Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 71.0% → 99.6%

Time: 35.2s

Alternatives: 26

Speedup: 4.7×

• 46.5% 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: 71.0% 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: 99.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

function code(x1, x2)
	t_0 = Float64(3.0 * Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = fma(x1, Float64(x1 * 3.0), Float64(2.0 * x2))
	t_3 = Float64(Float64(t_2 - x1) / fma(x1, x1, 1.0))
	t_4 = Float64(Float64(x1 * x1) + 1.0)
	t_5 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_4)
	t_6 = Float64(Float64(x1 - t_2) / fma(x1, x1, 1.0))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_4 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_5) * Float64(t_5 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_5 * 4.0) - 6.0)))) + Float64(t_1 * t_5)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_4)))) <= 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(Float64(x1 * Float64(2.0 * t_6)) * Float64(t_6 - -3.0))), fma(t_0, t_3, (x1 ^ 3.0))))));
	else
		tmp = Float64(6.0 * (x1 ^ 4.0));
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.5%

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

   3. Simplified 99.7%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.8%

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

Alternative 2: 99.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.5%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.6%

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

Alternative 3: 96.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \left(t\_0 + 2 \cdot x2\right) - x1\\ t_3 := -1 - x1 \cdot x1\\ t_4 := \frac{t\_2}{t\_3}\\ \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+63} \lor \neg \left(x1 \leq 1.2 \cdot 10^{+35}\right):\\ \;\;\;\;{x1}^{4} \cdot \left(6 + \frac{\frac{9 + 4 \cdot \left(2 \cdot x2 - 3\right)}{x1} - 3}{x1}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(t\_0 \cdot t\_4 - t\_3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_4\right) + \left(\frac{t\_2}{t\_1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x1 - 2 \cdot x2\right)\right)\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

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_3 (- -1.0 (* x1 x1)))
        (t_4 (/ t_2 t_3)))
   (if (or (<= x1 -5.5e+63) (not (<= x1 1.2e+35)))
     (*
      (pow x1 4.0)
      (+ 6.0 (/ (- (/ (+ 9.0 (* 4.0 (- (* 2.0 x2) 3.0))) x1) 3.0) x1)))
     (+
      x1
      (+
       (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))
       (+
        x1
        (-
         (* x1 (* x1 x1))
         (-
          (* t_0 t_4)
          (*
           t_3
           (+
            (* (* x1 x1) (+ 6.0 (* 4.0 t_4)))
            (* (- (/ t_2 t_1) 3.0) (* (* x1 2.0) (- x1 (* 2.0 x2))))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = (t_0 + (2.0 * x2)) - x1;
	double t_3 = -1.0 - (x1 * x1);
	double t_4 = t_2 / t_3;
	double tmp;
	if ((x1 <= -5.5e+63) || !(x1 <= 1.2e+35)) {
		tmp = pow(x1, 4.0) * (6.0 + ((((9.0 + (4.0 * ((2.0 * x2) - 3.0))) / x1) - 3.0) / x1));
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) - ((t_0 * t_4) - (t_3 * (((x1 * x1) * (6.0 + (4.0 * t_4))) + (((t_2 / t_1) - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: 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) + 1.0d0
    t_2 = (t_0 + (2.0d0 * x2)) - x1
    t_3 = (-1.0d0) - (x1 * x1)
    t_4 = t_2 / t_3
    if ((x1 <= (-5.5d+63)) .or. (.not. (x1 <= 1.2d+35))) then
        tmp = (x1 ** 4.0d0) * (6.0d0 + ((((9.0d0 + (4.0d0 * ((2.0d0 * x2) - 3.0d0))) / x1) - 3.0d0) / x1))
    else
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) - ((t_0 * t_4) - (t_3 * (((x1 * x1) * (6.0d0 + (4.0d0 * t_4))) + (((t_2 / t_1) - 3.0d0) * ((x1 * 2.0d0) * (x1 - (2.0d0 * x2))))))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = (t_0 + (2.0 * x2)) - x1;
	double t_3 = -1.0 - (x1 * x1);
	double t_4 = t_2 / t_3;
	double tmp;
	if ((x1 <= -5.5e+63) || !(x1 <= 1.2e+35)) {
		tmp = Math.pow(x1, 4.0) * (6.0 + ((((9.0 + (4.0 * ((2.0 * x2) - 3.0))) / x1) - 3.0) / x1));
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) - ((t_0 * t_4) - (t_3 * (((x1 * x1) * (6.0 + (4.0 * t_4))) + (((t_2 / t_1) - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = (t_0 + (2.0 * x2)) - x1
	t_3 = -1.0 - (x1 * x1)
	t_4 = t_2 / t_3
	tmp = 0
	if (x1 <= -5.5e+63) or not (x1 <= 1.2e+35):
		tmp = math.pow(x1, 4.0) * (6.0 + ((((9.0 + (4.0 * ((2.0 * x2) - 3.0))) / x1) - 3.0) / x1))
	else:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) - ((t_0 * t_4) - (t_3 * (((x1 * x1) * (6.0 + (4.0 * t_4))) + (((t_2 / t_1) - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(t_0 + Float64(2.0 * x2)) - x1)
	t_3 = Float64(-1.0 - Float64(x1 * x1))
	t_4 = Float64(t_2 / t_3)
	tmp = 0.0
	if ((x1 <= -5.5e+63) || !(x1 <= 1.2e+35))
		tmp = Float64((x1 ^ 4.0) * Float64(6.0 + Float64(Float64(Float64(Float64(9.0 + Float64(4.0 * Float64(Float64(2.0 * x2) - 3.0))) / x1) - 3.0) / 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 * t_4) - Float64(t_3 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_4))) + Float64(Float64(Float64(t_2 / t_1) - 3.0) * Float64(Float64(x1 * 2.0) * Float64(x1 - Float64(2.0 * x2)))))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = (t_0 + (2.0 * x2)) - x1;
	t_3 = -1.0 - (x1 * x1);
	t_4 = t_2 / t_3;
	tmp = 0.0;
	if ((x1 <= -5.5e+63) || ~((x1 <= 1.2e+35)))
		tmp = (x1 ^ 4.0) * (6.0 + ((((9.0 + (4.0 * ((2.0 * x2) - 3.0))) / x1) - 3.0) / x1));
	else
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) - ((t_0 * t_4) - (t_3 * (((x1 * x1) * (6.0 + (4.0 * t_4))) + (((t_2 / t_1) - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$3 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 / t$95$3), $MachinePrecision]}, If[Or[LessEqual[x1, -5.5e+63], N[Not[LessEqual[x1, 1.2e+35]], $MachinePrecision]], N[(N[Power[x1, 4.0], $MachinePrecision] * N[(6.0 + N[(N[(N[(N[(9.0 + N[(4.0 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision] - 3.0), $MachinePrecision] / x1), $MachinePrecision]), $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$4), $MachinePrecision] - N[(t$95$3 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t$95$2 / t$95$1), $MachinePrecision] - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(x1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -5.50000000000000004e63 or 1.20000000000000007e35 < x1

   1. Initial program 31.6%

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

   3. Simplified 31.6%

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

   5. Taylor expanded in x1 around -inf 99.9%

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

   if -5.50000000000000004e63 < x1 < 1.20000000000000007e35

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around 0 96.5%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+63} \lor \neg \left(x1 \leq 1.2 \cdot 10^{+35}\right):\\ \;\;\;\;{x1}^{4} \cdot \left(6 + \frac{\frac{9 + 4 \cdot \left(2 \cdot x2 - 3\right)}{x1} - 3}{x1}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x1 - 2 \cdot x2\right)\right)\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 - 2 \cdot x2\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := -1 - x1 \cdot x1\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := \left(t\_3 + 2 \cdot x2\right) - x1\\ t_5 := x1 \cdot x1 + 1\\ t_6 := \frac{t\_4}{t\_5}\\ t_7 := t\_6 - 3\\ \mathbf{if}\;x1 \leq -3.5 \cdot 10^{+66}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq -3.3 \cdot 10^{-6}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t\_5 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_6\right) \cdot t\_7 + \left(x1 \cdot x1\right) \cdot \left(t\_6 \cdot 4 - 6\right)\right) + t\_3 \cdot t\_6\right) + t\_1\right)\right) + 9\right)\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_3 - 2 \cdot x2\right) - x1}{t\_5} + \left(x1 + \left(t\_1 - \left(t\_3 \cdot t\_0 - t\_2 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{t\_4}{t\_2}\right) + t\_7 \cdot \left(\left(x1 \cdot 2\right) \cdot t\_0\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 9\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- x1 (* 2.0 x2)))
        (t_1 (* x1 (* x1 x1)))
        (t_2 (- -1.0 (* x1 x1)))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (- (+ t_3 (* 2.0 x2)) x1))
        (t_5 (+ (* x1 x1) 1.0))
        (t_6 (/ t_4 t_5))
        (t_7 (- t_6 3.0)))
   (if (<= x1 -3.5e+66)
     (* 6.0 (pow x1 4.0))
     (if (<= x1 -3.3e-6)
       (+
        x1
        (+
         (+
          x1
          (+
           (+
            (*
             t_5
             (+ (* (* (* x1 2.0) t_6) t_7) (* (* x1 x1) (- (* t_6 4.0) 6.0))))
            (* t_3 t_6))
           t_1))
         9.0))
       (if (<= x1 3.9e+102)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_3 (* 2.0 x2)) x1) t_5))
           (+
            x1
            (-
             t_1
             (-
              (* t_3 t_0)
              (*
               t_2
               (+
                (* (* x1 x1) (+ 6.0 (* 4.0 (/ t_4 t_2))))
                (* t_7 (* (* x1 2.0) t_0)))))))))
         (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 (+ (* x1 3.0) 9.0)) 2.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 - (2.0 * x2);
	double t_1 = x1 * (x1 * x1);
	double t_2 = -1.0 - (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = (t_3 + (2.0 * x2)) - x1;
	double t_5 = (x1 * x1) + 1.0;
	double t_6 = t_4 / t_5;
	double t_7 = t_6 - 3.0;
	double tmp;
	if (x1 <= -3.5e+66) {
		tmp = 6.0 * pow(x1, 4.0);
	} else if (x1 <= -3.3e-6) {
		tmp = x1 + ((x1 + (((t_5 * ((((x1 * 2.0) * t_6) * t_7) + ((x1 * x1) * ((t_6 * 4.0) - 6.0)))) + (t_3 * t_6)) + t_1)) + 9.0);
	} else if (x1 <= 3.9e+102) {
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_5)) + (x1 + (t_1 - ((t_3 * t_0) - (t_2 * (((x1 * x1) * (6.0 + (4.0 * (t_4 / t_2)))) + (t_7 * ((x1 * 2.0) * t_0))))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + 9.0)) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = x1 - (2.0d0 * x2)
    t_1 = x1 * (x1 * x1)
    t_2 = (-1.0d0) - (x1 * x1)
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = (t_3 + (2.0d0 * x2)) - x1
    t_5 = (x1 * x1) + 1.0d0
    t_6 = t_4 / t_5
    t_7 = t_6 - 3.0d0
    if (x1 <= (-3.5d+66)) then
        tmp = 6.0d0 * (x1 ** 4.0d0)
    else if (x1 <= (-3.3d-6)) then
        tmp = x1 + ((x1 + (((t_5 * ((((x1 * 2.0d0) * t_6) * t_7) + ((x1 * x1) * ((t_6 * 4.0d0) - 6.0d0)))) + (t_3 * t_6)) + t_1)) + 9.0d0)
    else if (x1 <= 3.9d+102) then
        tmp = x1 + ((3.0d0 * (((t_3 - (2.0d0 * x2)) - x1) / t_5)) + (x1 + (t_1 - ((t_3 * t_0) - (t_2 * (((x1 * x1) * (6.0d0 + (4.0d0 * (t_4 / t_2)))) + (t_7 * ((x1 * 2.0d0) * t_0))))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * ((x1 * 3.0d0) + 9.0d0)) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 - (2.0 * x2);
	double t_1 = x1 * (x1 * x1);
	double t_2 = -1.0 - (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = (t_3 + (2.0 * x2)) - x1;
	double t_5 = (x1 * x1) + 1.0;
	double t_6 = t_4 / t_5;
	double t_7 = t_6 - 3.0;
	double tmp;
	if (x1 <= -3.5e+66) {
		tmp = 6.0 * Math.pow(x1, 4.0);
	} else if (x1 <= -3.3e-6) {
		tmp = x1 + ((x1 + (((t_5 * ((((x1 * 2.0) * t_6) * t_7) + ((x1 * x1) * ((t_6 * 4.0) - 6.0)))) + (t_3 * t_6)) + t_1)) + 9.0);
	} else if (x1 <= 3.9e+102) {
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_5)) + (x1 + (t_1 - ((t_3 * t_0) - (t_2 * (((x1 * x1) * (6.0 + (4.0 * (t_4 / t_2)))) + (t_7 * ((x1 * 2.0) * t_0))))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + 9.0)) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 - (2.0 * x2)
	t_1 = x1 * (x1 * x1)
	t_2 = -1.0 - (x1 * x1)
	t_3 = x1 * (x1 * 3.0)
	t_4 = (t_3 + (2.0 * x2)) - x1
	t_5 = (x1 * x1) + 1.0
	t_6 = t_4 / t_5
	t_7 = t_6 - 3.0
	tmp = 0
	if x1 <= -3.5e+66:
		tmp = 6.0 * math.pow(x1, 4.0)
	elif x1 <= -3.3e-6:
		tmp = x1 + ((x1 + (((t_5 * ((((x1 * 2.0) * t_6) * t_7) + ((x1 * x1) * ((t_6 * 4.0) - 6.0)))) + (t_3 * t_6)) + t_1)) + 9.0)
	elif x1 <= 3.9e+102:
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_5)) + (x1 + (t_1 - ((t_3 * t_0) - (t_2 * (((x1 * x1) * (6.0 + (4.0 * (t_4 / t_2)))) + (t_7 * ((x1 * 2.0) * t_0))))))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + 9.0)) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 - Float64(2.0 * x2))
	t_1 = Float64(x1 * Float64(x1 * x1))
	t_2 = Float64(-1.0 - Float64(x1 * x1))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(Float64(t_3 + Float64(2.0 * x2)) - x1)
	t_5 = Float64(Float64(x1 * x1) + 1.0)
	t_6 = Float64(t_4 / t_5)
	t_7 = Float64(t_6 - 3.0)
	tmp = 0.0
	if (x1 <= -3.5e+66)
		tmp = Float64(6.0 * (x1 ^ 4.0));
	elseif (x1 <= -3.3e-6)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_5 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_6) * t_7) + Float64(Float64(x1 * x1) * Float64(Float64(t_6 * 4.0) - 6.0)))) + Float64(t_3 * t_6)) + t_1)) + 9.0));
	elseif (x1 <= 3.9e+102)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_3 - Float64(2.0 * x2)) - x1) / t_5)) + Float64(x1 + Float64(t_1 - Float64(Float64(t_3 * t_0) - Float64(t_2 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * Float64(t_4 / t_2)))) + Float64(t_7 * Float64(Float64(x1 * 2.0) * t_0)))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0)) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 - (2.0 * x2);
	t_1 = x1 * (x1 * x1);
	t_2 = -1.0 - (x1 * x1);
	t_3 = x1 * (x1 * 3.0);
	t_4 = (t_3 + (2.0 * x2)) - x1;
	t_5 = (x1 * x1) + 1.0;
	t_6 = t_4 / t_5;
	t_7 = t_6 - 3.0;
	tmp = 0.0;
	if (x1 <= -3.5e+66)
		tmp = 6.0 * (x1 ^ 4.0);
	elseif (x1 <= -3.3e-6)
		tmp = x1 + ((x1 + (((t_5 * ((((x1 * 2.0) * t_6) * t_7) + ((x1 * x1) * ((t_6 * 4.0) - 6.0)))) + (t_3 * t_6)) + t_1)) + 9.0);
	elseif (x1 <= 3.9e+102)
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_5)) + (x1 + (t_1 - ((t_3 * t_0) - (t_2 * (((x1 * x1) * (6.0 + (4.0 * (t_4 / t_2)))) + (t_7 * ((x1 * 2.0) * t_0))))))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + 9.0)) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$4 / t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$6 - 3.0), $MachinePrecision]}, If[LessEqual[x1, -3.5e+66], N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -3.3e-6], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$5 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$6), $MachinePrecision] * t$95$7), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$6 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 * t$95$6), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.9e+102], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$3 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$5), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$1 - N[(N[(t$95$3 * t$95$0), $MachinePrecision] - N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * N[(t$95$4 / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$7 * N[(N[(x1 * 2.0), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -3.4999999999999997e66

   1. Initial program 10.0%

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

   3. Simplified 9.9%

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

   5. Taylor expanded in x1 around inf 100.0%

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

   if -3.4999999999999997e66 < x1 < -3.30000000000000017e-6

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around inf 99.4%

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

   if -3.30000000000000017e-6 < x1 < 3.8999999999999998e102

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 98.9%

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

   4. Taylor expanded in x1 around 0 98.9%

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

   if 3.8999999999999998e102 < x1

   1. Initial program 26.8%

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

   3. Simplified 26.8%

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

   5. Taylor expanded in x1 around 0 8.3%

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

      1. associate-*r* 8.3%

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

      2. fmm-def 8.3%

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

      3. metadata-eval 8.3%

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

   7. Simplified 8.3%

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

   8. Taylor expanded in x1 around 0 92.7%

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

   9. Taylor expanded in x2 around 0 100.0%

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

       1. *-commutative 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.5 \cdot 10^{+66}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq -3.3 \cdot 10^{-6}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 9\right)\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x1 - 2 \cdot x2\right) - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x1 - 2 \cdot x2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 9\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 92.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -4.1 \cdot 10^{+15} \lor \neg \left(x1 \leq 4.7 \cdot 10^{+33}\right):\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 - x1 \cdot \left(x1 \cdot 3 + 9\right)\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -4.1e+15) (not (<= x1 4.7e+33)))
   (* 6.0 (pow x1 4.0))
   (-
    x1
    (-
     (+
      (* x1 (- 2.0 (* x1 (+ (* x1 3.0) 9.0))))
      (* x2 (- (* x1 (- 12.0 (* x1 6.0))) (* 8.0 (* x1 x2)))))
     (* x2 -6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -4.1e+15) || !(x1 <= 4.7e+33)) {
		tmp = 6.0 * pow(x1, 4.0);
	} else {
		tmp = x1 - (((x1 * (2.0 - (x1 * ((x1 * 3.0) + 9.0)))) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-4.1d+15)) .or. (.not. (x1 <= 4.7d+33))) then
        tmp = 6.0d0 * (x1 ** 4.0d0)
    else
        tmp = x1 - (((x1 * (2.0d0 - (x1 * ((x1 * 3.0d0) + 9.0d0)))) + (x2 * ((x1 * (12.0d0 - (x1 * 6.0d0))) - (8.0d0 * (x1 * x2))))) - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -4.1e+15) || !(x1 <= 4.7e+33)) {
		tmp = 6.0 * Math.pow(x1, 4.0);
	} else {
		tmp = x1 - (((x1 * (2.0 - (x1 * ((x1 * 3.0) + 9.0)))) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -4.1e+15) or not (x1 <= 4.7e+33):
		tmp = 6.0 * math.pow(x1, 4.0)
	else:
		tmp = x1 - (((x1 * (2.0 - (x1 * ((x1 * 3.0) + 9.0)))) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -4.1e+15) || !(x1 <= 4.7e+33))
		tmp = Float64(6.0 * (x1 ^ 4.0));
	else
		tmp = Float64(x1 - Float64(Float64(Float64(x1 * Float64(2.0 - Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0)))) + Float64(x2 * Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(8.0 * Float64(x1 * x2))))) - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -4.1e+15) || ~((x1 <= 4.7e+33)))
		tmp = 6.0 * (x1 ^ 4.0);
	else
		tmp = x1 - (((x1 * (2.0 - (x1 * ((x1 * 3.0) + 9.0)))) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -4.1e+15], N[Not[LessEqual[x1, 4.7e+33]], $MachinePrecision]], N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision], N[(x1 - N[(N[(N[(x1 * N[(2.0 - N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -4.1e15 or 4.6999999999999998e33 < x1

   1. Initial program 38.3%

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

   3. Simplified 38.3%

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

   5. Taylor expanded in x1 around inf 94.4%

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

   if -4.1e15 < x1 < 4.6999999999999998e33

   1. Initial program 99.5%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x1 around 0 86.9%

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

      1. associate-*r* 96.1%

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

      2. fmm-def 96.1%

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

      3. metadata-eval 96.1%

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

   7. Simplified 96.1%

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

   8. Taylor expanded in x1 around 0 87.1%

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

   9. Taylor expanded in x2 around 0 96.2%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right)\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.1 \cdot 10^{+15} \lor \neg \left(x1 \leq 4.7 \cdot 10^{+33}\right):\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 - x1 \cdot \left(x1 \cdot 3 + 9\right)\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 - 2 \cdot x2\\ t_1 := -1 - x1 \cdot x1\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := x1 \cdot x1 + 1\\ t_4 := \left(t\_2 + 2 \cdot x2\right) - x1\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+63}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_2 - 2 \cdot x2\right) - x1}{t\_3} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(t\_2 \cdot t\_0 - t\_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{t\_4}{t\_1}\right) + \left(\frac{t\_4}{t\_3} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot t\_0\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 9\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- x1 (* 2.0 x2)))
        (t_1 (- -1.0 (* x1 x1)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (- (+ t_2 (* 2.0 x2)) x1)))
   (if (<= x1 -5.6e+63)
     (* 6.0 (pow x1 4.0))
     (if (<= x1 3.9e+102)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_3))
         (+
          x1
          (-
           (* x1 (* x1 x1))
           (-
            (* t_2 t_0)
            (*
             t_1
             (+
              (* (* x1 x1) (+ 6.0 (* 4.0 (/ t_4 t_1))))
              (* (- (/ t_4 t_3) 3.0) (* (* x1 2.0) t_0)))))))))
       (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 (+ (* x1 3.0) 9.0)) 2.0))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 - (2.0 * x2);
	double t_1 = -1.0 - (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = (t_2 + (2.0 * x2)) - x1;
	double tmp;
	if (x1 <= -5.6e+63) {
		tmp = 6.0 * pow(x1, 4.0);
	} else if (x1 <= 3.9e+102) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_3)) + (x1 + ((x1 * (x1 * x1)) - ((t_2 * t_0) - (t_1 * (((x1 * x1) * (6.0 + (4.0 * (t_4 / t_1)))) + (((t_4 / t_3) - 3.0) * ((x1 * 2.0) * t_0))))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + 9.0)) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = x1 - (2.0d0 * x2)
    t_1 = (-1.0d0) - (x1 * x1)
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = (x1 * x1) + 1.0d0
    t_4 = (t_2 + (2.0d0 * x2)) - x1
    if (x1 <= (-5.6d+63)) then
        tmp = 6.0d0 * (x1 ** 4.0d0)
    else if (x1 <= 3.9d+102) then
        tmp = x1 + ((3.0d0 * (((t_2 - (2.0d0 * x2)) - x1) / t_3)) + (x1 + ((x1 * (x1 * x1)) - ((t_2 * t_0) - (t_1 * (((x1 * x1) * (6.0d0 + (4.0d0 * (t_4 / t_1)))) + (((t_4 / t_3) - 3.0d0) * ((x1 * 2.0d0) * t_0))))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * ((x1 * 3.0d0) + 9.0d0)) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 - (2.0 * x2);
	double t_1 = -1.0 - (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = (t_2 + (2.0 * x2)) - x1;
	double tmp;
	if (x1 <= -5.6e+63) {
		tmp = 6.0 * Math.pow(x1, 4.0);
	} else if (x1 <= 3.9e+102) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_3)) + (x1 + ((x1 * (x1 * x1)) - ((t_2 * t_0) - (t_1 * (((x1 * x1) * (6.0 + (4.0 * (t_4 / t_1)))) + (((t_4 / t_3) - 3.0) * ((x1 * 2.0) * t_0))))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + 9.0)) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 - (2.0 * x2)
	t_1 = -1.0 - (x1 * x1)
	t_2 = x1 * (x1 * 3.0)
	t_3 = (x1 * x1) + 1.0
	t_4 = (t_2 + (2.0 * x2)) - x1
	tmp = 0
	if x1 <= -5.6e+63:
		tmp = 6.0 * math.pow(x1, 4.0)
	elif x1 <= 3.9e+102:
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_3)) + (x1 + ((x1 * (x1 * x1)) - ((t_2 * t_0) - (t_1 * (((x1 * x1) * (6.0 + (4.0 * (t_4 / t_1)))) + (((t_4 / t_3) - 3.0) * ((x1 * 2.0) * t_0))))))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + 9.0)) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 - Float64(2.0 * x2))
	t_1 = Float64(-1.0 - Float64(x1 * x1))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(Float64(t_2 + Float64(2.0 * x2)) - x1)
	tmp = 0.0
	if (x1 <= -5.6e+63)
		tmp = Float64(6.0 * (x1 ^ 4.0));
	elseif (x1 <= 3.9e+102)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_3)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) - Float64(Float64(t_2 * t_0) - Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * Float64(t_4 / t_1)))) + Float64(Float64(Float64(t_4 / t_3) - 3.0) * Float64(Float64(x1 * 2.0) * t_0)))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0)) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 - (2.0 * x2);
	t_1 = -1.0 - (x1 * x1);
	t_2 = x1 * (x1 * 3.0);
	t_3 = (x1 * x1) + 1.0;
	t_4 = (t_2 + (2.0 * x2)) - x1;
	tmp = 0.0;
	if (x1 <= -5.6e+63)
		tmp = 6.0 * (x1 ^ 4.0);
	elseif (x1 <= 3.9e+102)
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_3)) + (x1 + ((x1 * (x1 * x1)) - ((t_2 * t_0) - (t_1 * (((x1 * x1) * (6.0 + (4.0 * (t_4 / t_1)))) + (((t_4 / t_3) - 3.0) * ((x1 * 2.0) * t_0))))))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + 9.0)) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, If[LessEqual[x1, -5.6e+63], N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.9e+102], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$2 * t$95$0), $MachinePrecision] - N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * N[(t$95$4 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t$95$4 / t$95$3), $MachinePrecision] - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.59999999999999974e63

   1. Initial program 11.7%

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

   3. Simplified 11.7%

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

   5. Taylor expanded in x1 around inf 98.3%

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

   if -5.59999999999999974e63 < x1 < 3.8999999999999998e102

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 96.8%

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

   4. Taylor expanded in x1 around 0 95.6%

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

   if 3.8999999999999998e102 < x1

   1. Initial program 26.8%

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

   3. Simplified 26.8%

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

   5. Taylor expanded in x1 around 0 8.3%

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

      1. associate-*r* 8.3%

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

      2. fmm-def 8.3%

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

      3. metadata-eval 8.3%

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

   7. Simplified 8.3%

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

   8. Taylor expanded in x1 around 0 92.7%

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

   9. Taylor expanded in x2 around 0 100.0%

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

       1. *-commutative 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+63}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x1 - 2 \cdot x2\right) - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x1 - 2 \cdot x2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 9\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 \cdot \left(x2 \cdot -2\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 \cdot \left(x1 \cdot x1\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := \frac{\left(t\_3 + 2 \cdot x2\right) - x1}{t\_1}\\ t_5 := \left(x1 \cdot x1\right) \cdot \left(t\_4 \cdot 4 - 6\right) + \left(t\_4 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2\right)\right)\\ t_6 := x1 \cdot \left(x1 \cdot 3 + 9\right)\\ \mathbf{if}\;x1 \leq -5.3 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -1:\\ \;\;\;\;x1 + \left(\left(x1 + \left(t\_2 + \left(t\_3 \cdot t\_4 + t\_1 \cdot t\_5\right)\right)\right) + t\_0\right)\\ \mathbf{elif}\;x1 \leq 3.3 \cdot 10^{-9}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 - t\_6\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{+102}:\\ \;\;\;\;x1 - \left(\left(\left(\left(t\_5 \cdot \left(-1 - x1 \cdot x1\right) - t\_3 \cdot \left(2 \cdot x2\right)\right) - t\_2\right) - x1\right) - t\_0\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(t\_6 - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 3.0 (* x2 -2.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* x1 (* x1 x1)))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (/ (- (+ t_3 (* 2.0 x2)) x1) t_1))
        (t_5
         (+
          (* (* x1 x1) (- (* t_4 4.0) 6.0))
          (* (- t_4 3.0) (* (* x1 2.0) (* 2.0 x2)))))
        (t_6 (* x1 (+ (* x1 3.0) 9.0))))
   (if (<= x1 -5.3e+102)
     (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0))))))
     (if (<= x1 -1.0)
       (+ x1 (+ (+ x1 (+ t_2 (+ (* t_3 t_4) (* t_1 t_5)))) t_0))
       (if (<= x1 3.3e-9)
         (-
          x1
          (-
           (+
            (* x1 (- 2.0 t_6))
            (* x2 (- (* x1 (- 12.0 (* x1 6.0))) (* 8.0 (* x1 x2)))))
           (* x2 -6.0)))
         (if (<= x1 3.9e+102)
           (-
            x1
            (-
             (- (- (- (* t_5 (- -1.0 (* x1 x1))) (* t_3 (* 2.0 x2))) t_2) x1)
             t_0))
           (+ x1 (+ (* x2 -6.0) (* x1 (- t_6 2.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 * (x2 * -2.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = ((t_3 + (2.0 * x2)) - x1) / t_1;
	double t_5 = ((x1 * x1) * ((t_4 * 4.0) - 6.0)) + ((t_4 - 3.0) * ((x1 * 2.0) * (2.0 * x2)));
	double t_6 = x1 * ((x1 * 3.0) + 9.0);
	double tmp;
	if (x1 <= -5.3e+102) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= -1.0) {
		tmp = x1 + ((x1 + (t_2 + ((t_3 * t_4) + (t_1 * t_5)))) + t_0);
	} else if (x1 <= 3.3e-9) {
		tmp = x1 - (((x1 * (2.0 - t_6)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	} else if (x1 <= 3.9e+102) {
		tmp = x1 - (((((t_5 * (-1.0 - (x1 * x1))) - (t_3 * (2.0 * x2))) - t_2) - x1) - t_0);
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_6 - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = 3.0d0 * (x2 * (-2.0d0))
    t_1 = (x1 * x1) + 1.0d0
    t_2 = x1 * (x1 * x1)
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = ((t_3 + (2.0d0 * x2)) - x1) / t_1
    t_5 = ((x1 * x1) * ((t_4 * 4.0d0) - 6.0d0)) + ((t_4 - 3.0d0) * ((x1 * 2.0d0) * (2.0d0 * x2)))
    t_6 = x1 * ((x1 * 3.0d0) + 9.0d0)
    if (x1 <= (-5.3d+102)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0))))))
    else if (x1 <= (-1.0d0)) then
        tmp = x1 + ((x1 + (t_2 + ((t_3 * t_4) + (t_1 * t_5)))) + t_0)
    else if (x1 <= 3.3d-9) then
        tmp = x1 - (((x1 * (2.0d0 - t_6)) + (x2 * ((x1 * (12.0d0 - (x1 * 6.0d0))) - (8.0d0 * (x1 * x2))))) - (x2 * (-6.0d0)))
    else if (x1 <= 3.9d+102) then
        tmp = x1 - (((((t_5 * ((-1.0d0) - (x1 * x1))) - (t_3 * (2.0d0 * x2))) - t_2) - x1) - t_0)
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (t_6 - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 * (x2 * -2.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = ((t_3 + (2.0 * x2)) - x1) / t_1;
	double t_5 = ((x1 * x1) * ((t_4 * 4.0) - 6.0)) + ((t_4 - 3.0) * ((x1 * 2.0) * (2.0 * x2)));
	double t_6 = x1 * ((x1 * 3.0) + 9.0);
	double tmp;
	if (x1 <= -5.3e+102) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= -1.0) {
		tmp = x1 + ((x1 + (t_2 + ((t_3 * t_4) + (t_1 * t_5)))) + t_0);
	} else if (x1 <= 3.3e-9) {
		tmp = x1 - (((x1 * (2.0 - t_6)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	} else if (x1 <= 3.9e+102) {
		tmp = x1 - (((((t_5 * (-1.0 - (x1 * x1))) - (t_3 * (2.0 * x2))) - t_2) - x1) - t_0);
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_6 - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 * (x2 * -2.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = x1 * (x1 * x1)
	t_3 = x1 * (x1 * 3.0)
	t_4 = ((t_3 + (2.0 * x2)) - x1) / t_1
	t_5 = ((x1 * x1) * ((t_4 * 4.0) - 6.0)) + ((t_4 - 3.0) * ((x1 * 2.0) * (2.0 * x2)))
	t_6 = x1 * ((x1 * 3.0) + 9.0)
	tmp = 0
	if x1 <= -5.3e+102:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))))
	elif x1 <= -1.0:
		tmp = x1 + ((x1 + (t_2 + ((t_3 * t_4) + (t_1 * t_5)))) + t_0)
	elif x1 <= 3.3e-9:
		tmp = x1 - (((x1 * (2.0 - t_6)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0))
	elif x1 <= 3.9e+102:
		tmp = x1 - (((((t_5 * (-1.0 - (x1 * x1))) - (t_3 * (2.0 * x2))) - t_2) - x1) - t_0)
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_6 - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 * Float64(x2 * -2.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	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_1)
	t_5 = Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_4 * 4.0) - 6.0)) + Float64(Float64(t_4 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(2.0 * x2))))
	t_6 = Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0))
	tmp = 0.0
	if (x1 <= -5.3e+102)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))))));
	elseif (x1 <= -1.0)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(t_2 + Float64(Float64(t_3 * t_4) + Float64(t_1 * t_5)))) + t_0));
	elseif (x1 <= 3.3e-9)
		tmp = Float64(x1 - Float64(Float64(Float64(x1 * Float64(2.0 - t_6)) + Float64(x2 * Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(8.0 * Float64(x1 * x2))))) - Float64(x2 * -6.0)));
	elseif (x1 <= 3.9e+102)
		tmp = Float64(x1 - Float64(Float64(Float64(Float64(Float64(t_5 * Float64(-1.0 - Float64(x1 * x1))) - Float64(t_3 * Float64(2.0 * x2))) - t_2) - x1) - t_0));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(t_6 - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 * (x2 * -2.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = x1 * (x1 * x1);
	t_3 = x1 * (x1 * 3.0);
	t_4 = ((t_3 + (2.0 * x2)) - x1) / t_1;
	t_5 = ((x1 * x1) * ((t_4 * 4.0) - 6.0)) + ((t_4 - 3.0) * ((x1 * 2.0) * (2.0 * x2)));
	t_6 = x1 * ((x1 * 3.0) + 9.0);
	tmp = 0.0;
	if (x1 <= -5.3e+102)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	elseif (x1 <= -1.0)
		tmp = x1 + ((x1 + (t_2 + ((t_3 * t_4) + (t_1 * t_5)))) + t_0);
	elseif (x1 <= 3.3e-9)
		tmp = x1 - (((x1 * (2.0 - t_6)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	elseif (x1 <= 3.9e+102)
		tmp = x1 - (((((t_5 * (-1.0 - (x1 * x1))) - (t_3 * (2.0 * x2))) - t_2) - x1) - t_0);
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_6 - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $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$1), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$4 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$4 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.3e+102], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.0], N[(x1 + N[(N[(x1 + N[(t$95$2 + N[(N[(t$95$3 * t$95$4), $MachinePrecision] + N[(t$95$1 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.3e-9], N[(x1 - N[(N[(N[(x1 * N[(2.0 - t$95$6), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.9e+102], N[(x1 - N[(N[(N[(N[(N[(t$95$5 * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$3 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] - x1), $MachinePrecision] - t$95$0), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(t$95$6 - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -5.2999999999999997e102

   1. Initial program 0.0%

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

   3. Simplified 22.2%

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

   5. Taylor expanded in x1 around 0 71.1%

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

   6. Taylor expanded in x2 around 0 100.0%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 1\right) \]

   8. Simplified 100.0%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 1\right) \]

   if -5.2999999999999997e102 < x1 < -1

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 79.9%

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

   4. Taylor expanded in x1 around 0 79.9%

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

      1. *-commutative 79.9%

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

   6. Simplified 79.9%

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

   7. Taylor expanded in x1 around 0 82.0%

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

      1. *-commutative 82.0%

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

   9. Simplified 82.0%

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

   if -1 < x1 < 3.30000000000000018e-9

   1. Initial program 99.5%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x1 around 0 89.3%

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

      1. associate-*r* 99.6%

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

      2. fmm-def 99.6%

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

      3. metadata-eval 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in x1 around 0 89.4%

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

   9. Taylor expanded in x2 around 0 99.6%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right)\right)}\right) \]

   if 3.30000000000000018e-9 < x1 < 3.8999999999999998e102

   1. Initial program 99.2%

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

   3. Taylor expanded in x1 around 0 96.5%

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

   4. Taylor expanded in x1 around 0 96.5%

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

      1. *-commutative 96.5%

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

   6. Simplified 96.5%

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

   7. Taylor expanded in x1 around 0 96.5%

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

   8. Taylor expanded in x1 around 0 99.2%

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

      1. *-commutative 99.2%

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

   10. Simplified 99.2%

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

   if 3.8999999999999998e102 < x1

   1. Initial program 26.8%

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

   3. Simplified 26.8%

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

   5. Taylor expanded in x1 around 0 8.3%

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

      1. associate-*r* 8.3%

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

      2. fmm-def 8.3%

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

      3. metadata-eval 8.3%

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

   7. Simplified 8.3%

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

   8. Taylor expanded in x1 around 0 92.7%

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

   9. Taylor expanded in x2 around 0 100.0%

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

       1. *-commutative 100.0%

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

   11. Simplified 100.0%

       \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot 3\right)} - 2\right)\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.3 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -1:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2\right)\right)\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 3.3 \cdot 10^{-9}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 - x1 \cdot \left(x1 \cdot 3 + 9\right)\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{+102}:\\ \;\;\;\;x1 - \left(\left(\left(\left(\left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2\right)\right)\right) \cdot \left(-1 - x1 \cdot x1\right) - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right) - 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 9\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 95.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\\ t_2 := x1 - \left(\left(\left(\left(\left(\left(x1 \cdot x1\right) \cdot \left(t\_1 \cdot 4 - 6\right) + \left(t\_1 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2\right)\right)\right) \cdot \left(-1 - x1 \cdot x1\right) - t\_0 \cdot \left(2 \cdot x2\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right) - 3 \cdot \left(x2 \cdot -2\right)\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3 + 9\right)\\ \mathbf{if}\;x1 \leq -2.12 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -1.3:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq 3.3 \cdot 10^{-9}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 - t\_3\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{+102}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(t\_3 - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (/ (- (+ t_0 (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
        (t_2
         (-
          x1
          (-
           (-
            (-
             (-
              (*
               (+
                (* (* x1 x1) (- (* t_1 4.0) 6.0))
                (* (- t_1 3.0) (* (* x1 2.0) (* 2.0 x2))))
               (- -1.0 (* x1 x1)))
              (* t_0 (* 2.0 x2)))
             (* x1 (* x1 x1)))
            x1)
           (* 3.0 (* x2 -2.0)))))
        (t_3 (* x1 (+ (* x1 3.0) 9.0))))
   (if (<= x1 -2.12e+102)
     (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0))))))
     (if (<= x1 -1.3)
       t_2
       (if (<= x1 3.3e-9)
         (-
          x1
          (-
           (+
            (* x1 (- 2.0 t_3))
            (* x2 (- (* x1 (- 12.0 (* x1 6.0))) (* 8.0 (* x1 x2)))))
           (* x2 -6.0)))
         (if (<= x1 3.9e+102)
           t_2
           (+ x1 (+ (* x2 -6.0) (* x1 (- t_3 2.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = ((t_0 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0);
	double t_2 = x1 - ((((((((x1 * x1) * ((t_1 * 4.0) - 6.0)) + ((t_1 - 3.0) * ((x1 * 2.0) * (2.0 * x2)))) * (-1.0 - (x1 * x1))) - (t_0 * (2.0 * x2))) - (x1 * (x1 * x1))) - x1) - (3.0 * (x2 * -2.0)));
	double t_3 = x1 * ((x1 * 3.0) + 9.0);
	double tmp;
	if (x1 <= -2.12e+102) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= -1.3) {
		tmp = t_2;
	} else if (x1 <= 3.3e-9) {
		tmp = x1 - (((x1 * (2.0 - t_3)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	} else if (x1 <= 3.9e+102) {
		tmp = t_2;
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_3 - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = ((t_0 + (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0)
    t_2 = x1 - ((((((((x1 * x1) * ((t_1 * 4.0d0) - 6.0d0)) + ((t_1 - 3.0d0) * ((x1 * 2.0d0) * (2.0d0 * x2)))) * ((-1.0d0) - (x1 * x1))) - (t_0 * (2.0d0 * x2))) - (x1 * (x1 * x1))) - x1) - (3.0d0 * (x2 * (-2.0d0))))
    t_3 = x1 * ((x1 * 3.0d0) + 9.0d0)
    if (x1 <= (-2.12d+102)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0))))))
    else if (x1 <= (-1.3d0)) then
        tmp = t_2
    else if (x1 <= 3.3d-9) then
        tmp = x1 - (((x1 * (2.0d0 - t_3)) + (x2 * ((x1 * (12.0d0 - (x1 * 6.0d0))) - (8.0d0 * (x1 * x2))))) - (x2 * (-6.0d0)))
    else if (x1 <= 3.9d+102) then
        tmp = t_2
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (t_3 - 2.0d0)))
    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 = ((t_0 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0);
	double t_2 = x1 - ((((((((x1 * x1) * ((t_1 * 4.0) - 6.0)) + ((t_1 - 3.0) * ((x1 * 2.0) * (2.0 * x2)))) * (-1.0 - (x1 * x1))) - (t_0 * (2.0 * x2))) - (x1 * (x1 * x1))) - x1) - (3.0 * (x2 * -2.0)));
	double t_3 = x1 * ((x1 * 3.0) + 9.0);
	double tmp;
	if (x1 <= -2.12e+102) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= -1.3) {
		tmp = t_2;
	} else if (x1 <= 3.3e-9) {
		tmp = x1 - (((x1 * (2.0 - t_3)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	} else if (x1 <= 3.9e+102) {
		tmp = t_2;
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_3 - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = ((t_0 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0)
	t_2 = x1 - ((((((((x1 * x1) * ((t_1 * 4.0) - 6.0)) + ((t_1 - 3.0) * ((x1 * 2.0) * (2.0 * x2)))) * (-1.0 - (x1 * x1))) - (t_0 * (2.0 * x2))) - (x1 * (x1 * x1))) - x1) - (3.0 * (x2 * -2.0)))
	t_3 = x1 * ((x1 * 3.0) + 9.0)
	tmp = 0
	if x1 <= -2.12e+102:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))))
	elif x1 <= -1.3:
		tmp = t_2
	elif x1 <= 3.3e-9:
		tmp = x1 - (((x1 * (2.0 - t_3)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0))
	elif x1 <= 3.9e+102:
		tmp = t_2
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_3 - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))
	t_2 = Float64(x1 - Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_1 * 4.0) - 6.0)) + Float64(Float64(t_1 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(2.0 * x2)))) * Float64(-1.0 - Float64(x1 * x1))) - Float64(t_0 * Float64(2.0 * x2))) - Float64(x1 * Float64(x1 * x1))) - x1) - Float64(3.0 * Float64(x2 * -2.0))))
	t_3 = Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0))
	tmp = 0.0
	if (x1 <= -2.12e+102)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))))));
	elseif (x1 <= -1.3)
		tmp = t_2;
	elseif (x1 <= 3.3e-9)
		tmp = Float64(x1 - Float64(Float64(Float64(x1 * Float64(2.0 - t_3)) + Float64(x2 * Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(8.0 * Float64(x1 * x2))))) - Float64(x2 * -6.0)));
	elseif (x1 <= 3.9e+102)
		tmp = t_2;
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(t_3 - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = ((t_0 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0);
	t_2 = x1 - ((((((((x1 * x1) * ((t_1 * 4.0) - 6.0)) + ((t_1 - 3.0) * ((x1 * 2.0) * (2.0 * x2)))) * (-1.0 - (x1 * x1))) - (t_0 * (2.0 * x2))) - (x1 * (x1 * x1))) - x1) - (3.0 * (x2 * -2.0)));
	t_3 = x1 * ((x1 * 3.0) + 9.0);
	tmp = 0.0;
	if (x1 <= -2.12e+102)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	elseif (x1 <= -1.3)
		tmp = t_2;
	elseif (x1 <= 3.3e-9)
		tmp = x1 - (((x1 * (2.0 - t_3)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	elseif (x1 <= 3.9e+102)
		tmp = t_2;
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_3 - 2.0)));
	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[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 - N[(N[(N[(N[(N[(N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$1 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$0 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] - N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.12e+102], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.3], t$95$2, If[LessEqual[x1, 3.3e-9], N[(x1 - N[(N[(N[(x1 * N[(2.0 - t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.9e+102], t$95$2, N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(t$95$3 - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.12000000000000003e102

   1. Initial program 0.0%

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

   3. Simplified 22.2%

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

   5. Taylor expanded in x1 around 0 71.1%

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

   6. Taylor expanded in x2 around 0 100.0%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 1\right) \]

   8. Simplified 100.0%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 1\right) \]

   if -2.12000000000000003e102 < x1 < -1.30000000000000004 or 3.30000000000000018e-9 < x1 < 3.8999999999999998e102

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 89.2%

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

   4. Taylor expanded in x1 around 0 89.2%

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

      1. *-commutative 89.2%

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

   6. Simplified 89.2%

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

   7. Taylor expanded in x1 around 0 85.2%

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

   8. Taylor expanded in x1 around 0 87.7%

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

      1. *-commutative 91.6%

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

   10. Simplified 87.7%

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

   if -1.30000000000000004 < x1 < 3.30000000000000018e-9

   1. Initial program 99.5%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x1 around 0 89.3%

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

      1. associate-*r* 99.6%

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

      2. fmm-def 99.6%

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

      3. metadata-eval 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in x1 around 0 89.4%

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

   9. Taylor expanded in x2 around 0 99.6%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right)\right)}\right) \]

   if 3.8999999999999998e102 < x1

   1. Initial program 26.8%

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

   3. Simplified 26.8%

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

   5. Taylor expanded in x1 around 0 8.3%

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

      1. associate-*r* 8.3%

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

      2. fmm-def 8.3%

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

      3. metadata-eval 8.3%

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

   7. Simplified 8.3%

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

   8. Taylor expanded in x1 around 0 92.7%

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

   9. Taylor expanded in x2 around 0 100.0%

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

       1. *-commutative 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.12 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -1.3:\\ \;\;\;\;x1 - \left(\left(\left(\left(\left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2\right)\right)\right) \cdot \left(-1 - x1 \cdot x1\right) - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right) - 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 3.3 \cdot 10^{-9}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 - x1 \cdot \left(x1 \cdot 3 + 9\right)\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{+102}:\\ \;\;\;\;x1 - \left(\left(\left(\left(\left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2\right)\right)\right) \cdot \left(-1 - x1 \cdot x1\right) - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right) - 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 9\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 94.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 \cdot \left(x2 \cdot -2\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 \cdot \left(x1 \cdot 3 + 9\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := \left(t\_3 + 2 \cdot x2\right) - x1\\ t_5 := \frac{t\_4}{-1 - x1 \cdot x1}\\ t_6 := \frac{t\_4}{t\_1}\\ t_7 := x1 \cdot \left(x1 \cdot x1\right)\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -4.1 \cdot 10^{+15}:\\ \;\;\;\;x1 + \left(t\_0 - \left(\left(\left(t\_3 \cdot t\_5 + t\_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_5\right) - x1 \cdot 2\right)\right) - t\_7\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 2.9 \cdot 10^{+33}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 - t\_2\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+101}:\\ \;\;\;\;x1 + \left(t\_0 + \left(x1 + \left(t\_7 + \left(t\_3 \cdot \left(2 \cdot x2\right) - t\_1 \cdot \left(\left(t\_6 - 3\right) \cdot \left(x1 \cdot \left(x1 \cdot 2\right)\right) - \left(x1 \cdot x1\right) \cdot \left(t\_6 \cdot 4 - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(t\_2 - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 3.0 (* x2 -2.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* x1 (+ (* x1 3.0) 9.0)))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (- (+ t_3 (* 2.0 x2)) x1))
        (t_5 (/ t_4 (- -1.0 (* x1 x1))))
        (t_6 (/ t_4 t_1))
        (t_7 (* x1 (* x1 x1))))
   (if (<= x1 -5e+102)
     (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0))))))
     (if (<= x1 -4.1e+15)
       (+
        x1
        (-
         t_0
         (-
          (-
           (+
            (* t_3 t_5)
            (* t_1 (- (* (* x1 x1) (+ 6.0 (* 4.0 t_5))) (* x1 2.0))))
           t_7)
          x1)))
       (if (<= x1 2.9e+33)
         (-
          x1
          (-
           (+
            (* x1 (- 2.0 t_2))
            (* x2 (- (* x1 (- 12.0 (* x1 6.0))) (* 8.0 (* x1 x2)))))
           (* x2 -6.0)))
         (if (<= x1 2e+101)
           (+
            x1
            (+
             t_0
             (+
              x1
              (+
               t_7
               (-
                (* t_3 (* 2.0 x2))
                (*
                 t_1
                 (-
                  (* (- t_6 3.0) (* x1 (* x1 2.0)))
                  (* (* x1 x1) (- (* t_6 4.0) 6.0)))))))))
           (+ x1 (+ (* x2 -6.0) (* x1 (- t_2 2.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 * (x2 * -2.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 * ((x1 * 3.0) + 9.0);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = (t_3 + (2.0 * x2)) - x1;
	double t_5 = t_4 / (-1.0 - (x1 * x1));
	double t_6 = t_4 / t_1;
	double t_7 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -5e+102) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= -4.1e+15) {
		tmp = x1 + (t_0 - ((((t_3 * t_5) + (t_1 * (((x1 * x1) * (6.0 + (4.0 * t_5))) - (x1 * 2.0)))) - t_7) - x1));
	} else if (x1 <= 2.9e+33) {
		tmp = x1 - (((x1 * (2.0 - t_2)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	} else if (x1 <= 2e+101) {
		tmp = x1 + (t_0 + (x1 + (t_7 + ((t_3 * (2.0 * x2)) - (t_1 * (((t_6 - 3.0) * (x1 * (x1 * 2.0))) - ((x1 * x1) * ((t_6 * 4.0) - 6.0))))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_2 - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = 3.0d0 * (x2 * (-2.0d0))
    t_1 = (x1 * x1) + 1.0d0
    t_2 = x1 * ((x1 * 3.0d0) + 9.0d0)
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = (t_3 + (2.0d0 * x2)) - x1
    t_5 = t_4 / ((-1.0d0) - (x1 * x1))
    t_6 = t_4 / t_1
    t_7 = x1 * (x1 * x1)
    if (x1 <= (-5d+102)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0))))))
    else if (x1 <= (-4.1d+15)) then
        tmp = x1 + (t_0 - ((((t_3 * t_5) + (t_1 * (((x1 * x1) * (6.0d0 + (4.0d0 * t_5))) - (x1 * 2.0d0)))) - t_7) - x1))
    else if (x1 <= 2.9d+33) then
        tmp = x1 - (((x1 * (2.0d0 - t_2)) + (x2 * ((x1 * (12.0d0 - (x1 * 6.0d0))) - (8.0d0 * (x1 * x2))))) - (x2 * (-6.0d0)))
    else if (x1 <= 2d+101) then
        tmp = x1 + (t_0 + (x1 + (t_7 + ((t_3 * (2.0d0 * x2)) - (t_1 * (((t_6 - 3.0d0) * (x1 * (x1 * 2.0d0))) - ((x1 * x1) * ((t_6 * 4.0d0) - 6.0d0))))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (t_2 - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 * (x2 * -2.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 * ((x1 * 3.0) + 9.0);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = (t_3 + (2.0 * x2)) - x1;
	double t_5 = t_4 / (-1.0 - (x1 * x1));
	double t_6 = t_4 / t_1;
	double t_7 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -5e+102) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= -4.1e+15) {
		tmp = x1 + (t_0 - ((((t_3 * t_5) + (t_1 * (((x1 * x1) * (6.0 + (4.0 * t_5))) - (x1 * 2.0)))) - t_7) - x1));
	} else if (x1 <= 2.9e+33) {
		tmp = x1 - (((x1 * (2.0 - t_2)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	} else if (x1 <= 2e+101) {
		tmp = x1 + (t_0 + (x1 + (t_7 + ((t_3 * (2.0 * x2)) - (t_1 * (((t_6 - 3.0) * (x1 * (x1 * 2.0))) - ((x1 * x1) * ((t_6 * 4.0) - 6.0))))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_2 - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 * (x2 * -2.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = x1 * ((x1 * 3.0) + 9.0)
	t_3 = x1 * (x1 * 3.0)
	t_4 = (t_3 + (2.0 * x2)) - x1
	t_5 = t_4 / (-1.0 - (x1 * x1))
	t_6 = t_4 / t_1
	t_7 = x1 * (x1 * x1)
	tmp = 0
	if x1 <= -5e+102:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))))
	elif x1 <= -4.1e+15:
		tmp = x1 + (t_0 - ((((t_3 * t_5) + (t_1 * (((x1 * x1) * (6.0 + (4.0 * t_5))) - (x1 * 2.0)))) - t_7) - x1))
	elif x1 <= 2.9e+33:
		tmp = x1 - (((x1 * (2.0 - t_2)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0))
	elif x1 <= 2e+101:
		tmp = x1 + (t_0 + (x1 + (t_7 + ((t_3 * (2.0 * x2)) - (t_1 * (((t_6 - 3.0) * (x1 * (x1 * 2.0))) - ((x1 * x1) * ((t_6 * 4.0) - 6.0))))))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_2 - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 * Float64(x2 * -2.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(Float64(t_3 + Float64(2.0 * x2)) - x1)
	t_5 = Float64(t_4 / Float64(-1.0 - Float64(x1 * x1)))
	t_6 = Float64(t_4 / t_1)
	t_7 = Float64(x1 * Float64(x1 * x1))
	tmp = 0.0
	if (x1 <= -5e+102)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))))));
	elseif (x1 <= -4.1e+15)
		tmp = Float64(x1 + Float64(t_0 - Float64(Float64(Float64(Float64(t_3 * t_5) + Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_5))) - Float64(x1 * 2.0)))) - t_7) - x1)));
	elseif (x1 <= 2.9e+33)
		tmp = Float64(x1 - Float64(Float64(Float64(x1 * Float64(2.0 - t_2)) + Float64(x2 * Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(8.0 * Float64(x1 * x2))))) - Float64(x2 * -6.0)));
	elseif (x1 <= 2e+101)
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(t_7 + Float64(Float64(t_3 * Float64(2.0 * x2)) - Float64(t_1 * Float64(Float64(Float64(t_6 - 3.0) * Float64(x1 * Float64(x1 * 2.0))) - Float64(Float64(x1 * x1) * Float64(Float64(t_6 * 4.0) - 6.0)))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(t_2 - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 * (x2 * -2.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = x1 * ((x1 * 3.0) + 9.0);
	t_3 = x1 * (x1 * 3.0);
	t_4 = (t_3 + (2.0 * x2)) - x1;
	t_5 = t_4 / (-1.0 - (x1 * x1));
	t_6 = t_4 / t_1;
	t_7 = x1 * (x1 * x1);
	tmp = 0.0;
	if (x1 <= -5e+102)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	elseif (x1 <= -4.1e+15)
		tmp = x1 + (t_0 - ((((t_3 * t_5) + (t_1 * (((x1 * x1) * (6.0 + (4.0 * t_5))) - (x1 * 2.0)))) - t_7) - x1));
	elseif (x1 <= 2.9e+33)
		tmp = x1 - (((x1 * (2.0 - t_2)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	elseif (x1 <= 2e+101)
		tmp = x1 + (t_0 + (x1 + (t_7 + ((t_3 * (2.0 * x2)) - (t_1 * (((t_6 - 3.0) * (x1 * (x1 * 2.0))) - ((x1 * x1) * ((t_6 * 4.0) - 6.0))))))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_2 - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$4 / t$95$1), $MachinePrecision]}, Block[{t$95$7 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5e+102], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -4.1e+15], N[(x1 + N[(t$95$0 - N[(N[(N[(N[(t$95$3 * t$95$5), $MachinePrecision] + N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$7), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.9e+33], N[(x1 - N[(N[(N[(x1 * N[(2.0 - t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+101], N[(x1 + N[(t$95$0 + N[(x1 + N[(t$95$7 + N[(N[(t$95$3 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 * N[(N[(N[(t$95$6 - 3.0), $MachinePrecision] * N[(x1 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$6 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(t$95$2 - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -5e102

   1. Initial program 0.0%

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

   3. Simplified 22.2%

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

   5. Taylor expanded in x1 around 0 71.1%

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

   6. Taylor expanded in x2 around 0 100.0%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 1\right) \]

   8. Simplified 100.0%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 1\right) \]

   if -5e102 < x1 < -4.1e15

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 78.3%

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

   4. Taylor expanded in x1 around 0 78.3%

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

      1. *-commutative 78.3%

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

   6. Simplified 78.3%

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

   7. Taylor expanded in x1 around inf 77.1%

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

      1. *-commutative 77.1%

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

   9. Simplified 77.1%

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

   if -4.1e15 < x1 < 2.90000000000000025e33

   1. Initial program 99.5%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x1 around 0 86.9%

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

      1. associate-*r* 96.1%

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

      2. fmm-def 96.1%

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

      3. metadata-eval 96.1%

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

   7. Simplified 96.1%

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

   8. Taylor expanded in x1 around 0 87.1%

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

   9. Taylor expanded in x2 around 0 96.2%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right)\right)}\right) \]

   if 2.90000000000000025e33 < x1 < 2e101

   1. Initial program 99.0%

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

   3. Taylor expanded in x1 around 0 99.4%

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

   4. Taylor expanded in x1 around 0 99.4%

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

      1. *-commutative 99.4%

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

   6. Simplified 99.4%

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

   7. Taylor expanded in x1 around 0 99.4%

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

   8. Taylor expanded in x1 around inf 99.4%

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

      1. neg-mul-1 99.4%

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

   10. Simplified 99.4%

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

   if 2e101 < x1

   1. Initial program 26.8%

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

   3. Simplified 26.8%

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

   5. Taylor expanded in x1 around 0 8.3%

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

      1. associate-*r* 8.3%

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

      2. fmm-def 8.3%

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

      3. metadata-eval 8.3%

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

   7. Simplified 8.3%

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

   8. Taylor expanded in x1 around 0 92.7%

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

   9. Taylor expanded in x2 around 0 100.0%

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

       1. *-commutative 100.0%

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

   11. Simplified 100.0%

       \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot 3\right)} - 2\right)\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -4.1 \cdot 10^{+15}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) - x1 \cdot 2\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 2.9 \cdot 10^{+33}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 - x1 \cdot \left(x1 \cdot 3 + 9\right)\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+101}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right) - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(x1 \cdot \left(x1 \cdot 2\right)\right) - \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 9\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 94.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3 + 9\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\left(t\_1 + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\\ t_3 := x1 + \left(3 \cdot \left(x2 \cdot -2\right) - \left(\left(\left(t\_1 \cdot t\_2 + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_2\right) - x1 \cdot 2\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -8 \cdot 10^{+15}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x1 \leq 2.9 \cdot 10^{+33}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 - t\_0\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 5.5 \cdot 10^{+102}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(t\_0 - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ (* x1 3.0) 9.0)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (/ (- (+ t_1 (* 2.0 x2)) x1) (- -1.0 (* x1 x1))))
        (t_3
         (+
          x1
          (-
           (* 3.0 (* x2 -2.0))
           (-
            (-
             (+
              (* t_1 t_2)
              (*
               (+ (* x1 x1) 1.0)
               (- (* (* x1 x1) (+ 6.0 (* 4.0 t_2))) (* x1 2.0))))
             (* x1 (* x1 x1)))
            x1)))))
   (if (<= x1 -5e+102)
     (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0))))))
     (if (<= x1 -8e+15)
       t_3
       (if (<= x1 2.9e+33)
         (-
          x1
          (-
           (+
            (* x1 (- 2.0 t_0))
            (* x2 (- (* x1 (- 12.0 (* x1 6.0))) (* 8.0 (* x1 x2)))))
           (* x2 -6.0)))
         (if (<= x1 5.5e+102)
           t_3
           (+ x1 (+ (* x2 -6.0) (* x1 (- t_0 2.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 3.0) + 9.0);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (2.0 * x2)) - x1) / (-1.0 - (x1 * x1));
	double t_3 = x1 + ((3.0 * (x2 * -2.0)) - ((((t_1 * t_2) + (((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 + (4.0 * t_2))) - (x1 * 2.0)))) - (x1 * (x1 * x1))) - x1));
	double tmp;
	if (x1 <= -5e+102) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= -8e+15) {
		tmp = t_3;
	} else if (x1 <= 2.9e+33) {
		tmp = x1 - (((x1 * (2.0 - t_0)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	} else if (x1 <= 5.5e+102) {
		tmp = t_3;
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_0 - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x1 * ((x1 * 3.0d0) + 9.0d0)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = ((t_1 + (2.0d0 * x2)) - x1) / ((-1.0d0) - (x1 * x1))
    t_3 = x1 + ((3.0d0 * (x2 * (-2.0d0))) - ((((t_1 * t_2) + (((x1 * x1) + 1.0d0) * (((x1 * x1) * (6.0d0 + (4.0d0 * t_2))) - (x1 * 2.0d0)))) - (x1 * (x1 * x1))) - x1))
    if (x1 <= (-5d+102)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0))))))
    else if (x1 <= (-8d+15)) then
        tmp = t_3
    else if (x1 <= 2.9d+33) then
        tmp = x1 - (((x1 * (2.0d0 - t_0)) + (x2 * ((x1 * (12.0d0 - (x1 * 6.0d0))) - (8.0d0 * (x1 * x2))))) - (x2 * (-6.0d0)))
    else if (x1 <= 5.5d+102) then
        tmp = t_3
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (t_0 - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 3.0) + 9.0);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (2.0 * x2)) - x1) / (-1.0 - (x1 * x1));
	double t_3 = x1 + ((3.0 * (x2 * -2.0)) - ((((t_1 * t_2) + (((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 + (4.0 * t_2))) - (x1 * 2.0)))) - (x1 * (x1 * x1))) - x1));
	double tmp;
	if (x1 <= -5e+102) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= -8e+15) {
		tmp = t_3;
	} else if (x1 <= 2.9e+33) {
		tmp = x1 - (((x1 * (2.0 - t_0)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	} else if (x1 <= 5.5e+102) {
		tmp = t_3;
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_0 - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((x1 * 3.0) + 9.0)
	t_1 = x1 * (x1 * 3.0)
	t_2 = ((t_1 + (2.0 * x2)) - x1) / (-1.0 - (x1 * x1))
	t_3 = x1 + ((3.0 * (x2 * -2.0)) - ((((t_1 * t_2) + (((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 + (4.0 * t_2))) - (x1 * 2.0)))) - (x1 * (x1 * x1))) - x1))
	tmp = 0
	if x1 <= -5e+102:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))))
	elif x1 <= -8e+15:
		tmp = t_3
	elif x1 <= 2.9e+33:
		tmp = x1 - (((x1 * (2.0 - t_0)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0))
	elif x1 <= 5.5e+102:
		tmp = t_3
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_0 - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / Float64(-1.0 - Float64(x1 * x1)))
	t_3 = Float64(x1 + Float64(Float64(3.0 * Float64(x2 * -2.0)) - Float64(Float64(Float64(Float64(t_1 * t_2) + Float64(Float64(Float64(x1 * x1) + 1.0) * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_2))) - Float64(x1 * 2.0)))) - Float64(x1 * Float64(x1 * x1))) - x1)))
	tmp = 0.0
	if (x1 <= -5e+102)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))))));
	elseif (x1 <= -8e+15)
		tmp = t_3;
	elseif (x1 <= 2.9e+33)
		tmp = Float64(x1 - Float64(Float64(Float64(x1 * Float64(2.0 - t_0)) + Float64(x2 * Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(8.0 * Float64(x1 * x2))))) - Float64(x2 * -6.0)));
	elseif (x1 <= 5.5e+102)
		tmp = t_3;
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(t_0 - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((x1 * 3.0) + 9.0);
	t_1 = x1 * (x1 * 3.0);
	t_2 = ((t_1 + (2.0 * x2)) - x1) / (-1.0 - (x1 * x1));
	t_3 = x1 + ((3.0 * (x2 * -2.0)) - ((((t_1 * t_2) + (((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 + (4.0 * t_2))) - (x1 * 2.0)))) - (x1 * (x1 * x1))) - x1));
	tmp = 0.0;
	if (x1 <= -5e+102)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	elseif (x1 <= -8e+15)
		tmp = t_3;
	elseif (x1 <= 2.9e+33)
		tmp = x1 - (((x1 * (2.0 - t_0)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	elseif (x1 <= 5.5e+102)
		tmp = t_3;
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_0 - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(t$95$1 * t$95$2), $MachinePrecision] + N[(N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision] * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5e+102], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -8e+15], t$95$3, If[LessEqual[x1, 2.9e+33], N[(x1 - N[(N[(N[(x1 * N[(2.0 - t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.5e+102], t$95$3, N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(t$95$0 - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5e102

   1. Initial program 0.0%

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

   3. Simplified 22.2%

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

   5. Taylor expanded in x1 around 0 71.1%

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

   6. Taylor expanded in x2 around 0 100.0%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 1\right) \]

   8. Simplified 100.0%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 1\right) \]

   if -5e102 < x1 < -8e15 or 2.90000000000000025e33 < x1 < 5.49999999999999981e102

   1. Initial program 99.2%

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

   3. Taylor expanded in x1 around 0 88.9%

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

   4. Taylor expanded in x1 around 0 88.9%

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

      1. *-commutative 88.9%

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

   6. Simplified 88.9%

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

   7. Taylor expanded in x1 around inf 88.0%

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

      1. *-commutative 88.0%

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

   9. Simplified 88.0%

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

   if -8e15 < x1 < 2.90000000000000025e33

   1. Initial program 99.5%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x1 around 0 86.9%

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

      1. associate-*r* 96.1%

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

      2. fmm-def 96.1%

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

      3. metadata-eval 96.1%

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

   7. Simplified 96.1%

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

   8. Taylor expanded in x1 around 0 87.1%

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

   9. Taylor expanded in x2 around 0 96.2%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right)\right)}\right) \]

   if 5.49999999999999981e102 < x1

   1. Initial program 26.8%

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

   3. Simplified 26.8%

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

   5. Taylor expanded in x1 around 0 8.3%

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

      1. associate-*r* 8.3%

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

      2. fmm-def 8.3%

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

      3. metadata-eval 8.3%

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

   7. Simplified 8.3%

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

   8. Taylor expanded in x1 around 0 92.7%

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

   9. Taylor expanded in x2 around 0 100.0%

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

       1. *-commutative 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -8 \cdot 10^{+15}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) - x1 \cdot 2\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 2.9 \cdot 10^{+33}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 - x1 \cdot \left(x1 \cdot 3 + 9\right)\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) - x1 \cdot 2\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 9\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 93.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := \left(t\_0 + 2 \cdot x2\right) - x1\\ t_2 := t\_0 \cdot \left(2 \cdot x2\right)\\ t_3 := x1 \cdot \left(x1 \cdot x1\right)\\ t_4 := 3 \cdot \left(x2 \cdot -2\right)\\ t_5 := x1 \cdot x1 + 1\\ t_6 := x1 \cdot \left(x1 \cdot 3 + 9\right)\\ \mathbf{if}\;x1 \leq -2.12 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -4.1 \cdot 10^{+15}:\\ \;\;\;\;x1 + \left(t\_4 + \left(x1 - \left(\left(t\_5 \cdot \left(\frac{-1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x1 - 2 \cdot x2\right)\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{t\_1}{-1 - x1 \cdot x1}\right)\right) - t\_2\right) - t\_3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.9 \cdot 10^{+33}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 - t\_6\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(t\_4 + \left(x1 + \left(t\_3 + \left(t\_2 + t\_5 \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(\frac{t\_1}{t\_5} \cdot 4 - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(t\_6 - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (- (+ t_0 (* 2.0 x2)) x1))
        (t_2 (* t_0 (* 2.0 x2)))
        (t_3 (* x1 (* x1 x1)))
        (t_4 (* 3.0 (* x2 -2.0)))
        (t_5 (+ (* x1 x1) 1.0))
        (t_6 (* x1 (+ (* x1 3.0) 9.0))))
   (if (<= x1 -2.12e+102)
     (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0))))))
     (if (<= x1 -4.1e+15)
       (+
        x1
        (+
         t_4
         (-
          x1
          (-
           (-
            (*
             t_5
             (+
              (* (/ -1.0 x1) (* (* x1 2.0) (- x1 (* 2.0 x2))))
              (* (* x1 x1) (+ 6.0 (* 4.0 (/ t_1 (- -1.0 (* x1 x1))))))))
            t_2)
           t_3))))
       (if (<= x1 2.9e+33)
         (-
          x1
          (-
           (+
            (* x1 (- 2.0 t_6))
            (* x2 (- (* x1 (- 12.0 (* x1 6.0))) (* 8.0 (* x1 x2)))))
           (* x2 -6.0)))
         (if (<= x1 5e+102)
           (+
            x1
            (+
             t_4
             (+
              x1
              (+
               t_3
               (+
                t_2
                (*
                 t_5
                 (+ (* x1 2.0) (* (* x1 x1) (- (* (/ t_1 t_5) 4.0) 6.0)))))))))
           (+ x1 (+ (* x2 -6.0) (* x1 (- t_6 2.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (t_0 + (2.0 * x2)) - x1;
	double t_2 = t_0 * (2.0 * x2);
	double t_3 = x1 * (x1 * x1);
	double t_4 = 3.0 * (x2 * -2.0);
	double t_5 = (x1 * x1) + 1.0;
	double t_6 = x1 * ((x1 * 3.0) + 9.0);
	double tmp;
	if (x1 <= -2.12e+102) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= -4.1e+15) {
		tmp = x1 + (t_4 + (x1 - (((t_5 * (((-1.0 / x1) * ((x1 * 2.0) * (x1 - (2.0 * x2)))) + ((x1 * x1) * (6.0 + (4.0 * (t_1 / (-1.0 - (x1 * x1)))))))) - t_2) - t_3)));
	} else if (x1 <= 2.9e+33) {
		tmp = x1 - (((x1 * (2.0 - t_6)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	} else if (x1 <= 5e+102) {
		tmp = x1 + (t_4 + (x1 + (t_3 + (t_2 + (t_5 * ((x1 * 2.0) + ((x1 * x1) * (((t_1 / t_5) * 4.0) - 6.0))))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_6 - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (t_0 + (2.0d0 * x2)) - x1
    t_2 = t_0 * (2.0d0 * x2)
    t_3 = x1 * (x1 * x1)
    t_4 = 3.0d0 * (x2 * (-2.0d0))
    t_5 = (x1 * x1) + 1.0d0
    t_6 = x1 * ((x1 * 3.0d0) + 9.0d0)
    if (x1 <= (-2.12d+102)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0))))))
    else if (x1 <= (-4.1d+15)) then
        tmp = x1 + (t_4 + (x1 - (((t_5 * ((((-1.0d0) / x1) * ((x1 * 2.0d0) * (x1 - (2.0d0 * x2)))) + ((x1 * x1) * (6.0d0 + (4.0d0 * (t_1 / ((-1.0d0) - (x1 * x1)))))))) - t_2) - t_3)))
    else if (x1 <= 2.9d+33) then
        tmp = x1 - (((x1 * (2.0d0 - t_6)) + (x2 * ((x1 * (12.0d0 - (x1 * 6.0d0))) - (8.0d0 * (x1 * x2))))) - (x2 * (-6.0d0)))
    else if (x1 <= 5d+102) then
        tmp = x1 + (t_4 + (x1 + (t_3 + (t_2 + (t_5 * ((x1 * 2.0d0) + ((x1 * x1) * (((t_1 / t_5) * 4.0d0) - 6.0d0))))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (t_6 - 2.0d0)))
    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 = (t_0 + (2.0 * x2)) - x1;
	double t_2 = t_0 * (2.0 * x2);
	double t_3 = x1 * (x1 * x1);
	double t_4 = 3.0 * (x2 * -2.0);
	double t_5 = (x1 * x1) + 1.0;
	double t_6 = x1 * ((x1 * 3.0) + 9.0);
	double tmp;
	if (x1 <= -2.12e+102) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= -4.1e+15) {
		tmp = x1 + (t_4 + (x1 - (((t_5 * (((-1.0 / x1) * ((x1 * 2.0) * (x1 - (2.0 * x2)))) + ((x1 * x1) * (6.0 + (4.0 * (t_1 / (-1.0 - (x1 * x1)))))))) - t_2) - t_3)));
	} else if (x1 <= 2.9e+33) {
		tmp = x1 - (((x1 * (2.0 - t_6)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	} else if (x1 <= 5e+102) {
		tmp = x1 + (t_4 + (x1 + (t_3 + (t_2 + (t_5 * ((x1 * 2.0) + ((x1 * x1) * (((t_1 / t_5) * 4.0) - 6.0))))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_6 - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (t_0 + (2.0 * x2)) - x1
	t_2 = t_0 * (2.0 * x2)
	t_3 = x1 * (x1 * x1)
	t_4 = 3.0 * (x2 * -2.0)
	t_5 = (x1 * x1) + 1.0
	t_6 = x1 * ((x1 * 3.0) + 9.0)
	tmp = 0
	if x1 <= -2.12e+102:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))))
	elif x1 <= -4.1e+15:
		tmp = x1 + (t_4 + (x1 - (((t_5 * (((-1.0 / x1) * ((x1 * 2.0) * (x1 - (2.0 * x2)))) + ((x1 * x1) * (6.0 + (4.0 * (t_1 / (-1.0 - (x1 * x1)))))))) - t_2) - t_3)))
	elif x1 <= 2.9e+33:
		tmp = x1 - (((x1 * (2.0 - t_6)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0))
	elif x1 <= 5e+102:
		tmp = x1 + (t_4 + (x1 + (t_3 + (t_2 + (t_5 * ((x1 * 2.0) + ((x1 * x1) * (((t_1 / t_5) * 4.0) - 6.0))))))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_6 - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(t_0 + Float64(2.0 * x2)) - x1)
	t_2 = Float64(t_0 * Float64(2.0 * x2))
	t_3 = Float64(x1 * Float64(x1 * x1))
	t_4 = Float64(3.0 * Float64(x2 * -2.0))
	t_5 = Float64(Float64(x1 * x1) + 1.0)
	t_6 = Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0))
	tmp = 0.0
	if (x1 <= -2.12e+102)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))))));
	elseif (x1 <= -4.1e+15)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 - Float64(Float64(Float64(t_5 * Float64(Float64(Float64(-1.0 / x1) * Float64(Float64(x1 * 2.0) * Float64(x1 - Float64(2.0 * x2)))) + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * Float64(t_1 / Float64(-1.0 - Float64(x1 * x1)))))))) - t_2) - t_3))));
	elseif (x1 <= 2.9e+33)
		tmp = Float64(x1 - Float64(Float64(Float64(x1 * Float64(2.0 - t_6)) + Float64(x2 * Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(8.0 * Float64(x1 * x2))))) - Float64(x2 * -6.0)));
	elseif (x1 <= 5e+102)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(t_3 + Float64(t_2 + Float64(t_5 * Float64(Float64(x1 * 2.0) + Float64(Float64(x1 * x1) * Float64(Float64(Float64(t_1 / t_5) * 4.0) - 6.0)))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(t_6 - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (t_0 + (2.0 * x2)) - x1;
	t_2 = t_0 * (2.0 * x2);
	t_3 = x1 * (x1 * x1);
	t_4 = 3.0 * (x2 * -2.0);
	t_5 = (x1 * x1) + 1.0;
	t_6 = x1 * ((x1 * 3.0) + 9.0);
	tmp = 0.0;
	if (x1 <= -2.12e+102)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	elseif (x1 <= -4.1e+15)
		tmp = x1 + (t_4 + (x1 - (((t_5 * (((-1.0 / x1) * ((x1 * 2.0) * (x1 - (2.0 * x2)))) + ((x1 * x1) * (6.0 + (4.0 * (t_1 / (-1.0 - (x1 * x1)))))))) - t_2) - t_3)));
	elseif (x1 <= 2.9e+33)
		tmp = x1 - (((x1 * (2.0 - t_6)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	elseif (x1 <= 5e+102)
		tmp = x1 + (t_4 + (x1 + (t_3 + (t_2 + (t_5 * ((x1 * 2.0) + ((x1 * x1) * (((t_1 / t_5) * 4.0) - 6.0))))))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_6 - 2.0)));
	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[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$6 = N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.12e+102], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -4.1e+15], N[(x1 + N[(t$95$4 + N[(x1 - N[(N[(N[(t$95$5 * N[(N[(N[(-1.0 / x1), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(x1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * N[(t$95$1 / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.9e+33], N[(x1 - N[(N[(N[(x1 * N[(2.0 - t$95$6), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+102], N[(x1 + N[(t$95$4 + N[(x1 + N[(t$95$3 + N[(t$95$2 + N[(t$95$5 * N[(N[(x1 * 2.0), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(N[(t$95$1 / t$95$5), $MachinePrecision] * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(t$95$6 - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -2.12000000000000003e102

   1. Initial program 0.0%

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

   3. Simplified 22.2%

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

   5. Taylor expanded in x1 around 0 71.1%

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

   6. Taylor expanded in x2 around 0 100.0%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 1\right) \]

   8. Simplified 100.0%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 1\right) \]

   if -2.12000000000000003e102 < x1 < -4.1e15

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 78.3%

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

   4. Taylor expanded in x1 around 0 78.3%

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

      1. *-commutative 78.3%

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

   6. Simplified 78.3%

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

   7. Taylor expanded in x1 around 0 72.8%

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

   8. Taylor expanded in x1 around inf 69.5%

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

   if -4.1e15 < x1 < 2.90000000000000025e33

   1. Initial program 99.5%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x1 around 0 86.9%

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

      1. associate-*r* 96.1%

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

      2. fmm-def 96.1%

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

      3. metadata-eval 96.1%

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

   7. Simplified 96.1%

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

   8. Taylor expanded in x1 around 0 87.1%

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

   9. Taylor expanded in x2 around 0 96.2%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right)\right)}\right) \]

   if 2.90000000000000025e33 < x1 < 5e102

   1. Initial program 99.0%

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

   3. Taylor expanded in x1 around 0 99.4%

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

   4. Taylor expanded in x1 around 0 99.4%

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

      1. *-commutative 99.4%

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

   6. Simplified 99.4%

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

   7. Taylor expanded in x1 around 0 99.4%

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

   8. Taylor expanded in x1 around inf 99.0%

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

      1. *-commutative 99.0%

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

   10. Simplified 99.0%

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

   if 5e102 < x1

   1. Initial program 26.8%

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

   3. Simplified 26.8%

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

   5. Taylor expanded in x1 around 0 8.3%

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

      1. associate-*r* 8.3%

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

      2. fmm-def 8.3%

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

      3. metadata-eval 8.3%

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

   7. Simplified 8.3%

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

   8. Taylor expanded in x1 around 0 92.7%

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

   9. Taylor expanded in x2 around 0 100.0%

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

       1. *-commutative 100.0%

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

   11. Simplified 100.0%

       \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot 3\right)} - 2\right)\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.12 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -4.1 \cdot 10^{+15}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 - \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\frac{-1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x1 - 2 \cdot x2\right)\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right) - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.9 \cdot 10^{+33}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 - x1 \cdot \left(x1 \cdot 3 + 9\right)\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 9\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 93.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3 + 9\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := t\_1 \cdot \left(2 \cdot x2\right)\\ t_3 := \left(t\_1 + 2 \cdot x2\right) - x1\\ t_4 := x1 \cdot x1 + 1\\ t_5 := 3 \cdot \left(x2 \cdot -2\right)\\ t_6 := x1 \cdot \left(x1 \cdot x1\right)\\ \mathbf{if}\;x1 \leq -2.12 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -4.1 \cdot 10^{+15}:\\ \;\;\;\;x1 + \left(t\_5 - \left(\left(\left(t\_4 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{t\_3}{-1 - x1 \cdot x1}\right) - x1 \cdot \left(2 + 2 \cdot \frac{3 - x2 \cdot 4}{x1}\right)\right) - t\_2\right) - t\_6\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 2.9 \cdot 10^{+33}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 - t\_0\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+101}:\\ \;\;\;\;x1 + \left(t\_5 + \left(x1 + \left(t\_6 + \left(t\_2 + t\_4 \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(\frac{t\_3}{t\_4} \cdot 4 - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(t\_0 - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ (* x1 3.0) 9.0)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (* t_1 (* 2.0 x2)))
        (t_3 (- (+ t_1 (* 2.0 x2)) x1))
        (t_4 (+ (* x1 x1) 1.0))
        (t_5 (* 3.0 (* x2 -2.0)))
        (t_6 (* x1 (* x1 x1))))
   (if (<= x1 -2.12e+102)
     (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0))))))
     (if (<= x1 -4.1e+15)
       (+
        x1
        (-
         t_5
         (-
          (-
           (-
            (*
             t_4
             (-
              (* (* x1 x1) (+ 6.0 (* 4.0 (/ t_3 (- -1.0 (* x1 x1))))))
              (* x1 (+ 2.0 (* 2.0 (/ (- 3.0 (* x2 4.0)) x1))))))
            t_2)
           t_6)
          x1)))
       (if (<= x1 2.9e+33)
         (-
          x1
          (-
           (+
            (* x1 (- 2.0 t_0))
            (* x2 (- (* x1 (- 12.0 (* x1 6.0))) (* 8.0 (* x1 x2)))))
           (* x2 -6.0)))
         (if (<= x1 2e+101)
           (+
            x1
            (+
             t_5
             (+
              x1
              (+
               t_6
               (+
                t_2
                (*
                 t_4
                 (+ (* x1 2.0) (* (* x1 x1) (- (* (/ t_3 t_4) 4.0) 6.0)))))))))
           (+ x1 (+ (* x2 -6.0) (* x1 (- t_0 2.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 3.0) + 9.0);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = t_1 * (2.0 * x2);
	double t_3 = (t_1 + (2.0 * x2)) - x1;
	double t_4 = (x1 * x1) + 1.0;
	double t_5 = 3.0 * (x2 * -2.0);
	double t_6 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -2.12e+102) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= -4.1e+15) {
		tmp = x1 + (t_5 - ((((t_4 * (((x1 * x1) * (6.0 + (4.0 * (t_3 / (-1.0 - (x1 * x1)))))) - (x1 * (2.0 + (2.0 * ((3.0 - (x2 * 4.0)) / x1)))))) - t_2) - t_6) - x1));
	} else if (x1 <= 2.9e+33) {
		tmp = x1 - (((x1 * (2.0 - t_0)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	} else if (x1 <= 2e+101) {
		tmp = x1 + (t_5 + (x1 + (t_6 + (t_2 + (t_4 * ((x1 * 2.0) + ((x1 * x1) * (((t_3 / t_4) * 4.0) - 6.0))))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_0 - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = x1 * ((x1 * 3.0d0) + 9.0d0)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = t_1 * (2.0d0 * x2)
    t_3 = (t_1 + (2.0d0 * x2)) - x1
    t_4 = (x1 * x1) + 1.0d0
    t_5 = 3.0d0 * (x2 * (-2.0d0))
    t_6 = x1 * (x1 * x1)
    if (x1 <= (-2.12d+102)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0))))))
    else if (x1 <= (-4.1d+15)) then
        tmp = x1 + (t_5 - ((((t_4 * (((x1 * x1) * (6.0d0 + (4.0d0 * (t_3 / ((-1.0d0) - (x1 * x1)))))) - (x1 * (2.0d0 + (2.0d0 * ((3.0d0 - (x2 * 4.0d0)) / x1)))))) - t_2) - t_6) - x1))
    else if (x1 <= 2.9d+33) then
        tmp = x1 - (((x1 * (2.0d0 - t_0)) + (x2 * ((x1 * (12.0d0 - (x1 * 6.0d0))) - (8.0d0 * (x1 * x2))))) - (x2 * (-6.0d0)))
    else if (x1 <= 2d+101) then
        tmp = x1 + (t_5 + (x1 + (t_6 + (t_2 + (t_4 * ((x1 * 2.0d0) + ((x1 * x1) * (((t_3 / t_4) * 4.0d0) - 6.0d0))))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (t_0 - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 3.0) + 9.0);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = t_1 * (2.0 * x2);
	double t_3 = (t_1 + (2.0 * x2)) - x1;
	double t_4 = (x1 * x1) + 1.0;
	double t_5 = 3.0 * (x2 * -2.0);
	double t_6 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -2.12e+102) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= -4.1e+15) {
		tmp = x1 + (t_5 - ((((t_4 * (((x1 * x1) * (6.0 + (4.0 * (t_3 / (-1.0 - (x1 * x1)))))) - (x1 * (2.0 + (2.0 * ((3.0 - (x2 * 4.0)) / x1)))))) - t_2) - t_6) - x1));
	} else if (x1 <= 2.9e+33) {
		tmp = x1 - (((x1 * (2.0 - t_0)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	} else if (x1 <= 2e+101) {
		tmp = x1 + (t_5 + (x1 + (t_6 + (t_2 + (t_4 * ((x1 * 2.0) + ((x1 * x1) * (((t_3 / t_4) * 4.0) - 6.0))))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_0 - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((x1 * 3.0) + 9.0)
	t_1 = x1 * (x1 * 3.0)
	t_2 = t_1 * (2.0 * x2)
	t_3 = (t_1 + (2.0 * x2)) - x1
	t_4 = (x1 * x1) + 1.0
	t_5 = 3.0 * (x2 * -2.0)
	t_6 = x1 * (x1 * x1)
	tmp = 0
	if x1 <= -2.12e+102:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))))
	elif x1 <= -4.1e+15:
		tmp = x1 + (t_5 - ((((t_4 * (((x1 * x1) * (6.0 + (4.0 * (t_3 / (-1.0 - (x1 * x1)))))) - (x1 * (2.0 + (2.0 * ((3.0 - (x2 * 4.0)) / x1)))))) - t_2) - t_6) - x1))
	elif x1 <= 2.9e+33:
		tmp = x1 - (((x1 * (2.0 - t_0)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0))
	elif x1 <= 2e+101:
		tmp = x1 + (t_5 + (x1 + (t_6 + (t_2 + (t_4 * ((x1 * 2.0) + ((x1 * x1) * (((t_3 / t_4) * 4.0) - 6.0))))))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_0 - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(t_1 * Float64(2.0 * x2))
	t_3 = Float64(Float64(t_1 + Float64(2.0 * x2)) - x1)
	t_4 = Float64(Float64(x1 * x1) + 1.0)
	t_5 = Float64(3.0 * Float64(x2 * -2.0))
	t_6 = Float64(x1 * Float64(x1 * x1))
	tmp = 0.0
	if (x1 <= -2.12e+102)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))))));
	elseif (x1 <= -4.1e+15)
		tmp = Float64(x1 + Float64(t_5 - Float64(Float64(Float64(Float64(t_4 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * Float64(t_3 / Float64(-1.0 - Float64(x1 * x1)))))) - Float64(x1 * Float64(2.0 + Float64(2.0 * Float64(Float64(3.0 - Float64(x2 * 4.0)) / x1)))))) - t_2) - t_6) - x1)));
	elseif (x1 <= 2.9e+33)
		tmp = Float64(x1 - Float64(Float64(Float64(x1 * Float64(2.0 - t_0)) + Float64(x2 * Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(8.0 * Float64(x1 * x2))))) - Float64(x2 * -6.0)));
	elseif (x1 <= 2e+101)
		tmp = Float64(x1 + Float64(t_5 + Float64(x1 + Float64(t_6 + Float64(t_2 + Float64(t_4 * Float64(Float64(x1 * 2.0) + Float64(Float64(x1 * x1) * Float64(Float64(Float64(t_3 / t_4) * 4.0) - 6.0)))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(t_0 - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((x1 * 3.0) + 9.0);
	t_1 = x1 * (x1 * 3.0);
	t_2 = t_1 * (2.0 * x2);
	t_3 = (t_1 + (2.0 * x2)) - x1;
	t_4 = (x1 * x1) + 1.0;
	t_5 = 3.0 * (x2 * -2.0);
	t_6 = x1 * (x1 * x1);
	tmp = 0.0;
	if (x1 <= -2.12e+102)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	elseif (x1 <= -4.1e+15)
		tmp = x1 + (t_5 - ((((t_4 * (((x1 * x1) * (6.0 + (4.0 * (t_3 / (-1.0 - (x1 * x1)))))) - (x1 * (2.0 + (2.0 * ((3.0 - (x2 * 4.0)) / x1)))))) - t_2) - t_6) - x1));
	elseif (x1 <= 2.9e+33)
		tmp = x1 - (((x1 * (2.0 - t_0)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	elseif (x1 <= 2e+101)
		tmp = x1 + (t_5 + (x1 + (t_6 + (t_2 + (t_4 * ((x1 * 2.0) + ((x1 * x1) * (((t_3 / t_4) * 4.0) - 6.0))))))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_0 - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$5 = N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.12e+102], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -4.1e+15], N[(x1 + N[(t$95$5 - N[(N[(N[(N[(t$95$4 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * N[(t$95$3 / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(2.0 + N[(2.0 * N[(N[(3.0 - N[(x2 * 4.0), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] - t$95$6), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.9e+33], N[(x1 - N[(N[(N[(x1 * N[(2.0 - t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+101], N[(x1 + N[(t$95$5 + N[(x1 + N[(t$95$6 + N[(t$95$2 + N[(t$95$4 * N[(N[(x1 * 2.0), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(N[(t$95$3 / t$95$4), $MachinePrecision] * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(t$95$0 - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -2.12000000000000003e102

   1. Initial program 0.0%

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

   3. Simplified 22.2%

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

   5. Taylor expanded in x1 around 0 71.1%

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

   6. Taylor expanded in x2 around 0 100.0%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 1\right) \]

   8. Simplified 100.0%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 1\right) \]

   if -2.12000000000000003e102 < x1 < -4.1e15

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 78.3%

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

   4. Taylor expanded in x1 around 0 78.3%

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

      1. *-commutative 78.3%

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

   6. Simplified 78.3%

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

   7. Taylor expanded in x1 around 0 72.8%

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

   8. Taylor expanded in x1 around -inf 69.3%

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

   if -4.1e15 < x1 < 2.90000000000000025e33

   1. Initial program 99.5%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x1 around 0 86.9%

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

      1. associate-*r* 96.1%

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

      2. fmm-def 96.1%

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

      3. metadata-eval 96.1%

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

   7. Simplified 96.1%

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

   8. Taylor expanded in x1 around 0 87.1%

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

   9. Taylor expanded in x2 around 0 96.2%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right)\right)}\right) \]

   if 2.90000000000000025e33 < x1 < 2e101

   1. Initial program 99.0%

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

   3. Taylor expanded in x1 around 0 99.4%

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

   4. Taylor expanded in x1 around 0 99.4%

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

      1. *-commutative 99.4%

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

   6. Simplified 99.4%

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

   7. Taylor expanded in x1 around 0 99.4%

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

   8. Taylor expanded in x1 around inf 99.0%

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

      1. *-commutative 99.0%

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

   10. Simplified 99.0%

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

   if 2e101 < x1

   1. Initial program 26.8%

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

   3. Simplified 26.8%

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

   5. Taylor expanded in x1 around 0 8.3%

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

      1. associate-*r* 8.3%

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

      2. fmm-def 8.3%

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

      3. metadata-eval 8.3%

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

   7. Simplified 8.3%

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

   8. Taylor expanded in x1 around 0 92.7%

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

   9. Taylor expanded in x2 around 0 100.0%

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

       1. *-commutative 100.0%

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

   11. Simplified 100.0%

       \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot 3\right)} - 2\right)\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.12 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -4.1 \cdot 10^{+15}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) - \left(\left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) - x1 \cdot \left(2 + 2 \cdot \frac{3 - x2 \cdot 4}{x1}\right)\right) - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 2.9 \cdot 10^{+33}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 - x1 \cdot \left(x1 \cdot 3 + 9\right)\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+101}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 9\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 93.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_0 \cdot \left(2 \cdot x2\right) + t\_1 \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1} \cdot 4 - 6\right)\right)\right)\right)\right)\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3 + 9\right)\\ \mathbf{if}\;x1 \leq -2.12 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -1.6 \cdot 10^{+16}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq 2.9 \cdot 10^{+33}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 - t\_3\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+102}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(t\_3 - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2
         (+
          x1
          (+
           (* 3.0 (* x2 -2.0))
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* t_0 (* 2.0 x2))
              (*
               t_1
               (+
                (* x1 2.0)
                (*
                 (* x1 x1)
                 (- (* (/ (- (+ t_0 (* 2.0 x2)) x1) t_1) 4.0) 6.0))))))))))
        (t_3 (* x1 (+ (* x1 3.0) 9.0))))
   (if (<= x1 -2.12e+102)
     (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0))))))
     (if (<= x1 -1.6e+16)
       t_2
       (if (<= x1 2.9e+33)
         (-
          x1
          (-
           (+
            (* x1 (- 2.0 t_3))
            (* x2 (- (* x1 (- 12.0 (* x1 6.0))) (* 8.0 (* x1 x2)))))
           (* x2 -6.0)))
         (if (<= x1 4e+102) t_2 (+ x1 (+ (* x2 -6.0) (* x1 (- t_3 2.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (2.0 * x2)) + (t_1 * ((x1 * 2.0) + ((x1 * x1) * (((((t_0 + (2.0 * x2)) - x1) / t_1) * 4.0) - 6.0))))))));
	double t_3 = x1 * ((x1 * 3.0) + 9.0);
	double tmp;
	if (x1 <= -2.12e+102) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= -1.6e+16) {
		tmp = t_2;
	} else if (x1 <= 2.9e+33) {
		tmp = x1 - (((x1 * (2.0 - t_3)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	} else if (x1 <= 4e+102) {
		tmp = t_2;
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_3 - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = x1 + ((3.0d0 * (x2 * (-2.0d0))) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (2.0d0 * x2)) + (t_1 * ((x1 * 2.0d0) + ((x1 * x1) * (((((t_0 + (2.0d0 * x2)) - x1) / t_1) * 4.0d0) - 6.0d0))))))))
    t_3 = x1 * ((x1 * 3.0d0) + 9.0d0)
    if (x1 <= (-2.12d+102)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0))))))
    else if (x1 <= (-1.6d+16)) then
        tmp = t_2
    else if (x1 <= 2.9d+33) then
        tmp = x1 - (((x1 * (2.0d0 - t_3)) + (x2 * ((x1 * (12.0d0 - (x1 * 6.0d0))) - (8.0d0 * (x1 * x2))))) - (x2 * (-6.0d0)))
    else if (x1 <= 4d+102) then
        tmp = t_2
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (t_3 - 2.0d0)))
    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 = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (2.0 * x2)) + (t_1 * ((x1 * 2.0) + ((x1 * x1) * (((((t_0 + (2.0 * x2)) - x1) / t_1) * 4.0) - 6.0))))))));
	double t_3 = x1 * ((x1 * 3.0) + 9.0);
	double tmp;
	if (x1 <= -2.12e+102) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= -1.6e+16) {
		tmp = t_2;
	} else if (x1 <= 2.9e+33) {
		tmp = x1 - (((x1 * (2.0 - t_3)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	} else if (x1 <= 4e+102) {
		tmp = t_2;
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_3 - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (2.0 * x2)) + (t_1 * ((x1 * 2.0) + ((x1 * x1) * (((((t_0 + (2.0 * x2)) - x1) / t_1) * 4.0) - 6.0))))))))
	t_3 = x1 * ((x1 * 3.0) + 9.0)
	tmp = 0
	if x1 <= -2.12e+102:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))))
	elif x1 <= -1.6e+16:
		tmp = t_2
	elif x1 <= 2.9e+33:
		tmp = x1 - (((x1 * (2.0 - t_3)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0))
	elif x1 <= 4e+102:
		tmp = t_2
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_3 - 2.0)))
	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(x1 + Float64(Float64(3.0 * Float64(x2 * -2.0)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * Float64(2.0 * x2)) + Float64(t_1 * Float64(Float64(x1 * 2.0) + Float64(Float64(x1 * x1) * Float64(Float64(Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1) * 4.0) - 6.0)))))))))
	t_3 = Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0))
	tmp = 0.0
	if (x1 <= -2.12e+102)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))))));
	elseif (x1 <= -1.6e+16)
		tmp = t_2;
	elseif (x1 <= 2.9e+33)
		tmp = Float64(x1 - Float64(Float64(Float64(x1 * Float64(2.0 - t_3)) + Float64(x2 * Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(8.0 * Float64(x1 * x2))))) - Float64(x2 * -6.0)));
	elseif (x1 <= 4e+102)
		tmp = t_2;
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(t_3 - 2.0))));
	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 = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (2.0 * x2)) + (t_1 * ((x1 * 2.0) + ((x1 * x1) * (((((t_0 + (2.0 * x2)) - x1) / t_1) * 4.0) - 6.0))))))));
	t_3 = x1 * ((x1 * 3.0) + 9.0);
	tmp = 0.0;
	if (x1 <= -2.12e+102)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	elseif (x1 <= -1.6e+16)
		tmp = t_2;
	elseif (x1 <= 2.9e+33)
		tmp = x1 - (((x1 * (2.0 - t_3)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	elseif (x1 <= 4e+102)
		tmp = t_2;
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_3 - 2.0)));
	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[(x1 + N[(N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(N[(x1 * 2.0), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision] * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.12e+102], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.6e+16], t$95$2, If[LessEqual[x1, 2.9e+33], N[(x1 - N[(N[(N[(x1 * N[(2.0 - t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4e+102], t$95$2, N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(t$95$3 - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.12000000000000003e102

   1. Initial program 0.0%

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

   3. Simplified 22.2%

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

   5. Taylor expanded in x1 around 0 71.1%

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

   6. Taylor expanded in x2 around 0 100.0%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 1\right) \]

   8. Simplified 100.0%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 1\right) \]

   if -2.12000000000000003e102 < x1 < -1.6e16 or 2.90000000000000025e33 < x1 < 3.99999999999999991e102

   1. Initial program 99.2%

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

   3. Taylor expanded in x1 around 0 88.9%

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

   4. Taylor expanded in x1 around 0 88.9%

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

      1. *-commutative 88.9%

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

   6. Simplified 88.9%

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

   7. Taylor expanded in x1 around 0 86.1%

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

   8. Taylor expanded in x1 around inf 84.1%

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

      1. *-commutative 88.0%

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

   10. Simplified 84.1%

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

   if -1.6e16 < x1 < 2.90000000000000025e33

   1. Initial program 99.5%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x1 around 0 86.9%

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

      1. associate-*r* 96.1%

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

      2. fmm-def 96.1%

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

      3. metadata-eval 96.1%

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

   7. Simplified 96.1%

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

   8. Taylor expanded in x1 around 0 87.1%

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

   9. Taylor expanded in x2 around 0 96.2%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right)\right)}\right) \]

   if 3.99999999999999991e102 < x1

   1. Initial program 26.8%

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

   3. Simplified 26.8%

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

   5. Taylor expanded in x1 around 0 8.3%

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

      1. associate-*r* 8.3%

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

      2. fmm-def 8.3%

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

      3. metadata-eval 8.3%

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

   7. Simplified 8.3%

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

   8. Taylor expanded in x1 around 0 92.7%

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

   9. Taylor expanded in x2 around 0 100.0%

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

       1. *-commutative 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.12 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -1.6 \cdot 10^{+16}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.9 \cdot 10^{+33}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 - x1 \cdot \left(x1 \cdot 3 + 9\right)\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 9\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 86.1% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3 + 9\right)\\ \mathbf{if}\;x1 \leq -2.9 \cdot 10^{+43}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+101}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 - t\_0\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(t\_0 - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ (* x1 3.0) 9.0))))
   (if (<= x1 -2.9e+43)
     (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0))))))
     (if (<= x1 2e+101)
       (-
        x1
        (-
         (+
          (* x1 (- 2.0 t_0))
          (* x2 (- (* x1 (- 12.0 (* x1 6.0))) (* 8.0 (* x1 x2)))))
         (* x2 -6.0)))
       (+ x1 (+ (* x2 -6.0) (* x1 (- t_0 2.0))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 3.0) + 9.0);
	double tmp;
	if (x1 <= -2.9e+43) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= 2e+101) {
		tmp = x1 - (((x1 * (2.0 - t_0)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_0 - 2.0)));
	}
	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 * 3.0d0) + 9.0d0)
    if (x1 <= (-2.9d+43)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0))))))
    else if (x1 <= 2d+101) then
        tmp = x1 - (((x1 * (2.0d0 - t_0)) + (x2 * ((x1 * (12.0d0 - (x1 * 6.0d0))) - (8.0d0 * (x1 * x2))))) - (x2 * (-6.0d0)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (t_0 - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 3.0) + 9.0);
	double tmp;
	if (x1 <= -2.9e+43) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= 2e+101) {
		tmp = x1 - (((x1 * (2.0 - t_0)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_0 - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((x1 * 3.0) + 9.0)
	tmp = 0
	if x1 <= -2.9e+43:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))))
	elif x1 <= 2e+101:
		tmp = x1 - (((x1 * (2.0 - t_0)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_0 - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0))
	tmp = 0.0
	if (x1 <= -2.9e+43)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))))));
	elseif (x1 <= 2e+101)
		tmp = Float64(x1 - Float64(Float64(Float64(x1 * Float64(2.0 - t_0)) + Float64(x2 * Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(8.0 * Float64(x1 * x2))))) - Float64(x2 * -6.0)));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(t_0 - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((x1 * 3.0) + 9.0);
	tmp = 0.0;
	if (x1 <= -2.9e+43)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	elseif (x1 <= 2e+101)
		tmp = x1 - (((x1 * (2.0 - t_0)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_0 - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.9e+43], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+101], N[(x1 - N[(N[(N[(x1 * N[(2.0 - t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(t$95$0 - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.9000000000000002e43

   1. Initial program 16.6%

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

   3. Simplified 35.1%

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

   5. Taylor expanded in x1 around 0 60.5%

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

   6. Taylor expanded in x2 around 0 84.6%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 84.6%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 1\right) \]

   8. Simplified 84.6%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 1\right) \]

   if -2.9000000000000002e43 < x1 < 2e101

   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%

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

   5. Taylor expanded in x1 around 0 76.0%

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

      1. associate-*r* 83.7%

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

      2. fmm-def 83.7%

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

      3. metadata-eval 83.7%

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

   7. Simplified 83.7%

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

   8. Taylor expanded in x1 around 0 75.7%

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

   9. Taylor expanded in x2 around 0 84.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right)\right)}\right) \]

   if 2e101 < x1

   1. Initial program 26.8%

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

   3. Simplified 26.8%

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

   5. Taylor expanded in x1 around 0 8.3%

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

      1. associate-*r* 8.3%

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

      2. fmm-def 8.3%

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

      3. metadata-eval 8.3%

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

   7. Simplified 8.3%

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

   8. Taylor expanded in x1 around 0 92.7%

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

   9. Taylor expanded in x2 around 0 100.0%

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

       1. *-commutative 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.9 \cdot 10^{+43}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+101}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 - x1 \cdot \left(x1 \cdot 3 + 9\right)\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 9\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 79.5% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -9.6 \cdot 10^{+39}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq 3.7 \cdot 10^{+102}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - 3 \cdot \left(x1 \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 9\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -9.6e+39)
   (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0))))))
   (if (<= x1 3.7e+102)
     (-
      x1
      (-
       (*
        x1
        (+
         2.0
         (-
          (* 4.0 (* x2 (- 3.0 (* 2.0 x2))))
          (* 3.0 (* x1 (- 3.0 (* x2 -2.0)))))))
       (* x2 -6.0)))
     (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 (+ (* x1 3.0) 9.0)) 2.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -9.6e+39) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= 3.7e+102) {
		tmp = x1 - ((x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (3.0 * (x1 * (3.0 - (x2 * -2.0))))))) - (x2 * -6.0));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + 9.0)) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-9.6d+39)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0))))))
    else if (x1 <= 3.7d+102) then
        tmp = x1 - ((x1 * (2.0d0 + ((4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))) - (3.0d0 * (x1 * (3.0d0 - (x2 * (-2.0d0)))))))) - (x2 * (-6.0d0)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * ((x1 * 3.0d0) + 9.0d0)) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -9.6e+39) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= 3.7e+102) {
		tmp = x1 - ((x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (3.0 * (x1 * (3.0 - (x2 * -2.0))))))) - (x2 * -6.0));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + 9.0)) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -9.6e+39:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))))
	elif x1 <= 3.7e+102:
		tmp = x1 - ((x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (3.0 * (x1 * (3.0 - (x2 * -2.0))))))) - (x2 * -6.0))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + 9.0)) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -9.6e+39)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))))));
	elseif (x1 <= 3.7e+102)
		tmp = Float64(x1 - Float64(Float64(x1 * Float64(2.0 + Float64(Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))) - Float64(3.0 * Float64(x1 * Float64(3.0 - Float64(x2 * -2.0))))))) - Float64(x2 * -6.0)));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0)) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -9.6e+39)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	elseif (x1 <= 3.7e+102)
		tmp = x1 - ((x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (3.0 * (x1 * (3.0 - (x2 * -2.0))))))) - (x2 * -6.0));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + 9.0)) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -9.6e+39], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.7e+102], N[(x1 - N[(N[(x1 * N[(2.0 + N[(N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * N[(x1 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -9.6000000000000004e39

   1. Initial program 20.9%

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

   3. Simplified 36.7%

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

   5. Taylor expanded in x1 around 0 57.5%

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

   6. Taylor expanded in x2 around 0 80.5%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 80.5%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 1\right) \]

   8. Simplified 80.5%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 1\right) \]

   if -9.6000000000000004e39 < x1 < 3.70000000000000023e102

   1. Initial program 99.4%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x1 around 0 76.8%

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

      1. associate-*r* 84.6%

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

      2. fmm-def 84.6%

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

      3. metadata-eval 84.6%

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

   7. Simplified 84.6%

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

   8. Taylor expanded in x1 around 0 77.1%

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

   if 3.70000000000000023e102 < x1

   1. Initial program 26.8%

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

   3. Simplified 26.8%

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

   5. Taylor expanded in x1 around 0 8.3%

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

      1. associate-*r* 8.3%

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

      2. fmm-def 8.3%

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

      3. metadata-eval 8.3%

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

   7. Simplified 8.3%

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

   8. Taylor expanded in x1 around 0 92.7%

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

   9. Taylor expanded in x2 around 0 100.0%

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

       1. *-commutative 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9.6 \cdot 10^{+39}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq 3.7 \cdot 10^{+102}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - 3 \cdot \left(x1 \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 9\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 78.6% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -3.35 \cdot 10^{+40}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -3.35e+40)
   (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0))))))
   (+
    x1
    (-
     (* x2 -6.0)
     (*
      x1
      (+
       2.0
       (+
        (* x1 (- (* 3.0 (- (* x2 -2.0) 3.0)) (* x1 3.0)))
        (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3.35e+40) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (4.0 * (x2 * (3.0 - (2.0 * 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 <= (-3.35d+40)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((x1 * ((3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)) - (x1 * 3.0d0))) + (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2))))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3.35e+40) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (4.0 * (x2 * (3.0 - (2.0 * x2))))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -3.35e+40:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (4.0 * (x2 * (3.0 - (2.0 * x2))))))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -3.35e+40)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(x1 * Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)) - Float64(x1 * 3.0))) + Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -3.35e+40)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (4.0 * (x2 * (3.0 - (2.0 * x2))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -3.35e+40], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(N[(x1 * N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -3.35000000000000011e40

   1. Initial program 20.9%

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

   3. Simplified 36.7%

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

   5. Taylor expanded in x1 around 0 57.5%

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

   6. Taylor expanded in x2 around 0 80.5%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 80.5%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 1\right) \]

   8. Simplified 80.5%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 1\right) \]

   if -3.35000000000000011e40 < x1

   1. Initial program 84.5%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in x1 around 0 62.7%

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

      1. associate-*r* 68.8%

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

      2. fmm-def 68.8%

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

      3. metadata-eval 68.8%

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

   7. Simplified 68.8%

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

   8. Taylor expanded in x1 around 0 80.3%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.35 \cdot 10^{+40}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 54.6% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{if}\;x2 \leq -1.95 \cdot 10^{+57}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x2 \leq 1.5 \cdot 10^{-76}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 - 2\right)\right)\\ \mathbf{elif}\;x2 \leq 6 \cdot 10^{+218}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x2 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ 2.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))))))
   (if (<= x2 -1.95e+57)
     t_0
     (if (<= x2 1.5e-76)
       (+ x1 (+ (* x2 -6.0) (* x1 (- (* x2 -12.0) 2.0))))
       (if (<= x2 6e+218)
         (+ x1 (+ (* x2 -6.0) (* x1 (* x2 (- (* x1 6.0) 12.0)))))
         t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	double tmp;
	if (x2 <= -1.95e+57) {
		tmp = t_0;
	} else if (x2 <= 1.5e-76) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x2 * -12.0) - 2.0)));
	} else if (x2 <= 6e+218) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (x2 * ((x1 * 6.0) - 12.0))));
	} 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 * (2.0d0 + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))))
    if (x2 <= (-1.95d+57)) then
        tmp = t_0
    else if (x2 <= 1.5d-76) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x2 * (-12.0d0)) - 2.0d0)))
    else if (x2 <= 6d+218) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (x2 * ((x1 * 6.0d0) - 12.0d0))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	double tmp;
	if (x2 <= -1.95e+57) {
		tmp = t_0;
	} else if (x2 <= 1.5e-76) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x2 * -12.0) - 2.0)));
	} else if (x2 <= 6e+218) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (x2 * ((x1 * 6.0) - 12.0))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))))
	tmp = 0
	if x2 <= -1.95e+57:
		tmp = t_0
	elif x2 <= 1.5e-76:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x2 * -12.0) - 2.0)))
	elif x2 <= 6e+218:
		tmp = x1 + ((x2 * -6.0) + (x1 * (x2 * ((x1 * 6.0) - 12.0))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(2.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))))
	tmp = 0.0
	if (x2 <= -1.95e+57)
		tmp = t_0;
	elseif (x2 <= 1.5e-76)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x2 * -12.0) - 2.0))));
	elseif (x2 <= 6e+218)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(x2 * Float64(Float64(x1 * 6.0) - 12.0)))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	tmp = 0.0;
	if (x2 <= -1.95e+57)
		tmp = t_0;
	elseif (x2 <= 1.5e-76)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x2 * -12.0) - 2.0)));
	elseif (x2 <= 6e+218)
		tmp = x1 + ((x2 * -6.0) + (x1 * (x2 * ((x1 * 6.0) - 12.0))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(2.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x2, -1.95e+57], t$95$0, If[LessEqual[x2, 1.5e-76], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x2, 6e+218], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(x2 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -1.94999999999999984e57 or 6.0000000000000001e218 < x2

   1. Initial program 72.0%

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

   3. Simplified 72.0%

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

   5. Taylor expanded in x1 around 0 59.4%

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

      1. associate-*r* 70.3%

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

      2. fmm-def 70.3%

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

      3. metadata-eval 70.3%

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

   7. Simplified 70.3%

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

   8. Taylor expanded in x1 around inf 60.2%

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

   9. Taylor expanded in x1 around 0 60.2%

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

   if -1.94999999999999984e57 < x2 < 1.50000000000000012e-76

   1. Initial program 71.9%

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

   3. Simplified 72.1%

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

   5. Taylor expanded in x1 around 0 49.0%

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

      1. associate-*r* 49.0%

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

      2. fmm-def 49.0%

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

      3. metadata-eval 49.0%

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

   7. Simplified 49.0%

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

   8. Taylor expanded in x1 around 0 66.7%

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

   9. Taylor expanded in x2 around 0 66.7%

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

   10. Taylor expanded in x1 around 0 48.1%

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

   12. Simplified 48.1%

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

   if 1.50000000000000012e-76 < x2 < 6.0000000000000001e218

   1. Initial program 65.9%

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

   3. Simplified 66.0%

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

   5. Taylor expanded in x1 around 0 40.7%

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

      1. associate-*r* 47.8%

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

      2. fmm-def 47.8%

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

      3. metadata-eval 47.8%

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

   7. Simplified 47.8%

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

   8. Taylor expanded in x1 around 0 55.2%

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

   9. Taylor expanded in x2 around 0 51.1%

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

   10. Taylor expanded in x2 around inf 66.0%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.95 \cdot 10^{+57}:\\ \;\;\;\;x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{elif}\;x2 \leq 1.5 \cdot 10^{-76}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 - 2\right)\right)\\ \mathbf{elif}\;x2 \leq 6 \cdot 10^{+218}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x2 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 41.3% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.9 \cdot 10^{+43}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + x1 \cdot 12\right)\\ \mathbf{elif}\;x1 \leq -2.4 \cdot 10^{-82} \lor \neg \left(x1 \leq 1.35 \cdot 10^{-176}\right):\\ \;\;\;\;x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -2.9e+43)
   (- x1 (* x2 (+ 6.0 (* x1 12.0))))
   (if (or (<= x1 -2.4e-82) (not (<= x1 1.35e-176)))
     (* x1 (+ 2.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))))
     (* x2 -6.0))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.9e+43) {
		tmp = x1 - (x2 * (6.0 + (x1 * 12.0)));
	} else if ((x1 <= -2.4e-82) || !(x1 <= 1.35e-176)) {
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-2.9d+43)) then
        tmp = x1 - (x2 * (6.0d0 + (x1 * 12.0d0)))
    else if ((x1 <= (-2.4d-82)) .or. (.not. (x1 <= 1.35d-176))) then
        tmp = x1 * (2.0d0 + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))))
    else
        tmp = x2 * (-6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.9e+43) {
		tmp = x1 - (x2 * (6.0 + (x1 * 12.0)));
	} else if ((x1 <= -2.4e-82) || !(x1 <= 1.35e-176)) {
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -2.9e+43:
		tmp = x1 - (x2 * (6.0 + (x1 * 12.0)))
	elif (x1 <= -2.4e-82) or not (x1 <= 1.35e-176):
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))))
	else:
		tmp = x2 * -6.0
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -2.9e+43)
		tmp = Float64(x1 - Float64(x2 * Float64(6.0 + Float64(x1 * 12.0))));
	elseif ((x1 <= -2.4e-82) || !(x1 <= 1.35e-176))
		tmp = Float64(x1 * Float64(2.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))));
	else
		tmp = Float64(x2 * -6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -2.9e+43)
		tmp = x1 - (x2 * (6.0 + (x1 * 12.0)));
	elseif ((x1 <= -2.4e-82) || ~((x1 <= 1.35e-176)))
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	else
		tmp = x2 * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -2.9e+43], N[(x1 - N[(x2 * N[(6.0 + N[(x1 * 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x1, -2.4e-82], N[Not[LessEqual[x1, 1.35e-176]], $MachinePrecision]], N[(x1 * N[(2.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * -6.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.9000000000000002e43

   1. Initial program 16.6%

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

   3. Simplified 16.6%

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

   5. Taylor expanded in x1 around 0 2.0%

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

      1. associate-*r* 2.0%

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

      2. fmm-def 2.0%

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

      3. metadata-eval 2.0%

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

   7. Simplified 2.0%

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

   8. Taylor expanded in x1 around 0 33.2%

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

   9. Taylor expanded in x2 around -inf 3.8%

      \[\leadsto x1 + \color{blue}{{x2}^{2} \cdot \left(-1 \cdot \frac{6 + 12 \cdot x1}{x2} + 8 \cdot x1\right)} \]

   10. Taylor expanded in x2 around 0 17.5%

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

   if -2.9000000000000002e43 < x1 < -2.40000000000000008e-82 or 1.3499999999999999e-176 < x1

   1. Initial program 76.8%

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

   3. Simplified 77.0%

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

   5. Taylor expanded in x1 around 0 51.0%

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

      1. associate-*r* 51.7%

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

      2. fmm-def 51.7%

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

      3. metadata-eval 51.7%

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

   7. Simplified 51.7%

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

   8. Taylor expanded in x1 around inf 38.9%

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

   9. Taylor expanded in x1 around 0 38.9%

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

   if -2.40000000000000008e-82 < x1 < 1.3499999999999999e-176

   1. Initial program 99.5%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x1 around 0 64.7%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.9 \cdot 10^{+43}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + x1 \cdot 12\right)\\ \mathbf{elif}\;x1 \leq -2.4 \cdot 10^{-82} \lor \neg \left(x1 \leq 1.35 \cdot 10^{-176}\right):\\ \;\;\;\;x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 79.3% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.9 \cdot 10^{+43}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 - x2 \cdot \left(12 - x2 \cdot 8\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 9\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -2.9e+43)
   (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0))))))
   (if (<= x1 3.9e+102)
     (+ (* x2 -6.0) (* x1 (- -1.0 (* x2 (- 12.0 (* x2 8.0))))))
     (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 (+ (* x1 3.0) 9.0)) 2.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.9e+43) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= 3.9e+102) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 - (x2 * (12.0 - (x2 * 8.0)))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + 9.0)) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-2.9d+43)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0))))))
    else if (x1 <= 3.9d+102) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) - (x2 * (12.0d0 - (x2 * 8.0d0)))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * ((x1 * 3.0d0) + 9.0d0)) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.9e+43) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= 3.9e+102) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 - (x2 * (12.0 - (x2 * 8.0)))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + 9.0)) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -2.9e+43:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))))
	elif x1 <= 3.9e+102:
		tmp = (x2 * -6.0) + (x1 * (-1.0 - (x2 * (12.0 - (x2 * 8.0)))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + 9.0)) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -2.9e+43)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))))));
	elseif (x1 <= 3.9e+102)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 - Float64(x2 * Float64(12.0 - Float64(x2 * 8.0))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0)) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -2.9e+43)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	elseif (x1 <= 3.9e+102)
		tmp = (x2 * -6.0) + (x1 * (-1.0 - (x2 * (12.0 - (x2 * 8.0)))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + 9.0)) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -2.9e+43], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.9e+102], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 - N[(x2 * N[(12.0 - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.9000000000000002e43

   1. Initial program 16.6%

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

   3. Simplified 35.1%

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

   5. Taylor expanded in x1 around 0 60.5%

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

   6. Taylor expanded in x2 around 0 84.6%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 84.6%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 1\right) \]

   8. Simplified 84.6%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 1\right) \]

   if -2.9000000000000002e43 < x1 < 3.8999999999999998e102

   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%

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

   5. Taylor expanded in x1 around 0 76.0%

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

      1. associate-*r* 83.7%

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

      2. fmm-def 83.7%

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

      3. metadata-eval 83.7%

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

   7. Simplified 83.7%

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

   8. Taylor expanded in x1 around 0 84.0%

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

   9. Taylor expanded in x2 around 0 84.0%

      \[\leadsto x1 + \mathsf{fma}\left(3, \frac{3 \cdot \left(x1 \cdot x1\right) - \mathsf{fma}\left(2, x2, x1\right)}{1}, x1 + \color{blue}{x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)}\right) \]

   10. Taylor expanded in x1 around 0 75.3%

       \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(x2 \cdot \left(8 \cdot x2 - 12\right) - 1\right)} \]

   if 3.8999999999999998e102 < x1

   1. Initial program 26.8%

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

   3. Simplified 26.8%

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

   5. Taylor expanded in x1 around 0 8.3%

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

      1. associate-*r* 8.3%

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

      2. fmm-def 8.3%

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

      3. metadata-eval 8.3%

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

   7. Simplified 8.3%

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

   8. Taylor expanded in x1 around 0 92.7%

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

   9. Taylor expanded in x2 around 0 100.0%

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

       1. *-commutative 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.9 \cdot 10^{+43}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 - x2 \cdot \left(12 - x2 \cdot 8\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 9\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 49.4% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -1.9 \cdot 10^{+56} \lor \neg \left(x2 \leq 1.15 \cdot 10^{+217}\right):\\ \;\;\;\;x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -1.9e+56) (not (<= x2 1.15e+217)))
   (* x1 (+ 2.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))))
   (+ x1 (+ (* x2 -6.0) (* x1 (- (* x2 -12.0) 2.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.9e+56) || !(x2 <= 1.15e+217)) {
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x2 * -12.0) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-1.9d+56)) .or. (.not. (x2 <= 1.15d+217))) then
        tmp = x1 * (2.0d0 + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x2 * (-12.0d0)) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.9e+56) || !(x2 <= 1.15e+217)) {
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x2 * -12.0) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -1.9e+56) or not (x2 <= 1.15e+217):
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x2 * -12.0) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -1.9e+56) || !(x2 <= 1.15e+217))
		tmp = Float64(x1 * Float64(2.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x2 * -12.0) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -1.9e+56) || ~((x2 <= 1.15e+217)))
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x2 * -12.0) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -1.9e+56], N[Not[LessEqual[x2, 1.15e+217]], $MachinePrecision]], N[(x1 * N[(2.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -1.89999999999999998e56 or 1.1499999999999999e217 < x2

   1. Initial program 72.0%

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

   3. Simplified 72.0%

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

   5. Taylor expanded in x1 around 0 59.4%

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

      1. associate-*r* 70.3%

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

      2. fmm-def 70.3%

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

      3. metadata-eval 70.3%

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

   7. Simplified 70.3%

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

   8. Taylor expanded in x1 around inf 60.2%

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

   9. Taylor expanded in x1 around 0 60.2%

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

   if -1.89999999999999998e56 < x2 < 1.1499999999999999e217

   1. Initial program 69.7%

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

   3. Simplified 69.9%

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

   5. Taylor expanded in x1 around 0 46.0%

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

      1. associate-*r* 48.6%

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

      2. fmm-def 48.6%

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

      3. metadata-eval 48.6%

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

   7. Simplified 48.6%

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

   8. Taylor expanded in x1 around 0 62.5%

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

   9. Taylor expanded in x2 around 0 61.1%

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

   10. Taylor expanded in x1 around 0 46.1%

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

   12. Simplified 46.1%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.9 \cdot 10^{+56} \lor \neg \left(x2 \leq 1.15 \cdot 10^{+217}\right):\\ \;\;\;\;x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 69.8% accurate, 6.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.9 \cdot 10^{+43}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 - x2 \cdot \left(12 - x2 \cdot 8\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -2.9e+43)
   (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0))))))
   (+ (* x2 -6.0) (* x1 (- -1.0 (* x2 (- 12.0 (* x2 8.0))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.9e+43) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 - (x2 * (12.0 - (x2 * 8.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-2.9d+43)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0))))))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) - (x2 * (12.0d0 - (x2 * 8.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.9e+43) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 - (x2 * (12.0 - (x2 * 8.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -2.9e+43:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))))
	else:
		tmp = (x2 * -6.0) + (x1 * (-1.0 - (x2 * (12.0 - (x2 * 8.0)))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -2.9e+43)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 - Float64(x2 * Float64(12.0 - Float64(x2 * 8.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -2.9e+43)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	else
		tmp = (x2 * -6.0) + (x1 * (-1.0 - (x2 * (12.0 - (x2 * 8.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -2.9e+43], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 - N[(x2 * N[(12.0 - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -2.9000000000000002e43

   1. Initial program 16.6%

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

   3. Simplified 35.1%

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

   5. Taylor expanded in x1 around 0 60.5%

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

   6. Taylor expanded in x2 around 0 84.6%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 84.6%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 1\right) \]

   8. Simplified 84.6%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 1\right) \]

   if -2.9000000000000002e43 < x1

   1. Initial program 84.7%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in x1 around 0 62.3%

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

      1. associate-*r* 68.4%

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

      2. fmm-def 68.4%

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

      3. metadata-eval 68.4%

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

   7. Simplified 68.4%

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

   8. Taylor expanded in x1 around 0 83.5%

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

   9. Taylor expanded in x2 around 0 83.5%

      \[\leadsto x1 + \mathsf{fma}\left(3, \frac{3 \cdot \left(x1 \cdot x1\right) - \mathsf{fma}\left(2, x2, x1\right)}{1}, x1 + \color{blue}{x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)}\right) \]

   10. Taylor expanded in x1 around 0 66.6%

       \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(x2 \cdot \left(8 \cdot x2 - 12\right) - 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.9 \cdot 10^{+43}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 - x2 \cdot \left(12 - x2 \cdot 8\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 63.4% accurate, 6.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq 3 \cdot 10^{-20}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 3e-20)
   (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0))))))
   (* x1 (+ 2.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= 3e-20) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else {
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= 3d-20) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0))))))
    else
        tmp = x1 * (2.0d0 + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= 3e-20) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else {
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= 3e-20:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))))
	else:
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= 3e-20)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))))));
	else
		tmp = Float64(x1 * Float64(2.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= 3e-20)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	else
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, 3e-20], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 * N[(2.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < 3.00000000000000029e-20

   1. Initial program 75.0%

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

   3. Simplified 72.9%

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

   5. Taylor expanded in x1 around 0 64.6%

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

   6. Taylor expanded in x2 around 0 71.8%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 71.8%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 1\right) \]

   8. Simplified 71.8%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 1\right) \]

   if 3.00000000000000029e-20 < x1

   1. Initial program 58.5%

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

   3. Simplified 58.6%

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

   5. Taylor expanded in x1 around 0 25.1%

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

      1. associate-*r* 25.1%

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

      2. fmm-def 25.1%

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

      3. metadata-eval 25.1%

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

   7. Simplified 25.1%

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

   8. Taylor expanded in x1 around inf 38.0%

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

   9. Taylor expanded in x1 around 0 38.0%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq 3 \cdot 10^{-20}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 31.7% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+153} \lor \neg \left(x1 \leq 1.35\right):\\ \;\;\;\;x1 - x1 \cdot \left(-1 - x2 \cdot -12\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -9.5e+153) (not (<= x1 1.35)))
   (- x1 (* x1 (- -1.0 (* x2 -12.0))))
   (* x2 -6.0)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -9.5e+153) || !(x1 <= 1.35)) {
		tmp = x1 - (x1 * (-1.0 - (x2 * -12.0)));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-9.5d+153)) .or. (.not. (x1 <= 1.35d0))) then
        tmp = x1 - (x1 * ((-1.0d0) - (x2 * (-12.0d0))))
    else
        tmp = x2 * (-6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -9.5e+153) || !(x1 <= 1.35)) {
		tmp = x1 - (x1 * (-1.0 - (x2 * -12.0)));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -9.5e+153) or not (x1 <= 1.35):
		tmp = x1 - (x1 * (-1.0 - (x2 * -12.0)))
	else:
		tmp = x2 * -6.0
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -9.5e+153) || !(x1 <= 1.35))
		tmp = Float64(x1 - Float64(x1 * Float64(-1.0 - Float64(x2 * -12.0))));
	else
		tmp = Float64(x2 * -6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -9.5e+153) || ~((x1 <= 1.35)))
		tmp = x1 - (x1 * (-1.0 - (x2 * -12.0)));
	else
		tmp = x2 * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -9.5e+153], N[Not[LessEqual[x1, 1.35]], $MachinePrecision]], N[(x1 - N[(x1 * N[(-1.0 - N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * -6.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -9.4999999999999995e153 or 1.3500000000000001 < x1

   1. Initial program 35.8%

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

   3. Simplified 35.8%

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

   5. Taylor expanded in x1 around 0 11.4%

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

      1. associate-*r* 11.4%

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

      2. fmm-def 11.4%

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

      3. metadata-eval 11.4%

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

   7. Simplified 11.4%

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

   8. Taylor expanded in x1 around inf 22.8%

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

   9. Taylor expanded in x2 around 0 15.9%

      \[\leadsto x1 + x1 \cdot \left(1 + \color{blue}{-12 \cdot x2}\right) \]
   10. Step-by-step derivation

       1. *-commutative 15.9%

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

   11. Simplified 15.9%

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

   if -9.4999999999999995e153 < x1 < 1.3500000000000001

   1. Initial program 92.5%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in x1 around 0 35.7%

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

4. Final simplification 27.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+153} \lor \neg \left(x1 \leq 1.35\right):\\ \;\;\;\;x1 - x1 \cdot \left(-1 - x2 \cdot -12\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 32.3% accurate, 14.1× speedup

Math

\[\begin{array}{l} \\ x1 - x2 \cdot \left(6 + x1 \cdot 12\right) \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (- x1 (* x2 (+ 6.0 (* x1 12.0)))))

C

double code(double x1, double x2) {
	return x1 - (x2 * (6.0 + (x1 * 12.0)));
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x1 - (x2 * (6.0d0 + (x1 * 12.0d0)))
end function

Java

public static double code(double x1, double x2) {
	return x1 - (x2 * (6.0 + (x1 * 12.0)));
}

Python

def code(x1, x2):
	return x1 - (x2 * (6.0 + (x1 * 12.0)))

Julia

function code(x1, x2)
	return Float64(x1 - Float64(x2 * Float64(6.0 + Float64(x1 * 12.0))))
end

MATLAB

function tmp = code(x1, x2)
	tmp = x1 - (x2 * (6.0 + (x1 * 12.0)));
end

Wolfram

code[x1_, x2_] := N[(x1 - N[(x2 * N[(6.0 + N[(x1 * 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.3%

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

3. Simplified 70.5%

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

5. Taylor expanded in x1 around 0 49.6%

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

   1. associate-*r* 54.4%

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

   2. fmm-def 54.4%

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

   3. metadata-eval 54.4%

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

7. Simplified 54.4%

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

8. Taylor expanded in x1 around 0 72.9%

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

9. Taylor expanded in x2 around -inf 40.0%

   \[\leadsto x1 + \color{blue}{{x2}^{2} \cdot \left(-1 \cdot \frac{6 + 12 \cdot x1}{x2} + 8 \cdot x1\right)} \]

10. Taylor expanded in x2 around 0 27.5%

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

11. Final simplification 27.5%

    \[\leadsto x1 - x2 \cdot \left(6 + x1 \cdot 12\right) \]
12. Add Preprocessing

Alternative 25: 26.6% accurate, 42.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 70.3%

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

3. Simplified 70.5%

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

5. Taylor expanded in x1 around 0 22.6%

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

6. Final simplification 22.6%

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

Alternative 26: 3.2% accurate, 127.0× speedup

Math

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

FPCore

(FPCore (x1 x2) :precision binary64 x1)

C

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

Fortran

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

Java

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

Python

def code(x1, x2):
	return x1

Julia

function code(x1, x2)
	return x1
end

MATLAB

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

Wolfram

code[x1_, x2_] := x1

Derivation

1. Initial program 70.3%

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

3. Simplified 70.5%

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

5. Taylor expanded in x1 around 0 49.6%

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

   1. associate-*r* 54.4%

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

   2. fmm-def 54.4%

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

   3. metadata-eval 54.4%

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

7. Simplified 54.4%

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

8. Taylor expanded in x1 around 0 72.9%

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

9. Taylor expanded in x2 around -inf 40.0%

   \[\leadsto x1 + \color{blue}{{x2}^{2} \cdot \left(-1 \cdot \frac{6 + 12 \cdot x1}{x2} + 8 \cdot x1\right)} \]

10. Taylor expanded in x2 around 0 3.1%

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

Reproduce

herbie shell --seed 2024149 
(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))))))