -5e-114], t$95$1, If[LessEqual[x1, 7.8e-235], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 4.1e+130], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -7.8999999999999996e90 or 4.09999999999999978e130 < x1

   1. Initial program 8.0%

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

   2. Taylor expanded in x2 around inf 0.2%

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

      1. associate-*r/ 0.2%

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

      2. unpow2 0.2%

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

      3. +-commutative 0.2%

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

      4. unpow2 0.2%

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

      5. fma-udef 0.2%

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

   4. Simplified 0.2%

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

   5. Taylor expanded in x1 around 0 62.0%

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

      1. *-commutative 62.0%

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

      2. fma-def 62.0%

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

      3. +-commutative 62.0%

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

      4. fma-def 71.3%

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

      5. *-commutative 71.3%

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

      6. fma-neg 71.3%

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

      7. metadata-eval 71.3%

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

      8. unpow2 71.3%

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

      9. associate-*r* 71.3%

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

      10. *-commutative 71.3%

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

      11. associate-*l* 71.3%

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

      12. unpow2 71.3%

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

      13. cancel-sign-sub-inv 71.3%

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

      14. metadata-eval 71.3%

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

      15. +-commutative 71.3%

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

      16. count-2 71.3%

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

   7. Simplified 71.3%

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

   8. Taylor expanded in x2 around 0 83.9%

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

      1. associate-+r+ 83.9%

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

      2. distribute-rgt1-in 83.9%

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

      3. metadata-eval 83.9%

         \[\leadsto \color{blue}{-1} \cdot x1 + 9 \cdot {x1}^{2} \]

      4. neg-mul-1 83.9%

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

      5. +-commutative 83.9%

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

      6. unsub-neg 83.9%

         \[\leadsto \color{blue}{9 \cdot {x1}^{2} - x1} \]

      7. *-commutative 83.9%

         \[\leadsto \color{blue}{{x1}^{2} \cdot 9} - x1 \]

      8. unpow2 83.9%

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

      9. associate-*l* 83.9%

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

   10. Simplified 83.9%

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

   if -7.8999999999999996e90 < x1 < -4.99999999999999989e-114 or 7.79999999999999939e-235 < x1 < 4.09999999999999978e130

   1. Initial program 99.3%

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

   2. Taylor expanded in x2 around inf 70.8%

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

      1. associate-*r/ 70.8%

         \[\leadsto x1 + \left(\left(\color{blue}{\frac{8 \cdot \left(x1 \cdot {x2}^{2}\right)}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. unpow2 70.8%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \color{blue}{\left(x2 \cdot x2\right)}\right)}{1 + {x1}^{2}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      3. +-commutative 70.8%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{{x1}^{2} + 1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      4. unpow2 70.8%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{x1 \cdot x1} + 1} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      5. fma-udef 70.8%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Simplified 70.8%

      \[\leadsto x1 + \left(\left(\color{blue}{\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Taylor expanded in x1 around 0 68.5%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 68.5%

         \[\leadsto x1 + \left(\color{blue}{x2 \cdot -6} + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)\right) \]

      2. fma-def 68.5%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x2, -6, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)} \]

      3. +-commutative 68.5%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \color{blue}{x1 \cdot \left(8 \cdot {x2}^{2} - 2\right) + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)}\right) \]

      4. fma-def 68.5%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \color{blue}{\mathsf{fma}\left(x1, 8 \cdot {x2}^{2} - 2, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)}\right) \]

      5. *-commutative 68.5%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \color{blue}{{x2}^{2} \cdot 8} - 2, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      6. fma-neg 68.5%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \color{blue}{\mathsf{fma}\left({x2}^{2}, 8, -2\right)}, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      7. metadata-eval 68.5%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left({x2}^{2}, 8, \color{blue}{-2}\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      8. unpow2 68.5%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(\color{blue}{x2 \cdot x2}, 8, -2\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      9. associate-*r* 68.5%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{\left(3 \cdot {x1}^{2}\right) \cdot \left(3 - -2 \cdot x2\right)}\right)\right) \]

      10. *-commutative 68.5%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{\left({x1}^{2} \cdot 3\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      11. associate-*l* 68.5%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{{x1}^{2} \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right)\right)}\right)\right) \]

      12. unpow2 68.5%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{\left(x1 \cdot x1\right)} \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      13. cancel-sign-sub-inv 68.5%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \color{blue}{\left(3 + \left(--2\right) \cdot x2\right)}\right)\right)\right) \]

      14. metadata-eval 68.5%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(3 + \color{blue}{2} \cdot x2\right)\right)\right)\right) \]

      15. +-commutative 68.5%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \color{blue}{\left(2 \cdot x2 + 3\right)}\right)\right)\right) \]

      16. count-2 68.5%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(\color{blue}{\left(x2 + x2\right)} + 3\right)\right)\right)\right) \]

   7. Simplified 68.5%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(\left(x2 + x2\right) + 3\right)\right)\right)\right)} \]

   8. Taylor expanded in x1 around 0 69.0%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(8 \cdot {x2}^{2} - 1\right)} \]
   9. Step-by-step derivation

      1. pow1 69.0%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{{\left(8 \cdot {x2}^{2}\right)}^{1}} - 1\right) \]

      2. pow2 69.0%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left({\left(8 \cdot \color{blue}{\left(x2 \cdot x2\right)}\right)}^{1} - 1\right) \]

      3. *-commutative 69.0%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left({\color{blue}{\left(\left(x2 \cdot x2\right) \cdot 8\right)}}^{1} - 1\right) \]

   10. Applied egg-rr 69.0%

       \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{{\left(\left(x2 \cdot x2\right) \cdot 8\right)}^{1}} - 1\right) \]
   11. Step-by-step derivation

       1. unpow1 69.0%

          \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{\left(x2 \cdot x2\right) \cdot 8} - 1\right) \]

       2. associate-*l* 69.0%

          \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x2 \cdot \left(x2 \cdot 8\right)} - 1\right) \]

   12. Simplified 69.0%

       \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x2 \cdot \left(x2 \cdot 8\right)} - 1\right) \]

   if -4.99999999999999989e-114 < x1 < 7.79999999999999939e-235

   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 x2 around inf 87.4%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{x1 \cdot {x2}^{2}}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   3. Step-by-step derivation

      1. associate-*r/ 87.4%

         \[\leadsto x1 + \left(\left(\color{blue}{\frac{8 \cdot \left(x1 \cdot {x2}^{2}\right)}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. unpow2 87.4%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \color{blue}{\left(x2 \cdot x2\right)}\right)}{1 + {x1}^{2}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      3. +-commutative 87.4%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{{x1}^{2} + 1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      4. unpow2 87.4%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{x1 \cdot x1} + 1} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      5. fma-udef 87.4%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Simplified 87.4%

      \[\leadsto x1 + \left(\left(\color{blue}{\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Taylor expanded in x1 around 0 87.6%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 87.6%

         \[\leadsto x1 + \left(\color{blue}{x2 \cdot -6} + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)\right) \]

      2. fma-def 87.8%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x2, -6, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)} \]

      3. +-commutative 87.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \color{blue}{x1 \cdot \left(8 \cdot {x2}^{2} - 2\right) + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)}\right) \]

      4. fma-def 87.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \color{blue}{\mathsf{fma}\left(x1, 8 \cdot {x2}^{2} - 2, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)}\right) \]

      5. *-commutative 87.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \color{blue}{{x2}^{2} \cdot 8} - 2, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      6. fma-neg 87.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \color{blue}{\mathsf{fma}\left({x2}^{2}, 8, -2\right)}, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      7. metadata-eval 87.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left({x2}^{2}, 8, \color{blue}{-2}\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      8. unpow2 87.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(\color{blue}{x2 \cdot x2}, 8, -2\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      9. associate-*r* 87.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{\left(3 \cdot {x1}^{2}\right) \cdot \left(3 - -2 \cdot x2\right)}\right)\right) \]

      10. *-commutative 87.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{\left({x1}^{2} \cdot 3\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      11. associate-*l* 87.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{{x1}^{2} \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right)\right)}\right)\right) \]

      12. unpow2 87.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{\left(x1 \cdot x1\right)} \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      13. cancel-sign-sub-inv 87.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \color{blue}{\left(3 + \left(--2\right) \cdot x2\right)}\right)\right)\right) \]

      14. metadata-eval 87.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(3 + \color{blue}{2} \cdot x2\right)\right)\right)\right) \]

      15. +-commutative 87.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \color{blue}{\left(2 \cdot x2 + 3\right)}\right)\right)\right) \]

      16. count-2 87.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(\color{blue}{\left(x2 + x2\right)} + 3\right)\right)\right)\right) \]

   7. Simplified 87.8%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(\left(x2 + x2\right) + 3\right)\right)\right)\right)} \]

   8. Taylor expanded in x1 around 0 87.7%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(8 \cdot {x2}^{2} - 1\right)} \]

   9. Taylor expanded in x2 around 0 99.7%

      \[\leadsto \color{blue}{-6 \cdot x2 + -1 \cdot x1} \]
   10. Step-by-step derivation

       1. *-commutative 99.7%

          \[\leadsto \color{blue}{x2 \cdot -6} + -1 \cdot x1 \]

       2. mul-1-neg 99.7%

          \[\leadsto x2 \cdot -6 + \color{blue}{\left(-x1\right)} \]

       3. unsub-neg 99.7%

          \[\leadsto \color{blue}{x2 \cdot -6 - x1} \]

   11. Simplified 99.7%

       \[\leadsto \color{blue}{x2 \cdot -6 - x1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.9 \cdot 10^{+90}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \mathbf{elif}\;x1 \leq -5 \cdot 10^{-114}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot \left(x2 \cdot 8\right)\right) + x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 7.8 \cdot 10^{-235}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 4.1 \cdot 10^{+130}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot \left(x2 \cdot 8\right)\right) + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \end{array} \]

Alternative 21: 65.6% accurate, 7.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 9\right) - x1\\ t_1 := \frac{x2 \cdot x2}{\frac{x1}{8}}\\ \mathbf{if}\;x1 \leq -1.3 \cdot 10^{+89}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq -6.8 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq -4.2 \cdot 10^{-25}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{-25}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 2.5 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* x1 (* x1 9.0)) x1)) (t_1 (/ (* x2 x2) (/ x1 8.0))))
   (if (<= x1 -1.3e+89)
     t_0
     (if (<= x1 -6.8e+40)
       t_1
       (if (<= x1 -4.2e-25)
         t_0
         (if (<= x1 3.9e-25)
           (- (* x2 -6.0) x1)
           (if (<= x1 2.5e+77) t_1 t_0)))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * (x1 * 9.0)) - x1;
	double t_1 = (x2 * x2) / (x1 / 8.0);
	double tmp;
	if (x1 <= -1.3e+89) {
		tmp = t_0;
	} else if (x1 <= -6.8e+40) {
		tmp = t_1;
	} else if (x1 <= -4.2e-25) {
		tmp = t_0;
	} else if (x1 <= 3.9e-25) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 2.5e+77) {
		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 * 9.0d0)) - x1
    t_1 = (x2 * x2) / (x1 / 8.0d0)
    if (x1 <= (-1.3d+89)) then
        tmp = t_0
    else if (x1 <= (-6.8d+40)) then
        tmp = t_1
    else if (x1 <= (-4.2d-25)) then
        tmp = t_0
    else if (x1 <= 3.9d-25) then
        tmp = (x2 * (-6.0d0)) - x1
    else if (x1 <= 2.5d+77) 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 * 9.0)) - x1;
	double t_1 = (x2 * x2) / (x1 / 8.0);
	double tmp;
	if (x1 <= -1.3e+89) {
		tmp = t_0;
	} else if (x1 <= -6.8e+40) {
		tmp = t_1;
	} else if (x1 <= -4.2e-25) {
		tmp = t_0;
	} else if (x1 <= 3.9e-25) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 2.5e+77) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * (x1 * 9.0)) - x1
	t_1 = (x2 * x2) / (x1 / 8.0)
	tmp = 0
	if x1 <= -1.3e+89:
		tmp = t_0
	elif x1 <= -6.8e+40:
		tmp = t_1
	elif x1 <= -4.2e-25:
		tmp = t_0
	elif x1 <= 3.9e-25:
		tmp = (x2 * -6.0) - x1
	elif x1 <= 2.5e+77:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * Float64(x1 * 9.0)) - x1)
	t_1 = Float64(Float64(x2 * x2) / Float64(x1 / 8.0))
	tmp = 0.0
	if (x1 <= -1.3e+89)
		tmp = t_0;
	elseif (x1 <= -6.8e+40)
		tmp = t_1;
	elseif (x1 <= -4.2e-25)
		tmp = t_0;
	elseif (x1 <= 3.9e-25)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	elseif (x1 <= 2.5e+77)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * (x1 * 9.0)) - x1;
	t_1 = (x2 * x2) / (x1 / 8.0);
	tmp = 0.0;
	if (x1 <= -1.3e+89)
		tmp = t_0;
	elseif (x1 <= -6.8e+40)
		tmp = t_1;
	elseif (x1 <= -4.2e-25)
		tmp = t_0;
	elseif (x1 <= 3.9e-25)
		tmp = (x2 * -6.0) - x1;
	elseif (x1 <= 2.5e+77)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x2 * x2), $MachinePrecision] / N[(x1 / 8.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.3e+89], t$95$0, If[LessEqual[x1, -6.8e+40], t$95$1, If[LessEqual[x1, -4.2e-25], t$95$0, If[LessEqual[x1, 3.9e-25], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 2.5e+77], t$95$1, t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.3e89 or -6.79999999999999977e40 < x1 < -4.20000000000000005e-25 or 2.50000000000000002e77 < x1

   1. Initial program 26.5%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x2 around inf 7.0%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{x1 \cdot {x2}^{2}}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   3. Step-by-step derivation

      1. associate-*r/ 7.0%

         \[\leadsto x1 + \left(\left(\color{blue}{\frac{8 \cdot \left(x1 \cdot {x2}^{2}\right)}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. unpow2 7.0%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \color{blue}{\left(x2 \cdot x2\right)}\right)}{1 + {x1}^{2}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      3. +-commutative 7.0%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{{x1}^{2} + 1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      4. unpow2 7.0%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{x1 \cdot x1} + 1} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      5. fma-udef 7.0%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Simplified 7.0%

      \[\leadsto x1 + \left(\left(\color{blue}{\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Taylor expanded in x1 around 0 57.6%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 57.6%

         \[\leadsto x1 + \left(\color{blue}{x2 \cdot -6} + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)\right) \]

      2. fma-def 57.6%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x2, -6, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)} \]

      3. +-commutative 57.6%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \color{blue}{x1 \cdot \left(8 \cdot {x2}^{2} - 2\right) + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)}\right) \]

      4. fma-def 65.0%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \color{blue}{\mathsf{fma}\left(x1, 8 \cdot {x2}^{2} - 2, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)}\right) \]

      5. *-commutative 65.0%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \color{blue}{{x2}^{2} \cdot 8} - 2, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      6. fma-neg 65.0%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \color{blue}{\mathsf{fma}\left({x2}^{2}, 8, -2\right)}, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      7. metadata-eval 65.0%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left({x2}^{2}, 8, \color{blue}{-2}\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      8. unpow2 65.0%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(\color{blue}{x2 \cdot x2}, 8, -2\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      9. associate-*r* 65.0%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{\left(3 \cdot {x1}^{2}\right) \cdot \left(3 - -2 \cdot x2\right)}\right)\right) \]

      10. *-commutative 65.0%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{\left({x1}^{2} \cdot 3\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      11. associate-*l* 65.0%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{{x1}^{2} \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right)\right)}\right)\right) \]

      12. unpow2 65.0%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{\left(x1 \cdot x1\right)} \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      13. cancel-sign-sub-inv 65.0%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \color{blue}{\left(3 + \left(--2\right) \cdot x2\right)}\right)\right)\right) \]

      14. metadata-eval 65.0%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(3 + \color{blue}{2} \cdot x2\right)\right)\right)\right) \]

      15. +-commutative 65.0%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \color{blue}{\left(2 \cdot x2 + 3\right)}\right)\right)\right) \]

      16. count-2 65.0%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(\color{blue}{\left(x2 + x2\right)} + 3\right)\right)\right)\right) \]

   7. Simplified 65.0%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(\left(x2 + x2\right) + 3\right)\right)\right)\right)} \]

   8. Taylor expanded in x2 around 0 71.0%

      \[\leadsto \color{blue}{x1 + \left(-2 \cdot x1 + 9 \cdot {x1}^{2}\right)} \]
   9. Step-by-step derivation

      1. associate-+r+ 71.0%

         \[\leadsto \color{blue}{\left(x1 + -2 \cdot x1\right) + 9 \cdot {x1}^{2}} \]

      2. distribute-rgt1-in 71.0%

         \[\leadsto \color{blue}{\left(-2 + 1\right) \cdot x1} + 9 \cdot {x1}^{2} \]

      3. metadata-eval 71.0%

         \[\leadsto \color{blue}{-1} \cdot x1 + 9 \cdot {x1}^{2} \]

      4. neg-mul-1 71.0%

         \[\leadsto \color{blue}{\left(-x1\right)} + 9 \cdot {x1}^{2} \]

      5. +-commutative 71.0%

         \[\leadsto \color{blue}{9 \cdot {x1}^{2} + \left(-x1\right)} \]

      6. unsub-neg 71.0%

         \[\leadsto \color{blue}{9 \cdot {x1}^{2} - x1} \]

      7. *-commutative 71.0%

         \[\leadsto \color{blue}{{x1}^{2} \cdot 9} - x1 \]

      8. unpow2 71.0%

         \[\leadsto \color{blue}{\left(x1 \cdot x1\right)} \cdot 9 - x1 \]

      9. associate-*l* 71.0%

         \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot 9\right)} - x1 \]

   10. Simplified 71.0%

       \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot 9\right) - x1} \]

   if -1.3e89 < x1 < -6.79999999999999977e40 or 3.9e-25 < x1 < 2.50000000000000002e77

   1. Initial program 99.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x2 around inf 52.8%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{x1 \cdot {x2}^{2}}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   3. Step-by-step derivation

      1. associate-*r/ 52.8%

         \[\leadsto x1 + \left(\left(\color{blue}{\frac{8 \cdot \left(x1 \cdot {x2}^{2}\right)}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. unpow2 52.8%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \color{blue}{\left(x2 \cdot x2\right)}\right)}{1 + {x1}^{2}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      3. +-commutative 52.8%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{{x1}^{2} + 1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      4. unpow2 52.8%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{x1 \cdot x1} + 1} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      5. fma-udef 52.8%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Simplified 52.8%

      \[\leadsto x1 + \left(\left(\color{blue}{\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Taylor expanded in x1 around -inf 48.5%

      \[\leadsto x1 + \color{blue}{\left(9 + \left(x1 + -1 \cdot \frac{3 + -8 \cdot {x2}^{2}}{x1}\right)\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 48.5%

         \[\leadsto x1 + \color{blue}{\left(\left(9 + x1\right) + -1 \cdot \frac{3 + -8 \cdot {x2}^{2}}{x1}\right)} \]

      2. +-commutative 48.5%

         \[\leadsto x1 + \left(\color{blue}{\left(x1 + 9\right)} + -1 \cdot \frac{3 + -8 \cdot {x2}^{2}}{x1}\right) \]

      3. mul-1-neg 48.5%

         \[\leadsto x1 + \left(\left(x1 + 9\right) + \color{blue}{\left(-\frac{3 + -8 \cdot {x2}^{2}}{x1}\right)}\right) \]

      4. *-commutative 48.5%

         \[\leadsto x1 + \left(\left(x1 + 9\right) + \left(-\frac{3 + \color{blue}{{x2}^{2} \cdot -8}}{x1}\right)\right) \]

      5. unpow2 48.5%

         \[\leadsto x1 + \left(\left(x1 + 9\right) + \left(-\frac{3 + \color{blue}{\left(x2 \cdot x2\right)} \cdot -8}{x1}\right)\right) \]

   7. Simplified 48.5%

      \[\leadsto x1 + \color{blue}{\left(\left(x1 + 9\right) + \left(-\frac{3 + \left(x2 \cdot x2\right) \cdot -8}{x1}\right)\right)} \]

   8. Taylor expanded in x2 around inf 47.8%

      \[\leadsto \color{blue}{8 \cdot \frac{{x2}^{2}}{x1}} \]
   9. Step-by-step derivation

      1. associate-*r/ 47.8%

         \[\leadsto \color{blue}{\frac{8 \cdot {x2}^{2}}{x1}} \]

      2. *-commutative 47.8%

         \[\leadsto \frac{\color{blue}{{x2}^{2} \cdot 8}}{x1} \]

      3. associate-/l* 47.8%

         \[\leadsto \color{blue}{\frac{{x2}^{2}}{\frac{x1}{8}}} \]

      4. unpow2 47.8%

         \[\leadsto \frac{\color{blue}{x2 \cdot x2}}{\frac{x1}{8}} \]

   10. Simplified 47.8%

       \[\leadsto \color{blue}{\frac{x2 \cdot x2}{\frac{x1}{8}}} \]

   if -4.20000000000000005e-25 < x1 < 3.9e-25

   1. Initial program 99.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x2 around inf 88.5%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{x1 \cdot {x2}^{2}}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   3. Step-by-step derivation

      1. associate-*r/ 88.5%

         \[\leadsto x1 + \left(\left(\color{blue}{\frac{8 \cdot \left(x1 \cdot {x2}^{2}\right)}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. unpow2 88.5%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \color{blue}{\left(x2 \cdot x2\right)}\right)}{1 + {x1}^{2}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      3. +-commutative 88.5%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{{x1}^{2} + 1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      4. unpow2 88.5%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{x1 \cdot x1} + 1} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      5. fma-udef 88.5%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Simplified 88.5%

      \[\leadsto x1 + \left(\left(\color{blue}{\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Taylor expanded in x1 around 0 88.9%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 88.9%

         \[\leadsto x1 + \left(\color{blue}{x2 \cdot -6} + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)\right) \]

      2. fma-def 89.1%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x2, -6, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)} \]

      3. +-commutative 89.1%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \color{blue}{x1 \cdot \left(8 \cdot {x2}^{2} - 2\right) + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)}\right) \]

      4. fma-def 89.1%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \color{blue}{\mathsf{fma}\left(x1, 8 \cdot {x2}^{2} - 2, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)}\right) \]

      5. *-commutative 89.1%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \color{blue}{{x2}^{2} \cdot 8} - 2, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      6. fma-neg 89.1%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \color{blue}{\mathsf{fma}\left({x2}^{2}, 8, -2\right)}, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      7. metadata-eval 89.1%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left({x2}^{2}, 8, \color{blue}{-2}\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      8. unpow2 89.1%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(\color{blue}{x2 \cdot x2}, 8, -2\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      9. associate-*r* 89.1%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{\left(3 \cdot {x1}^{2}\right) \cdot \left(3 - -2 \cdot x2\right)}\right)\right) \]

      10. *-commutative 89.1%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{\left({x1}^{2} \cdot 3\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      11. associate-*l* 89.1%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{{x1}^{2} \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right)\right)}\right)\right) \]

      12. unpow2 89.1%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{\left(x1 \cdot x1\right)} \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      13. cancel-sign-sub-inv 89.1%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \color{blue}{\left(3 + \left(--2\right) \cdot x2\right)}\right)\right)\right) \]

      14. metadata-eval 89.1%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(3 + \color{blue}{2} \cdot x2\right)\right)\right)\right) \]

      15. +-commutative 89.1%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \color{blue}{\left(2 \cdot x2 + 3\right)}\right)\right)\right) \]

      16. count-2 89.1%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(\color{blue}{\left(x2 + x2\right)} + 3\right)\right)\right)\right) \]

   7. Simplified 89.1%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(\left(x2 + x2\right) + 3\right)\right)\right)\right)} \]

   8. Taylor expanded in x1 around 0 88.9%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(8 \cdot {x2}^{2} - 1\right)} \]

   9. Taylor expanded in x2 around 0 81.1%

      \[\leadsto \color{blue}{-6 \cdot x2 + -1 \cdot x1} \]
   10. Step-by-step derivation

       1. *-commutative 81.1%

          \[\leadsto \color{blue}{x2 \cdot -6} + -1 \cdot x1 \]

       2. mul-1-neg 81.1%

          \[\leadsto x2 \cdot -6 + \color{blue}{\left(-x1\right)} \]

       3. unsub-neg 81.1%

          \[\leadsto \color{blue}{x2 \cdot -6 - x1} \]

   11. Simplified 81.1%

       \[\leadsto \color{blue}{x2 \cdot -6 - x1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.3 \cdot 10^{+89}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \mathbf{elif}\;x1 \leq -6.8 \cdot 10^{+40}:\\ \;\;\;\;\frac{x2 \cdot x2}{\frac{x1}{8}}\\ \mathbf{elif}\;x1 \leq -4.2 \cdot 10^{-25}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{-25}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 2.5 \cdot 10^{+77}:\\ \;\;\;\;\frac{x2 \cdot x2}{\frac{x1}{8}}\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \end{array} \]

Alternative 22: 63.6% accurate, 11.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -4.2 \cdot 10^{-25} \lor \neg \left(x1 \leq 3 \cdot 10^{-9}\right):\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -4.2e-25) (not (<= x1 3e-9)))
   (- (* x1 (* x1 9.0)) x1)
   (- (* x2 -6.0) x1)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -4.2e-25) || !(x1 <= 3e-9)) {
		tmp = (x1 * (x1 * 9.0)) - x1;
	} else {
		tmp = (x2 * -6.0) - x1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-4.2d-25)) .or. (.not. (x1 <= 3d-9))) then
        tmp = (x1 * (x1 * 9.0d0)) - x1
    else
        tmp = (x2 * (-6.0d0)) - x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -4.2e-25) || !(x1 <= 3e-9)) {
		tmp = (x1 * (x1 * 9.0)) - x1;
	} else {
		tmp = (x2 * -6.0) - x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -4.2e-25) or not (x1 <= 3e-9):
		tmp = (x1 * (x1 * 9.0)) - x1
	else:
		tmp = (x2 * -6.0) - x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -4.2e-25) || !(x1 <= 3e-9))
		tmp = Float64(Float64(x1 * Float64(x1 * 9.0)) - x1);
	else
		tmp = Float64(Float64(x2 * -6.0) - x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -4.2e-25) || ~((x1 <= 3e-9)))
		tmp = (x1 * (x1 * 9.0)) - x1;
	else
		tmp = (x2 * -6.0) - x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -4.2e-25], N[Not[LessEqual[x1, 3e-9]], $MachinePrecision]], N[(N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -4.20000000000000005e-25 or 2.99999999999999998e-9 < x1

   1. Initial program 42.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x2 around inf 15.7%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{x1 \cdot {x2}^{2}}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   3. Step-by-step derivation

      1. associate-*r/ 15.7%

         \[\leadsto x1 + \left(\left(\color{blue}{\frac{8 \cdot \left(x1 \cdot {x2}^{2}\right)}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. unpow2 15.7%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \color{blue}{\left(x2 \cdot x2\right)}\right)}{1 + {x1}^{2}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      3. +-commutative 15.7%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{{x1}^{2} + 1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      4. unpow2 15.7%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{x1 \cdot x1} + 1} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      5. fma-udef 15.7%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Simplified 15.7%

      \[\leadsto x1 + \left(\left(\color{blue}{\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Taylor expanded in x1 around 0 51.7%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 51.7%

         \[\leadsto x1 + \left(\color{blue}{x2 \cdot -6} + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)\right) \]

      2. fma-def 51.7%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x2, -6, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)} \]

      3. +-commutative 51.7%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \color{blue}{x1 \cdot \left(8 \cdot {x2}^{2} - 2\right) + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)}\right) \]

      4. fma-def 57.6%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \color{blue}{\mathsf{fma}\left(x1, 8 \cdot {x2}^{2} - 2, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)}\right) \]

      5. *-commutative 57.6%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \color{blue}{{x2}^{2} \cdot 8} - 2, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      6. fma-neg 57.6%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \color{blue}{\mathsf{fma}\left({x2}^{2}, 8, -2\right)}, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      7. metadata-eval 57.6%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left({x2}^{2}, 8, \color{blue}{-2}\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      8. unpow2 57.6%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(\color{blue}{x2 \cdot x2}, 8, -2\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      9. associate-*r* 57.6%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{\left(3 \cdot {x1}^{2}\right) \cdot \left(3 - -2 \cdot x2\right)}\right)\right) \]

      10. *-commutative 57.6%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{\left({x1}^{2} \cdot 3\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      11. associate-*l* 57.6%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{{x1}^{2} \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right)\right)}\right)\right) \]

      12. unpow2 57.6%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{\left(x1 \cdot x1\right)} \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      13. cancel-sign-sub-inv 57.6%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \color{blue}{\left(3 + \left(--2\right) \cdot x2\right)}\right)\right)\right) \]

      14. metadata-eval 57.6%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(3 + \color{blue}{2} \cdot x2\right)\right)\right)\right) \]

      15. +-commutative 57.6%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \color{blue}{\left(2 \cdot x2 + 3\right)}\right)\right)\right) \]

      16. count-2 57.6%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(\color{blue}{\left(x2 + x2\right)} + 3\right)\right)\right)\right) \]

   7. Simplified 57.6%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(\left(x2 + x2\right) + 3\right)\right)\right)\right)} \]

   8. Taylor expanded in x2 around 0 57.3%

      \[\leadsto \color{blue}{x1 + \left(-2 \cdot x1 + 9 \cdot {x1}^{2}\right)} \]
   9. Step-by-step derivation

      1. associate-+r+ 57.3%

         \[\leadsto \color{blue}{\left(x1 + -2 \cdot x1\right) + 9 \cdot {x1}^{2}} \]

      2. distribute-rgt1-in 57.3%

         \[\leadsto \color{blue}{\left(-2 + 1\right) \cdot x1} + 9 \cdot {x1}^{2} \]

      3. metadata-eval 57.3%

         \[\leadsto \color{blue}{-1} \cdot x1 + 9 \cdot {x1}^{2} \]

      4. neg-mul-1 57.3%

         \[\leadsto \color{blue}{\left(-x1\right)} + 9 \cdot {x1}^{2} \]

      5. +-commutative 57.3%

         \[\leadsto \color{blue}{9 \cdot {x1}^{2} + \left(-x1\right)} \]

      6. unsub-neg 57.3%

         \[\leadsto \color{blue}{9 \cdot {x1}^{2} - x1} \]

      7. *-commutative 57.3%

         \[\leadsto \color{blue}{{x1}^{2} \cdot 9} - x1 \]

      8. unpow2 57.3%

         \[\leadsto \color{blue}{\left(x1 \cdot x1\right)} \cdot 9 - x1 \]

      9. associate-*l* 57.3%

         \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot 9\right)} - x1 \]

   10. Simplified 57.3%

       \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot 9\right) - x1} \]

   if -4.20000000000000005e-25 < x1 < 2.99999999999999998e-9

   1. Initial program 99.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x2 around inf 88.3%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{x1 \cdot {x2}^{2}}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   3. Step-by-step derivation

      1. associate-*r/ 88.3%

         \[\leadsto x1 + \left(\left(\color{blue}{\frac{8 \cdot \left(x1 \cdot {x2}^{2}\right)}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. unpow2 88.3%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \color{blue}{\left(x2 \cdot x2\right)}\right)}{1 + {x1}^{2}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      3. +-commutative 88.3%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{{x1}^{2} + 1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      4. unpow2 88.3%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{x1 \cdot x1} + 1} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      5. fma-udef 88.3%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Simplified 88.3%

      \[\leadsto x1 + \left(\left(\color{blue}{\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Taylor expanded in x1 around 0 88.7%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 88.7%

         \[\leadsto x1 + \left(\color{blue}{x2 \cdot -6} + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)\right) \]

      2. fma-def 88.8%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x2, -6, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)} \]

      3. +-commutative 88.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \color{blue}{x1 \cdot \left(8 \cdot {x2}^{2} - 2\right) + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)}\right) \]

      4. fma-def 88.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \color{blue}{\mathsf{fma}\left(x1, 8 \cdot {x2}^{2} - 2, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)}\right) \]

      5. *-commutative 88.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \color{blue}{{x2}^{2} \cdot 8} - 2, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      6. fma-neg 88.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \color{blue}{\mathsf{fma}\left({x2}^{2}, 8, -2\right)}, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      7. metadata-eval 88.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left({x2}^{2}, 8, \color{blue}{-2}\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      8. unpow2 88.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(\color{blue}{x2 \cdot x2}, 8, -2\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      9. associate-*r* 88.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{\left(3 \cdot {x1}^{2}\right) \cdot \left(3 - -2 \cdot x2\right)}\right)\right) \]

      10. *-commutative 88.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{\left({x1}^{2} \cdot 3\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      11. associate-*l* 88.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{{x1}^{2} \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right)\right)}\right)\right) \]

      12. unpow2 88.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{\left(x1 \cdot x1\right)} \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      13. cancel-sign-sub-inv 88.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \color{blue}{\left(3 + \left(--2\right) \cdot x2\right)}\right)\right)\right) \]

      14. metadata-eval 88.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(3 + \color{blue}{2} \cdot x2\right)\right)\right)\right) \]

      15. +-commutative 88.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \color{blue}{\left(2 \cdot x2 + 3\right)}\right)\right)\right) \]

      16. count-2 88.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(\color{blue}{\left(x2 + x2\right)} + 3\right)\right)\right)\right) \]

   7. Simplified 88.8%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(\left(x2 + x2\right) + 3\right)\right)\right)\right)} \]

   8. Taylor expanded in x1 around 0 88.7%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(8 \cdot {x2}^{2} - 1\right)} \]

   9. Taylor expanded in x2 around 0 78.3%

      \[\leadsto \color{blue}{-6 \cdot x2 + -1 \cdot x1} \]
   10. Step-by-step derivation

       1. *-commutative 78.3%

          \[\leadsto \color{blue}{x2 \cdot -6} + -1 \cdot x1 \]

       2. mul-1-neg 78.3%

          \[\leadsto x2 \cdot -6 + \color{blue}{\left(-x1\right)} \]

       3. unsub-neg 78.3%

          \[\leadsto \color{blue}{x2 \cdot -6 - x1} \]

   11. Simplified 78.3%

       \[\leadsto \color{blue}{x2 \cdot -6 - x1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.2 \cdot 10^{-25} \lor \neg \left(x1 \leq 3 \cdot 10^{-9}\right):\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \]

Alternative 23: 31.8% accurate, 13.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -2.2 \cdot 10^{-113}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 1.62 \cdot 10^{-158}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 -2.2e-113)
   (* x2 -6.0)
   (if (<= x2 1.62e-158) (+ x1 (* x1 -2.0)) (* x2 -6.0))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= -2.2e-113) {
		tmp = x2 * -6.0;
	} else if (x2 <= 1.62e-158) {
		tmp = x1 + (x1 * -2.0);
	} 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 (x2 <= (-2.2d-113)) then
        tmp = x2 * (-6.0d0)
    else if (x2 <= 1.62d-158) then
        tmp = x1 + (x1 * (-2.0d0))
    else
        tmp = x2 * (-6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x2 <= -2.2e-113) {
		tmp = x2 * -6.0;
	} else if (x2 <= 1.62e-158) {
		tmp = x1 + (x1 * -2.0);
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= -2.2e-113:
		tmp = x2 * -6.0
	elif x2 <= 1.62e-158:
		tmp = x1 + (x1 * -2.0)
	else:
		tmp = x2 * -6.0
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= -2.2e-113)
		tmp = Float64(x2 * -6.0);
	elseif (x2 <= 1.62e-158)
		tmp = Float64(x1 + Float64(x1 * -2.0));
	else
		tmp = Float64(x2 * -6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= -2.2e-113)
		tmp = x2 * -6.0;
	elseif (x2 <= 1.62e-158)
		tmp = x1 + (x1 * -2.0);
	else
		tmp = x2 * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, -2.2e-113], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x2, 1.62e-158], N[(x1 + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision], N[(x2 * -6.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x2 < -2.20000000000000004e-113 or 1.62000000000000002e-158 < x2

   1. Initial program 71.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x2 around inf 52.2%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{x1 \cdot {x2}^{2}}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   3. Step-by-step derivation

      1. associate-*r/ 52.2%

         \[\leadsto x1 + \left(\left(\color{blue}{\frac{8 \cdot \left(x1 \cdot {x2}^{2}\right)}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. unpow2 52.2%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \color{blue}{\left(x2 \cdot x2\right)}\right)}{1 + {x1}^{2}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      3. +-commutative 52.2%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{{x1}^{2} + 1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      4. unpow2 52.2%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{x1 \cdot x1} + 1} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      5. fma-udef 52.2%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Simplified 52.2%

      \[\leadsto x1 + \left(\left(\color{blue}{\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Taylor expanded in x1 around 0 67.5%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 67.5%

         \[\leadsto x1 + \left(\color{blue}{x2 \cdot -6} + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)\right) \]

      2. fma-def 67.6%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x2, -6, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)} \]

      3. +-commutative 67.6%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \color{blue}{x1 \cdot \left(8 \cdot {x2}^{2} - 2\right) + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)}\right) \]

      4. fma-def 71.4%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \color{blue}{\mathsf{fma}\left(x1, 8 \cdot {x2}^{2} - 2, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)}\right) \]

      5. *-commutative 71.4%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \color{blue}{{x2}^{2} \cdot 8} - 2, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      6. fma-neg 71.4%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \color{blue}{\mathsf{fma}\left({x2}^{2}, 8, -2\right)}, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      7. metadata-eval 71.4%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left({x2}^{2}, 8, \color{blue}{-2}\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      8. unpow2 71.4%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(\color{blue}{x2 \cdot x2}, 8, -2\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      9. associate-*r* 71.4%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{\left(3 \cdot {x1}^{2}\right) \cdot \left(3 - -2 \cdot x2\right)}\right)\right) \]

      10. *-commutative 71.4%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{\left({x1}^{2} \cdot 3\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      11. associate-*l* 71.4%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{{x1}^{2} \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right)\right)}\right)\right) \]

      12. unpow2 71.4%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{\left(x1 \cdot x1\right)} \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      13. cancel-sign-sub-inv 71.4%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \color{blue}{\left(3 + \left(--2\right) \cdot x2\right)}\right)\right)\right) \]

      14. metadata-eval 71.4%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(3 + \color{blue}{2} \cdot x2\right)\right)\right)\right) \]

      15. +-commutative 71.4%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \color{blue}{\left(2 \cdot x2 + 3\right)}\right)\right)\right) \]

      16. count-2 71.4%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(\color{blue}{\left(x2 + x2\right)} + 3\right)\right)\right)\right) \]

   7. Simplified 71.4%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(\left(x2 + x2\right) + 3\right)\right)\right)\right)} \]

   8. Taylor expanded in x1 around 0 34.7%

      \[\leadsto \color{blue}{-6 \cdot x2} \]
   9. Step-by-step derivation

      1. *-commutative 34.7%

         \[\leadsto \color{blue}{x2 \cdot -6} \]

   10. Simplified 34.7%

       \[\leadsto \color{blue}{x2 \cdot -6} \]

   if -2.20000000000000004e-113 < x2 < 1.62000000000000002e-158

   1. Initial program 74.8%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 59.4%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 59.7%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2 + -1 \cdot x1\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg 59.7%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(-2 \cdot x2 + \color{blue}{\left(-x1\right)}\right)\right) \]

      2. unsub-neg 59.7%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2 - x1\right)}\right) \]

      3. *-commutative 59.7%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{x2 \cdot -2} - x1\right)\right) \]

   5. Simplified 59.7%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2 - x1\right)}\right) \]

   6. Taylor expanded in x2 around 0 43.2%

      \[\leadsto x1 + \color{blue}{\left(x1 + -3 \cdot x1\right)} \]
   7. Step-by-step derivation

      1. distribute-rgt1-in 43.7%

         \[\leadsto x1 + \color{blue}{\left(-3 + 1\right) \cdot x1} \]

      2. metadata-eval 43.7%

         \[\leadsto x1 + \color{blue}{-2} \cdot x1 \]

      3. *-commutative 43.7%

         \[\leadsto x1 + \color{blue}{x1 \cdot -2} \]

   8. Simplified 43.7%

      \[\leadsto x1 + \color{blue}{x1 \cdot -2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -2.2 \cdot 10^{-113}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 1.62 \cdot 10^{-158}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]

Alternative 24: 32.1% accurate, 13.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -1.38 \cdot 10^{-111}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 1.45 \cdot 10^{-159}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 -1.38e-111)
   (* x2 -6.0)
   (if (<= x2 1.45e-159) (+ x1 (* x1 -2.0)) (+ x1 (* x2 -6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= -1.38e-111) {
		tmp = x2 * -6.0;
	} else if (x2 <= 1.45e-159) {
		tmp = x1 + (x1 * -2.0);
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x2 <= (-1.38d-111)) then
        tmp = x2 * (-6.0d0)
    else if (x2 <= 1.45d-159) then
        tmp = x1 + (x1 * (-2.0d0))
    else
        tmp = x1 + (x2 * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x2 <= -1.38e-111) {
		tmp = x2 * -6.0;
	} else if (x2 <= 1.45e-159) {
		tmp = x1 + (x1 * -2.0);
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= -1.38e-111:
		tmp = x2 * -6.0
	elif x2 <= 1.45e-159:
		tmp = x1 + (x1 * -2.0)
	else:
		tmp = x1 + (x2 * -6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= -1.38e-111)
		tmp = Float64(x2 * -6.0);
	elseif (x2 <= 1.45e-159)
		tmp = Float64(x1 + Float64(x1 * -2.0));
	else
		tmp = Float64(x1 + Float64(x2 * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= -1.38e-111)
		tmp = x2 * -6.0;
	elseif (x2 <= 1.45e-159)
		tmp = x1 + (x1 * -2.0);
	else
		tmp = x1 + (x2 * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, -1.38e-111], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x2, 1.45e-159], N[(x1 + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -1.38000000000000004e-111

   1. Initial program 79.2%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x2 around inf 58.4%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{x1 \cdot {x2}^{2}}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   3. Step-by-step derivation

      1. associate-*r/ 58.4%

         \[\leadsto x1 + \left(\left(\color{blue}{\frac{8 \cdot \left(x1 \cdot {x2}^{2}\right)}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. unpow2 58.4%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \color{blue}{\left(x2 \cdot x2\right)}\right)}{1 + {x1}^{2}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      3. +-commutative 58.4%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{{x1}^{2} + 1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      4. unpow2 58.4%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{x1 \cdot x1} + 1} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      5. fma-udef 58.4%

         \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Simplified 58.4%

      \[\leadsto x1 + \left(\left(\color{blue}{\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Taylor expanded in x1 around 0 65.0%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 65.0%

         \[\leadsto x1 + \left(\color{blue}{x2 \cdot -6} + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)\right) \]

      2. fma-def 65.1%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x2, -6, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)} \]

      3. +-commutative 65.1%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \color{blue}{x1 \cdot \left(8 \cdot {x2}^{2} - 2\right) + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)}\right) \]

      4. fma-def 65.1%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \color{blue}{\mathsf{fma}\left(x1, 8 \cdot {x2}^{2} - 2, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)}\right) \]

      5. *-commutative 65.1%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \color{blue}{{x2}^{2} \cdot 8} - 2, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      6. fma-neg 65.1%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \color{blue}{\mathsf{fma}\left({x2}^{2}, 8, -2\right)}, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      7. metadata-eval 65.1%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left({x2}^{2}, 8, \color{blue}{-2}\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      8. unpow2 65.1%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(\color{blue}{x2 \cdot x2}, 8, -2\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      9. associate-*r* 65.1%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{\left(3 \cdot {x1}^{2}\right) \cdot \left(3 - -2 \cdot x2\right)}\right)\right) \]

      10. *-commutative 65.1%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{\left({x1}^{2} \cdot 3\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      11. associate-*l* 65.1%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{{x1}^{2} \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right)\right)}\right)\right) \]

      12. unpow2 65.1%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{\left(x1 \cdot x1\right)} \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      13. cancel-sign-sub-inv 65.1%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \color{blue}{\left(3 + \left(--2\right) \cdot x2\right)}\right)\right)\right) \]

      14. metadata-eval 65.1%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(3 + \color{blue}{2} \cdot x2\right)\right)\right)\right) \]

      15. +-commutative 65.1%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \color{blue}{\left(2 \cdot x2 + 3\right)}\right)\right)\right) \]

      16. count-2 65.1%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(\color{blue}{\left(x2 + x2\right)} + 3\right)\right)\right)\right) \]

   7. Simplified 65.1%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(\left(x2 + x2\right) + 3\right)\right)\right)\right)} \]

   8. Taylor expanded in x1 around 0 43.7%

      \[\leadsto \color{blue}{-6 \cdot x2} \]
   9. Step-by-step derivation

      1. *-commutative 43.7%

         \[\leadsto \color{blue}{x2 \cdot -6} \]

   10. Simplified 43.7%

       \[\leadsto \color{blue}{x2 \cdot -6} \]

   if -1.38000000000000004e-111 < x2 < 1.44999999999999995e-159

   1. Initial program 74.8%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 59.4%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 59.7%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2 + -1 \cdot x1\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg 59.7%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(-2 \cdot x2 + \color{blue}{\left(-x1\right)}\right)\right) \]

      2. unsub-neg 59.7%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2 - x1\right)}\right) \]

      3. *-commutative 59.7%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{x2 \cdot -2} - x1\right)\right) \]

   5. Simplified 59.7%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2 - x1\right)}\right) \]

   6. Taylor expanded in x2 around 0 43.2%

      \[\leadsto x1 + \color{blue}{\left(x1 + -3 \cdot x1\right)} \]
   7. Step-by-step derivation

      1. distribute-rgt1-in 43.7%

         \[\leadsto x1 + \color{blue}{\left(-3 + 1\right) \cdot x1} \]

      2. metadata-eval 43.7%

         \[\leadsto x1 + \color{blue}{-2} \cdot x1 \]

      3. *-commutative 43.7%

         \[\leadsto x1 + \color{blue}{x1 \cdot -2} \]

   8. Simplified 43.7%

      \[\leadsto x1 + \color{blue}{x1 \cdot -2} \]

   if 1.44999999999999995e-159 < x2

   1. Initial program 66.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 46.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 29.4%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 29.4%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 29.4%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
3. Recombined 3 regimes into one program.

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.38 \cdot 10^{-111}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 1.45 \cdot 10^{-159}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \]

Alternative 25: 38.2% accurate, 25.4× speedup

Math

\[\begin{array}{l} \\ x2 \cdot -6 - x1 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (- (* x2 -6.0) x1))

C

double code(double x1, double x2) {
	return (x2 * -6.0) - x1;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = (x2 * (-6.0d0)) - x1
end function

Java

public static double code(double x1, double x2) {
	return (x2 * -6.0) - x1;
}

Python

def code(x1, x2):
	return (x2 * -6.0) - x1

Julia

function code(x1, x2)
	return Float64(Float64(x2 * -6.0) - x1)
end

MATLAB

function tmp = code(x1, x2)
	tmp = (x2 * -6.0) - x1;
end

Wolfram

code[x1_, x2_] := N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision]

Derivation

1. Initial program 72.6%

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

2. Taylor expanded in x2 around inf 54.3%

   \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{x1 \cdot {x2}^{2}}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Step-by-step derivation

   1. associate-*r/ 54.3%

      \[\leadsto x1 + \left(\left(\color{blue}{\frac{8 \cdot \left(x1 \cdot {x2}^{2}\right)}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. unpow2 54.3%

      \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \color{blue}{\left(x2 \cdot x2\right)}\right)}{1 + {x1}^{2}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. +-commutative 54.3%

      \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{{x1}^{2} + 1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. unpow2 54.3%

      \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{x1 \cdot x1} + 1} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. fma-udef 54.3%

      \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

4. Simplified 54.3%

   \[\leadsto x1 + \left(\left(\color{blue}{\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

5. Taylor expanded in x1 around 0 71.4%

   \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)\right)} \]
6. Step-by-step derivation

   1. *-commutative 71.4%

      \[\leadsto x1 + \left(\color{blue}{x2 \cdot -6} + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)\right) \]

   2. fma-def 71.4%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x2, -6, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)} \]

   3. +-commutative 71.4%

      \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \color{blue}{x1 \cdot \left(8 \cdot {x2}^{2} - 2\right) + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)}\right) \]

   4. fma-def 74.2%

      \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \color{blue}{\mathsf{fma}\left(x1, 8 \cdot {x2}^{2} - 2, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)}\right) \]

   5. *-commutative 74.2%

      \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \color{blue}{{x2}^{2} \cdot 8} - 2, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

   6. fma-neg 74.2%

      \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \color{blue}{\mathsf{fma}\left({x2}^{2}, 8, -2\right)}, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

   7. metadata-eval 74.2%

      \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left({x2}^{2}, 8, \color{blue}{-2}\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

   8. unpow2 74.2%

      \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(\color{blue}{x2 \cdot x2}, 8, -2\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

   9. associate-*r* 74.2%

      \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{\left(3 \cdot {x1}^{2}\right) \cdot \left(3 - -2 \cdot x2\right)}\right)\right) \]

   10. *-commutative 74.2%

       \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{\left({x1}^{2} \cdot 3\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

   11. associate-*l* 74.2%

       \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{{x1}^{2} \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right)\right)}\right)\right) \]

   12. unpow2 74.2%

       \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{\left(x1 \cdot x1\right)} \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

   13. cancel-sign-sub-inv 74.2%

       \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \color{blue}{\left(3 + \left(--2\right) \cdot x2\right)}\right)\right)\right) \]

   14. metadata-eval 74.2%

       \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(3 + \color{blue}{2} \cdot x2\right)\right)\right)\right) \]

   15. +-commutative 74.2%

       \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \color{blue}{\left(2 \cdot x2 + 3\right)}\right)\right)\right) \]

   16. count-2 74.2%

       \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(\color{blue}{\left(x2 + x2\right)} + 3\right)\right)\right)\right) \]

7. Simplified 74.2%

   \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(\left(x2 + x2\right) + 3\right)\right)\right)\right)} \]

8. Taylor expanded in x1 around 0 61.0%

   \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(8 \cdot {x2}^{2} - 1\right)} \]

9. Taylor expanded in x2 around 0 44.1%

   \[\leadsto \color{blue}{-6 \cdot x2 + -1 \cdot x1} \]
10. Step-by-step derivation

    1. *-commutative 44.1%

       \[\leadsto \color{blue}{x2 \cdot -6} + -1 \cdot x1 \]

    2. mul-1-neg 44.1%

       \[\leadsto x2 \cdot -6 + \color{blue}{\left(-x1\right)} \]

    3. unsub-neg 44.1%

       \[\leadsto \color{blue}{x2 \cdot -6 - x1} \]

11. Simplified 44.1%

    \[\leadsto \color{blue}{x2 \cdot -6 - x1} \]

12. Final simplification 44.1%

    \[\leadsto x2 \cdot -6 - x1 \]

Alternative 26: 26.0% accurate, 42.3× speedup

Math

\[\begin{array}{l} \\ x2 \cdot -6 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (* x2 -6.0))

C

double code(double x1, double x2) {
	return x2 * -6.0;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x2 * (-6.0d0)
end function

Java

public static double code(double x1, double x2) {
	return x2 * -6.0;
}

Python

def code(x1, x2):
	return x2 * -6.0

Julia

function code(x1, x2)
	return Float64(x2 * -6.0)
end

MATLAB

function tmp = code(x1, x2)
	tmp = x2 * -6.0;
end

Wolfram

code[x1_, x2_] := N[(x2 * -6.0), $MachinePrecision]

Derivation

1. Initial program 72.6%

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

2. Taylor expanded in x2 around inf 54.3%

   \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{x1 \cdot {x2}^{2}}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Step-by-step derivation

   1. associate-*r/ 54.3%

      \[\leadsto x1 + \left(\left(\color{blue}{\frac{8 \cdot \left(x1 \cdot {x2}^{2}\right)}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. unpow2 54.3%

      \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \color{blue}{\left(x2 \cdot x2\right)}\right)}{1 + {x1}^{2}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. +-commutative 54.3%

      \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{{x1}^{2} + 1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. unpow2 54.3%

      \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{x1 \cdot x1} + 1} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. fma-udef 54.3%

      \[\leadsto x1 + \left(\left(\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

4. Simplified 54.3%

   \[\leadsto x1 + \left(\left(\color{blue}{\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

5. Taylor expanded in x1 around 0 71.4%

   \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)\right)} \]
6. Step-by-step derivation

   1. *-commutative 71.4%

      \[\leadsto x1 + \left(\color{blue}{x2 \cdot -6} + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)\right) \]

   2. fma-def 71.4%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x2, -6, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)} \]

   3. +-commutative 71.4%

      \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \color{blue}{x1 \cdot \left(8 \cdot {x2}^{2} - 2\right) + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)}\right) \]

   4. fma-def 74.2%

      \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \color{blue}{\mathsf{fma}\left(x1, 8 \cdot {x2}^{2} - 2, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)}\right) \]

   5. *-commutative 74.2%

      \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \color{blue}{{x2}^{2} \cdot 8} - 2, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

   6. fma-neg 74.2%

      \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \color{blue}{\mathsf{fma}\left({x2}^{2}, 8, -2\right)}, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

   7. metadata-eval 74.2%

      \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left({x2}^{2}, 8, \color{blue}{-2}\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

   8. unpow2 74.2%

      \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(\color{blue}{x2 \cdot x2}, 8, -2\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

   9. associate-*r* 74.2%

      \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{\left(3 \cdot {x1}^{2}\right) \cdot \left(3 - -2 \cdot x2\right)}\right)\right) \]

   10. *-commutative 74.2%

       \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{\left({x1}^{2} \cdot 3\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

   11. associate-*l* 74.2%

       \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{{x1}^{2} \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right)\right)}\right)\right) \]

   12. unpow2 74.2%

       \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \color{blue}{\left(x1 \cdot x1\right)} \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

   13. cancel-sign-sub-inv 74.2%

       \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \color{blue}{\left(3 + \left(--2\right) \cdot x2\right)}\right)\right)\right) \]

   14. metadata-eval 74.2%

       \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(3 + \color{blue}{2} \cdot x2\right)\right)\right)\right) \]

   15. +-commutative 74.2%

       \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \color{blue}{\left(2 \cdot x2 + 3\right)}\right)\right)\right) \]

   16. count-2 74.2%

       \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(\color{blue}{\left(x2 + x2\right)} + 3\right)\right)\right)\right) \]

7. Simplified 74.2%

   \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot x2, 8, -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(\left(x2 + x2\right) + 3\right)\right)\right)\right)} \]

8. Taylor expanded in x1 around 0 30.2%

   \[\leadsto \color{blue}{-6 \cdot x2} \]
9. Step-by-step derivation

   1. *-commutative 30.2%

      \[\leadsto \color{blue}{x2 \cdot -6} \]

10. Simplified 30.2%

    \[\leadsto \color{blue}{x2 \cdot -6} \]

11. Final simplification 30.2%

    \[\leadsto x2 \cdot -6 \]

Reproduce

herbie shell --seed 2023283 
(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))))))