Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 69.9% → 99.5%

Time: 43.5s

Alternatives: 27

Speedup: 4.7×

• 46.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 69.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 - x1 \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right)\\ t_3 := \frac{t\_2 - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\\ t_4 := x1 \cdot \left(x1 \cdot 3\right)\\ t_5 := \frac{x1 - t\_2}{\mathsf{fma}\left(x1, x1, 1\right)}\\ t_6 := \left(t\_4 + 2 \cdot x2\right) - x1\\ t_7 := \frac{t\_6}{t\_1}\\ t_8 := 3 \cdot \left(x1 \cdot x1\right)\\ \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(t\_4 \cdot t\_7 - t\_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - t\_7 \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot t\_7\right) \cdot \left(3 + \frac{t\_6}{t\_0}\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{x1 + \left(2 \cdot x2 - t\_4\right)}{t\_0}\right) \leq \infty:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{t\_8 - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 + \mathsf{fma}\left(\mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot \mathsf{fma}\left(t\_3, 4, -6\right), \left(x1 \cdot \left(2 \cdot t\_5\right)\right) \cdot \left(t\_5 - -3\right)\right), \mathsf{fma}\left(t\_8, t\_3, {x1}^{3}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{x1}^{4} \cdot \left(6 + \frac{\frac{15 - \left(6 + -4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1} - 3}{x1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- -1.0 (* x1 x1)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (fma x1 (* x1 3.0) (* 2.0 x2)))
        (t_3 (/ (- t_2 x1) (fma x1 x1 1.0)))
        (t_4 (* x1 (* x1 3.0)))
        (t_5 (/ (- x1 t_2) (fma x1 x1 1.0)))
        (t_6 (- (+ t_4 (* 2.0 x2)) x1))
        (t_7 (/ t_6 t_1))
        (t_8 (* 3.0 (* x1 x1))))
   (if (<=
        (+
         x1
         (+
          (+
           x1
           (+
            (-
             (* t_4 t_7)
             (*
              t_1
              (+
               (* (* x1 x1) (- 6.0 (* t_7 4.0)))
               (* (* (* x1 2.0) t_7) (+ 3.0 (/ t_6 t_0))))))
            (* x1 (* x1 x1))))
          (* 3.0 (/ (+ x1 (- (* 2.0 x2) t_4)) t_0))))
        INFINITY)
     (+
      x1
      (fma
       3.0
       (/ (- t_8 (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_5)) (- t_5 -3.0)))
         (fma t_8 t_3 (pow x1 3.0))))))
     (*
      (pow x1 4.0)
      (+
       6.0
       (/ (- (/ (- 15.0 (+ 6.0 (* -4.0 (- (* 2.0 x2) 3.0)))) x1) 3.0) x1))))))

C

double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = (x1 * x1) + 1.0;
	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 * 3.0);
	double t_5 = (x1 - t_2) / fma(x1, x1, 1.0);
	double t_6 = (t_4 + (2.0 * x2)) - x1;
	double t_7 = t_6 / t_1;
	double t_8 = 3.0 * (x1 * x1);
	double tmp;
	if ((x1 + ((x1 + (((t_4 * t_7) - (t_1 * (((x1 * x1) * (6.0 - (t_7 * 4.0))) + (((x1 * 2.0) * t_7) * (3.0 + (t_6 / t_0)))))) + (x1 * (x1 * x1)))) + (3.0 * ((x1 + ((2.0 * x2) - t_4)) / t_0)))) <= ((double) INFINITY)) {
		tmp = x1 + fma(3.0, ((t_8 - 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_5)) * (t_5 - -3.0))), fma(t_8, t_3, pow(x1, 3.0)))));
	} else {
		tmp = pow(x1, 4.0) * (6.0 + ((((15.0 - (6.0 + (-4.0 * ((2.0 * x2) - 3.0)))) / x1) - 3.0) / x1));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(-1.0 - Float64(x1 * x1))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	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(x1 * Float64(x1 * 3.0))
	t_5 = Float64(Float64(x1 - t_2) / fma(x1, x1, 1.0))
	t_6 = Float64(Float64(t_4 + Float64(2.0 * x2)) - x1)
	t_7 = Float64(t_6 / t_1)
	t_8 = Float64(3.0 * Float64(x1 * x1))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_4 * t_7) - Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(t_7 * 4.0))) + Float64(Float64(Float64(x1 * 2.0) * t_7) * Float64(3.0 + Float64(t_6 / t_0)))))) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(x1 + Float64(Float64(2.0 * x2) - t_4)) / t_0)))) <= Inf)
		tmp = Float64(x1 + fma(3.0, Float64(Float64(t_8 - 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_5)) * Float64(t_5 - -3.0))), fma(t_8, t_3, (x1 ^ 3.0))))));
	else
		tmp = Float64((x1 ^ 4.0) * Float64(6.0 + Float64(Float64(Float64(Float64(15.0 - Float64(6.0 + Float64(-4.0 * Float64(Float64(2.0 * x2) - 3.0)))) / x1) - 3.0) / x1)));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $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[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 - t$95$2), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(t$95$4 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$6 / t$95$1), $MachinePrecision]}, Block[{t$95$8 = N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$4 * t$95$7), $MachinePrecision] - N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(t$95$7 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$7), $MachinePrecision] * N[(3.0 + N[(t$95$6 / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x1 + N[(N[(2.0 * x2), $MachinePrecision] - t$95$4), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(3.0 * N[(N[(t$95$8 - 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$5), $MachinePrecision]), $MachinePrecision] * N[(t$95$5 - -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$8 * t$95$3 + N[Power[x1, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Power[x1, 4.0], $MachinePrecision] * N[(6.0 + N[(N[(N[(N[(15.0 - N[(6.0 + N[(-4.0 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision] - 3.0), $MachinePrecision] / x1), $MachinePrecision]), $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 99.2%

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

   3. Simplified 99.5%

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

   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 17.2%

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

   5. Taylor expanded in x1 around -inf 100.0%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1}\right) \leq \infty:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{3 \cdot \left(x1 \cdot x1\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 + \mathsf{fma}\left(\mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, 4, -6\right), \left(x1 \cdot \left(2 \cdot \frac{x1 - \mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right) \cdot \left(\frac{x1 - \mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right)}{\mathsf{fma}\left(x1, x1, 1\right)} - -3\right)\right), \mathsf{fma}\left(3 \cdot \left(x1 \cdot x1\right), \frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, {x1}^{3}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{x1}^{4} \cdot \left(6 + \frac{\frac{15 - \left(6 + -4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1} - 3}{x1}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 - x1 \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 \cdot \left(x1 \cdot x1\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := 3 \cdot \frac{x1 + \left(2 \cdot x2 - t\_3\right)}{t\_0}\\ t_5 := \left(t\_3 + 2 \cdot x2\right) - x1\\ t_6 := \frac{t\_5}{t\_0}\\ t_7 := \frac{t\_5}{t\_1}\\ t_8 := \left(\left(x1 \cdot 2\right) \cdot t\_7\right) \cdot \left(3 + t\_6\right)\\ \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(t\_3 \cdot t\_7 - t\_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - t\_7 \cdot 4\right) + t\_8\right)\right) + t\_2\right)\right) + t\_4\right) \leq \infty:\\ \;\;\;\;x1 + \left(t\_4 + \left(x1 + \left(t\_2 - \left(t\_3 \cdot t\_6 + t\_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{1}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1 - \mathsf{fma}\left(3, {x1}^{2}, 2 \cdot x2\right)}}\right) + t\_8\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{x1}^{4} \cdot \left(6 + \frac{\frac{15 - \left(6 + -4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1} - 3}{x1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- -1.0 (* x1 x1)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* x1 (* x1 x1)))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (* 3.0 (/ (+ x1 (- (* 2.0 x2) t_3)) t_0)))
        (t_5 (- (+ t_3 (* 2.0 x2)) x1))
        (t_6 (/ t_5 t_0))
        (t_7 (/ t_5 t_1))
        (t_8 (* (* (* x1 2.0) t_7) (+ 3.0 t_6))))
   (if (<=
        (+
         x1
         (+
          (+
           x1
           (+
            (- (* t_3 t_7) (* t_1 (+ (* (* x1 x1) (- 6.0 (* t_7 4.0))) t_8)))
            t_2))
          t_4))
        INFINITY)
     (+
      x1
      (+
       t_4
       (+
        x1
        (-
         t_2
         (+
          (* t_3 t_6)
          (*
           t_1
           (+
            (*
             (* x1 x1)
             (+
              6.0
              (*
               4.0
               (/
                1.0
                (/
                 (fma x1 x1 1.0)
                 (- x1 (fma 3.0 (pow x1 2.0) (* 2.0 x2))))))))
            t_8)))))))
     (*
      (pow x1 4.0)
      (+
       6.0
       (/ (- (/ (- 15.0 (+ 6.0 (* -4.0 (- (* 2.0 x2) 3.0)))) x1) 3.0) x1))))))

C

double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = 3.0 * ((x1 + ((2.0 * x2) - t_3)) / t_0);
	double t_5 = (t_3 + (2.0 * x2)) - x1;
	double t_6 = t_5 / t_0;
	double t_7 = t_5 / t_1;
	double t_8 = ((x1 * 2.0) * t_7) * (3.0 + t_6);
	double tmp;
	if ((x1 + ((x1 + (((t_3 * t_7) - (t_1 * (((x1 * x1) * (6.0 - (t_7 * 4.0))) + t_8))) + t_2)) + t_4)) <= ((double) INFINITY)) {
		tmp = x1 + (t_4 + (x1 + (t_2 - ((t_3 * t_6) + (t_1 * (((x1 * x1) * (6.0 + (4.0 * (1.0 / (fma(x1, x1, 1.0) / (x1 - fma(3.0, pow(x1, 2.0), (2.0 * x2)))))))) + t_8))))));
	} else {
		tmp = pow(x1, 4.0) * (6.0 + ((((15.0 - (6.0 + (-4.0 * ((2.0 * x2) - 3.0)))) / x1) - 3.0) / x1));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(-1.0 - Float64(x1 * x1))
	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(3.0 * Float64(Float64(x1 + Float64(Float64(2.0 * x2) - t_3)) / t_0))
	t_5 = Float64(Float64(t_3 + Float64(2.0 * x2)) - x1)
	t_6 = Float64(t_5 / t_0)
	t_7 = Float64(t_5 / t_1)
	t_8 = Float64(Float64(Float64(x1 * 2.0) * t_7) * Float64(3.0 + t_6))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_3 * t_7) - Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(t_7 * 4.0))) + t_8))) + t_2)) + t_4)) <= Inf)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(t_2 - Float64(Float64(t_3 * t_6) + Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * Float64(1.0 / Float64(fma(x1, x1, 1.0) / Float64(x1 - fma(3.0, (x1 ^ 2.0), Float64(2.0 * x2)))))))) + t_8)))))));
	else
		tmp = Float64((x1 ^ 4.0) * Float64(6.0 + Float64(Float64(Float64(Float64(15.0 - Float64(6.0 + Float64(-4.0 * Float64(Float64(2.0 * x2) - 3.0)))) / x1) - 3.0) / x1)));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(-1.0 - N[(x1 * x1), $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[(3.0 * N[(N[(x1 + N[(N[(2.0 * x2), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$5 / t$95$0), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$5 / t$95$1), $MachinePrecision]}, Block[{t$95$8 = N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$7), $MachinePrecision] * N[(3.0 + t$95$6), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$3 * t$95$7), $MachinePrecision] - N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(t$95$7 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(t$95$4 + N[(x1 + N[(t$95$2 - N[(N[(t$95$3 * t$95$6), $MachinePrecision] + N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * N[(1.0 / N[(N[(x1 * x1 + 1.0), $MachinePrecision] / N[(x1 - N[(3.0 * N[Power[x1, 2.0], $MachinePrecision] + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Power[x1, 4.0], $MachinePrecision] * N[(6.0 + N[(N[(N[(N[(15.0 - N[(6.0 + N[(-4.0 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision] - 3.0), $MachinePrecision] / x1), $MachinePrecision]), $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 99.2%

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

      1. fma-define 99.2%

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

      2. *-commutative 99.2%

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

      3. fma-define 99.2%

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

      4. clear-num 99.2%

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

      5. inv-pow 99.2%

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

      6. *-commutative 99.2%

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

      7. fma-define 99.2%

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

      8. associate-*r* 99.2%

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

      9. fma-define 99.2%

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

      10. pow2 99.2%

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

   4. Applied egg-rr 99.2%

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

      1. unpow-1 99.2%

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

   6. Simplified 99.2%

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

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

   1. Initial program 0.0%

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

   3. Simplified 17.2%

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

   5. Taylor expanded in x1 around -inf 100.0%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1}\right) \leq \infty:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{1}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1 - \mathsf{fma}\left(3, {x1}^{2}, 2 \cdot x2\right)}}\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{x1}^{4} \cdot \left(6 + \frac{\frac{15 - \left(6 + -4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1} - 3}{x1}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 - x1 \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 \cdot \left(x1 \cdot x1\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := x1 + \left(2 \cdot x2 - t\_3\right)\\ t_5 := \left(t\_3 + 2 \cdot x2\right) - x1\\ t_6 := \frac{t\_5}{t\_0}\\ t_7 := \frac{t\_5}{t\_1}\\ t_8 := \left(\left(x1 \cdot 2\right) \cdot t\_7\right) \cdot \left(3 + t\_6\right)\\ \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(t\_3 \cdot t\_7 - t\_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - t\_7 \cdot 4\right) + t\_8\right)\right) + t\_2\right)\right) + 3 \cdot \frac{t\_4}{t\_0}\right) \leq \infty:\\ \;\;\;\;x1 - \left(3 \cdot \frac{t\_4}{t\_1} + \left(\left(\left(t\_3 \cdot t\_6 + t\_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(2 \cdot x2 + 3 \cdot {x1}^{2}\right) - x1}{t\_0}\right) + t\_8\right)\right) - t\_2\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{x1}^{4} \cdot \left(6 + \frac{\frac{15 - \left(6 + -4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1} - 3}{x1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- -1.0 (* x1 x1)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* x1 (* x1 x1)))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (+ x1 (- (* 2.0 x2) t_3)))
        (t_5 (- (+ t_3 (* 2.0 x2)) x1))
        (t_6 (/ t_5 t_0))
        (t_7 (/ t_5 t_1))
        (t_8 (* (* (* x1 2.0) t_7) (+ 3.0 t_6))))
   (if (<=
        (+
         x1
         (+
          (+
           x1
           (+
            (- (* t_3 t_7) (* t_1 (+ (* (* x1 x1) (- 6.0 (* t_7 4.0))) t_8)))
            t_2))
          (* 3.0 (/ t_4 t_0))))
        INFINITY)
     (-
      x1
      (+
       (* 3.0 (/ t_4 t_1))
       (-
        (-
         (+
          (* t_3 t_6)
          (*
           t_1
           (+
            (*
             (* x1 x1)
             (+
              6.0
              (* 4.0 (/ (- (+ (* 2.0 x2) (* 3.0 (pow x1 2.0))) x1) t_0))))
            t_8)))
         t_2)
        x1)))
     (*
      (pow x1 4.0)
      (+
       6.0
       (/ (- (/ (- 15.0 (+ 6.0 (* -4.0 (- (* 2.0 x2) 3.0)))) x1) 3.0) x1))))))

C

double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = x1 + ((2.0 * x2) - t_3);
	double t_5 = (t_3 + (2.0 * x2)) - x1;
	double t_6 = t_5 / t_0;
	double t_7 = t_5 / t_1;
	double t_8 = ((x1 * 2.0) * t_7) * (3.0 + t_6);
	double tmp;
	if ((x1 + ((x1 + (((t_3 * t_7) - (t_1 * (((x1 * x1) * (6.0 - (t_7 * 4.0))) + t_8))) + t_2)) + (3.0 * (t_4 / t_0)))) <= ((double) INFINITY)) {
		tmp = x1 - ((3.0 * (t_4 / t_1)) + ((((t_3 * t_6) + (t_1 * (((x1 * x1) * (6.0 + (4.0 * ((((2.0 * x2) + (3.0 * pow(x1, 2.0))) - x1) / t_0)))) + t_8))) - t_2) - x1));
	} else {
		tmp = pow(x1, 4.0) * (6.0 + ((((15.0 - (6.0 + (-4.0 * ((2.0 * x2) - 3.0)))) / x1) - 3.0) / x1));
	}
	return tmp;
}

Java

public static double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = x1 + ((2.0 * x2) - t_3);
	double t_5 = (t_3 + (2.0 * x2)) - x1;
	double t_6 = t_5 / t_0;
	double t_7 = t_5 / t_1;
	double t_8 = ((x1 * 2.0) * t_7) * (3.0 + t_6);
	double tmp;
	if ((x1 + ((x1 + (((t_3 * t_7) - (t_1 * (((x1 * x1) * (6.0 - (t_7 * 4.0))) + t_8))) + t_2)) + (3.0 * (t_4 / t_0)))) <= Double.POSITIVE_INFINITY) {
		tmp = x1 - ((3.0 * (t_4 / t_1)) + ((((t_3 * t_6) + (t_1 * (((x1 * x1) * (6.0 + (4.0 * ((((2.0 * x2) + (3.0 * Math.pow(x1, 2.0))) - x1) / t_0)))) + t_8))) - t_2) - x1));
	} else {
		tmp = Math.pow(x1, 4.0) * (6.0 + ((((15.0 - (6.0 + (-4.0 * ((2.0 * x2) - 3.0)))) / x1) - 3.0) / x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = -1.0 - (x1 * x1)
	t_1 = (x1 * x1) + 1.0
	t_2 = x1 * (x1 * x1)
	t_3 = x1 * (x1 * 3.0)
	t_4 = x1 + ((2.0 * x2) - t_3)
	t_5 = (t_3 + (2.0 * x2)) - x1
	t_6 = t_5 / t_0
	t_7 = t_5 / t_1
	t_8 = ((x1 * 2.0) * t_7) * (3.0 + t_6)
	tmp = 0
	if (x1 + ((x1 + (((t_3 * t_7) - (t_1 * (((x1 * x1) * (6.0 - (t_7 * 4.0))) + t_8))) + t_2)) + (3.0 * (t_4 / t_0)))) <= math.inf:
		tmp = x1 - ((3.0 * (t_4 / t_1)) + ((((t_3 * t_6) + (t_1 * (((x1 * x1) * (6.0 + (4.0 * ((((2.0 * x2) + (3.0 * math.pow(x1, 2.0))) - x1) / t_0)))) + t_8))) - t_2) - x1))
	else:
		tmp = math.pow(x1, 4.0) * (6.0 + ((((15.0 - (6.0 + (-4.0 * ((2.0 * x2) - 3.0)))) / x1) - 3.0) / x1))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(-1.0 - Float64(x1 * x1))
	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(x1 + Float64(Float64(2.0 * x2) - t_3))
	t_5 = Float64(Float64(t_3 + Float64(2.0 * x2)) - x1)
	t_6 = Float64(t_5 / t_0)
	t_7 = Float64(t_5 / t_1)
	t_8 = Float64(Float64(Float64(x1 * 2.0) * t_7) * Float64(3.0 + t_6))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_3 * t_7) - Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(t_7 * 4.0))) + t_8))) + t_2)) + Float64(3.0 * Float64(t_4 / t_0)))) <= Inf)
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(t_4 / t_1)) + Float64(Float64(Float64(Float64(t_3 * t_6) + Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * Float64(Float64(Float64(Float64(2.0 * x2) + Float64(3.0 * (x1 ^ 2.0))) - x1) / t_0)))) + t_8))) - t_2) - x1)));
	else
		tmp = Float64((x1 ^ 4.0) * Float64(6.0 + Float64(Float64(Float64(Float64(15.0 - Float64(6.0 + Float64(-4.0 * Float64(Float64(2.0 * x2) - 3.0)))) / x1) - 3.0) / x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = -1.0 - (x1 * x1);
	t_1 = (x1 * x1) + 1.0;
	t_2 = x1 * (x1 * x1);
	t_3 = x1 * (x1 * 3.0);
	t_4 = x1 + ((2.0 * x2) - t_3);
	t_5 = (t_3 + (2.0 * x2)) - x1;
	t_6 = t_5 / t_0;
	t_7 = t_5 / t_1;
	t_8 = ((x1 * 2.0) * t_7) * (3.0 + t_6);
	tmp = 0.0;
	if ((x1 + ((x1 + (((t_3 * t_7) - (t_1 * (((x1 * x1) * (6.0 - (t_7 * 4.0))) + t_8))) + t_2)) + (3.0 * (t_4 / t_0)))) <= Inf)
		tmp = x1 - ((3.0 * (t_4 / t_1)) + ((((t_3 * t_6) + (t_1 * (((x1 * x1) * (6.0 + (4.0 * ((((2.0 * x2) + (3.0 * (x1 ^ 2.0))) - x1) / t_0)))) + t_8))) - t_2) - x1));
	else
		tmp = (x1 ^ 4.0) * (6.0 + ((((15.0 - (6.0 + (-4.0 * ((2.0 * x2) - 3.0)))) / x1) - 3.0) / x1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(-1.0 - N[(x1 * x1), $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[(x1 + N[(N[(2.0 * x2), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$5 / t$95$0), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$5 / t$95$1), $MachinePrecision]}, Block[{t$95$8 = N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$7), $MachinePrecision] * N[(3.0 + t$95$6), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$3 * t$95$7), $MachinePrecision] - N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(t$95$7 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(t$95$4 / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 - N[(N[(3.0 * N[(t$95$4 / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(t$95$3 * t$95$6), $MachinePrecision] + N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * N[(N[(N[(N[(2.0 * x2), $MachinePrecision] + N[(3.0 * N[Power[x1, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Power[x1, 4.0], $MachinePrecision] * N[(6.0 + N[(N[(N[(N[(15.0 - N[(6.0 + N[(-4.0 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision] - 3.0), $MachinePrecision] / x1), $MachinePrecision]), $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 99.2%

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

   3. Taylor expanded in x1 around 0 99.2%

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

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

   1. Initial program 0.0%

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

   3. Simplified 17.2%

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

   5. Taylor expanded in x1 around -inf 100.0%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1}\right) \leq \infty:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} + \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(2 \cdot x2 + 3 \cdot {x1}^{2}\right) - x1}{-1 - x1 \cdot x1}\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{x1}^{4} \cdot \left(6 + \frac{\frac{15 - \left(6 + -4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1} - 3}{x1}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 - x1 \cdot x1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \left(t\_1 + 2 \cdot x2\right) - x1\\ t_3 := x1 \cdot x1 + 1\\ t_4 := \frac{t\_2}{t\_3}\\ t_5 := x1 + \left(\left(x1 + \left(\left(t\_1 \cdot t\_4 - t\_3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - t\_4 \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot t\_4\right) \cdot \left(3 + \frac{t\_2}{t\_0}\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{x1 + \left(2 \cdot x2 - t\_1\right)}{t\_0}\right)\\ \mathbf{if}\;t\_5 \leq \infty:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;{x1}^{4} \cdot \left(6 + \frac{\frac{15 - \left(6 + -4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1} - 3}{x1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- -1.0 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (- (+ t_1 (* 2.0 x2)) x1))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (/ t_2 t_3))
        (t_5
         (+
          x1
          (+
           (+
            x1
            (+
             (-
              (* t_1 t_4)
              (*
               t_3
               (+
                (* (* x1 x1) (- 6.0 (* t_4 4.0)))
                (* (* (* x1 2.0) t_4) (+ 3.0 (/ t_2 t_0))))))
             (* x1 (* x1 x1))))
           (* 3.0 (/ (+ x1 (- (* 2.0 x2) t_1)) t_0))))))
   (if (<= t_5 INFINITY)
     t_5
     (*
      (pow x1 4.0)
      (+
       6.0
       (/ (- (/ (- 15.0 (+ 6.0 (* -4.0 (- (* 2.0 x2) 3.0)))) x1) 3.0) x1))))))

C

double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (t_1 + (2.0 * x2)) - x1;
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = t_2 / t_3;
	double t_5 = x1 + ((x1 + (((t_1 * t_4) - (t_3 * (((x1 * x1) * (6.0 - (t_4 * 4.0))) + (((x1 * 2.0) * t_4) * (3.0 + (t_2 / t_0)))))) + (x1 * (x1 * x1)))) + (3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_0)));
	double tmp;
	if (t_5 <= ((double) INFINITY)) {
		tmp = t_5;
	} else {
		tmp = pow(x1, 4.0) * (6.0 + ((((15.0 - (6.0 + (-4.0 * ((2.0 * x2) - 3.0)))) / x1) - 3.0) / x1));
	}
	return tmp;
}

Java

public static double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (t_1 + (2.0 * x2)) - x1;
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = t_2 / t_3;
	double t_5 = x1 + ((x1 + (((t_1 * t_4) - (t_3 * (((x1 * x1) * (6.0 - (t_4 * 4.0))) + (((x1 * 2.0) * t_4) * (3.0 + (t_2 / t_0)))))) + (x1 * (x1 * x1)))) + (3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_0)));
	double tmp;
	if (t_5 <= Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else {
		tmp = Math.pow(x1, 4.0) * (6.0 + ((((15.0 - (6.0 + (-4.0 * ((2.0 * x2) - 3.0)))) / x1) - 3.0) / x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = -1.0 - (x1 * x1)
	t_1 = x1 * (x1 * 3.0)
	t_2 = (t_1 + (2.0 * x2)) - x1
	t_3 = (x1 * x1) + 1.0
	t_4 = t_2 / t_3
	t_5 = x1 + ((x1 + (((t_1 * t_4) - (t_3 * (((x1 * x1) * (6.0 - (t_4 * 4.0))) + (((x1 * 2.0) * t_4) * (3.0 + (t_2 / t_0)))))) + (x1 * (x1 * x1)))) + (3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_0)))
	tmp = 0
	if t_5 <= math.inf:
		tmp = t_5
	else:
		tmp = math.pow(x1, 4.0) * (6.0 + ((((15.0 - (6.0 + (-4.0 * ((2.0 * x2) - 3.0)))) / x1) - 3.0) / x1))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(-1.0 - Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(t_1 + Float64(2.0 * x2)) - x1)
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(t_2 / t_3)
	t_5 = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_1 * t_4) - Float64(t_3 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(t_4 * 4.0))) + Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(3.0 + Float64(t_2 / t_0)))))) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(x1 + Float64(Float64(2.0 * x2) - t_1)) / t_0))))
	tmp = 0.0
	if (t_5 <= Inf)
		tmp = t_5;
	else
		tmp = Float64((x1 ^ 4.0) * Float64(6.0 + Float64(Float64(Float64(Float64(15.0 - Float64(6.0 + Float64(-4.0 * Float64(Float64(2.0 * x2) - 3.0)))) / x1) - 3.0) / x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = -1.0 - (x1 * x1);
	t_1 = x1 * (x1 * 3.0);
	t_2 = (t_1 + (2.0 * x2)) - x1;
	t_3 = (x1 * x1) + 1.0;
	t_4 = t_2 / t_3;
	t_5 = x1 + ((x1 + (((t_1 * t_4) - (t_3 * (((x1 * x1) * (6.0 - (t_4 * 4.0))) + (((x1 * 2.0) * t_4) * (3.0 + (t_2 / t_0)))))) + (x1 * (x1 * x1)))) + (3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_0)));
	tmp = 0.0;
	if (t_5 <= Inf)
		tmp = t_5;
	else
		tmp = (x1 ^ 4.0) * (6.0 + ((((15.0 - (6.0 + (-4.0 * ((2.0 * x2) - 3.0)))) / x1) - 3.0) / x1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$1 * t$95$4), $MachinePrecision] - N[(t$95$3 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(t$95$4 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(3.0 + N[(t$95$2 / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x1 + N[(N[(2.0 * x2), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$5, Infinity], t$95$5, N[(N[Power[x1, 4.0], $MachinePrecision] * N[(6.0 + N[(N[(N[(N[(15.0 - N[(6.0 + N[(-4.0 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision] - 3.0), $MachinePrecision] / x1), $MachinePrecision]), $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 99.2%

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

   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 17.2%

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

   5. Taylor expanded in x1 around -inf 100.0%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1}\right) \leq \infty:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1}\right)\\ \mathbf{else}:\\ \;\;\;\;{x1}^{4} \cdot \left(6 + \frac{\frac{15 - \left(6 + -4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1} - 3}{x1}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \left(t\_2 + 2 \cdot x2\right) - x1\\ t_4 := \frac{t\_3}{t\_0}\\ t_5 := -1 - x1 \cdot x1\\ \mathbf{if}\;x1 \leq -4 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x2 \cdot 8\right) + x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - \left(x2 \cdot 6 + x1 \cdot \left(x2 \cdot \left(24 + x2 \cdot -8\right) - 19\right)\right)\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t\_2 \cdot t\_4 - t\_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - t\_4 \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot t\_4\right) \cdot \left(3 + \frac{t\_3}{t\_5}\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{x1 + \left(2 \cdot x2 - t\_2\right)}{t\_5}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (+ x1 (+ x1 (+ (* x1 -18.0) (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (- (+ t_2 (* 2.0 x2)) x1))
        (t_4 (/ t_3 t_0))
        (t_5 (- -1.0 (* x1 x1))))
   (if (<= x1 -4e+146)
     t_1
     (if (<= x1 -5.6e+102)
       (-
        (* x2 -6.0)
        (*
         x1
         (-
          (+
           (* x2 (- 12.0 (* x2 8.0)))
           (*
            x1
            (-
             (* 3.0 (- (* x2 -2.0) 3.0))
             (+ (* x2 6.0) (* x1 (- (* x2 (+ 24.0 (* x2 -8.0))) 19.0))))))
          -1.0)))
       (if (<= x1 2e+153)
         (+
          x1
          (+
           (+
            x1
            (+
             (-
              (* t_2 t_4)
              (*
               t_0
               (+
                (* (* x1 x1) (- 6.0 (* t_4 4.0)))
                (* (* (* x1 2.0) t_4) (+ 3.0 (/ t_3 t_5))))))
             (* x1 (* x1 x1))))
           (* 3.0 (/ (+ x1 (- (* 2.0 x2) t_2)) t_5))))
         t_1)))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = (t_2 + (2.0 * x2)) - x1;
	double t_4 = t_3 / t_0;
	double t_5 = -1.0 - (x1 * x1);
	double tmp;
	if (x1 <= -4e+146) {
		tmp = t_1;
	} else if (x1 <= -5.6e+102) {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0));
	} else if (x1 <= 2e+153) {
		tmp = x1 + ((x1 + (((t_2 * t_4) - (t_0 * (((x1 * x1) * (6.0 - (t_4 * 4.0))) + (((x1 * 2.0) * t_4) * (3.0 + (t_3 / t_5)))))) + (x1 * (x1 * x1)))) + (3.0 * ((x1 + ((2.0 * x2) - t_2)) / t_5)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 + (x1 + ((x1 * (-18.0d0)) + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0))))))
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = (t_2 + (2.0d0 * x2)) - x1
    t_4 = t_3 / t_0
    t_5 = (-1.0d0) - (x1 * x1)
    if (x1 <= (-4d+146)) then
        tmp = t_1
    else if (x1 <= (-5.6d+102)) then
        tmp = (x2 * (-6.0d0)) - (x1 * (((x2 * (12.0d0 - (x2 * 8.0d0))) + (x1 * ((3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)) - ((x2 * 6.0d0) + (x1 * ((x2 * (24.0d0 + (x2 * (-8.0d0)))) - 19.0d0)))))) - (-1.0d0)))
    else if (x1 <= 2d+153) then
        tmp = x1 + ((x1 + (((t_2 * t_4) - (t_0 * (((x1 * x1) * (6.0d0 - (t_4 * 4.0d0))) + (((x1 * 2.0d0) * t_4) * (3.0d0 + (t_3 / t_5)))))) + (x1 * (x1 * x1)))) + (3.0d0 * ((x1 + ((2.0d0 * x2) - t_2)) / t_5)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = (t_2 + (2.0 * x2)) - x1;
	double t_4 = t_3 / t_0;
	double t_5 = -1.0 - (x1 * x1);
	double tmp;
	if (x1 <= -4e+146) {
		tmp = t_1;
	} else if (x1 <= -5.6e+102) {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0));
	} else if (x1 <= 2e+153) {
		tmp = x1 + ((x1 + (((t_2 * t_4) - (t_0 * (((x1 * x1) * (6.0 - (t_4 * 4.0))) + (((x1 * 2.0) * t_4) * (3.0 + (t_3 / t_5)))))) + (x1 * (x1 * x1)))) + (3.0 * ((x1 + ((2.0 * x2) - t_2)) / t_5)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))))
	t_2 = x1 * (x1 * 3.0)
	t_3 = (t_2 + (2.0 * x2)) - x1
	t_4 = t_3 / t_0
	t_5 = -1.0 - (x1 * x1)
	tmp = 0
	if x1 <= -4e+146:
		tmp = t_1
	elif x1 <= -5.6e+102:
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0))
	elif x1 <= 2e+153:
		tmp = x1 + ((x1 + (((t_2 * t_4) - (t_0 * (((x1 * x1) * (6.0 - (t_4 * 4.0))) + (((x1 * 2.0) * t_4) * (3.0 + (t_3 / t_5)))))) + (x1 * (x1 * x1)))) + (3.0 * ((x1 + ((2.0 * x2) - t_2)) / t_5)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 + Float64(x1 + Float64(Float64(x1 * -18.0) + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0))))))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(t_2 + Float64(2.0 * x2)) - x1)
	t_4 = Float64(t_3 / t_0)
	t_5 = Float64(-1.0 - Float64(x1 * x1))
	tmp = 0.0
	if (x1 <= -4e+146)
		tmp = t_1;
	elseif (x1 <= -5.6e+102)
		tmp = Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(Float64(Float64(x2 * Float64(12.0 - Float64(x2 * 8.0))) + Float64(x1 * Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)) - Float64(Float64(x2 * 6.0) + Float64(x1 * Float64(Float64(x2 * Float64(24.0 + Float64(x2 * -8.0))) - 19.0)))))) - -1.0)));
	elseif (x1 <= 2e+153)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_2 * t_4) - Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(t_4 * 4.0))) + Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(3.0 + Float64(t_3 / t_5)))))) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(x1 + Float64(Float64(2.0 * x2) - t_2)) / t_5))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	t_2 = x1 * (x1 * 3.0);
	t_3 = (t_2 + (2.0 * x2)) - x1;
	t_4 = t_3 / t_0;
	t_5 = -1.0 - (x1 * x1);
	tmp = 0.0;
	if (x1 <= -4e+146)
		tmp = t_1;
	elseif (x1 <= -5.6e+102)
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0));
	elseif (x1 <= 2e+153)
		tmp = x1 + ((x1 + (((t_2 * t_4) - (t_0 * (((x1 * x1) * (6.0 - (t_4 * 4.0))) + (((x1 * 2.0) * t_4) * (3.0 + (t_3 / t_5)))))) + (x1 * (x1 * x1)))) + (3.0 * ((x1 + ((2.0 * x2) - t_2)) / t_5)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x1 + N[(N[(x1 * -18.0), $MachinePrecision] + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 / t$95$0), $MachinePrecision]}, Block[{t$95$5 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4e+146], t$95$1, If[LessEqual[x1, -5.6e+102], N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(N[(N[(x2 * N[(12.0 - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - N[(N[(x2 * 6.0), $MachinePrecision] + N[(x1 * N[(N[(x2 * N[(24.0 + N[(x2 * -8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+153], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$2 * t$95$4), $MachinePrecision] - N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(t$95$4 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(3.0 + N[(t$95$3 / t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x1 + N[(N[(2.0 * x2), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision] / t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.99999999999999973e146 or 2e153 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x1 around 0 66.7%

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

   6. Taylor expanded in x2 around 0 98.3%

      \[\leadsto x1 + \color{blue}{\left(x1 + \left(-18 \cdot x1 + 3 \cdot \left(x1 \cdot \left(3 \cdot x1 - 1\right)\right)\right)\right)} \]

   if -3.99999999999999973e146 < x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x2 around 0 77.8%

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

   6. Taylor expanded in x1 around 0 100.0%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x1 \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + x1 \cdot \left(x2 \cdot \left(24 + -8 \cdot x2\right) - 19\right)\right)\right) + x2 \cdot \left(8 \cdot x2 - 12\right)\right) - 1\right)} \]

   if -5.60000000000000037e102 < x1 < 2e153

   1. Initial program 98.7%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+146}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x2 \cdot 8\right) + x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - \left(x2 \cdot 6 + x1 \cdot \left(x2 \cdot \left(24 + x2 \cdot -8\right) - 19\right)\right)\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x2 \cdot -2 - 3\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \left(t\_2 + 2 \cdot x2\right) - x1\\ t_4 := x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ t_5 := \frac{t\_3}{t\_0}\\ \mathbf{if}\;x1 \leq -4 \cdot 10^{+146}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x2 \cdot 8\right) + x1 \cdot \left(3 \cdot t\_1 - \left(x2 \cdot 6 + x1 \cdot \left(x2 \cdot \left(24 + x2 \cdot -8\right) - 19\right)\right)\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_2 \cdot \left(2 \cdot x2\right) - t\_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - t\_5 \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot t\_5\right) \cdot \left(3 + \frac{t\_3}{-1 - x1 \cdot x1}\right)\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 - x1 \cdot t\_1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (- (* x2 -2.0) 3.0))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (- (+ t_2 (* 2.0 x2)) x1))
        (t_4 (+ x1 (+ x1 (+ (* x1 -18.0) (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))))
        (t_5 (/ t_3 t_0)))
   (if (<= x1 -4e+146)
     t_4
     (if (<= x1 -5.6e+102)
       (-
        (* x2 -6.0)
        (*
         x1
         (-
          (+
           (* x2 (- 12.0 (* x2 8.0)))
           (*
            x1
            (-
             (* 3.0 t_1)
             (+ (* x2 6.0) (* x1 (- (* x2 (+ 24.0 (* x2 -8.0))) 19.0))))))
          -1.0)))
       (if (<= x1 4.5e+153)
         (+
          x1
          (+
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (-
              (* t_2 (* 2.0 x2))
              (*
               t_0
               (+
                (* (* x1 x1) (- 6.0 (* t_5 4.0)))
                (* (* (* x1 2.0) t_5) (+ 3.0 (/ t_3 (- -1.0 (* x1 x1))))))))))
           (* 3.0 (+ (* x2 -2.0) (* x1 (- -1.0 (* x1 t_1)))))))
         t_4)))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = (x2 * -2.0) - 3.0;
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = (t_2 + (2.0 * x2)) - x1;
	double t_4 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	double t_5 = t_3 / t_0;
	double tmp;
	if (x1 <= -4e+146) {
		tmp = t_4;
	} else if (x1 <= -5.6e+102) {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * t_1) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0));
	} else if (x1 <= 4.5e+153) {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_2 * (2.0 * x2)) - (t_0 * (((x1 * x1) * (6.0 - (t_5 * 4.0))) + (((x1 * 2.0) * t_5) * (3.0 + (t_3 / (-1.0 - (x1 * x1)))))))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 - (x1 * t_1))))));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = (x2 * (-2.0d0)) - 3.0d0
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = (t_2 + (2.0d0 * x2)) - x1
    t_4 = x1 + (x1 + ((x1 * (-18.0d0)) + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0))))))
    t_5 = t_3 / t_0
    if (x1 <= (-4d+146)) then
        tmp = t_4
    else if (x1 <= (-5.6d+102)) then
        tmp = (x2 * (-6.0d0)) - (x1 * (((x2 * (12.0d0 - (x2 * 8.0d0))) + (x1 * ((3.0d0 * t_1) - ((x2 * 6.0d0) + (x1 * ((x2 * (24.0d0 + (x2 * (-8.0d0)))) - 19.0d0)))))) - (-1.0d0)))
    else if (x1 <= 4.5d+153) then
        tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_2 * (2.0d0 * x2)) - (t_0 * (((x1 * x1) * (6.0d0 - (t_5 * 4.0d0))) + (((x1 * 2.0d0) * t_5) * (3.0d0 + (t_3 / ((-1.0d0) - (x1 * x1)))))))))) + (3.0d0 * ((x2 * (-2.0d0)) + (x1 * ((-1.0d0) - (x1 * t_1))))))
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = (x2 * -2.0) - 3.0;
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = (t_2 + (2.0 * x2)) - x1;
	double t_4 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	double t_5 = t_3 / t_0;
	double tmp;
	if (x1 <= -4e+146) {
		tmp = t_4;
	} else if (x1 <= -5.6e+102) {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * t_1) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0));
	} else if (x1 <= 4.5e+153) {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_2 * (2.0 * x2)) - (t_0 * (((x1 * x1) * (6.0 - (t_5 * 4.0))) + (((x1 * 2.0) * t_5) * (3.0 + (t_3 / (-1.0 - (x1 * x1)))))))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 - (x1 * t_1))))));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = (x2 * -2.0) - 3.0
	t_2 = x1 * (x1 * 3.0)
	t_3 = (t_2 + (2.0 * x2)) - x1
	t_4 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))))
	t_5 = t_3 / t_0
	tmp = 0
	if x1 <= -4e+146:
		tmp = t_4
	elif x1 <= -5.6e+102:
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * t_1) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0))
	elif x1 <= 4.5e+153:
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_2 * (2.0 * x2)) - (t_0 * (((x1 * x1) * (6.0 - (t_5 * 4.0))) + (((x1 * 2.0) * t_5) * (3.0 + (t_3 / (-1.0 - (x1 * x1)))))))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 - (x1 * t_1))))))
	else:
		tmp = t_4
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(Float64(x2 * -2.0) - 3.0)
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(t_2 + Float64(2.0 * x2)) - x1)
	t_4 = Float64(x1 + Float64(x1 + Float64(Float64(x1 * -18.0) + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0))))))
	t_5 = Float64(t_3 / t_0)
	tmp = 0.0
	if (x1 <= -4e+146)
		tmp = t_4;
	elseif (x1 <= -5.6e+102)
		tmp = Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(Float64(Float64(x2 * Float64(12.0 - Float64(x2 * 8.0))) + Float64(x1 * Float64(Float64(3.0 * t_1) - Float64(Float64(x2 * 6.0) + Float64(x1 * Float64(Float64(x2 * Float64(24.0 + Float64(x2 * -8.0))) - 19.0)))))) - -1.0)));
	elseif (x1 <= 4.5e+153)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_2 * Float64(2.0 * x2)) - Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(t_5 * 4.0))) + Float64(Float64(Float64(x1 * 2.0) * t_5) * Float64(3.0 + Float64(t_3 / Float64(-1.0 - Float64(x1 * x1)))))))))) + Float64(3.0 * Float64(Float64(x2 * -2.0) + Float64(x1 * Float64(-1.0 - Float64(x1 * t_1)))))));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = (x2 * -2.0) - 3.0;
	t_2 = x1 * (x1 * 3.0);
	t_3 = (t_2 + (2.0 * x2)) - x1;
	t_4 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	t_5 = t_3 / t_0;
	tmp = 0.0;
	if (x1 <= -4e+146)
		tmp = t_4;
	elseif (x1 <= -5.6e+102)
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * t_1) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0));
	elseif (x1 <= 4.5e+153)
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_2 * (2.0 * x2)) - (t_0 * (((x1 * x1) * (6.0 - (t_5 * 4.0))) + (((x1 * 2.0) * t_5) * (3.0 + (t_3 / (-1.0 - (x1 * x1)))))))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 - (x1 * t_1))))));
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(x1 + N[(N[(x1 * -18.0), $MachinePrecision] + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$3 / t$95$0), $MachinePrecision]}, If[LessEqual[x1, -4e+146], t$95$4, If[LessEqual[x1, -5.6e+102], N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(N[(N[(x2 * N[(12.0 - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(3.0 * t$95$1), $MachinePrecision] - N[(N[(x2 * 6.0), $MachinePrecision] + N[(x1 * N[(N[(x2 * N[(24.0 + N[(x2 * -8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.5e+153], N[(x1 + N[(N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(t$95$5 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$5), $MachinePrecision] * N[(3.0 + N[(t$95$3 / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] + N[(x1 * N[(-1.0 - N[(x1 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.99999999999999973e146 or 4.5000000000000001e153 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x1 around 0 66.7%

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

   6. Taylor expanded in x2 around 0 98.3%

      \[\leadsto x1 + \color{blue}{\left(x1 + \left(-18 \cdot x1 + 3 \cdot \left(x1 \cdot \left(3 \cdot x1 - 1\right)\right)\right)\right)} \]

   if -3.99999999999999973e146 < x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x2 around 0 77.8%

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

   6. Taylor expanded in x1 around 0 100.0%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x1 \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + x1 \cdot \left(x2 \cdot \left(24 + -8 \cdot x2\right) - 19\right)\right)\right) + x2 \cdot \left(8 \cdot x2 - 12\right)\right) - 1\right)} \]

   if -5.60000000000000037e102 < x1 < 4.5000000000000001e153

   1. Initial program 98.7%

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

   3. Taylor expanded in x1 around 0 95.5%

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

   4. Taylor expanded in x1 around 0 97.2%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+146}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x2 \cdot 8\right) + x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - \left(x2 \cdot 6 + x1 \cdot \left(x2 \cdot \left(24 + x2 \cdot -8\right) - 19\right)\right)\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right) - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 - x1 \cdot \left(x2 \cdot -2 - 3\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \left(t\_1 + 2 \cdot x2\right) - x1\\ t_3 := x1 \cdot x1 + 1\\ t_4 := \frac{t\_2}{t\_3}\\ \mathbf{if}\;x1 \leq -4 \cdot 10^{+146}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x2 \cdot 8\right) + x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - \left(x2 \cdot 6 + x1 \cdot \left(x2 \cdot \left(24 + x2 \cdot -8\right) - 19\right)\right)\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - t\_1\right)}{t\_3} - \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_1 - t\_3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - t\_4 \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot t\_4\right) \cdot \left(3 + \frac{t\_2}{-1 - x1 \cdot x1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (+ x1 (+ (* x1 -18.0) (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (- (+ t_1 (* 2.0 x2)) x1))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (/ t_2 t_3)))
   (if (<= x1 -4e+146)
     t_0
     (if (<= x1 -5.6e+102)
       (-
        (* x2 -6.0)
        (*
         x1
         (-
          (+
           (* x2 (- 12.0 (* x2 8.0)))
           (*
            x1
            (-
             (* 3.0 (- (* x2 -2.0) 3.0))
             (+ (* x2 6.0) (* x1 (- (* x2 (+ 24.0 (* x2 -8.0))) 19.0))))))
          -1.0)))
       (if (<= x1 2e+153)
         (-
          x1
          (-
           (* 3.0 (/ (+ x1 (- (* 2.0 x2) t_1)) t_3))
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (-
              (* 3.0 t_1)
              (*
               t_3
               (+
                (* (* x1 x1) (- 6.0 (* t_4 4.0)))
                (*
                 (* (* x1 2.0) t_4)
                 (+ 3.0 (/ t_2 (- -1.0 (* x1 x1))))))))))))
         t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (t_1 + (2.0 * x2)) - x1;
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = t_2 / t_3;
	double tmp;
	if (x1 <= -4e+146) {
		tmp = t_0;
	} else if (x1 <= -5.6e+102) {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0));
	} else if (x1 <= 2e+153) {
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_3)) - (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) - (t_3 * (((x1 * x1) * (6.0 - (t_4 * 4.0))) + (((x1 * 2.0) * t_4) * (3.0 + (t_2 / (-1.0 - (x1 * x1)))))))))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = x1 + (x1 + ((x1 * (-18.0d0)) + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0))))))
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (t_1 + (2.0d0 * x2)) - x1
    t_3 = (x1 * x1) + 1.0d0
    t_4 = t_2 / t_3
    if (x1 <= (-4d+146)) then
        tmp = t_0
    else if (x1 <= (-5.6d+102)) then
        tmp = (x2 * (-6.0d0)) - (x1 * (((x2 * (12.0d0 - (x2 * 8.0d0))) + (x1 * ((3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)) - ((x2 * 6.0d0) + (x1 * ((x2 * (24.0d0 + (x2 * (-8.0d0)))) - 19.0d0)))))) - (-1.0d0)))
    else if (x1 <= 2d+153) then
        tmp = x1 - ((3.0d0 * ((x1 + ((2.0d0 * x2) - t_1)) / t_3)) - (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_1) - (t_3 * (((x1 * x1) * (6.0d0 - (t_4 * 4.0d0))) + (((x1 * 2.0d0) * t_4) * (3.0d0 + (t_2 / ((-1.0d0) - (x1 * x1)))))))))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (t_1 + (2.0 * x2)) - x1;
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = t_2 / t_3;
	double tmp;
	if (x1 <= -4e+146) {
		tmp = t_0;
	} else if (x1 <= -5.6e+102) {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0));
	} else if (x1 <= 2e+153) {
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_3)) - (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) - (t_3 * (((x1 * x1) * (6.0 - (t_4 * 4.0))) + (((x1 * 2.0) * t_4) * (3.0 + (t_2 / (-1.0 - (x1 * x1)))))))))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))))
	t_1 = x1 * (x1 * 3.0)
	t_2 = (t_1 + (2.0 * x2)) - x1
	t_3 = (x1 * x1) + 1.0
	t_4 = t_2 / t_3
	tmp = 0
	if x1 <= -4e+146:
		tmp = t_0
	elif x1 <= -5.6e+102:
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0))
	elif x1 <= 2e+153:
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_3)) - (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) - (t_3 * (((x1 * x1) * (6.0 - (t_4 * 4.0))) + (((x1 * 2.0) * t_4) * (3.0 + (t_2 / (-1.0 - (x1 * x1)))))))))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 + Float64(Float64(x1 * -18.0) + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0))))))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(t_1 + Float64(2.0 * x2)) - x1)
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(t_2 / t_3)
	tmp = 0.0
	if (x1 <= -4e+146)
		tmp = t_0;
	elseif (x1 <= -5.6e+102)
		tmp = Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(Float64(Float64(x2 * Float64(12.0 - Float64(x2 * 8.0))) + Float64(x1 * Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)) - Float64(Float64(x2 * 6.0) + Float64(x1 * Float64(Float64(x2 * Float64(24.0 + Float64(x2 * -8.0))) - 19.0)))))) - -1.0)));
	elseif (x1 <= 2e+153)
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(Float64(x1 + Float64(Float64(2.0 * x2) - t_1)) / t_3)) - Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_1) - Float64(t_3 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(t_4 * 4.0))) + Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(3.0 + Float64(t_2 / Float64(-1.0 - Float64(x1 * x1))))))))))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	t_1 = x1 * (x1 * 3.0);
	t_2 = (t_1 + (2.0 * x2)) - x1;
	t_3 = (x1 * x1) + 1.0;
	t_4 = t_2 / t_3;
	tmp = 0.0;
	if (x1 <= -4e+146)
		tmp = t_0;
	elseif (x1 <= -5.6e+102)
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0));
	elseif (x1 <= 2e+153)
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_3)) - (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) - (t_3 * (((x1 * x1) * (6.0 - (t_4 * 4.0))) + (((x1 * 2.0) * t_4) * (3.0 + (t_2 / (-1.0 - (x1 * x1)))))))))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 + N[(N[(x1 * -18.0), $MachinePrecision] + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 / t$95$3), $MachinePrecision]}, If[LessEqual[x1, -4e+146], t$95$0, If[LessEqual[x1, -5.6e+102], N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(N[(N[(x2 * N[(12.0 - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - N[(N[(x2 * 6.0), $MachinePrecision] + N[(x1 * N[(N[(x2 * N[(24.0 + N[(x2 * -8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+153], N[(x1 - N[(N[(3.0 * N[(N[(x1 + N[(N[(2.0 * x2), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] - N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$1), $MachinePrecision] - N[(t$95$3 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(t$95$4 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(3.0 + N[(t$95$2 / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.99999999999999973e146 or 2e153 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x1 around 0 66.7%

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

   6. Taylor expanded in x2 around 0 98.3%

      \[\leadsto x1 + \color{blue}{\left(x1 + \left(-18 \cdot x1 + 3 \cdot \left(x1 \cdot \left(3 \cdot x1 - 1\right)\right)\right)\right)} \]

   if -3.99999999999999973e146 < x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x2 around 0 77.8%

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

   6. Taylor expanded in x1 around 0 100.0%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x1 \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + x1 \cdot \left(x2 \cdot \left(24 + -8 \cdot x2\right) - 19\right)\right)\right) + x2 \cdot \left(8 \cdot x2 - 12\right)\right) - 1\right)} \]

   if -5.60000000000000037e102 < x1 < 2e153

   1. Initial program 98.7%

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

   3. Taylor expanded in x1 around inf 96.4%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+146}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x2 \cdot 8\right) + x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - \left(x2 \cdot 6 + x1 \cdot \left(x2 \cdot \left(24 + x2 \cdot -8\right) - 19\right)\right)\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} - \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 95.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \left(t\_1 + 2 \cdot x2\right) - x1\\ t_3 := \frac{t\_2}{x1 \cdot x1 + 1}\\ t_4 := -1 - x1 \cdot x1\\ \mathbf{if}\;x1 \leq -4 \cdot 10^{+146}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x2 \cdot 8\right) + x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - \left(x2 \cdot 6 + x1 \cdot \left(x2 \cdot \left(24 + x2 \cdot -8\right) - 19\right)\right)\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - t\_1\right)}{t\_4} - \left(\left(\left(t\_1 \cdot \frac{t\_2}{t\_4} + \left(\left(\left(x1 \cdot 2\right) \cdot t\_3\right) \cdot \left(t\_3 - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right) \cdot t\_4\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (+ x1 (+ (* x1 -18.0) (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (- (+ t_1 (* 2.0 x2)) x1))
        (t_3 (/ t_2 (+ (* x1 x1) 1.0)))
        (t_4 (- -1.0 (* x1 x1))))
   (if (<= x1 -4e+146)
     t_0
     (if (<= x1 -5.6e+102)
       (-
        (* x2 -6.0)
        (*
         x1
         (-
          (+
           (* x2 (- 12.0 (* x2 8.0)))
           (*
            x1
            (-
             (* 3.0 (- (* x2 -2.0) 3.0))
             (+ (* x2 6.0) (* x1 (- (* x2 (+ 24.0 (* x2 -8.0))) 19.0))))))
          -1.0)))
       (if (<= x1 2e+153)
         (+
          x1
          (-
           (* 3.0 (/ (+ x1 (- (* 2.0 x2) t_1)) t_4))
           (-
            (-
             (+
              (* t_1 (/ t_2 t_4))
              (* (+ (* (* (* x1 2.0) t_3) (- t_3 3.0)) (* (* x1 x1) 6.0)) t_4))
             (* x1 (* x1 x1)))
            x1)))
         t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (t_1 + (2.0 * x2)) - x1;
	double t_3 = t_2 / ((x1 * x1) + 1.0);
	double t_4 = -1.0 - (x1 * x1);
	double tmp;
	if (x1 <= -4e+146) {
		tmp = t_0;
	} else if (x1 <= -5.6e+102) {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0));
	} else if (x1 <= 2e+153) {
		tmp = x1 + ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_4)) - ((((t_1 * (t_2 / t_4)) + (((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * 6.0)) * t_4)) - (x1 * (x1 * x1))) - x1));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = x1 + (x1 + ((x1 * (-18.0d0)) + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0))))))
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (t_1 + (2.0d0 * x2)) - x1
    t_3 = t_2 / ((x1 * x1) + 1.0d0)
    t_4 = (-1.0d0) - (x1 * x1)
    if (x1 <= (-4d+146)) then
        tmp = t_0
    else if (x1 <= (-5.6d+102)) then
        tmp = (x2 * (-6.0d0)) - (x1 * (((x2 * (12.0d0 - (x2 * 8.0d0))) + (x1 * ((3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)) - ((x2 * 6.0d0) + (x1 * ((x2 * (24.0d0 + (x2 * (-8.0d0)))) - 19.0d0)))))) - (-1.0d0)))
    else if (x1 <= 2d+153) then
        tmp = x1 + ((3.0d0 * ((x1 + ((2.0d0 * x2) - t_1)) / t_4)) - ((((t_1 * (t_2 / t_4)) + (((((x1 * 2.0d0) * t_3) * (t_3 - 3.0d0)) + ((x1 * x1) * 6.0d0)) * t_4)) - (x1 * (x1 * x1))) - x1))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (t_1 + (2.0 * x2)) - x1;
	double t_3 = t_2 / ((x1 * x1) + 1.0);
	double t_4 = -1.0 - (x1 * x1);
	double tmp;
	if (x1 <= -4e+146) {
		tmp = t_0;
	} else if (x1 <= -5.6e+102) {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0));
	} else if (x1 <= 2e+153) {
		tmp = x1 + ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_4)) - ((((t_1 * (t_2 / t_4)) + (((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * 6.0)) * t_4)) - (x1 * (x1 * x1))) - x1));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))))
	t_1 = x1 * (x1 * 3.0)
	t_2 = (t_1 + (2.0 * x2)) - x1
	t_3 = t_2 / ((x1 * x1) + 1.0)
	t_4 = -1.0 - (x1 * x1)
	tmp = 0
	if x1 <= -4e+146:
		tmp = t_0
	elif x1 <= -5.6e+102:
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0))
	elif x1 <= 2e+153:
		tmp = x1 + ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_4)) - ((((t_1 * (t_2 / t_4)) + (((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * 6.0)) * t_4)) - (x1 * (x1 * x1))) - x1))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 + Float64(Float64(x1 * -18.0) + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0))))))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(t_1 + Float64(2.0 * x2)) - x1)
	t_3 = Float64(t_2 / Float64(Float64(x1 * x1) + 1.0))
	t_4 = Float64(-1.0 - Float64(x1 * x1))
	tmp = 0.0
	if (x1 <= -4e+146)
		tmp = t_0;
	elseif (x1 <= -5.6e+102)
		tmp = Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(Float64(Float64(x2 * Float64(12.0 - Float64(x2 * 8.0))) + Float64(x1 * Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)) - Float64(Float64(x2 * 6.0) + Float64(x1 * Float64(Float64(x2 * Float64(24.0 + Float64(x2 * -8.0))) - 19.0)))))) - -1.0)));
	elseif (x1 <= 2e+153)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 + Float64(Float64(2.0 * x2) - t_1)) / t_4)) - Float64(Float64(Float64(Float64(t_1 * Float64(t_2 / t_4)) + Float64(Float64(Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(t_3 - 3.0)) + Float64(Float64(x1 * x1) * 6.0)) * t_4)) - Float64(x1 * Float64(x1 * x1))) - x1)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	t_1 = x1 * (x1 * 3.0);
	t_2 = (t_1 + (2.0 * x2)) - x1;
	t_3 = t_2 / ((x1 * x1) + 1.0);
	t_4 = -1.0 - (x1 * x1);
	tmp = 0.0;
	if (x1 <= -4e+146)
		tmp = t_0;
	elseif (x1 <= -5.6e+102)
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0));
	elseif (x1 <= 2e+153)
		tmp = x1 + ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_4)) - ((((t_1 * (t_2 / t_4)) + (((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * 6.0)) * t_4)) - (x1 * (x1 * x1))) - x1));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 + N[(N[(x1 * -18.0), $MachinePrecision] + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4e+146], t$95$0, If[LessEqual[x1, -5.6e+102], N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(N[(N[(x2 * N[(12.0 - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - N[(N[(x2 * 6.0), $MachinePrecision] + N[(x1 * N[(N[(x2 * N[(24.0 + N[(x2 * -8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+153], N[(x1 + N[(N[(3.0 * N[(N[(x1 + N[(N[(2.0 * x2), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(t$95$1 * N[(t$95$2 / t$95$4), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.99999999999999973e146 or 2e153 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x1 around 0 66.7%

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

   6. Taylor expanded in x2 around 0 98.3%

      \[\leadsto x1 + \color{blue}{\left(x1 + \left(-18 \cdot x1 + 3 \cdot \left(x1 \cdot \left(3 \cdot x1 - 1\right)\right)\right)\right)} \]

   if -3.99999999999999973e146 < x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x2 around 0 77.8%

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

   6. Taylor expanded in x1 around 0 100.0%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x1 \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + x1 \cdot \left(x2 \cdot \left(24 + -8 \cdot x2\right) - 19\right)\right)\right) + x2 \cdot \left(8 \cdot x2 - 12\right)\right) - 1\right)} \]

   if -5.60000000000000037e102 < x1 < 2e153

   1. Initial program 98.7%

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

   3. Taylor expanded in x1 around inf 94.8%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+146}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x2 \cdot 8\right) + x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - \left(x2 \cdot 6 + x1 \cdot \left(x2 \cdot \left(24 + x2 \cdot -8\right) - 19\right)\right)\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right) \cdot \left(-1 - x1 \cdot x1\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 95.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := -1 - x1 \cdot x1\\ t_2 := x1 \cdot \left(x1 \cdot x1\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := \left(t\_3 + 2 \cdot x2\right) - x1\\ t_5 := x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ t_6 := \frac{t\_4}{t\_0}\\ t_7 := \left(x1 \cdot 2\right) \cdot t\_6\\ \mathbf{if}\;x1 \leq -4 \cdot 10^{+146}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x2 \cdot 8\right) + x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - \left(x2 \cdot 6 + x1 \cdot \left(x2 \cdot \left(24 + x2 \cdot -8\right) - 19\right)\right)\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq -5 \cdot 10^{-53}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) - \left(\left(\left(t\_3 \cdot \left(\frac{1}{x1} - 3\right) + t\_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - t\_6 \cdot 4\right) + t\_7 \cdot \left(3 + \frac{t\_4}{t\_1}\right)\right)\right) - t\_2\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - t\_3\right)}{t\_1} + \left(x1 - \left(\left(\left(t\_7 \cdot \left(t\_6 - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right) \cdot t\_1 - t\_3 \cdot \left(2 \cdot x2\right)\right) - t\_2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (- -1.0 (* x1 x1)))
        (t_2 (* x1 (* x1 x1)))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (- (+ t_3 (* 2.0 x2)) x1))
        (t_5 (+ x1 (+ x1 (+ (* x1 -18.0) (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))))
        (t_6 (/ t_4 t_0))
        (t_7 (* (* x1 2.0) t_6)))
   (if (<= x1 -4e+146)
     t_5
     (if (<= x1 -5.6e+102)
       (-
        (* x2 -6.0)
        (*
         x1
         (-
          (+
           (* x2 (- 12.0 (* x2 8.0)))
           (*
            x1
            (-
             (* 3.0 (- (* x2 -2.0) 3.0))
             (+ (* x2 6.0) (* x1 (- (* x2 (+ 24.0 (* x2 -8.0))) 19.0))))))
          -1.0)))
       (if (<= x1 -5e-53)
         (+
          x1
          (-
           (* 3.0 (* x2 -2.0))
           (-
            (-
             (+
              (* t_3 (- (/ 1.0 x1) 3.0))
              (*
               t_0
               (+
                (* (* x1 x1) (- 6.0 (* t_6 4.0)))
                (* t_7 (+ 3.0 (/ t_4 t_1))))))
             t_2)
            x1)))
         (if (<= x1 4.5e+153)
           (+
            x1
            (+
             (* 3.0 (/ (+ x1 (- (* 2.0 x2) t_3)) t_1))
             (-
              x1
              (-
               (-
                (* (+ (* t_7 (- t_6 3.0)) (* (* x1 x1) 6.0)) t_1)
                (* t_3 (* 2.0 x2)))
               t_2))))
           t_5))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = -1.0 - (x1 * x1);
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = (t_3 + (2.0 * x2)) - x1;
	double t_5 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	double t_6 = t_4 / t_0;
	double t_7 = (x1 * 2.0) * t_6;
	double tmp;
	if (x1 <= -4e+146) {
		tmp = t_5;
	} else if (x1 <= -5.6e+102) {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0));
	} else if (x1 <= -5e-53) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) - ((((t_3 * ((1.0 / x1) - 3.0)) + (t_0 * (((x1 * x1) * (6.0 - (t_6 * 4.0))) + (t_7 * (3.0 + (t_4 / t_1)))))) - t_2) - x1));
	} else if (x1 <= 4.5e+153) {
		tmp = x1 + ((3.0 * ((x1 + ((2.0 * x2) - t_3)) / t_1)) + (x1 - (((((t_7 * (t_6 - 3.0)) + ((x1 * x1) * 6.0)) * t_1) - (t_3 * (2.0 * x2))) - t_2)));
	} else {
		tmp = t_5;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = (-1.0d0) - (x1 * x1)
    t_2 = x1 * (x1 * x1)
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = (t_3 + (2.0d0 * x2)) - x1
    t_5 = x1 + (x1 + ((x1 * (-18.0d0)) + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0))))))
    t_6 = t_4 / t_0
    t_7 = (x1 * 2.0d0) * t_6
    if (x1 <= (-4d+146)) then
        tmp = t_5
    else if (x1 <= (-5.6d+102)) then
        tmp = (x2 * (-6.0d0)) - (x1 * (((x2 * (12.0d0 - (x2 * 8.0d0))) + (x1 * ((3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)) - ((x2 * 6.0d0) + (x1 * ((x2 * (24.0d0 + (x2 * (-8.0d0)))) - 19.0d0)))))) - (-1.0d0)))
    else if (x1 <= (-5d-53)) then
        tmp = x1 + ((3.0d0 * (x2 * (-2.0d0))) - ((((t_3 * ((1.0d0 / x1) - 3.0d0)) + (t_0 * (((x1 * x1) * (6.0d0 - (t_6 * 4.0d0))) + (t_7 * (3.0d0 + (t_4 / t_1)))))) - t_2) - x1))
    else if (x1 <= 4.5d+153) then
        tmp = x1 + ((3.0d0 * ((x1 + ((2.0d0 * x2) - t_3)) / t_1)) + (x1 - (((((t_7 * (t_6 - 3.0d0)) + ((x1 * x1) * 6.0d0)) * t_1) - (t_3 * (2.0d0 * x2))) - t_2)))
    else
        tmp = t_5
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = -1.0 - (x1 * x1);
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = (t_3 + (2.0 * x2)) - x1;
	double t_5 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	double t_6 = t_4 / t_0;
	double t_7 = (x1 * 2.0) * t_6;
	double tmp;
	if (x1 <= -4e+146) {
		tmp = t_5;
	} else if (x1 <= -5.6e+102) {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0));
	} else if (x1 <= -5e-53) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) - ((((t_3 * ((1.0 / x1) - 3.0)) + (t_0 * (((x1 * x1) * (6.0 - (t_6 * 4.0))) + (t_7 * (3.0 + (t_4 / t_1)))))) - t_2) - x1));
	} else if (x1 <= 4.5e+153) {
		tmp = x1 + ((3.0 * ((x1 + ((2.0 * x2) - t_3)) / t_1)) + (x1 - (((((t_7 * (t_6 - 3.0)) + ((x1 * x1) * 6.0)) * t_1) - (t_3 * (2.0 * x2))) - t_2)));
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = -1.0 - (x1 * x1)
	t_2 = x1 * (x1 * x1)
	t_3 = x1 * (x1 * 3.0)
	t_4 = (t_3 + (2.0 * x2)) - x1
	t_5 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))))
	t_6 = t_4 / t_0
	t_7 = (x1 * 2.0) * t_6
	tmp = 0
	if x1 <= -4e+146:
		tmp = t_5
	elif x1 <= -5.6e+102:
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0))
	elif x1 <= -5e-53:
		tmp = x1 + ((3.0 * (x2 * -2.0)) - ((((t_3 * ((1.0 / x1) - 3.0)) + (t_0 * (((x1 * x1) * (6.0 - (t_6 * 4.0))) + (t_7 * (3.0 + (t_4 / t_1)))))) - t_2) - x1))
	elif x1 <= 4.5e+153:
		tmp = x1 + ((3.0 * ((x1 + ((2.0 * x2) - t_3)) / t_1)) + (x1 - (((((t_7 * (t_6 - 3.0)) + ((x1 * x1) * 6.0)) * t_1) - (t_3 * (2.0 * x2))) - t_2)))
	else:
		tmp = t_5
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(-1.0 - Float64(x1 * x1))
	t_2 = Float64(x1 * 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(x1 + Float64(x1 + Float64(Float64(x1 * -18.0) + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0))))))
	t_6 = Float64(t_4 / t_0)
	t_7 = Float64(Float64(x1 * 2.0) * t_6)
	tmp = 0.0
	if (x1 <= -4e+146)
		tmp = t_5;
	elseif (x1 <= -5.6e+102)
		tmp = Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(Float64(Float64(x2 * Float64(12.0 - Float64(x2 * 8.0))) + Float64(x1 * Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)) - Float64(Float64(x2 * 6.0) + Float64(x1 * Float64(Float64(x2 * Float64(24.0 + Float64(x2 * -8.0))) - 19.0)))))) - -1.0)));
	elseif (x1 <= -5e-53)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(x2 * -2.0)) - Float64(Float64(Float64(Float64(t_3 * Float64(Float64(1.0 / x1) - 3.0)) + Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(t_6 * 4.0))) + Float64(t_7 * Float64(3.0 + Float64(t_4 / t_1)))))) - t_2) - x1)));
	elseif (x1 <= 4.5e+153)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 + Float64(Float64(2.0 * x2) - t_3)) / t_1)) + Float64(x1 - Float64(Float64(Float64(Float64(Float64(t_7 * Float64(t_6 - 3.0)) + Float64(Float64(x1 * x1) * 6.0)) * t_1) - Float64(t_3 * Float64(2.0 * x2))) - t_2))));
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = -1.0 - (x1 * x1);
	t_2 = x1 * (x1 * x1);
	t_3 = x1 * (x1 * 3.0);
	t_4 = (t_3 + (2.0 * x2)) - x1;
	t_5 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	t_6 = t_4 / t_0;
	t_7 = (x1 * 2.0) * t_6;
	tmp = 0.0;
	if (x1 <= -4e+146)
		tmp = t_5;
	elseif (x1 <= -5.6e+102)
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0));
	elseif (x1 <= -5e-53)
		tmp = x1 + ((3.0 * (x2 * -2.0)) - ((((t_3 * ((1.0 / x1) - 3.0)) + (t_0 * (((x1 * x1) * (6.0 - (t_6 * 4.0))) + (t_7 * (3.0 + (t_4 / t_1)))))) - t_2) - x1));
	elseif (x1 <= 4.5e+153)
		tmp = x1 + ((3.0 * ((x1 + ((2.0 * x2) - t_3)) / t_1)) + (x1 - (((((t_7 * (t_6 - 3.0)) + ((x1 * x1) * 6.0)) * t_1) - (t_3 * (2.0 * x2))) - t_2)));
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $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[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(x1 + N[(N[(x1 * -18.0), $MachinePrecision] + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$4 / t$95$0), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x1 * 2.0), $MachinePrecision] * t$95$6), $MachinePrecision]}, If[LessEqual[x1, -4e+146], t$95$5, If[LessEqual[x1, -5.6e+102], N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(N[(N[(x2 * N[(12.0 - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - N[(N[(x2 * 6.0), $MachinePrecision] + N[(x1 * N[(N[(x2 * N[(24.0 + N[(x2 * -8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5e-53], N[(x1 + N[(N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(t$95$3 * N[(N[(1.0 / x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(t$95$6 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$7 * N[(3.0 + N[(t$95$4 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.5e+153], N[(x1 + N[(N[(3.0 * N[(N[(x1 + N[(N[(2.0 * x2), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 - N[(N[(N[(N[(N[(t$95$7 * N[(t$95$6 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] - N[(t$95$3 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$5]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -3.99999999999999973e146 or 4.5000000000000001e153 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x1 around 0 66.7%

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

   6. Taylor expanded in x2 around 0 98.3%

      \[\leadsto x1 + \color{blue}{\left(x1 + \left(-18 \cdot x1 + 3 \cdot \left(x1 \cdot \left(3 \cdot x1 - 1\right)\right)\right)\right)} \]

   if -3.99999999999999973e146 < x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x2 around 0 77.8%

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

   6. Taylor expanded in x1 around 0 100.0%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x1 \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + x1 \cdot \left(x2 \cdot \left(24 + -8 \cdot x2\right) - 19\right)\right)\right) + x2 \cdot \left(8 \cdot x2 - 12\right)\right) - 1\right)} \]

   if -5.60000000000000037e102 < x1 < -5e-53

   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 inf 85.1%

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

   4. Taylor expanded in x1 around 0 99.1%

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

      1. *-commutative 99.1%

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

   6. Simplified 99.1%

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

   if -5e-53 < x1 < 4.5000000000000001e153

   1. Initial program 98.6%

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

   3. Taylor expanded in x1 around 0 97.2%

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

   4. Taylor expanded in x1 around inf 96.3%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+146}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x2 \cdot 8\right) + x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - \left(x2 \cdot 6 + x1 \cdot \left(x2 \cdot \left(24 + x2 \cdot -8\right) - 19\right)\right)\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq -5 \cdot 10^{-53}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(\frac{1}{x1} - 3\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} + \left(x1 - \left(\left(\left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right) \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)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 94.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\left(t\_1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\\ t_3 := -1 - x1 \cdot x1\\ \mathbf{if}\;x1 \leq -4 \cdot 10^{+146}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -1 \cdot 10^{+105}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x2 \cdot 8\right) + x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - \left(x2 \cdot 6 + x1 \cdot \left(x2 \cdot \left(24 + x2 \cdot -8\right) - 19\right)\right)\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - t\_1\right)}{t\_3} + \left(x1 - \left(\left(\left(\left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right) \cdot t\_3 - t\_1 \cdot \left(2 \cdot x2\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (+ x1 (+ (* x1 -18.0) (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (/ (- (+ t_1 (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
        (t_3 (- -1.0 (* x1 x1))))
   (if (<= x1 -4e+146)
     t_0
     (if (<= x1 -1e+105)
       (-
        (* x2 -6.0)
        (*
         x1
         (-
          (+
           (* x2 (- 12.0 (* x2 8.0)))
           (*
            x1
            (-
             (* 3.0 (- (* x2 -2.0) 3.0))
             (+ (* x2 6.0) (* x1 (- (* x2 (+ 24.0 (* x2 -8.0))) 19.0))))))
          -1.0)))
       (if (<= x1 4.5e+153)
         (+
          x1
          (+
           (* 3.0 (/ (+ x1 (- (* 2.0 x2) t_1)) t_3))
           (-
            x1
            (-
             (-
              (* (+ (* (* (* x1 2.0) t_2) (- t_2 3.0)) (* (* x1 x1) 6.0)) t_3)
              (* t_1 (* 2.0 x2)))
             (* x1 (* x1 x1))))))
         t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0);
	double t_3 = -1.0 - (x1 * x1);
	double tmp;
	if (x1 <= -4e+146) {
		tmp = t_0;
	} else if (x1 <= -1e+105) {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0));
	} else if (x1 <= 4.5e+153) {
		tmp = x1 + ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_3)) + (x1 - (((((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)) * t_3) - (t_1 * (2.0 * x2))) - (x1 * (x1 * x1)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x1 + (x1 + ((x1 * (-18.0d0)) + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0))))))
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = ((t_1 + (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0)
    t_3 = (-1.0d0) - (x1 * x1)
    if (x1 <= (-4d+146)) then
        tmp = t_0
    else if (x1 <= (-1d+105)) then
        tmp = (x2 * (-6.0d0)) - (x1 * (((x2 * (12.0d0 - (x2 * 8.0d0))) + (x1 * ((3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)) - ((x2 * 6.0d0) + (x1 * ((x2 * (24.0d0 + (x2 * (-8.0d0)))) - 19.0d0)))))) - (-1.0d0)))
    else if (x1 <= 4.5d+153) then
        tmp = x1 + ((3.0d0 * ((x1 + ((2.0d0 * x2) - t_1)) / t_3)) + (x1 - (((((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * 6.0d0)) * t_3) - (t_1 * (2.0d0 * x2))) - (x1 * (x1 * x1)))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0);
	double t_3 = -1.0 - (x1 * x1);
	double tmp;
	if (x1 <= -4e+146) {
		tmp = t_0;
	} else if (x1 <= -1e+105) {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0));
	} else if (x1 <= 4.5e+153) {
		tmp = x1 + ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_3)) + (x1 - (((((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)) * t_3) - (t_1 * (2.0 * x2))) - (x1 * (x1 * x1)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))))
	t_1 = x1 * (x1 * 3.0)
	t_2 = ((t_1 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0)
	t_3 = -1.0 - (x1 * x1)
	tmp = 0
	if x1 <= -4e+146:
		tmp = t_0
	elif x1 <= -1e+105:
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0))
	elif x1 <= 4.5e+153:
		tmp = x1 + ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_3)) + (x1 - (((((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)) * t_3) - (t_1 * (2.0 * x2))) - (x1 * (x1 * x1)))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 + Float64(Float64(x1 * -18.0) + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0))))))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))
	t_3 = Float64(-1.0 - Float64(x1 * x1))
	tmp = 0.0
	if (x1 <= -4e+146)
		tmp = t_0;
	elseif (x1 <= -1e+105)
		tmp = Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(Float64(Float64(x2 * Float64(12.0 - Float64(x2 * 8.0))) + Float64(x1 * Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)) - Float64(Float64(x2 * 6.0) + Float64(x1 * Float64(Float64(x2 * Float64(24.0 + Float64(x2 * -8.0))) - 19.0)))))) - -1.0)));
	elseif (x1 <= 4.5e+153)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 + Float64(Float64(2.0 * x2) - t_1)) / t_3)) + Float64(x1 - Float64(Float64(Float64(Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * 6.0)) * t_3) - Float64(t_1 * Float64(2.0 * x2))) - Float64(x1 * Float64(x1 * x1))))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	t_1 = x1 * (x1 * 3.0);
	t_2 = ((t_1 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0);
	t_3 = -1.0 - (x1 * x1);
	tmp = 0.0;
	if (x1 <= -4e+146)
		tmp = t_0;
	elseif (x1 <= -1e+105)
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0));
	elseif (x1 <= 4.5e+153)
		tmp = x1 + ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_3)) + (x1 - (((((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)) * t_3) - (t_1 * (2.0 * x2))) - (x1 * (x1 * x1)))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 + N[(N[(x1 * -18.0), $MachinePrecision] + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4e+146], t$95$0, If[LessEqual[x1, -1e+105], N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(N[(N[(x2 * N[(12.0 - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - N[(N[(x2 * 6.0), $MachinePrecision] + N[(x1 * N[(N[(x2 * N[(24.0 + N[(x2 * -8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.5e+153], N[(x1 + N[(N[(3.0 * N[(N[(x1 + N[(N[(2.0 * x2), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x1 - N[(N[(N[(N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] * t$95$3), $MachinePrecision] - N[(t$95$1 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.99999999999999973e146 or 4.5000000000000001e153 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x1 around 0 66.7%

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

   6. Taylor expanded in x2 around 0 98.3%

      \[\leadsto x1 + \color{blue}{\left(x1 + \left(-18 \cdot x1 + 3 \cdot \left(x1 \cdot \left(3 \cdot x1 - 1\right)\right)\right)\right)} \]

   if -3.99999999999999973e146 < x1 < -9.9999999999999994e104

   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 100.0%

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

   5. Taylor expanded in x2 around 0 77.8%

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

   6. Taylor expanded in x1 around 0 100.0%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x1 \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + x1 \cdot \left(x2 \cdot \left(24 + -8 \cdot x2\right) - 19\right)\right)\right) + x2 \cdot \left(8 \cdot x2 - 12\right)\right) - 1\right)} \]

   if -9.9999999999999994e104 < x1 < 4.5000000000000001e153

   1. Initial program 98.7%

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

   3. Taylor expanded in x1 around 0 95.5%

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

   4. Taylor expanded in x1 around inf 94.4%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+146}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1 \cdot 10^{+105}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x2 \cdot 8\right) + x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - \left(x2 \cdot 6 + x1 \cdot \left(x2 \cdot \left(24 + x2 \cdot -8\right) - 19\right)\right)\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} + \left(x1 - \left(\left(\left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right) \cdot \left(-1 - x1 \cdot x1\right) - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 93.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ t_3 := 3 \cdot \left(x2 \cdot -2\right)\\ t_4 := x1 \cdot \left(x1 \cdot 3\right)\\ t_5 := \frac{\left(t\_4 + 2 \cdot x2\right) - x1}{t\_1}\\ t_6 := t\_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - t\_5 \cdot 4\right) - \left(t\_5 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot 3\right)\right)\\ \mathbf{if}\;x1 \leq -4 \cdot 10^{+146}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x2 \cdot 8\right) + x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - \left(x2 \cdot 6 + x1 \cdot \left(x2 \cdot \left(24 + x2 \cdot -8\right) - 19\right)\right)\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq -460000000000:\\ \;\;\;\;x1 + \left(t\_3 + \left(x1 + \left(t\_0 - \left(t\_6 - t\_4 \cdot \left(2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(t\_3 + \left(x1 + \left(t\_0 + \left(3 \cdot t\_4 - t\_6\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (+ x1 (+ x1 (+ (* x1 -18.0) (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))))
        (t_3 (* 3.0 (* x2 -2.0)))
        (t_4 (* x1 (* x1 3.0)))
        (t_5 (/ (- (+ t_4 (* 2.0 x2)) x1) t_1))
        (t_6
         (*
          t_1
          (-
           (* (* x1 x1) (- 6.0 (* t_5 4.0)))
           (* (- t_5 3.0) (* (* x1 2.0) 3.0))))))
   (if (<= x1 -4e+146)
     t_2
     (if (<= x1 -5.6e+102)
       (-
        (* x2 -6.0)
        (*
         x1
         (-
          (+
           (* x2 (- 12.0 (* x2 8.0)))
           (*
            x1
            (-
             (* 3.0 (- (* x2 -2.0) 3.0))
             (+ (* x2 6.0) (* x1 (- (* x2 (+ 24.0 (* x2 -8.0))) 19.0))))))
          -1.0)))
       (if (<= x1 -460000000000.0)
         (+ x1 (+ t_3 (+ x1 (- t_0 (- t_6 (* t_4 (* 2.0 x2)))))))
         (if (<= x1 7.0)
           (- (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0)) x1)
           (if (<= x1 2e+153)
             (+ x1 (+ t_3 (+ x1 (+ t_0 (- (* 3.0 t_4) t_6)))))
             t_2)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	double t_3 = 3.0 * (x2 * -2.0);
	double t_4 = x1 * (x1 * 3.0);
	double t_5 = ((t_4 + (2.0 * x2)) - x1) / t_1;
	double t_6 = t_1 * (((x1 * x1) * (6.0 - (t_5 * 4.0))) - ((t_5 - 3.0) * ((x1 * 2.0) * 3.0)));
	double tmp;
	if (x1 <= -4e+146) {
		tmp = t_2;
	} else if (x1 <= -5.6e+102) {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0));
	} else if (x1 <= -460000000000.0) {
		tmp = x1 + (t_3 + (x1 + (t_0 - (t_6 - (t_4 * (2.0 * x2))))));
	} else if (x1 <= 7.0) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else if (x1 <= 2e+153) {
		tmp = x1 + (t_3 + (x1 + (t_0 + ((3.0 * t_4) - t_6))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = x1 * (x1 * x1)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = x1 + (x1 + ((x1 * (-18.0d0)) + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0))))))
    t_3 = 3.0d0 * (x2 * (-2.0d0))
    t_4 = x1 * (x1 * 3.0d0)
    t_5 = ((t_4 + (2.0d0 * x2)) - x1) / t_1
    t_6 = t_1 * (((x1 * x1) * (6.0d0 - (t_5 * 4.0d0))) - ((t_5 - 3.0d0) * ((x1 * 2.0d0) * 3.0d0)))
    if (x1 <= (-4d+146)) then
        tmp = t_2
    else if (x1 <= (-5.6d+102)) then
        tmp = (x2 * (-6.0d0)) - (x1 * (((x2 * (12.0d0 - (x2 * 8.0d0))) + (x1 * ((3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)) - ((x2 * 6.0d0) + (x1 * ((x2 * (24.0d0 + (x2 * (-8.0d0)))) - 19.0d0)))))) - (-1.0d0)))
    else if (x1 <= (-460000000000.0d0)) then
        tmp = x1 + (t_3 + (x1 + (t_0 - (t_6 - (t_4 * (2.0d0 * x2))))))
    else if (x1 <= 7.0d0) then
        tmp = (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)) - x1
    else if (x1 <= 2d+153) then
        tmp = x1 + (t_3 + (x1 + (t_0 + ((3.0d0 * t_4) - t_6))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	double t_3 = 3.0 * (x2 * -2.0);
	double t_4 = x1 * (x1 * 3.0);
	double t_5 = ((t_4 + (2.0 * x2)) - x1) / t_1;
	double t_6 = t_1 * (((x1 * x1) * (6.0 - (t_5 * 4.0))) - ((t_5 - 3.0) * ((x1 * 2.0) * 3.0)));
	double tmp;
	if (x1 <= -4e+146) {
		tmp = t_2;
	} else if (x1 <= -5.6e+102) {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0));
	} else if (x1 <= -460000000000.0) {
		tmp = x1 + (t_3 + (x1 + (t_0 - (t_6 - (t_4 * (2.0 * x2))))));
	} else if (x1 <= 7.0) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else if (x1 <= 2e+153) {
		tmp = x1 + (t_3 + (x1 + (t_0 + ((3.0 * t_4) - t_6))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = (x1 * x1) + 1.0
	t_2 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))))
	t_3 = 3.0 * (x2 * -2.0)
	t_4 = x1 * (x1 * 3.0)
	t_5 = ((t_4 + (2.0 * x2)) - x1) / t_1
	t_6 = t_1 * (((x1 * x1) * (6.0 - (t_5 * 4.0))) - ((t_5 - 3.0) * ((x1 * 2.0) * 3.0)))
	tmp = 0
	if x1 <= -4e+146:
		tmp = t_2
	elif x1 <= -5.6e+102:
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0))
	elif x1 <= -460000000000.0:
		tmp = x1 + (t_3 + (x1 + (t_0 - (t_6 - (t_4 * (2.0 * x2))))))
	elif x1 <= 7.0:
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1
	elif x1 <= 2e+153:
		tmp = x1 + (t_3 + (x1 + (t_0 + ((3.0 * t_4) - t_6))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(x1 + Float64(x1 + Float64(Float64(x1 * -18.0) + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0))))))
	t_3 = Float64(3.0 * Float64(x2 * -2.0))
	t_4 = Float64(x1 * Float64(x1 * 3.0))
	t_5 = Float64(Float64(Float64(t_4 + Float64(2.0 * x2)) - x1) / t_1)
	t_6 = Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(t_5 * 4.0))) - Float64(Float64(t_5 - 3.0) * Float64(Float64(x1 * 2.0) * 3.0))))
	tmp = 0.0
	if (x1 <= -4e+146)
		tmp = t_2;
	elseif (x1 <= -5.6e+102)
		tmp = Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(Float64(Float64(x2 * Float64(12.0 - Float64(x2 * 8.0))) + Float64(x1 * Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)) - Float64(Float64(x2 * 6.0) + Float64(x1 * Float64(Float64(x2 * Float64(24.0 + Float64(x2 * -8.0))) - 19.0)))))) - -1.0)));
	elseif (x1 <= -460000000000.0)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(t_0 - Float64(t_6 - Float64(t_4 * Float64(2.0 * x2)))))));
	elseif (x1 <= 7.0)
		tmp = Float64(Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0)) - x1);
	elseif (x1 <= 2e+153)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(t_0 + Float64(Float64(3.0 * t_4) - t_6)))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = (x1 * x1) + 1.0;
	t_2 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	t_3 = 3.0 * (x2 * -2.0);
	t_4 = x1 * (x1 * 3.0);
	t_5 = ((t_4 + (2.0 * x2)) - x1) / t_1;
	t_6 = t_1 * (((x1 * x1) * (6.0 - (t_5 * 4.0))) - ((t_5 - 3.0) * ((x1 * 2.0) * 3.0)));
	tmp = 0.0;
	if (x1 <= -4e+146)
		tmp = t_2;
	elseif (x1 <= -5.6e+102)
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0));
	elseif (x1 <= -460000000000.0)
		tmp = x1 + (t_3 + (x1 + (t_0 - (t_6 - (t_4 * (2.0 * x2))))));
	elseif (x1 <= 7.0)
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	elseif (x1 <= 2e+153)
		tmp = x1 + (t_3 + (x1 + (t_0 + ((3.0 * t_4) - t_6))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(x1 + N[(N[(x1 * -18.0), $MachinePrecision] + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(t$95$4 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(t$95$5 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$5 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4e+146], t$95$2, If[LessEqual[x1, -5.6e+102], N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(N[(N[(x2 * N[(12.0 - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - N[(N[(x2 * 6.0), $MachinePrecision] + N[(x1 * N[(N[(x2 * N[(24.0 + N[(x2 * -8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -460000000000.0], N[(x1 + N[(t$95$3 + N[(x1 + N[(t$95$0 - N[(t$95$6 - N[(t$95$4 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7.0], N[(N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 2e+153], N[(x1 + N[(t$95$3 + N[(x1 + N[(t$95$0 + N[(N[(3.0 * t$95$4), $MachinePrecision] - t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -3.99999999999999973e146 or 2e153 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x1 around 0 66.7%

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

   6. Taylor expanded in x2 around 0 98.3%

      \[\leadsto x1 + \color{blue}{\left(x1 + \left(-18 \cdot x1 + 3 \cdot \left(x1 \cdot \left(3 \cdot x1 - 1\right)\right)\right)\right)} \]

   if -3.99999999999999973e146 < x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x2 around 0 77.8%

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

   6. Taylor expanded in x1 around 0 100.0%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x1 \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + x1 \cdot \left(x2 \cdot \left(24 + -8 \cdot x2\right) - 19\right)\right)\right) + x2 \cdot \left(8 \cdot x2 - 12\right)\right) - 1\right)} \]

   if -5.60000000000000037e102 < x1 < -4.6e11

   1. Initial program 99.1%

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

   3. Taylor expanded in x1 around inf 80.9%

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

   4. Taylor expanded in x1 around 0 80.9%

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

      1. *-commutative 99.1%

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

   6. Simplified 80.9%

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

   7. Taylor expanded in x1 around 0 81.0%

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

   if -4.6e11 < x1 < 7

   1. Initial program 99.2%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in x1 around 0 85.3%

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

      1. fma-define 85.4%

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

      2. associate-*r* 85.4%

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

      3. fmm-def 85.4%

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

      4. *-commutative 85.4%

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

      5. *-commutative 85.4%

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

      6. metadata-eval 85.4%

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

   7. Simplified 85.4%

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

   8. Taylor expanded in x2 around 0 94.8%

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

   if 7 < x1 < 2e153

   1. Initial program 96.2%

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

   3. Taylor expanded in x1 around inf 75.7%

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

   4. Taylor expanded in x1 around 0 75.7%

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

      1. *-commutative 96.3%

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

   6. Simplified 75.7%

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

   7. Taylor expanded in x1 around inf 75.8%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot 3\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{3}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+146}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x2 \cdot 8\right) + x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - \left(x2 \cdot 6 + x1 \cdot \left(x2 \cdot \left(24 + x2 \cdot -8\right) - 19\right)\right)\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq -460000000000:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4\right) - \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot 3\right)\right) - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4\right) - \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 93.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ t_3 := \left(x1 \cdot 2\right) \cdot 3\\ t_4 := x1 \cdot \left(x1 \cdot 3\right)\\ t_5 := 3 \cdot t\_4\\ t_6 := \frac{\left(t\_4 + 2 \cdot x2\right) - x1}{t\_1}\\ t_7 := \left(x1 \cdot x1\right) \cdot \left(6 - t\_6 \cdot 4\right)\\ \mathbf{if}\;x1 \leq -4 \cdot 10^{+146}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x2 \cdot 8\right) + x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - \left(x2 \cdot 6 + x1 \cdot \left(x2 \cdot \left(24 + x2 \cdot -8\right) - 19\right)\right)\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq -460000000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - t\_4\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(t\_0 - \left(t\_1 \cdot \left(\frac{1}{x1} \cdot t\_3 + t\_7\right) - t\_5\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7.8:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(t\_0 + \left(t\_5 - t\_1 \cdot \left(t\_7 - \left(t\_6 - 3\right) \cdot t\_3\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (+ x1 (+ x1 (+ (* x1 -18.0) (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))))
        (t_3 (* (* x1 2.0) 3.0))
        (t_4 (* x1 (* x1 3.0)))
        (t_5 (* 3.0 t_4))
        (t_6 (/ (- (+ t_4 (* 2.0 x2)) x1) t_1))
        (t_7 (* (* x1 x1) (- 6.0 (* t_6 4.0)))))
   (if (<= x1 -4e+146)
     t_2
     (if (<= x1 -5.6e+102)
       (-
        (* x2 -6.0)
        (*
         x1
         (-
          (+
           (* x2 (- 12.0 (* x2 8.0)))
           (*
            x1
            (-
             (* 3.0 (- (* x2 -2.0) 3.0))
             (+ (* x2 6.0) (* x1 (- (* x2 (+ 24.0 (* x2 -8.0))) 19.0))))))
          -1.0)))
       (if (<= x1 -460000000000.0)
         (+
          x1
          (+
           (* 3.0 (/ (+ x1 (- (* 2.0 x2) t_4)) (- -1.0 (* x1 x1))))
           (+ x1 (- t_0 (- (* t_1 (+ (* (/ 1.0 x1) t_3) t_7)) t_5)))))
         (if (<= x1 7.8)
           (- (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0)) x1)
           (if (<= x1 2e+153)
             (+
              x1
              (+
               (* 3.0 (* x2 -2.0))
               (+ x1 (+ t_0 (- t_5 (* t_1 (- t_7 (* (- t_6 3.0) t_3))))))))
             t_2)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	double t_3 = (x1 * 2.0) * 3.0;
	double t_4 = x1 * (x1 * 3.0);
	double t_5 = 3.0 * t_4;
	double t_6 = ((t_4 + (2.0 * x2)) - x1) / t_1;
	double t_7 = (x1 * x1) * (6.0 - (t_6 * 4.0));
	double tmp;
	if (x1 <= -4e+146) {
		tmp = t_2;
	} else if (x1 <= -5.6e+102) {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0));
	} else if (x1 <= -460000000000.0) {
		tmp = x1 + ((3.0 * ((x1 + ((2.0 * x2) - t_4)) / (-1.0 - (x1 * x1)))) + (x1 + (t_0 - ((t_1 * (((1.0 / x1) * t_3) + t_7)) - t_5))));
	} else if (x1 <= 7.8) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else if (x1 <= 2e+153) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (t_0 + (t_5 - (t_1 * (t_7 - ((t_6 - 3.0) * t_3)))))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = x1 * (x1 * x1)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = x1 + (x1 + ((x1 * (-18.0d0)) + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0))))))
    t_3 = (x1 * 2.0d0) * 3.0d0
    t_4 = x1 * (x1 * 3.0d0)
    t_5 = 3.0d0 * t_4
    t_6 = ((t_4 + (2.0d0 * x2)) - x1) / t_1
    t_7 = (x1 * x1) * (6.0d0 - (t_6 * 4.0d0))
    if (x1 <= (-4d+146)) then
        tmp = t_2
    else if (x1 <= (-5.6d+102)) then
        tmp = (x2 * (-6.0d0)) - (x1 * (((x2 * (12.0d0 - (x2 * 8.0d0))) + (x1 * ((3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)) - ((x2 * 6.0d0) + (x1 * ((x2 * (24.0d0 + (x2 * (-8.0d0)))) - 19.0d0)))))) - (-1.0d0)))
    else if (x1 <= (-460000000000.0d0)) then
        tmp = x1 + ((3.0d0 * ((x1 + ((2.0d0 * x2) - t_4)) / ((-1.0d0) - (x1 * x1)))) + (x1 + (t_0 - ((t_1 * (((1.0d0 / x1) * t_3) + t_7)) - t_5))))
    else if (x1 <= 7.8d0) then
        tmp = (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)) - x1
    else if (x1 <= 2d+153) then
        tmp = x1 + ((3.0d0 * (x2 * (-2.0d0))) + (x1 + (t_0 + (t_5 - (t_1 * (t_7 - ((t_6 - 3.0d0) * t_3)))))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	double t_3 = (x1 * 2.0) * 3.0;
	double t_4 = x1 * (x1 * 3.0);
	double t_5 = 3.0 * t_4;
	double t_6 = ((t_4 + (2.0 * x2)) - x1) / t_1;
	double t_7 = (x1 * x1) * (6.0 - (t_6 * 4.0));
	double tmp;
	if (x1 <= -4e+146) {
		tmp = t_2;
	} else if (x1 <= -5.6e+102) {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0));
	} else if (x1 <= -460000000000.0) {
		tmp = x1 + ((3.0 * ((x1 + ((2.0 * x2) - t_4)) / (-1.0 - (x1 * x1)))) + (x1 + (t_0 - ((t_1 * (((1.0 / x1) * t_3) + t_7)) - t_5))));
	} else if (x1 <= 7.8) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else if (x1 <= 2e+153) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (t_0 + (t_5 - (t_1 * (t_7 - ((t_6 - 3.0) * t_3)))))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = (x1 * x1) + 1.0
	t_2 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))))
	t_3 = (x1 * 2.0) * 3.0
	t_4 = x1 * (x1 * 3.0)
	t_5 = 3.0 * t_4
	t_6 = ((t_4 + (2.0 * x2)) - x1) / t_1
	t_7 = (x1 * x1) * (6.0 - (t_6 * 4.0))
	tmp = 0
	if x1 <= -4e+146:
		tmp = t_2
	elif x1 <= -5.6e+102:
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0))
	elif x1 <= -460000000000.0:
		tmp = x1 + ((3.0 * ((x1 + ((2.0 * x2) - t_4)) / (-1.0 - (x1 * x1)))) + (x1 + (t_0 - ((t_1 * (((1.0 / x1) * t_3) + t_7)) - t_5))))
	elif x1 <= 7.8:
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1
	elif x1 <= 2e+153:
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (t_0 + (t_5 - (t_1 * (t_7 - ((t_6 - 3.0) * t_3)))))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(x1 + Float64(x1 + Float64(Float64(x1 * -18.0) + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0))))))
	t_3 = Float64(Float64(x1 * 2.0) * 3.0)
	t_4 = Float64(x1 * Float64(x1 * 3.0))
	t_5 = Float64(3.0 * t_4)
	t_6 = Float64(Float64(Float64(t_4 + Float64(2.0 * x2)) - x1) / t_1)
	t_7 = Float64(Float64(x1 * x1) * Float64(6.0 - Float64(t_6 * 4.0)))
	tmp = 0.0
	if (x1 <= -4e+146)
		tmp = t_2;
	elseif (x1 <= -5.6e+102)
		tmp = Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(Float64(Float64(x2 * Float64(12.0 - Float64(x2 * 8.0))) + Float64(x1 * Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)) - Float64(Float64(x2 * 6.0) + Float64(x1 * Float64(Float64(x2 * Float64(24.0 + Float64(x2 * -8.0))) - 19.0)))))) - -1.0)));
	elseif (x1 <= -460000000000.0)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 + Float64(Float64(2.0 * x2) - t_4)) / Float64(-1.0 - Float64(x1 * x1)))) + Float64(x1 + Float64(t_0 - Float64(Float64(t_1 * Float64(Float64(Float64(1.0 / x1) * t_3) + t_7)) - t_5)))));
	elseif (x1 <= 7.8)
		tmp = Float64(Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0)) - x1);
	elseif (x1 <= 2e+153)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(x2 * -2.0)) + Float64(x1 + Float64(t_0 + Float64(t_5 - Float64(t_1 * Float64(t_7 - Float64(Float64(t_6 - 3.0) * t_3))))))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = (x1 * x1) + 1.0;
	t_2 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	t_3 = (x1 * 2.0) * 3.0;
	t_4 = x1 * (x1 * 3.0);
	t_5 = 3.0 * t_4;
	t_6 = ((t_4 + (2.0 * x2)) - x1) / t_1;
	t_7 = (x1 * x1) * (6.0 - (t_6 * 4.0));
	tmp = 0.0;
	if (x1 <= -4e+146)
		tmp = t_2;
	elseif (x1 <= -5.6e+102)
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0));
	elseif (x1 <= -460000000000.0)
		tmp = x1 + ((3.0 * ((x1 + ((2.0 * x2) - t_4)) / (-1.0 - (x1 * x1)))) + (x1 + (t_0 - ((t_1 * (((1.0 / x1) * t_3) + t_7)) - t_5))));
	elseif (x1 <= 7.8)
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	elseif (x1 <= 2e+153)
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (t_0 + (t_5 - (t_1 * (t_7 - ((t_6 - 3.0) * t_3)))))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(x1 + N[(N[(x1 * -18.0), $MachinePrecision] + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * 2.0), $MachinePrecision] * 3.0), $MachinePrecision]}, Block[{t$95$4 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(3.0 * t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$4 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(t$95$6 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4e+146], t$95$2, If[LessEqual[x1, -5.6e+102], N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(N[(N[(x2 * N[(12.0 - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - N[(N[(x2 * 6.0), $MachinePrecision] + N[(x1 * N[(N[(x2 * N[(24.0 + N[(x2 * -8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -460000000000.0], N[(x1 + N[(N[(3.0 * N[(N[(x1 + N[(N[(2.0 * x2), $MachinePrecision] - t$95$4), $MachinePrecision]), $MachinePrecision] / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$0 - N[(N[(t$95$1 * N[(N[(N[(1.0 / x1), $MachinePrecision] * t$95$3), $MachinePrecision] + t$95$7), $MachinePrecision]), $MachinePrecision] - t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7.8], N[(N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 2e+153], N[(x1 + N[(N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$0 + N[(t$95$5 - N[(t$95$1 * N[(t$95$7 - N[(N[(t$95$6 - 3.0), $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -3.99999999999999973e146 or 2e153 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x1 around 0 66.7%

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

   6. Taylor expanded in x2 around 0 98.3%

      \[\leadsto x1 + \color{blue}{\left(x1 + \left(-18 \cdot x1 + 3 \cdot \left(x1 \cdot \left(3 \cdot x1 - 1\right)\right)\right)\right)} \]

   if -3.99999999999999973e146 < x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x2 around 0 77.8%

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

   6. Taylor expanded in x1 around 0 100.0%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x1 \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + x1 \cdot \left(x2 \cdot \left(24 + -8 \cdot x2\right) - 19\right)\right)\right) + x2 \cdot \left(8 \cdot x2 - 12\right)\right) - 1\right)} \]

   if -5.60000000000000037e102 < x1 < -4.6e11

   1. Initial program 99.1%

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

   3. Taylor expanded in x1 around inf 80.9%

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

   4. Taylor expanded in x1 around inf 80.9%

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

   5. Taylor expanded in x1 around inf 80.9%

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

   if -4.6e11 < x1 < 7.79999999999999982

   1. Initial program 99.2%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in x1 around 0 85.3%

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

      1. fma-define 85.4%

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

      2. associate-*r* 85.4%

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

      3. fmm-def 85.4%

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

      4. *-commutative 85.4%

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

      5. *-commutative 85.4%

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

      6. metadata-eval 85.4%

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

   7. Simplified 85.4%

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

   8. Taylor expanded in x2 around 0 94.8%

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

   if 7.79999999999999982 < x1 < 2e153

   1. Initial program 96.2%

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

   3. Taylor expanded in x1 around inf 75.7%

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

   4. Taylor expanded in x1 around 0 75.7%

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

      1. *-commutative 96.3%

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

   6. Simplified 75.7%

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

   7. Taylor expanded in x1 around inf 75.8%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot 3\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{3}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+146}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x2 \cdot 8\right) + x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - \left(x2 \cdot 6 + x1 \cdot \left(x2 \cdot \left(24 + x2 \cdot -8\right) - 19\right)\right)\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq -460000000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\frac{1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4\right)\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7.8:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4\right) - \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 93.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := x1 + \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - t\_1\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(t\_2 \cdot \left(\frac{1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(t\_1 + 2 \cdot x2\right) - x1}{t\_2} \cdot 4\right)\right) - 3 \cdot t\_1\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -4 \cdot 10^{+146}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x2 \cdot 8\right) + x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - \left(x2 \cdot 6 + x1 \cdot \left(x2 \cdot \left(24 + x2 \cdot -8\right) - 19\right)\right)\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq -460000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x1 \leq 5.7 \cdot 10^{+29}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (+ x1 (+ (* x1 -18.0) (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3
         (+
          x1
          (+
           (* 3.0 (/ (+ x1 (- (* 2.0 x2) t_1)) (- -1.0 (* x1 x1))))
           (+
            x1
            (-
             (* x1 (* x1 x1))
             (-
              (*
               t_2
               (+
                (* (/ 1.0 x1) (* (* x1 2.0) 3.0))
                (*
                 (* x1 x1)
                 (- 6.0 (* (/ (- (+ t_1 (* 2.0 x2)) x1) t_2) 4.0)))))
              (* 3.0 t_1))))))))
   (if (<= x1 -4e+146)
     t_0
     (if (<= x1 -5.6e+102)
       (-
        (* x2 -6.0)
        (*
         x1
         (-
          (+
           (* x2 (- 12.0 (* x2 8.0)))
           (*
            x1
            (-
             (* 3.0 (- (* x2 -2.0) 3.0))
             (+ (* x2 6.0) (* x1 (- (* x2 (+ 24.0 (* x2 -8.0))) 19.0))))))
          -1.0)))
       (if (<= x1 -460000000000.0)
         t_3
         (if (<= x1 5.7e+29)
           (- (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0)) x1)
           (if (<= x1 2e+153) t_3 t_0)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = x1 + ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / (-1.0 - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) - ((t_2 * (((1.0 / x1) * ((x1 * 2.0) * 3.0)) + ((x1 * x1) * (6.0 - ((((t_1 + (2.0 * x2)) - x1) / t_2) * 4.0))))) - (3.0 * t_1)))));
	double tmp;
	if (x1 <= -4e+146) {
		tmp = t_0;
	} else if (x1 <= -5.6e+102) {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0));
	} else if (x1 <= -460000000000.0) {
		tmp = t_3;
	} else if (x1 <= 5.7e+29) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else if (x1 <= 2e+153) {
		tmp = t_3;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x1 + (x1 + ((x1 * (-18.0d0)) + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0))))))
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = x1 + ((3.0d0 * ((x1 + ((2.0d0 * x2) - t_1)) / ((-1.0d0) - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) - ((t_2 * (((1.0d0 / x1) * ((x1 * 2.0d0) * 3.0d0)) + ((x1 * x1) * (6.0d0 - ((((t_1 + (2.0d0 * x2)) - x1) / t_2) * 4.0d0))))) - (3.0d0 * t_1)))))
    if (x1 <= (-4d+146)) then
        tmp = t_0
    else if (x1 <= (-5.6d+102)) then
        tmp = (x2 * (-6.0d0)) - (x1 * (((x2 * (12.0d0 - (x2 * 8.0d0))) + (x1 * ((3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)) - ((x2 * 6.0d0) + (x1 * ((x2 * (24.0d0 + (x2 * (-8.0d0)))) - 19.0d0)))))) - (-1.0d0)))
    else if (x1 <= (-460000000000.0d0)) then
        tmp = t_3
    else if (x1 <= 5.7d+29) then
        tmp = (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)) - x1
    else if (x1 <= 2d+153) then
        tmp = t_3
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = x1 + ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / (-1.0 - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) - ((t_2 * (((1.0 / x1) * ((x1 * 2.0) * 3.0)) + ((x1 * x1) * (6.0 - ((((t_1 + (2.0 * x2)) - x1) / t_2) * 4.0))))) - (3.0 * t_1)))));
	double tmp;
	if (x1 <= -4e+146) {
		tmp = t_0;
	} else if (x1 <= -5.6e+102) {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0));
	} else if (x1 <= -460000000000.0) {
		tmp = t_3;
	} else if (x1 <= 5.7e+29) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else if (x1 <= 2e+153) {
		tmp = t_3;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))))
	t_1 = x1 * (x1 * 3.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = x1 + ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / (-1.0 - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) - ((t_2 * (((1.0 / x1) * ((x1 * 2.0) * 3.0)) + ((x1 * x1) * (6.0 - ((((t_1 + (2.0 * x2)) - x1) / t_2) * 4.0))))) - (3.0 * t_1)))))
	tmp = 0
	if x1 <= -4e+146:
		tmp = t_0
	elif x1 <= -5.6e+102:
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0))
	elif x1 <= -460000000000.0:
		tmp = t_3
	elif x1 <= 5.7e+29:
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1
	elif x1 <= 2e+153:
		tmp = t_3
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 + Float64(Float64(x1 * -18.0) + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0))))))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 + Float64(Float64(2.0 * x2) - t_1)) / Float64(-1.0 - Float64(x1 * x1)))) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) - Float64(Float64(t_2 * Float64(Float64(Float64(1.0 / x1) * Float64(Float64(x1 * 2.0) * 3.0)) + Float64(Float64(x1 * x1) * Float64(6.0 - Float64(Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_2) * 4.0))))) - Float64(3.0 * t_1))))))
	tmp = 0.0
	if (x1 <= -4e+146)
		tmp = t_0;
	elseif (x1 <= -5.6e+102)
		tmp = Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(Float64(Float64(x2 * Float64(12.0 - Float64(x2 * 8.0))) + Float64(x1 * Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)) - Float64(Float64(x2 * 6.0) + Float64(x1 * Float64(Float64(x2 * Float64(24.0 + Float64(x2 * -8.0))) - 19.0)))))) - -1.0)));
	elseif (x1 <= -460000000000.0)
		tmp = t_3;
	elseif (x1 <= 5.7e+29)
		tmp = Float64(Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0)) - x1);
	elseif (x1 <= 2e+153)
		tmp = t_3;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	t_1 = x1 * (x1 * 3.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = x1 + ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / (-1.0 - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) - ((t_2 * (((1.0 / x1) * ((x1 * 2.0) * 3.0)) + ((x1 * x1) * (6.0 - ((((t_1 + (2.0 * x2)) - x1) / t_2) * 4.0))))) - (3.0 * t_1)))));
	tmp = 0.0;
	if (x1 <= -4e+146)
		tmp = t_0;
	elseif (x1 <= -5.6e+102)
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0));
	elseif (x1 <= -460000000000.0)
		tmp = t_3;
	elseif (x1 <= 5.7e+29)
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	elseif (x1 <= 2e+153)
		tmp = t_3;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 + N[(N[(x1 * -18.0), $MachinePrecision] + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(N[(3.0 * N[(N[(x1 + N[(N[(2.0 * x2), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision] / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$2 * N[(N[(N[(1.0 / x1), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4e+146], t$95$0, If[LessEqual[x1, -5.6e+102], N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(N[(N[(x2 * N[(12.0 - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - N[(N[(x2 * 6.0), $MachinePrecision] + N[(x1 * N[(N[(x2 * N[(24.0 + N[(x2 * -8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -460000000000.0], t$95$3, If[LessEqual[x1, 5.7e+29], N[(N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 2e+153], t$95$3, t$95$0]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -3.99999999999999973e146 or 2e153 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x1 around 0 66.7%

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

   6. Taylor expanded in x2 around 0 98.3%

      \[\leadsto x1 + \color{blue}{\left(x1 + \left(-18 \cdot x1 + 3 \cdot \left(x1 \cdot \left(3 \cdot x1 - 1\right)\right)\right)\right)} \]

   if -3.99999999999999973e146 < x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x2 around 0 77.8%

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

   6. Taylor expanded in x1 around 0 100.0%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x1 \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + x1 \cdot \left(x2 \cdot \left(24 + -8 \cdot x2\right) - 19\right)\right)\right) + x2 \cdot \left(8 \cdot x2 - 12\right)\right) - 1\right)} \]

   if -5.60000000000000037e102 < x1 < -4.6e11 or 5.6999999999999999e29 < x1 < 2e153

   1. Initial program 97.0%

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

   3. Taylor expanded in x1 around inf 86.4%

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

   4. Taylor expanded in x1 around inf 86.4%

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

   5. Taylor expanded in x1 around inf 86.4%

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

   if -4.6e11 < x1 < 5.6999999999999999e29

   1. Initial program 99.2%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in x1 around 0 82.4%

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

      1. fma-define 82.5%

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

      2. associate-*r* 82.5%

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

      3. fmm-def 82.5%

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

      4. *-commutative 82.5%

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

      5. *-commutative 82.5%

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

      6. metadata-eval 82.5%

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

   7. Simplified 82.5%

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

   8. Taylor expanded in x2 around 0 91.3%

      \[\leadsto \color{blue}{-1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+146}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x2 \cdot 8\right) + x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - \left(x2 \cdot 6 + x1 \cdot \left(x2 \cdot \left(24 + x2 \cdot -8\right) - 19\right)\right)\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq -460000000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\frac{1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4\right)\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5.7 \cdot 10^{+29}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\frac{1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4\right)\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 91.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(3 - 2 \cdot x2\right)\\ t_1 := x1 + \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} + \left(x1 - x1 \cdot \left(x1 \cdot \left(3 + \left(x1 \cdot \left(3 + \left(\left(x1 \cdot \left(6 + \left(4 \cdot \left(2 \cdot x2 - 3\right) - x2 \cdot 8\right)\right) + t\_0\right) - 6 \cdot \left(3 + x2 \cdot -2\right)\right)\right) - x2 \cdot 8\right)\right) + t\_0\right)\right)\right)\\ t_2 := x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq -520000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq 22:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 6.0 (- 3.0 (* 2.0 x2))))
        (t_1
         (+
          x1
          (+
           (*
            3.0
            (/ (+ x1 (- (* 2.0 x2) (* x1 (* x1 3.0)))) (- -1.0 (* x1 x1))))
           (-
            x1
            (*
             x1
             (+
              (*
               x1
               (+
                3.0
                (-
                 (*
                  x1
                  (+
                   3.0
                   (-
                    (+
                     (* x1 (+ 6.0 (- (* 4.0 (- (* 2.0 x2) 3.0)) (* x2 8.0))))
                     t_0)
                    (* 6.0 (+ 3.0 (* x2 -2.0))))))
                 (* x2 8.0))))
              t_0))))))
        (t_2
         (+ x1 (+ x1 (+ (* x1 -18.0) (* 3.0 (* x1 (+ (* x1 3.0) -1.0))))))))
   (if (<= x1 -4.5e+153)
     t_2
     (if (<= x1 -520000000000.0)
       t_1
       (if (<= x1 22.0)
         (- (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0)) x1)
         (if (<= x1 4.5e+153) t_1 t_2))))))

C

double code(double x1, double x2) {
	double t_0 = 6.0 * (3.0 - (2.0 * x2));
	double t_1 = x1 + ((3.0 * ((x1 + ((2.0 * x2) - (x1 * (x1 * 3.0)))) / (-1.0 - (x1 * x1)))) + (x1 - (x1 * ((x1 * (3.0 + ((x1 * (3.0 + (((x1 * (6.0 + ((4.0 * ((2.0 * x2) - 3.0)) - (x2 * 8.0)))) + t_0) - (6.0 * (3.0 + (x2 * -2.0)))))) - (x2 * 8.0)))) + t_0))));
	double t_2 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = t_2;
	} else if (x1 <= -520000000000.0) {
		tmp = t_1;
	} else if (x1 <= 22.0) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else if (x1 <= 4.5e+153) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = 6.0d0 * (3.0d0 - (2.0d0 * x2))
    t_1 = x1 + ((3.0d0 * ((x1 + ((2.0d0 * x2) - (x1 * (x1 * 3.0d0)))) / ((-1.0d0) - (x1 * x1)))) + (x1 - (x1 * ((x1 * (3.0d0 + ((x1 * (3.0d0 + (((x1 * (6.0d0 + ((4.0d0 * ((2.0d0 * x2) - 3.0d0)) - (x2 * 8.0d0)))) + t_0) - (6.0d0 * (3.0d0 + (x2 * (-2.0d0))))))) - (x2 * 8.0d0)))) + t_0))))
    t_2 = x1 + (x1 + ((x1 * (-18.0d0)) + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0))))))
    if (x1 <= (-4.5d+153)) then
        tmp = t_2
    else if (x1 <= (-520000000000.0d0)) then
        tmp = t_1
    else if (x1 <= 22.0d0) then
        tmp = (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)) - x1
    else if (x1 <= 4.5d+153) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 6.0 * (3.0 - (2.0 * x2));
	double t_1 = x1 + ((3.0 * ((x1 + ((2.0 * x2) - (x1 * (x1 * 3.0)))) / (-1.0 - (x1 * x1)))) + (x1 - (x1 * ((x1 * (3.0 + ((x1 * (3.0 + (((x1 * (6.0 + ((4.0 * ((2.0 * x2) - 3.0)) - (x2 * 8.0)))) + t_0) - (6.0 * (3.0 + (x2 * -2.0)))))) - (x2 * 8.0)))) + t_0))));
	double t_2 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = t_2;
	} else if (x1 <= -520000000000.0) {
		tmp = t_1;
	} else if (x1 <= 22.0) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else if (x1 <= 4.5e+153) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 6.0 * (3.0 - (2.0 * x2))
	t_1 = x1 + ((3.0 * ((x1 + ((2.0 * x2) - (x1 * (x1 * 3.0)))) / (-1.0 - (x1 * x1)))) + (x1 - (x1 * ((x1 * (3.0 + ((x1 * (3.0 + (((x1 * (6.0 + ((4.0 * ((2.0 * x2) - 3.0)) - (x2 * 8.0)))) + t_0) - (6.0 * (3.0 + (x2 * -2.0)))))) - (x2 * 8.0)))) + t_0))))
	t_2 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))))
	tmp = 0
	if x1 <= -4.5e+153:
		tmp = t_2
	elif x1 <= -520000000000.0:
		tmp = t_1
	elif x1 <= 22.0:
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1
	elif x1 <= 4.5e+153:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(6.0 * Float64(3.0 - Float64(2.0 * x2)))
	t_1 = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 + Float64(Float64(2.0 * x2) - Float64(x1 * Float64(x1 * 3.0)))) / Float64(-1.0 - Float64(x1 * x1)))) + Float64(x1 - Float64(x1 * Float64(Float64(x1 * Float64(3.0 + Float64(Float64(x1 * Float64(3.0 + Float64(Float64(Float64(x1 * Float64(6.0 + Float64(Float64(4.0 * Float64(Float64(2.0 * x2) - 3.0)) - Float64(x2 * 8.0)))) + t_0) - Float64(6.0 * Float64(3.0 + Float64(x2 * -2.0)))))) - Float64(x2 * 8.0)))) + t_0)))))
	t_2 = Float64(x1 + Float64(x1 + Float64(Float64(x1 * -18.0) + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0))))))
	tmp = 0.0
	if (x1 <= -4.5e+153)
		tmp = t_2;
	elseif (x1 <= -520000000000.0)
		tmp = t_1;
	elseif (x1 <= 22.0)
		tmp = Float64(Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0)) - x1);
	elseif (x1 <= 4.5e+153)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 6.0 * (3.0 - (2.0 * x2));
	t_1 = x1 + ((3.0 * ((x1 + ((2.0 * x2) - (x1 * (x1 * 3.0)))) / (-1.0 - (x1 * x1)))) + (x1 - (x1 * ((x1 * (3.0 + ((x1 * (3.0 + (((x1 * (6.0 + ((4.0 * ((2.0 * x2) - 3.0)) - (x2 * 8.0)))) + t_0) - (6.0 * (3.0 + (x2 * -2.0)))))) - (x2 * 8.0)))) + t_0))));
	t_2 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	tmp = 0.0;
	if (x1 <= -4.5e+153)
		tmp = t_2;
	elseif (x1 <= -520000000000.0)
		tmp = t_1;
	elseif (x1 <= 22.0)
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	elseif (x1 <= 4.5e+153)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(6.0 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(N[(3.0 * N[(N[(x1 + N[(N[(2.0 * x2), $MachinePrecision] - N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 - N[(x1 * N[(N[(x1 * N[(3.0 + N[(N[(x1 * N[(3.0 + N[(N[(N[(x1 * N[(6.0 + N[(N[(4.0 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision] - N[(6.0 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(x1 + N[(N[(x1 * -18.0), $MachinePrecision] + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.5e+153], t$95$2, If[LessEqual[x1, -520000000000.0], t$95$1, If[LessEqual[x1, 22.0], N[(N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 4.5e+153], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4.5000000000000001e153 or 4.5000000000000001e153 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x1 around 0 67.9%

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

   6. Taylor expanded in x2 around 0 100.0%

      \[\leadsto x1 + \color{blue}{\left(x1 + \left(-18 \cdot x1 + 3 \cdot \left(x1 \cdot \left(3 \cdot x1 - 1\right)\right)\right)\right)} \]

   if -4.5000000000000001e153 < x1 < -5.2e11 or 22 < x1 < 4.5000000000000001e153

   1. Initial program 81.6%

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

   3. Taylor expanded in x1 around inf 65.2%

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

   4. Taylor expanded in x1 around inf 65.2%

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

   5. Taylor expanded in x1 around 0 67.3%

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

   if -5.2e11 < x1 < 22

   1. Initial program 99.2%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in x1 around 0 85.3%

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

      1. fma-define 85.4%

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

      2. associate-*r* 85.4%

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

      3. fmm-def 85.4%

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

      4. *-commutative 85.4%

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

      5. *-commutative 85.4%

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

      6. metadata-eval 85.4%

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

   7. Simplified 85.4%

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

   8. Taylor expanded in x2 around 0 94.8%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -520000000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} + \left(x1 - x1 \cdot \left(x1 \cdot \left(3 + \left(x1 \cdot \left(3 + \left(\left(x1 \cdot \left(6 + \left(4 \cdot \left(2 \cdot x2 - 3\right) - x2 \cdot 8\right)\right) + 6 \cdot \left(3 - 2 \cdot x2\right)\right) - 6 \cdot \left(3 + x2 \cdot -2\right)\right)\right) - x2 \cdot 8\right)\right) + 6 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 22:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} + \left(x1 - x1 \cdot \left(x1 \cdot \left(3 + \left(x1 \cdot \left(3 + \left(\left(x1 \cdot \left(6 + \left(4 \cdot \left(2 \cdot x2 - 3\right) - x2 \cdot 8\right)\right) + 6 \cdot \left(3 - 2 \cdot x2\right)\right) - 6 \cdot \left(3 + x2 \cdot -2\right)\right)\right) - x2 \cdot 8\right)\right) + 6 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 91.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(3 - 2 \cdot x2\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := -1 - x1 \cdot x1\\ t_3 := x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ t_4 := 3 \cdot \frac{x1 + \left(2 \cdot x2 - t\_1\right)}{t\_2}\\ \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x1 \leq -460000000000:\\ \;\;\;\;x1 + \left(t\_4 + \left(x1 - x1 \cdot \left(x1 \cdot \left(3 + \left(x1 \cdot \left(3 + \left(\left(x1 \cdot \left(6 + \left(4 \cdot \left(2 \cdot x2 - 3\right) - x2 \cdot 8\right)\right) + t\_0\right) - 6 \cdot \left(3 + x2 \cdot -2\right)\right)\right) - x2 \cdot 8\right)\right) + t\_0\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5.7 \cdot 10^{+29}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(t\_4 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(\left(x1 \cdot x1\right) \cdot 6 + \left(\frac{\left(t\_1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot 3\right)\right) \cdot t\_2 - 3 \cdot t\_1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 6.0 (- 3.0 (* 2.0 x2))))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (- -1.0 (* x1 x1)))
        (t_3 (+ x1 (+ x1 (+ (* x1 -18.0) (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))))
        (t_4 (* 3.0 (/ (+ x1 (- (* 2.0 x2) t_1)) t_2))))
   (if (<= x1 -4.5e+153)
     t_3
     (if (<= x1 -460000000000.0)
       (+
        x1
        (+
         t_4
         (-
          x1
          (*
           x1
           (+
            (*
             x1
             (+
              3.0
              (-
               (*
                x1
                (+
                 3.0
                 (-
                  (+
                   (* x1 (+ 6.0 (- (* 4.0 (- (* 2.0 x2) 3.0)) (* x2 8.0))))
                   t_0)
                  (* 6.0 (+ 3.0 (* x2 -2.0))))))
               (* x2 8.0))))
            t_0)))))
       (if (<= x1 5.7e+29)
         (- (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0)) x1)
         (if (<= x1 2e+153)
           (+
            x1
            (+
             t_4
             (+
              x1
              (-
               (* x1 (* x1 x1))
               (-
                (*
                 (+
                  (* (* x1 x1) 6.0)
                  (*
                   (- (/ (- (+ t_1 (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)
                   (* (* x1 2.0) 3.0)))
                 t_2)
                (* 3.0 t_1))))))
           t_3))))))

C

double code(double x1, double x2) {
	double t_0 = 6.0 * (3.0 - (2.0 * x2));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = -1.0 - (x1 * x1);
	double t_3 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	double t_4 = 3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_2);
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = t_3;
	} else if (x1 <= -460000000000.0) {
		tmp = x1 + (t_4 + (x1 - (x1 * ((x1 * (3.0 + ((x1 * (3.0 + (((x1 * (6.0 + ((4.0 * ((2.0 * x2) - 3.0)) - (x2 * 8.0)))) + t_0) - (6.0 * (3.0 + (x2 * -2.0)))))) - (x2 * 8.0)))) + t_0))));
	} else if (x1 <= 5.7e+29) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else if (x1 <= 2e+153) {
		tmp = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) - (((((x1 * x1) * 6.0) + (((((t_1 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0)) - 3.0) * ((x1 * 2.0) * 3.0))) * t_2) - (3.0 * t_1)))));
	} else {
		tmp = t_3;
	}
	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 = 6.0d0 * (3.0d0 - (2.0d0 * x2))
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (-1.0d0) - (x1 * x1)
    t_3 = x1 + (x1 + ((x1 * (-18.0d0)) + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0))))))
    t_4 = 3.0d0 * ((x1 + ((2.0d0 * x2) - t_1)) / t_2)
    if (x1 <= (-4.5d+153)) then
        tmp = t_3
    else if (x1 <= (-460000000000.0d0)) then
        tmp = x1 + (t_4 + (x1 - (x1 * ((x1 * (3.0d0 + ((x1 * (3.0d0 + (((x1 * (6.0d0 + ((4.0d0 * ((2.0d0 * x2) - 3.0d0)) - (x2 * 8.0d0)))) + t_0) - (6.0d0 * (3.0d0 + (x2 * (-2.0d0))))))) - (x2 * 8.0d0)))) + t_0))))
    else if (x1 <= 5.7d+29) then
        tmp = (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)) - x1
    else if (x1 <= 2d+153) then
        tmp = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) - (((((x1 * x1) * 6.0d0) + (((((t_1 + (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0)) - 3.0d0) * ((x1 * 2.0d0) * 3.0d0))) * t_2) - (3.0d0 * t_1)))))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 6.0 * (3.0 - (2.0 * x2));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = -1.0 - (x1 * x1);
	double t_3 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	double t_4 = 3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_2);
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = t_3;
	} else if (x1 <= -460000000000.0) {
		tmp = x1 + (t_4 + (x1 - (x1 * ((x1 * (3.0 + ((x1 * (3.0 + (((x1 * (6.0 + ((4.0 * ((2.0 * x2) - 3.0)) - (x2 * 8.0)))) + t_0) - (6.0 * (3.0 + (x2 * -2.0)))))) - (x2 * 8.0)))) + t_0))));
	} else if (x1 <= 5.7e+29) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else if (x1 <= 2e+153) {
		tmp = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) - (((((x1 * x1) * 6.0) + (((((t_1 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0)) - 3.0) * ((x1 * 2.0) * 3.0))) * t_2) - (3.0 * t_1)))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 6.0 * (3.0 - (2.0 * x2))
	t_1 = x1 * (x1 * 3.0)
	t_2 = -1.0 - (x1 * x1)
	t_3 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))))
	t_4 = 3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_2)
	tmp = 0
	if x1 <= -4.5e+153:
		tmp = t_3
	elif x1 <= -460000000000.0:
		tmp = x1 + (t_4 + (x1 - (x1 * ((x1 * (3.0 + ((x1 * (3.0 + (((x1 * (6.0 + ((4.0 * ((2.0 * x2) - 3.0)) - (x2 * 8.0)))) + t_0) - (6.0 * (3.0 + (x2 * -2.0)))))) - (x2 * 8.0)))) + t_0))))
	elif x1 <= 5.7e+29:
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1
	elif x1 <= 2e+153:
		tmp = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) - (((((x1 * x1) * 6.0) + (((((t_1 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0)) - 3.0) * ((x1 * 2.0) * 3.0))) * t_2) - (3.0 * t_1)))))
	else:
		tmp = t_3
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(6.0 * Float64(3.0 - Float64(2.0 * x2)))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(-1.0 - Float64(x1 * x1))
	t_3 = Float64(x1 + Float64(x1 + Float64(Float64(x1 * -18.0) + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0))))))
	t_4 = Float64(3.0 * Float64(Float64(x1 + Float64(Float64(2.0 * x2) - t_1)) / t_2))
	tmp = 0.0
	if (x1 <= -4.5e+153)
		tmp = t_3;
	elseif (x1 <= -460000000000.0)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 - Float64(x1 * Float64(Float64(x1 * Float64(3.0 + Float64(Float64(x1 * Float64(3.0 + Float64(Float64(Float64(x1 * Float64(6.0 + Float64(Float64(4.0 * Float64(Float64(2.0 * x2) - 3.0)) - Float64(x2 * 8.0)))) + t_0) - Float64(6.0 * Float64(3.0 + Float64(x2 * -2.0)))))) - Float64(x2 * 8.0)))) + t_0)))));
	elseif (x1 <= 5.7e+29)
		tmp = Float64(Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0)) - x1);
	elseif (x1 <= 2e+153)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) - Float64(Float64(Float64(Float64(Float64(x1 * x1) * 6.0) + Float64(Float64(Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0)) - 3.0) * Float64(Float64(x1 * 2.0) * 3.0))) * t_2) - Float64(3.0 * t_1))))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 6.0 * (3.0 - (2.0 * x2));
	t_1 = x1 * (x1 * 3.0);
	t_2 = -1.0 - (x1 * x1);
	t_3 = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	t_4 = 3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_2);
	tmp = 0.0;
	if (x1 <= -4.5e+153)
		tmp = t_3;
	elseif (x1 <= -460000000000.0)
		tmp = x1 + (t_4 + (x1 - (x1 * ((x1 * (3.0 + ((x1 * (3.0 + (((x1 * (6.0 + ((4.0 * ((2.0 * x2) - 3.0)) - (x2 * 8.0)))) + t_0) - (6.0 * (3.0 + (x2 * -2.0)))))) - (x2 * 8.0)))) + t_0))));
	elseif (x1 <= 5.7e+29)
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	elseif (x1 <= 2e+153)
		tmp = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) - (((((x1 * x1) * 6.0) + (((((t_1 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0)) - 3.0) * ((x1 * 2.0) * 3.0))) * t_2) - (3.0 * t_1)))));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(6.0 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(x1 + N[(N[(x1 * -18.0), $MachinePrecision] + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(N[(x1 + N[(N[(2.0 * x2), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.5e+153], t$95$3, If[LessEqual[x1, -460000000000.0], N[(x1 + N[(t$95$4 + N[(x1 - N[(x1 * N[(N[(x1 * N[(3.0 + N[(N[(x1 * N[(3.0 + N[(N[(N[(x1 * N[(6.0 + N[(N[(4.0 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision] - N[(6.0 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.7e+29], N[(N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 2e+153], N[(x1 + N[(t$95$4 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision] + N[(N[(N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] - N[(3.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.5000000000000001e153 or 2e153 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x1 around 0 67.9%

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

   6. Taylor expanded in x2 around 0 100.0%

      \[\leadsto x1 + \color{blue}{\left(x1 + \left(-18 \cdot x1 + 3 \cdot \left(x1 \cdot \left(3 \cdot x1 - 1\right)\right)\right)\right)} \]

   if -4.5000000000000001e153 < x1 < -4.6e11

   1. Initial program 66.1%

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

   3. Taylor expanded in x1 around inf 53.9%

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

   4. Taylor expanded in x1 around inf 53.9%

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

   5. Taylor expanded in x1 around 0 70.9%

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

   if -4.6e11 < x1 < 5.6999999999999999e29

   1. Initial program 99.2%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in x1 around 0 82.4%

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

      1. fma-define 82.5%

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

      2. associate-*r* 82.5%

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

      3. fmm-def 82.5%

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

      4. *-commutative 82.5%

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

      5. *-commutative 82.5%

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

      6. metadata-eval 82.5%

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

   7. Simplified 82.5%

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

   8. Taylor expanded in x2 around 0 91.3%

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

   if 5.6999999999999999e29 < x1 < 2e153

   1. Initial program 95.1%

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

   3. Taylor expanded in x1 around inf 91.2%

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

   4. Taylor expanded in x1 around inf 91.2%

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

   5. Taylor expanded in x1 around inf 82.5%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -460000000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} + \left(x1 - x1 \cdot \left(x1 \cdot \left(3 + \left(x1 \cdot \left(3 + \left(\left(x1 \cdot \left(6 + \left(4 \cdot \left(2 \cdot x2 - 3\right) - x2 \cdot 8\right)\right) + 6 \cdot \left(3 - 2 \cdot x2\right)\right) - 6 \cdot \left(3 + x2 \cdot -2\right)\right)\right) - x2 \cdot 8\right)\right) + 6 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5.7 \cdot 10^{+29}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(\left(x1 \cdot x1\right) \cdot 6 + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot 3\right)\right) \cdot \left(-1 - x1 \cdot x1\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 83.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot x2 - 3\\ t_1 := 6 \cdot t\_0\\ \mathbf{if}\;x1 \leq -4 \cdot 10^{+146}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.8 \cdot 10^{+71}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + x1 \cdot \left(t\_1 - x1 \cdot \left(12 - \left(x2 \cdot 6 - \left(x1 \cdot \left(6 - \left(6 \cdot \left(3 + x2 \cdot -2\right) + \left(t\_1 - x1 \cdot \left(6 + \left(3 \cdot t\_0 + \left(4 \cdot t\_0 - x2 \cdot 8\right)\right)\right)\right)\right)\right) - x2 \cdot 8\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.14 \cdot 10^{+30}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 - 6 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - \left(x1 + 3\right)\right) - -1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* 2.0 x2) 3.0)) (t_1 (* 6.0 t_0)))
   (if (<= x1 -4e+146)
     (+ x1 (+ x1 (+ (* x1 -18.0) (* 3.0 (* x1 (+ (* x1 3.0) -1.0))))))
     (if (<= x1 -5.8e+71)
       (+
        x1
        (+
         (* 3.0 (* x2 -2.0))
         (+
          x1
          (*
           x1
           (-
            t_1
            (*
             x1
             (-
              12.0
              (-
               (* x2 6.0)
               (-
                (*
                 x1
                 (-
                  6.0
                  (+
                   (* 6.0 (+ 3.0 (* x2 -2.0)))
                   (-
                    t_1
                    (*
                     x1
                     (+ 6.0 (+ (* 3.0 t_0) (- (* 4.0 t_0) (* x2 8.0)))))))))
                (* x2 8.0))))))))))
       (if (<= x1 1.14e+30)
         (- (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0)) x1)
         (+
          x1
          (+
           (- x1 (* 6.0 (* x1 (- 3.0 (* 2.0 x2)))))
           (*
            3.0
            (-
             (* x2 -2.0)
             (* x1 (- (* x1 (- (* x2 -2.0) (+ x1 3.0))) -1.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = 6.0 * t_0;
	double tmp;
	if (x1 <= -4e+146) {
		tmp = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	} else if (x1 <= -5.8e+71) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (x1 * (t_1 - (x1 * (12.0 - ((x2 * 6.0) - ((x1 * (6.0 - ((6.0 * (3.0 + (x2 * -2.0))) + (t_1 - (x1 * (6.0 + ((3.0 * t_0) + ((4.0 * t_0) - (x2 * 8.0))))))))) - (x2 * 8.0)))))))));
	} else if (x1 <= 1.14e+30) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else {
		tmp = x1 + ((x1 - (6.0 * (x1 * (3.0 - (2.0 * x2))))) + (3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - (x1 + 3.0))) - -1.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (2.0d0 * x2) - 3.0d0
    t_1 = 6.0d0 * t_0
    if (x1 <= (-4d+146)) then
        tmp = x1 + (x1 + ((x1 * (-18.0d0)) + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0))))))
    else if (x1 <= (-5.8d+71)) then
        tmp = x1 + ((3.0d0 * (x2 * (-2.0d0))) + (x1 + (x1 * (t_1 - (x1 * (12.0d0 - ((x2 * 6.0d0) - ((x1 * (6.0d0 - ((6.0d0 * (3.0d0 + (x2 * (-2.0d0)))) + (t_1 - (x1 * (6.0d0 + ((3.0d0 * t_0) + ((4.0d0 * t_0) - (x2 * 8.0d0))))))))) - (x2 * 8.0d0)))))))))
    else if (x1 <= 1.14d+30) then
        tmp = (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)) - x1
    else
        tmp = x1 + ((x1 - (6.0d0 * (x1 * (3.0d0 - (2.0d0 * x2))))) + (3.0d0 * ((x2 * (-2.0d0)) - (x1 * ((x1 * ((x2 * (-2.0d0)) - (x1 + 3.0d0))) - (-1.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = 6.0 * t_0;
	double tmp;
	if (x1 <= -4e+146) {
		tmp = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	} else if (x1 <= -5.8e+71) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (x1 * (t_1 - (x1 * (12.0 - ((x2 * 6.0) - ((x1 * (6.0 - ((6.0 * (3.0 + (x2 * -2.0))) + (t_1 - (x1 * (6.0 + ((3.0 * t_0) + ((4.0 * t_0) - (x2 * 8.0))))))))) - (x2 * 8.0)))))))));
	} else if (x1 <= 1.14e+30) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else {
		tmp = x1 + ((x1 - (6.0 * (x1 * (3.0 - (2.0 * x2))))) + (3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - (x1 + 3.0))) - -1.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (2.0 * x2) - 3.0
	t_1 = 6.0 * t_0
	tmp = 0
	if x1 <= -4e+146:
		tmp = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))))
	elif x1 <= -5.8e+71:
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (x1 * (t_1 - (x1 * (12.0 - ((x2 * 6.0) - ((x1 * (6.0 - ((6.0 * (3.0 + (x2 * -2.0))) + (t_1 - (x1 * (6.0 + ((3.0 * t_0) + ((4.0 * t_0) - (x2 * 8.0))))))))) - (x2 * 8.0)))))))))
	elif x1 <= 1.14e+30:
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1
	else:
		tmp = x1 + ((x1 - (6.0 * (x1 * (3.0 - (2.0 * x2))))) + (3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - (x1 + 3.0))) - -1.0)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(2.0 * x2) - 3.0)
	t_1 = Float64(6.0 * t_0)
	tmp = 0.0
	if (x1 <= -4e+146)
		tmp = Float64(x1 + Float64(x1 + Float64(Float64(x1 * -18.0) + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0))))));
	elseif (x1 <= -5.8e+71)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(x2 * -2.0)) + Float64(x1 + Float64(x1 * Float64(t_1 - Float64(x1 * Float64(12.0 - Float64(Float64(x2 * 6.0) - Float64(Float64(x1 * Float64(6.0 - Float64(Float64(6.0 * Float64(3.0 + Float64(x2 * -2.0))) + Float64(t_1 - Float64(x1 * Float64(6.0 + Float64(Float64(3.0 * t_0) + Float64(Float64(4.0 * t_0) - Float64(x2 * 8.0))))))))) - Float64(x2 * 8.0))))))))));
	elseif (x1 <= 1.14e+30)
		tmp = Float64(Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0)) - x1);
	else
		tmp = Float64(x1 + Float64(Float64(x1 - Float64(6.0 * Float64(x1 * Float64(3.0 - Float64(2.0 * x2))))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - Float64(x1 * Float64(Float64(x1 * Float64(Float64(x2 * -2.0) - Float64(x1 + 3.0))) - -1.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (2.0 * x2) - 3.0;
	t_1 = 6.0 * t_0;
	tmp = 0.0;
	if (x1 <= -4e+146)
		tmp = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	elseif (x1 <= -5.8e+71)
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (x1 * (t_1 - (x1 * (12.0 - ((x2 * 6.0) - ((x1 * (6.0 - ((6.0 * (3.0 + (x2 * -2.0))) + (t_1 - (x1 * (6.0 + ((3.0 * t_0) + ((4.0 * t_0) - (x2 * 8.0))))))))) - (x2 * 8.0)))))))));
	elseif (x1 <= 1.14e+30)
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	else
		tmp = x1 + ((x1 - (6.0 * (x1 * (3.0 - (2.0 * x2))))) + (3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - (x1 + 3.0))) - -1.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * t$95$0), $MachinePrecision]}, If[LessEqual[x1, -4e+146], N[(x1 + N[(x1 + N[(N[(x1 * -18.0), $MachinePrecision] + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5.8e+71], N[(x1 + N[(N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x1 * N[(t$95$1 - N[(x1 * N[(12.0 - N[(N[(x2 * 6.0), $MachinePrecision] - N[(N[(x1 * N[(6.0 - N[(N[(6.0 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 - N[(x1 * N[(6.0 + N[(N[(3.0 * t$95$0), $MachinePrecision] + N[(N[(4.0 * t$95$0), $MachinePrecision] - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.14e+30], N[(N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], N[(x1 + N[(N[(x1 - N[(6.0 * N[(x1 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - N[(x1 * N[(N[(x1 * N[(N[(x2 * -2.0), $MachinePrecision] - N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -3.99999999999999973e146

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x1 around 0 38.5%

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

   6. Taylor expanded in x2 around 0 96.5%

      \[\leadsto x1 + \color{blue}{\left(x1 + \left(-18 \cdot x1 + 3 \cdot \left(x1 \cdot \left(3 \cdot x1 - 1\right)\right)\right)\right)} \]

   if -3.99999999999999973e146 < x1 < -5.80000000000000014e71

   1. Initial program 49.9%

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

   3. Taylor expanded in x1 around inf 49.9%

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

   4. Taylor expanded in x1 around 0 49.9%

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

      1. *-commutative 49.9%

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

   6. Simplified 49.9%

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

   7. Taylor expanded in x1 around 0 72.7%

      \[\leadsto x1 + \left(\left(\color{blue}{x1 \cdot \left(6 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(\left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(6 \cdot \left(3 + -2 \cdot x2\right) + \left(6 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(\left(3 \cdot \left(3 - 2 \cdot x2\right) + \left(4 \cdot \left(3 - 2 \cdot x2\right) + 8 \cdot x2\right)\right) - 6\right)\right)\right) - 6\right)\right)\right) - 12\right)\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   if -5.80000000000000014e71 < x1 < 1.14e30

   1. Initial program 99.1%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in x1 around 0 78.4%

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

      1. fma-define 78.5%

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

      2. associate-*r* 78.5%

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

      3. fmm-def 78.5%

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

      4. *-commutative 78.5%

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

      5. *-commutative 78.5%

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

      6. metadata-eval 78.5%

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

   7. Simplified 78.5%

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

   8. Taylor expanded in x2 around 0 86.7%

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

   if 1.14e30 < x1

   1. Initial program 42.9%

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

   3. Taylor expanded in x1 around inf 41.1%

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

   4. Taylor expanded in x1 around 0 8.8%

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

   5. Taylor expanded in x1 around 0 78.1%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+146}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.8 \cdot 10^{+71}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + x1 \cdot \left(6 \cdot \left(2 \cdot x2 - 3\right) - x1 \cdot \left(12 - \left(x2 \cdot 6 - \left(x1 \cdot \left(6 - \left(6 \cdot \left(3 + x2 \cdot -2\right) + \left(6 \cdot \left(2 \cdot x2 - 3\right) - x1 \cdot \left(6 + \left(3 \cdot \left(2 \cdot x2 - 3\right) + \left(4 \cdot \left(2 \cdot x2 - 3\right) - x2 \cdot 8\right)\right)\right)\right)\right)\right) - x2 \cdot 8\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.14 \cdot 10^{+30}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 - 6 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - \left(x1 + 3\right)\right) - -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 82.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+146}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -6.2 \cdot 10^{+71}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x2 \cdot 8\right) + x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - \left(x2 \cdot 6 + x1 \cdot \left(x2 \cdot \left(24 + x2 \cdot -8\right) - 19\right)\right)\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq 1.14 \cdot 10^{+30}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 - 6 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - \left(x1 + 3\right)\right) - -1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -4e+146)
   (+ x1 (+ x1 (+ (* x1 -18.0) (* 3.0 (* x1 (+ (* x1 3.0) -1.0))))))
   (if (<= x1 -6.2e+71)
     (-
      (* x2 -6.0)
      (*
       x1
       (-
        (+
         (* x2 (- 12.0 (* x2 8.0)))
         (*
          x1
          (-
           (* 3.0 (- (* x2 -2.0) 3.0))
           (+ (* x2 6.0) (* x1 (- (* x2 (+ 24.0 (* x2 -8.0))) 19.0))))))
        -1.0)))
     (if (<= x1 1.14e+30)
       (- (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0)) x1)
       (+
        x1
        (+
         (- x1 (* 6.0 (* x1 (- 3.0 (* 2.0 x2)))))
         (*
          3.0
          (-
           (* x2 -2.0)
           (* x1 (- (* x1 (- (* x2 -2.0) (+ x1 3.0))) -1.0))))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -4e+146) {
		tmp = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	} else if (x1 <= -6.2e+71) {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0));
	} else if (x1 <= 1.14e+30) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else {
		tmp = x1 + ((x1 - (6.0 * (x1 * (3.0 - (2.0 * x2))))) + (3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - (x1 + 3.0))) - -1.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-4d+146)) then
        tmp = x1 + (x1 + ((x1 * (-18.0d0)) + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0))))))
    else if (x1 <= (-6.2d+71)) then
        tmp = (x2 * (-6.0d0)) - (x1 * (((x2 * (12.0d0 - (x2 * 8.0d0))) + (x1 * ((3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)) - ((x2 * 6.0d0) + (x1 * ((x2 * (24.0d0 + (x2 * (-8.0d0)))) - 19.0d0)))))) - (-1.0d0)))
    else if (x1 <= 1.14d+30) then
        tmp = (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)) - x1
    else
        tmp = x1 + ((x1 - (6.0d0 * (x1 * (3.0d0 - (2.0d0 * x2))))) + (3.0d0 * ((x2 * (-2.0d0)) - (x1 * ((x1 * ((x2 * (-2.0d0)) - (x1 + 3.0d0))) - (-1.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -4e+146) {
		tmp = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	} else if (x1 <= -6.2e+71) {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0));
	} else if (x1 <= 1.14e+30) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else {
		tmp = x1 + ((x1 - (6.0 * (x1 * (3.0 - (2.0 * x2))))) + (3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - (x1 + 3.0))) - -1.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -4e+146:
		tmp = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))))
	elif x1 <= -6.2e+71:
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0))
	elif x1 <= 1.14e+30:
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1
	else:
		tmp = x1 + ((x1 - (6.0 * (x1 * (3.0 - (2.0 * x2))))) + (3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - (x1 + 3.0))) - -1.0)))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -4e+146)
		tmp = Float64(x1 + Float64(x1 + Float64(Float64(x1 * -18.0) + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0))))));
	elseif (x1 <= -6.2e+71)
		tmp = Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(Float64(Float64(x2 * Float64(12.0 - Float64(x2 * 8.0))) + Float64(x1 * Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)) - Float64(Float64(x2 * 6.0) + Float64(x1 * Float64(Float64(x2 * Float64(24.0 + Float64(x2 * -8.0))) - 19.0)))))) - -1.0)));
	elseif (x1 <= 1.14e+30)
		tmp = Float64(Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0)) - x1);
	else
		tmp = Float64(x1 + Float64(Float64(x1 - Float64(6.0 * Float64(x1 * Float64(3.0 - Float64(2.0 * x2))))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - Float64(x1 * Float64(Float64(x1 * Float64(Float64(x2 * -2.0) - Float64(x1 + 3.0))) - -1.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -4e+146)
		tmp = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	elseif (x1 <= -6.2e+71)
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) + (x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - ((x2 * 6.0) + (x1 * ((x2 * (24.0 + (x2 * -8.0))) - 19.0)))))) - -1.0));
	elseif (x1 <= 1.14e+30)
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	else
		tmp = x1 + ((x1 - (6.0 * (x1 * (3.0 - (2.0 * x2))))) + (3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - (x1 + 3.0))) - -1.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -4e+146], N[(x1 + N[(x1 + N[(N[(x1 * -18.0), $MachinePrecision] + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -6.2e+71], N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(N[(N[(x2 * N[(12.0 - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - N[(N[(x2 * 6.0), $MachinePrecision] + N[(x1 * N[(N[(x2 * N[(24.0 + N[(x2 * -8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.14e+30], N[(N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], N[(x1 + N[(N[(x1 - N[(6.0 * N[(x1 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - N[(x1 * N[(N[(x1 * N[(N[(x2 * -2.0), $MachinePrecision] - N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -3.99999999999999973e146

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x1 around 0 38.5%

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

   6. Taylor expanded in x2 around 0 96.5%

      \[\leadsto x1 + \color{blue}{\left(x1 + \left(-18 \cdot x1 + 3 \cdot \left(x1 \cdot \left(3 \cdot x1 - 1\right)\right)\right)\right)} \]

   if -3.99999999999999973e146 < x1 < -6.20000000000000036e71

   1. Initial program 49.9%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x2 around 0 88.9%

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

   6. Taylor expanded in x1 around 0 64.4%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x1 \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + x1 \cdot \left(x2 \cdot \left(24 + -8 \cdot x2\right) - 19\right)\right)\right) + x2 \cdot \left(8 \cdot x2 - 12\right)\right) - 1\right)} \]

   if -6.20000000000000036e71 < x1 < 1.14e30

   1. Initial program 99.1%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in x1 around 0 78.4%

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

      1. fma-define 78.5%

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

      2. associate-*r* 78.5%

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

      3. fmm-def 78.5%

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

      4. *-commutative 78.5%

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

      5. *-commutative 78.5%

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

      6. metadata-eval 78.5%

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

   7. Simplified 78.5%

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

   8. Taylor expanded in x2 around 0 86.7%

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

   if 1.14e30 < x1

   1. Initial program 42.9%

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

   3. Taylor expanded in x1 around inf 41.1%

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

   4. Taylor expanded in x1 around 0 8.8%

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

   5. Taylor expanded in x1 around 0 78.1%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+146}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -6.2 \cdot 10^{+71}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x2 \cdot 8\right) + x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - \left(x2 \cdot 6 + x1 \cdot \left(x2 \cdot \left(24 + x2 \cdot -8\right) - 19\right)\right)\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq 1.14 \cdot 10^{+30}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 - 6 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - \left(x1 + 3\right)\right) - -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 80.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+128}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -6.2 \cdot 10^{+71}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 - x1 \cdot \left(x2 \cdot -2 - 3\right)\right)\right) + x2 \cdot \left(\frac{x1 \cdot -17}{x2} - x1 \cdot -12\right)\right)\\ \mathbf{elif}\;x1 \leq 8.2 \cdot 10^{+29}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 - 6 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - \left(x1 + 3\right)\right) - -1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -9.5e+128)
   (+ x1 (+ x1 (+ (* x1 -18.0) (* 3.0 (* x1 (+ (* x1 3.0) -1.0))))))
   (if (<= x1 -6.2e+71)
     (+
      x1
      (+
       (* 3.0 (+ (* x2 -2.0) (* x1 (- -1.0 (* x1 (- (* x2 -2.0) 3.0))))))
       (* x2 (- (/ (* x1 -17.0) x2) (* x1 -12.0)))))
     (if (<= x1 8.2e+29)
       (- (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0)) x1)
       (+
        x1
        (+
         (- x1 (* 6.0 (* x1 (- 3.0 (* 2.0 x2)))))
         (*
          3.0
          (-
           (* x2 -2.0)
           (* x1 (- (* x1 (- (* x2 -2.0) (+ x1 3.0))) -1.0))))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -9.5e+128) {
		tmp = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	} else if (x1 <= -6.2e+71) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) + (x1 * (-1.0 - (x1 * ((x2 * -2.0) - 3.0)))))) + (x2 * (((x1 * -17.0) / x2) - (x1 * -12.0))));
	} else if (x1 <= 8.2e+29) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else {
		tmp = x1 + ((x1 - (6.0 * (x1 * (3.0 - (2.0 * x2))))) + (3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - (x1 + 3.0))) - -1.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-9.5d+128)) then
        tmp = x1 + (x1 + ((x1 * (-18.0d0)) + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0))))))
    else if (x1 <= (-6.2d+71)) then
        tmp = x1 + ((3.0d0 * ((x2 * (-2.0d0)) + (x1 * ((-1.0d0) - (x1 * ((x2 * (-2.0d0)) - 3.0d0)))))) + (x2 * (((x1 * (-17.0d0)) / x2) - (x1 * (-12.0d0)))))
    else if (x1 <= 8.2d+29) then
        tmp = (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)) - x1
    else
        tmp = x1 + ((x1 - (6.0d0 * (x1 * (3.0d0 - (2.0d0 * x2))))) + (3.0d0 * ((x2 * (-2.0d0)) - (x1 * ((x1 * ((x2 * (-2.0d0)) - (x1 + 3.0d0))) - (-1.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -9.5e+128) {
		tmp = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	} else if (x1 <= -6.2e+71) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) + (x1 * (-1.0 - (x1 * ((x2 * -2.0) - 3.0)))))) + (x2 * (((x1 * -17.0) / x2) - (x1 * -12.0))));
	} else if (x1 <= 8.2e+29) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else {
		tmp = x1 + ((x1 - (6.0 * (x1 * (3.0 - (2.0 * x2))))) + (3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - (x1 + 3.0))) - -1.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -9.5e+128:
		tmp = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))))
	elif x1 <= -6.2e+71:
		tmp = x1 + ((3.0 * ((x2 * -2.0) + (x1 * (-1.0 - (x1 * ((x2 * -2.0) - 3.0)))))) + (x2 * (((x1 * -17.0) / x2) - (x1 * -12.0))))
	elif x1 <= 8.2e+29:
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1
	else:
		tmp = x1 + ((x1 - (6.0 * (x1 * (3.0 - (2.0 * x2))))) + (3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - (x1 + 3.0))) - -1.0)))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -9.5e+128)
		tmp = Float64(x1 + Float64(x1 + Float64(Float64(x1 * -18.0) + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0))))));
	elseif (x1 <= -6.2e+71)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) + Float64(x1 * Float64(-1.0 - Float64(x1 * Float64(Float64(x2 * -2.0) - 3.0)))))) + Float64(x2 * Float64(Float64(Float64(x1 * -17.0) / x2) - Float64(x1 * -12.0)))));
	elseif (x1 <= 8.2e+29)
		tmp = Float64(Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0)) - x1);
	else
		tmp = Float64(x1 + Float64(Float64(x1 - Float64(6.0 * Float64(x1 * Float64(3.0 - Float64(2.0 * x2))))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - Float64(x1 * Float64(Float64(x1 * Float64(Float64(x2 * -2.0) - Float64(x1 + 3.0))) - -1.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -9.5e+128)
		tmp = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	elseif (x1 <= -6.2e+71)
		tmp = x1 + ((3.0 * ((x2 * -2.0) + (x1 * (-1.0 - (x1 * ((x2 * -2.0) - 3.0)))))) + (x2 * (((x1 * -17.0) / x2) - (x1 * -12.0))));
	elseif (x1 <= 8.2e+29)
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	else
		tmp = x1 + ((x1 - (6.0 * (x1 * (3.0 - (2.0 * x2))))) + (3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - (x1 + 3.0))) - -1.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -9.5e+128], N[(x1 + N[(x1 + N[(N[(x1 * -18.0), $MachinePrecision] + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -6.2e+71], N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] + N[(x1 * N[(-1.0 - N[(x1 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(N[(x1 * -17.0), $MachinePrecision] / x2), $MachinePrecision] - N[(x1 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 8.2e+29], N[(N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], N[(x1 + N[(N[(x1 - N[(6.0 * N[(x1 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - N[(x1 * N[(N[(x1 * N[(N[(x2 * -2.0), $MachinePrecision] - N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -9.50000000000000014e128

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around 0 0.6%

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

   5. Taylor expanded in x1 around 0 34.8%

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

   6. Taylor expanded in x2 around 0 87.4%

      \[\leadsto x1 + \color{blue}{\left(x1 + \left(-18 \cdot x1 + 3 \cdot \left(x1 \cdot \left(3 \cdot x1 - 1\right)\right)\right)\right)} \]

   if -9.50000000000000014e128 < x1 < -6.20000000000000036e71

   1. Initial program 59.9%

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

   3. Taylor expanded in x1 around inf 59.9%

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

   4. Taylor expanded in x1 around 0 3.1%

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

   5. Taylor expanded in x1 around 0 23.9%

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

   6. Taylor expanded in x2 around -inf 42.9%

      \[\leadsto x1 + \left(\color{blue}{-1 \cdot \left(x2 \cdot \left(-12 \cdot x1 + -1 \cdot \frac{x1 + -18 \cdot x1}{x2}\right)\right)} + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]
   7. Step-by-step derivation

      1. mul-1-neg 42.9%

         \[\leadsto x1 + \left(\color{blue}{\left(-x2 \cdot \left(-12 \cdot x1 + -1 \cdot \frac{x1 + -18 \cdot x1}{x2}\right)\right)} + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]

      2. distribute-rgt-neg-in 42.9%

         \[\leadsto x1 + \left(\color{blue}{x2 \cdot \left(-\left(-12 \cdot x1 + -1 \cdot \frac{x1 + -18 \cdot x1}{x2}\right)\right)} + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]

      3. mul-1-neg 42.9%

         \[\leadsto x1 + \left(x2 \cdot \left(-\left(-12 \cdot x1 + \color{blue}{\left(-\frac{x1 + -18 \cdot x1}{x2}\right)}\right)\right) + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]

      4. unsub-neg 42.9%

         \[\leadsto x1 + \left(x2 \cdot \left(-\color{blue}{\left(-12 \cdot x1 - \frac{x1 + -18 \cdot x1}{x2}\right)}\right) + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]

      5. *-commutative 42.9%

         \[\leadsto x1 + \left(x2 \cdot \left(-\left(\color{blue}{x1 \cdot -12} - \frac{x1 + -18 \cdot x1}{x2}\right)\right) + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]

      6. distribute-rgt1-in 42.9%

         \[\leadsto x1 + \left(x2 \cdot \left(-\left(x1 \cdot -12 - \frac{\color{blue}{\left(-18 + 1\right) \cdot x1}}{x2}\right)\right) + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]

      7. metadata-eval 42.9%

         \[\leadsto x1 + \left(x2 \cdot \left(-\left(x1 \cdot -12 - \frac{\color{blue}{-17} \cdot x1}{x2}\right)\right) + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]

   8. Simplified 42.9%

      \[\leadsto x1 + \left(\color{blue}{x2 \cdot \left(-\left(x1 \cdot -12 - \frac{-17 \cdot x1}{x2}\right)\right)} + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]

   if -6.20000000000000036e71 < x1 < 8.2000000000000007e29

   1. Initial program 99.1%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in x1 around 0 78.4%

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

      1. fma-define 78.5%

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

      2. associate-*r* 78.5%

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

      3. fmm-def 78.5%

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

      4. *-commutative 78.5%

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

      5. *-commutative 78.5%

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

      6. metadata-eval 78.5%

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

   7. Simplified 78.5%

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

   8. Taylor expanded in x2 around 0 86.7%

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

   if 8.2000000000000007e29 < x1

   1. Initial program 42.9%

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

   3. Taylor expanded in x1 around inf 41.1%

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

   4. Taylor expanded in x1 around 0 8.8%

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

   5. Taylor expanded in x1 around 0 78.1%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+128}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -6.2 \cdot 10^{+71}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 - x1 \cdot \left(x2 \cdot -2 - 3\right)\right)\right) + x2 \cdot \left(\frac{x1 \cdot -17}{x2} - x1 \cdot -12\right)\right)\\ \mathbf{elif}\;x1 \leq 8.2 \cdot 10^{+29}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 - 6 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - \left(x1 + 3\right)\right) - -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 77.4% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 - x1 \cdot \left(x2 \cdot -2 - 3\right)\right)\right)\\ \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+128}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.4 \cdot 10^{+71}:\\ \;\;\;\;x1 + \left(t\_0 + x2 \cdot \left(\frac{x1 \cdot -17}{x2} - x1 \cdot -12\right)\right)\\ \mathbf{elif}\;x1 \leq 9.8 \cdot 10^{+29}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(t\_0 + x1 \cdot -17\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (* 3.0 (+ (* x2 -2.0) (* x1 (- -1.0 (* x1 (- (* x2 -2.0) 3.0))))))))
   (if (<= x1 -9.5e+128)
     (+ x1 (+ x1 (+ (* x1 -18.0) (* 3.0 (* x1 (+ (* x1 3.0) -1.0))))))
     (if (<= x1 -5.4e+71)
       (+ x1 (+ t_0 (* x2 (- (/ (* x1 -17.0) x2) (* x1 -12.0)))))
       (if (<= x1 9.8e+29)
         (- (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0)) x1)
         (+ x1 (+ t_0 (* x1 -17.0))))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 * ((x2 * -2.0) + (x1 * (-1.0 - (x1 * ((x2 * -2.0) - 3.0)))));
	double tmp;
	if (x1 <= -9.5e+128) {
		tmp = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	} else if (x1 <= -5.4e+71) {
		tmp = x1 + (t_0 + (x2 * (((x1 * -17.0) / x2) - (x1 * -12.0))));
	} else if (x1 <= 9.8e+29) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else {
		tmp = x1 + (t_0 + (x1 * -17.0));
	}
	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 = 3.0d0 * ((x2 * (-2.0d0)) + (x1 * ((-1.0d0) - (x1 * ((x2 * (-2.0d0)) - 3.0d0)))))
    if (x1 <= (-9.5d+128)) then
        tmp = x1 + (x1 + ((x1 * (-18.0d0)) + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0))))))
    else if (x1 <= (-5.4d+71)) then
        tmp = x1 + (t_0 + (x2 * (((x1 * (-17.0d0)) / x2) - (x1 * (-12.0d0)))))
    else if (x1 <= 9.8d+29) then
        tmp = (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)) - x1
    else
        tmp = x1 + (t_0 + (x1 * (-17.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 * ((x2 * -2.0) + (x1 * (-1.0 - (x1 * ((x2 * -2.0) - 3.0)))));
	double tmp;
	if (x1 <= -9.5e+128) {
		tmp = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	} else if (x1 <= -5.4e+71) {
		tmp = x1 + (t_0 + (x2 * (((x1 * -17.0) / x2) - (x1 * -12.0))));
	} else if (x1 <= 9.8e+29) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else {
		tmp = x1 + (t_0 + (x1 * -17.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 * ((x2 * -2.0) + (x1 * (-1.0 - (x1 * ((x2 * -2.0) - 3.0)))))
	tmp = 0
	if x1 <= -9.5e+128:
		tmp = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))))
	elif x1 <= -5.4e+71:
		tmp = x1 + (t_0 + (x2 * (((x1 * -17.0) / x2) - (x1 * -12.0))))
	elif x1 <= 9.8e+29:
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1
	else:
		tmp = x1 + (t_0 + (x1 * -17.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 * Float64(Float64(x2 * -2.0) + Float64(x1 * Float64(-1.0 - Float64(x1 * Float64(Float64(x2 * -2.0) - 3.0))))))
	tmp = 0.0
	if (x1 <= -9.5e+128)
		tmp = Float64(x1 + Float64(x1 + Float64(Float64(x1 * -18.0) + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0))))));
	elseif (x1 <= -5.4e+71)
		tmp = Float64(x1 + Float64(t_0 + Float64(x2 * Float64(Float64(Float64(x1 * -17.0) / x2) - Float64(x1 * -12.0)))));
	elseif (x1 <= 9.8e+29)
		tmp = Float64(Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0)) - x1);
	else
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 * -17.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 * ((x2 * -2.0) + (x1 * (-1.0 - (x1 * ((x2 * -2.0) - 3.0)))));
	tmp = 0.0;
	if (x1 <= -9.5e+128)
		tmp = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	elseif (x1 <= -5.4e+71)
		tmp = x1 + (t_0 + (x2 * (((x1 * -17.0) / x2) - (x1 * -12.0))));
	elseif (x1 <= 9.8e+29)
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	else
		tmp = x1 + (t_0 + (x1 * -17.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] + N[(x1 * N[(-1.0 - N[(x1 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -9.5e+128], N[(x1 + N[(x1 + N[(N[(x1 * -18.0), $MachinePrecision] + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5.4e+71], N[(x1 + N[(t$95$0 + N[(x2 * N[(N[(N[(x1 * -17.0), $MachinePrecision] / x2), $MachinePrecision] - N[(x1 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 9.8e+29], N[(N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], N[(x1 + N[(t$95$0 + N[(x1 * -17.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -9.50000000000000014e128

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around 0 0.6%

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

   5. Taylor expanded in x1 around 0 34.8%

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

   6. Taylor expanded in x2 around 0 87.4%

      \[\leadsto x1 + \color{blue}{\left(x1 + \left(-18 \cdot x1 + 3 \cdot \left(x1 \cdot \left(3 \cdot x1 - 1\right)\right)\right)\right)} \]

   if -9.50000000000000014e128 < x1 < -5.39999999999999993e71

   1. Initial program 59.9%

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

   3. Taylor expanded in x1 around inf 59.9%

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

   4. Taylor expanded in x1 around 0 3.1%

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

   5. Taylor expanded in x1 around 0 23.9%

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

   6. Taylor expanded in x2 around -inf 42.9%

      \[\leadsto x1 + \left(\color{blue}{-1 \cdot \left(x2 \cdot \left(-12 \cdot x1 + -1 \cdot \frac{x1 + -18 \cdot x1}{x2}\right)\right)} + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]
   7. Step-by-step derivation

      1. mul-1-neg 42.9%

         \[\leadsto x1 + \left(\color{blue}{\left(-x2 \cdot \left(-12 \cdot x1 + -1 \cdot \frac{x1 + -18 \cdot x1}{x2}\right)\right)} + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]

      2. distribute-rgt-neg-in 42.9%

         \[\leadsto x1 + \left(\color{blue}{x2 \cdot \left(-\left(-12 \cdot x1 + -1 \cdot \frac{x1 + -18 \cdot x1}{x2}\right)\right)} + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]

      3. mul-1-neg 42.9%

         \[\leadsto x1 + \left(x2 \cdot \left(-\left(-12 \cdot x1 + \color{blue}{\left(-\frac{x1 + -18 \cdot x1}{x2}\right)}\right)\right) + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]

      4. unsub-neg 42.9%

         \[\leadsto x1 + \left(x2 \cdot \left(-\color{blue}{\left(-12 \cdot x1 - \frac{x1 + -18 \cdot x1}{x2}\right)}\right) + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]

      5. *-commutative 42.9%

         \[\leadsto x1 + \left(x2 \cdot \left(-\left(\color{blue}{x1 \cdot -12} - \frac{x1 + -18 \cdot x1}{x2}\right)\right) + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]

      6. distribute-rgt1-in 42.9%

         \[\leadsto x1 + \left(x2 \cdot \left(-\left(x1 \cdot -12 - \frac{\color{blue}{\left(-18 + 1\right) \cdot x1}}{x2}\right)\right) + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]

      7. metadata-eval 42.9%

         \[\leadsto x1 + \left(x2 \cdot \left(-\left(x1 \cdot -12 - \frac{\color{blue}{-17} \cdot x1}{x2}\right)\right) + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]

   8. Simplified 42.9%

      \[\leadsto x1 + \left(\color{blue}{x2 \cdot \left(-\left(x1 \cdot -12 - \frac{-17 \cdot x1}{x2}\right)\right)} + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]

   if -5.39999999999999993e71 < x1 < 9.8000000000000003e29

   1. Initial program 99.1%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in x1 around 0 78.4%

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

      1. fma-define 78.5%

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

      2. associate-*r* 78.5%

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

      3. fmm-def 78.5%

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

      4. *-commutative 78.5%

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

      5. *-commutative 78.5%

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

      6. metadata-eval 78.5%

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

   7. Simplified 78.5%

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

   8. Taylor expanded in x2 around 0 86.7%

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

   if 9.8000000000000003e29 < x1

   1. Initial program 42.9%

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

   3. Taylor expanded in x1 around inf 41.1%

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

   4. Taylor expanded in x1 around 0 8.8%

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

   5. Taylor expanded in x1 around 0 66.7%

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

   6. Taylor expanded in x2 around 0 66.7%

      \[\leadsto x1 + \left(\color{blue}{\left(x1 + -18 \cdot x1\right)} + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]
   7. Step-by-step derivation

      1. distribute-rgt1-in 66.7%

         \[\leadsto x1 + \left(\color{blue}{\left(-18 + 1\right) \cdot x1} + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]

      2. metadata-eval 66.7%

         \[\leadsto x1 + \left(\color{blue}{-17} \cdot x1 + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]

   8. Simplified 66.7%

      \[\leadsto x1 + \left(\color{blue}{-17 \cdot x1} + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+128}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.4 \cdot 10^{+71}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 - x1 \cdot \left(x2 \cdot -2 - 3\right)\right)\right) + x2 \cdot \left(\frac{x1 \cdot -17}{x2} - x1 \cdot -12\right)\right)\\ \mathbf{elif}\;x1 \leq 9.8 \cdot 10^{+29}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 - x1 \cdot \left(x2 \cdot -2 - 3\right)\right)\right) + x1 \cdot -17\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 76.3% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -6.2 \cdot 10^{+71}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.14 \cdot 10^{+30}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 - x1 \cdot \left(x2 \cdot -2 - 3\right)\right)\right) + x1 \cdot -17\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -6.2e+71)
   (+ x1 (+ x1 (+ (* x1 -18.0) (* 3.0 (* x1 (+ (* x1 3.0) -1.0))))))
   (if (<= x1 1.14e+30)
     (- (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0)) x1)
     (+
      x1
      (+
       (* 3.0 (+ (* x2 -2.0) (* x1 (- -1.0 (* x1 (- (* x2 -2.0) 3.0))))))
       (* x1 -17.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -6.2e+71) {
		tmp = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	} else if (x1 <= 1.14e+30) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else {
		tmp = x1 + ((3.0 * ((x2 * -2.0) + (x1 * (-1.0 - (x1 * ((x2 * -2.0) - 3.0)))))) + (x1 * -17.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-6.2d+71)) then
        tmp = x1 + (x1 + ((x1 * (-18.0d0)) + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0))))))
    else if (x1 <= 1.14d+30) then
        tmp = (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)) - x1
    else
        tmp = x1 + ((3.0d0 * ((x2 * (-2.0d0)) + (x1 * ((-1.0d0) - (x1 * ((x2 * (-2.0d0)) - 3.0d0)))))) + (x1 * (-17.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -6.2e+71) {
		tmp = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	} else if (x1 <= 1.14e+30) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else {
		tmp = x1 + ((3.0 * ((x2 * -2.0) + (x1 * (-1.0 - (x1 * ((x2 * -2.0) - 3.0)))))) + (x1 * -17.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -6.2e+71:
		tmp = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))))
	elif x1 <= 1.14e+30:
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1
	else:
		tmp = x1 + ((3.0 * ((x2 * -2.0) + (x1 * (-1.0 - (x1 * ((x2 * -2.0) - 3.0)))))) + (x1 * -17.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -6.2e+71)
		tmp = Float64(x1 + Float64(x1 + Float64(Float64(x1 * -18.0) + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0))))));
	elseif (x1 <= 1.14e+30)
		tmp = Float64(Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0)) - x1);
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) + Float64(x1 * Float64(-1.0 - Float64(x1 * Float64(Float64(x2 * -2.0) - 3.0)))))) + Float64(x1 * -17.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -6.2e+71)
		tmp = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	elseif (x1 <= 1.14e+30)
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	else
		tmp = x1 + ((3.0 * ((x2 * -2.0) + (x1 * (-1.0 - (x1 * ((x2 * -2.0) - 3.0)))))) + (x1 * -17.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -6.2e+71], N[(x1 + N[(x1 + N[(N[(x1 * -18.0), $MachinePrecision] + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.14e+30], N[(N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] + N[(x1 * N[(-1.0 - N[(x1 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * -17.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -6.20000000000000036e71

   1. Initial program 20.4%

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

   3. Taylor expanded in x1 around inf 20.4%

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

   4. Taylor expanded in x1 around 0 1.4%

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

   5. Taylor expanded in x1 around 0 31.1%

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

   6. Taylor expanded in x2 around 0 59.5%

      \[\leadsto x1 + \color{blue}{\left(x1 + \left(-18 \cdot x1 + 3 \cdot \left(x1 \cdot \left(3 \cdot x1 - 1\right)\right)\right)\right)} \]

   if -6.20000000000000036e71 < x1 < 1.14e30

   1. Initial program 99.1%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in x1 around 0 78.4%

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

      1. fma-define 78.5%

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

      2. associate-*r* 78.5%

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

      3. fmm-def 78.5%

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

      4. *-commutative 78.5%

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

      5. *-commutative 78.5%

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

      6. metadata-eval 78.5%

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

   7. Simplified 78.5%

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

   8. Taylor expanded in x2 around 0 86.7%

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

   if 1.14e30 < x1

   1. Initial program 42.9%

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

   3. Taylor expanded in x1 around inf 41.1%

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

   4. Taylor expanded in x1 around 0 8.8%

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

   5. Taylor expanded in x1 around 0 66.7%

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

   6. Taylor expanded in x2 around 0 66.7%

      \[\leadsto x1 + \left(\color{blue}{\left(x1 + -18 \cdot x1\right)} + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]
   7. Step-by-step derivation

      1. distribute-rgt1-in 66.7%

         \[\leadsto x1 + \left(\color{blue}{\left(-18 + 1\right) \cdot x1} + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]

      2. metadata-eval 66.7%

         \[\leadsto x1 + \left(\color{blue}{-17} \cdot x1 + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]

   8. Simplified 66.7%

      \[\leadsto x1 + \left(\color{blue}{-17 \cdot x1} + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6.2 \cdot 10^{+71}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.14 \cdot 10^{+30}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 - x1 \cdot \left(x2 \cdot -2 - 3\right)\right)\right) + x1 \cdot -17\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 79.8% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -6.2 \cdot 10^{+71} \lor \neg \left(x1 \leq 4.5 \cdot 10^{+153}\right):\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -6.2e+71) (not (<= x1 4.5e+153)))
   (+ x1 (+ x1 (+ (* x1 -18.0) (* 3.0 (* x1 (+ (* x1 3.0) -1.0))))))
   (- (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0)) x1)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -6.2e+71) || !(x1 <= 4.5e+153)) {
		tmp = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	} else {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-6.2d+71)) .or. (.not. (x1 <= 4.5d+153))) then
        tmp = x1 + (x1 + ((x1 * (-18.0d0)) + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0))))))
    else
        tmp = (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)) - x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -6.2e+71) || !(x1 <= 4.5e+153)) {
		tmp = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	} else {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -6.2e+71) or not (x1 <= 4.5e+153):
		tmp = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))))
	else:
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -6.2e+71) || !(x1 <= 4.5e+153))
		tmp = Float64(x1 + Float64(x1 + Float64(Float64(x1 * -18.0) + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0))))));
	else
		tmp = Float64(Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0)) - x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -6.2e+71) || ~((x1 <= 4.5e+153)))
		tmp = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	else
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -6.2e+71], N[Not[LessEqual[x1, 4.5e+153]], $MachinePrecision]], N[(x1 + N[(x1 + N[(N[(x1 * -18.0), $MachinePrecision] + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -6.20000000000000036e71 or 4.5000000000000001e153 < x1

   1. Initial program 12.5%

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

   3. Taylor expanded in x1 around inf 12.5%

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

   4. Taylor expanded in x1 around 0 0.9%

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

   5. Taylor expanded in x1 around 0 55.1%

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

   6. Taylor expanded in x2 around 0 75.3%

      \[\leadsto x1 + \color{blue}{\left(x1 + \left(-18 \cdot x1 + 3 \cdot \left(x1 \cdot \left(3 \cdot x1 - 1\right)\right)\right)\right)} \]

   if -6.20000000000000036e71 < x1 < 4.5000000000000001e153

   1. Initial program 98.6%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in x1 around 0 71.6%

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

      1. fma-define 71.7%

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

      2. associate-*r* 71.7%

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

      3. fmm-def 71.7%

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

      4. *-commutative 71.7%

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

      5. *-commutative 71.7%

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

      6. metadata-eval 71.7%

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

   7. Simplified 71.7%

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

   8. Taylor expanded in x2 around 0 78.8%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6.2 \cdot 10^{+71} \lor \neg \left(x1 \leq 4.5 \cdot 10^{+153}\right):\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 73.9% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -6.2 \cdot 10^{+71} \lor \neg \left(x1 \leq 4.5 \cdot 10^{+153}\right):\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(x2 \cdot \left(12 - x2 \cdot 8\right) - -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -6.2e+71) (not (<= x1 4.5e+153)))
   (+ x1 (+ x1 (+ (* x1 -18.0) (* 3.0 (* x1 (+ (* x1 3.0) -1.0))))))
   (- (* x2 -6.0) (* x1 (- (* x2 (- 12.0 (* x2 8.0))) -1.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -6.2e+71) || !(x1 <= 4.5e+153)) {
		tmp = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	} else {
		tmp = (x2 * -6.0) - (x1 * ((x2 * (12.0 - (x2 * 8.0))) - -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-6.2d+71)) .or. (.not. (x1 <= 4.5d+153))) then
        tmp = x1 + (x1 + ((x1 * (-18.0d0)) + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0))))))
    else
        tmp = (x2 * (-6.0d0)) - (x1 * ((x2 * (12.0d0 - (x2 * 8.0d0))) - (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -6.2e+71) || !(x1 <= 4.5e+153)) {
		tmp = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	} else {
		tmp = (x2 * -6.0) - (x1 * ((x2 * (12.0 - (x2 * 8.0))) - -1.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -6.2e+71) or not (x1 <= 4.5e+153):
		tmp = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))))
	else:
		tmp = (x2 * -6.0) - (x1 * ((x2 * (12.0 - (x2 * 8.0))) - -1.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -6.2e+71) || !(x1 <= 4.5e+153))
		tmp = Float64(x1 + Float64(x1 + Float64(Float64(x1 * -18.0) + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0))))));
	else
		tmp = Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(Float64(x2 * Float64(12.0 - Float64(x2 * 8.0))) - -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -6.2e+71) || ~((x1 <= 4.5e+153)))
		tmp = x1 + (x1 + ((x1 * -18.0) + (3.0 * (x1 * ((x1 * 3.0) + -1.0)))));
	else
		tmp = (x2 * -6.0) - (x1 * ((x2 * (12.0 - (x2 * 8.0))) - -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -6.2e+71], N[Not[LessEqual[x1, 4.5e+153]], $MachinePrecision]], N[(x1 + N[(x1 + N[(N[(x1 * -18.0), $MachinePrecision] + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(N[(x2 * N[(12.0 - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -6.20000000000000036e71 or 4.5000000000000001e153 < x1

   1. Initial program 12.5%

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

   3. Taylor expanded in x1 around inf 12.5%

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

   4. Taylor expanded in x1 around 0 0.9%

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

   5. Taylor expanded in x1 around 0 55.1%

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

   6. Taylor expanded in x2 around 0 75.3%

      \[\leadsto x1 + \color{blue}{\left(x1 + \left(-18 \cdot x1 + 3 \cdot \left(x1 \cdot \left(3 \cdot x1 - 1\right)\right)\right)\right)} \]

   if -6.20000000000000036e71 < x1 < 4.5000000000000001e153

   1. Initial program 98.6%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in x2 around 0 98.5%

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

   6. Taylor expanded in x1 around 0 71.6%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6.2 \cdot 10^{+71} \lor \neg \left(x1 \leq 4.5 \cdot 10^{+153}\right):\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -18 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(x2 \cdot \left(12 - x2 \cdot 8\right) - -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 46.0% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -7.4 \cdot 10^{-90} \lor \neg \left(x1 \leq 9.2 \cdot 10^{-124}\right):\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot \left(x2 \cdot 8 - 12\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -7.4e-90) (not (<= x1 9.2e-124)))
   (* x1 (+ -1.0 (* x2 (- (* x2 8.0) 12.0))))
   (* x2 -6.0)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -7.4e-90) || !(x1 <= 9.2e-124)) {
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-7.4d-90)) .or. (.not. (x1 <= 9.2d-124))) then
        tmp = x1 * ((-1.0d0) + (x2 * ((x2 * 8.0d0) - 12.0d0)))
    else
        tmp = x2 * (-6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -7.4e-90) || !(x1 <= 9.2e-124)) {
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -7.4e-90) or not (x1 <= 9.2e-124):
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)))
	else:
		tmp = x2 * -6.0
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -7.4e-90) || !(x1 <= 9.2e-124))
		tmp = Float64(x1 * Float64(-1.0 + Float64(x2 * Float64(Float64(x2 * 8.0) - 12.0))));
	else
		tmp = Float64(x2 * -6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -7.4e-90) || ~((x1 <= 9.2e-124)))
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)));
	else
		tmp = x2 * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -7.4e-90], N[Not[LessEqual[x1, 9.2e-124]], $MachinePrecision]], N[(x1 * N[(-1.0 + N[(x2 * N[(N[(x2 * 8.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * -6.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -7.40000000000000035e-90 or 9.20000000000000048e-124 < x1

   1. Initial program 60.9%

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

   3. Simplified 67.1%

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

   5. Taylor expanded in x1 around 0 40.6%

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

      1. fma-define 40.6%

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

      2. associate-*r* 40.6%

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

      3. fmm-def 40.6%

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

      4. *-commutative 40.6%

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

      5. *-commutative 40.6%

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

      6. metadata-eval 40.6%

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

   7. Simplified 40.6%

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

   8. Taylor expanded in x2 around 0 40.6%

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

   9. Taylor expanded in x1 around inf 35.5%

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

   if -7.40000000000000035e-90 < x1 < 9.20000000000000048e-124

   1. Initial program 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x1 around 0 68.5%

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

      1. *-commutative 68.5%

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

   7. Simplified 68.5%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.4 \cdot 10^{-90} \lor \neg \left(x1 \leq 9.2 \cdot 10^{-124}\right):\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot \left(x2 \cdot 8 - 12\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 57.6% accurate, 6.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+71}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(x2 \cdot \left(12 - x2 \cdot 8\right) - -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -5.5e+71)
   (- (* x2 (- (* x1 -12.0) 6.0)) x1)
   (- (* x2 -6.0) (* x1 (- (* x2 (- 12.0 (* x2 8.0))) -1.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -5.5e+71) {
		tmp = (x2 * ((x1 * -12.0) - 6.0)) - x1;
	} else {
		tmp = (x2 * -6.0) - (x1 * ((x2 * (12.0 - (x2 * 8.0))) - -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-5.5d+71)) then
        tmp = (x2 * ((x1 * (-12.0d0)) - 6.0d0)) - x1
    else
        tmp = (x2 * (-6.0d0)) - (x1 * ((x2 * (12.0d0 - (x2 * 8.0d0))) - (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -5.5e+71) {
		tmp = (x2 * ((x1 * -12.0) - 6.0)) - x1;
	} else {
		tmp = (x2 * -6.0) - (x1 * ((x2 * (12.0 - (x2 * 8.0))) - -1.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -5.5e+71:
		tmp = (x2 * ((x1 * -12.0) - 6.0)) - x1
	else:
		tmp = (x2 * -6.0) - (x1 * ((x2 * (12.0 - (x2 * 8.0))) - -1.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -5.5e+71)
		tmp = Float64(Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)) - x1);
	else
		tmp = Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(Float64(x2 * Float64(12.0 - Float64(x2 * 8.0))) - -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -5.5e+71)
		tmp = (x2 * ((x1 * -12.0) - 6.0)) - x1;
	else
		tmp = (x2 * -6.0) - (x1 * ((x2 * (12.0 - (x2 * 8.0))) - -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -5.5e+71], N[(N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(N[(x2 * N[(12.0 - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -5.5e71

   1. Initial program 20.4%

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

   3. Simplified 43.2%

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

   5. Taylor expanded in x1 around 0 2.3%

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

      1. fma-define 2.3%

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

      2. associate-*r* 2.3%

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

      3. fmm-def 2.3%

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

      4. *-commutative 2.3%

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

      5. *-commutative 2.3%

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

      6. metadata-eval 2.3%

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

   7. Simplified 2.3%

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

   8. Taylor expanded in x2 around 0 18.9%

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

   if -5.5e71 < x1

   1. Initial program 85.6%

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

   3. Simplified 79.6%

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

   5. Taylor expanded in x2 around 0 85.5%

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

   6. Taylor expanded in x1 around 0 67.4%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+71}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(x2 \cdot \left(12 - x2 \cdot 8\right) - -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 47.2% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq 5.1 \cdot 10^{+104}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot \left(x2 \cdot 8 - 12\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 5.1e+104)
   (- (* x2 (- (* x1 -12.0) 6.0)) x1)
   (* x1 (+ -1.0 (* x2 (- (* x2 8.0) 12.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= 5.1e+104) {
		tmp = (x2 * ((x1 * -12.0) - 6.0)) - x1;
	} else {
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x2 <= 5.1d+104) then
        tmp = (x2 * ((x1 * (-12.0d0)) - 6.0d0)) - x1
    else
        tmp = x1 * ((-1.0d0) + (x2 * ((x2 * 8.0d0) - 12.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x2 <= 5.1e+104) {
		tmp = (x2 * ((x1 * -12.0) - 6.0)) - x1;
	} else {
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= 5.1e+104:
		tmp = (x2 * ((x1 * -12.0) - 6.0)) - x1
	else:
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= 5.1e+104)
		tmp = Float64(Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)) - x1);
	else
		tmp = Float64(x1 * Float64(-1.0 + Float64(x2 * Float64(Float64(x2 * 8.0) - 12.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= 5.1e+104)
		tmp = (x2 * ((x1 * -12.0) - 6.0)) - x1;
	else
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, 5.1e+104], N[(N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], N[(x1 * N[(-1.0 + N[(x2 * N[(N[(x2 * 8.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < 5.1000000000000002e104

   1. Initial program 75.7%

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

   3. Simplified 75.8%

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

   5. Taylor expanded in x1 around 0 53.2%

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

      1. fma-define 53.2%

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

      2. associate-*r* 53.2%

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

      3. fmm-def 53.2%

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

      4. *-commutative 53.2%

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

      5. *-commutative 53.2%

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

      6. metadata-eval 53.2%

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

   7. Simplified 53.2%

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

   8. Taylor expanded in x2 around 0 51.9%

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

   if 5.1000000000000002e104 < x2

   1. Initial program 68.6%

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

   3. Simplified 62.9%

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

   5. Taylor expanded in x1 around 0 69.4%

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

      1. fma-define 69.5%

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

      2. associate-*r* 69.5%

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

      3. fmm-def 69.5%

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

      4. *-commutative 69.5%

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

      5. *-commutative 69.5%

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

      6. metadata-eval 69.5%

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

   7. Simplified 69.5%

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

   8. Taylor expanded in x2 around 0 69.5%

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

   9. Taylor expanded in x1 around inf 63.5%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq 5.1 \cdot 10^{+104}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot \left(x2 \cdot 8 - 12\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 30.4% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -5.8 \cdot 10^{-148} \lor \neg \left(x2 \leq 5.5 \cdot 10^{-252}\right):\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -5.8e-148) (not (<= x2 5.5e-252))) (* x2 -6.0) (- x1)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -5.8e-148) || !(x2 <= 5.5e-252)) {
		tmp = x2 * -6.0;
	} else {
		tmp = -x1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-5.8d-148)) .or. (.not. (x2 <= 5.5d-252))) then
        tmp = x2 * (-6.0d0)
    else
        tmp = -x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -5.8e-148) || !(x2 <= 5.5e-252)) {
		tmp = x2 * -6.0;
	} else {
		tmp = -x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -5.8e-148) or not (x2 <= 5.5e-252):
		tmp = x2 * -6.0
	else:
		tmp = -x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -5.8e-148) || !(x2 <= 5.5e-252))
		tmp = Float64(x2 * -6.0);
	else
		tmp = Float64(-x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -5.8e-148) || ~((x2 <= 5.5e-252)))
		tmp = x2 * -6.0;
	else
		tmp = -x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -5.8e-148], N[Not[LessEqual[x2, 5.5e-252]], $MachinePrecision]], N[(x2 * -6.0), $MachinePrecision], (-x1)]

Derivation

1. Split input into 2 regimes

2. if x2 < -5.7999999999999997e-148 or 5.5e-252 < x2

   1. Initial program 73.0%

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

   3. Simplified 73.0%

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

   5. Taylor expanded in x1 around 0 32.1%

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

      1. *-commutative 32.1%

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

   7. Simplified 32.1%

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

   if -5.7999999999999997e-148 < x2 < 5.5e-252

   1. Initial program 81.5%

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

   3. Simplified 82.5%

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

   5. Taylor expanded in x1 around 0 58.1%

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

      1. fma-define 58.1%

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

      2. associate-*r* 58.1%

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

      3. fmm-def 58.1%

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

      4. *-commutative 58.1%

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

      5. *-commutative 58.1%

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

      6. metadata-eval 58.1%

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

   7. Simplified 58.1%

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

   8. Taylor expanded in x2 around 0 49.8%

      \[\leadsto \color{blue}{-1 \cdot x1} \]
   9. Step-by-step derivation

      1. mul-1-neg 49.8%

         \[\leadsto \color{blue}{-x1} \]

   10. Simplified 49.8%

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

4. Final simplification 34.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -5.8 \cdot 10^{-148} \lor \neg \left(x2 \leq 5.5 \cdot 10^{-252}\right):\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 14.2% accurate, 63.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x1, x2):
	return -x1

Julia

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

MATLAB

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

Wolfram

code[x1_, x2_] := (-x1)

Derivation

1. Initial program 74.4%

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

3. Simplified 73.3%

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

5. Taylor expanded in x1 around 0 56.2%

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

   1. fma-define 56.3%

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

   2. associate-*r* 56.3%

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

   3. fmm-def 56.3%

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

   4. *-commutative 56.3%

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

   5. *-commutative 56.3%

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

   6. metadata-eval 56.3%

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

7. Simplified 56.3%

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

8. Taylor expanded in x2 around 0 14.8%

   \[\leadsto \color{blue}{-1 \cdot x1} \]
9. Step-by-step derivation

   1. mul-1-neg 14.8%

      \[\leadsto \color{blue}{-x1} \]

10. Simplified 14.8%

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

Reproduce

herbie shell --seed 2024181 
(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))))))