Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.0% → 95.3%

Time: 1.4min

Alternatives: 20

Speedup: 1.3×

• 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: 70.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\mathsf{fma}\left(x1, x1 \cdot 3, x2 \cdot 2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\\ t_1 := 3 \cdot \left(x1 \cdot x1\right)\\ t_2 := \frac{t\_1 - \mathsf{fma}\left(x2, -2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\\ t_3 := \frac{t\_1 - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\\ t_4 := \frac{\mathsf{fma}\left(x2, -2, x1\right) - t\_1}{\mathsf{fma}\left(x1, x1, 1\right)}\\ \mathbf{if}\;x1 \leq -7.6 \cdot 10^{+153}:\\ \;\;\;\;6 + \left(x1 \cdot -17 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right) + -6 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq -2 \cdot 10^{-22}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, t\_3, t\_1 \cdot t\_2 + \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + x1 \cdot \left(2 \cdot \left(t\_4 \cdot \left(t\_4 - -3\right)\right) + x1 \cdot \mathsf{fma}\left(t\_2, 4, -6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{+104}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, t\_3, x1 + \mathsf{fma}\left(\mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot \mathsf{fma}\left(t\_0, 4, -6\right), \left(x1 \cdot \left(2 \cdot t\_0\right)\right) \cdot \left(-3 + t\_0\right)\right), \mathsf{fma}\left(t\_1, t\_0, {x1}^{3}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\right)\right) + 3 \cdot \mathsf{fma}\left(x2, -2, {x1}^{2} \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right) - x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (/ (- (fma x1 (* x1 3.0) (* x2 2.0)) x1) (fma x1 x1 1.0)))
        (t_1 (* 3.0 (* x1 x1)))
        (t_2 (/ (- t_1 (fma x2 -2.0 x1)) (fma x1 x1 1.0)))
        (t_3 (/ (- t_1 (fma 2.0 x2 x1)) (fma x1 x1 1.0)))
        (t_4 (/ (- (fma x2 -2.0 x1) t_1) (fma x1 x1 1.0))))
   (if (<= x1 -7.6e+153)
     (+
      6.0
      (+
       (* x1 -17.0)
       (+ (* 3.0 (* (pow x1 2.0) (- 3.0 (* x2 -2.0)))) (* -6.0 x2))))
     (if (<= x1 -2e-22)
       (+
        x1
        (fma
         3.0
         t_3
         (+
          (* t_1 t_2)
          (*
           (fma x1 x1 1.0)
           (+
            x1
            (*
             x1
             (+ (* 2.0 (* t_4 (- t_4 -3.0))) (* x1 (fma t_2 4.0 -6.0)))))))))
       (if (<= x1 1e+104)
         (+
          x1
          (fma
           3.0
           t_3
           (+
            x1
            (fma
             (fma x1 x1 1.0)
             (fma
              x1
              (* x1 (fma t_0 4.0 -6.0))
              (* (* x1 (* 2.0 t_0)) (+ -3.0 t_0)))
             (fma t_1 t_0 (pow x1 3.0))))))
         (+
          x1
          (+
           (- x1 (* 4.0 (* x1 (* x2 (- 3.0 (* x2 2.0))))))
           (*
            3.0
            (fma
             x2
             -2.0
             (- (* (pow x1 2.0) (+ x1 (+ 3.0 (* x2 2.0)))) x1))))))))))

C

double code(double x1, double x2) {
	double t_0 = (fma(x1, (x1 * 3.0), (x2 * 2.0)) - x1) / fma(x1, x1, 1.0);
	double t_1 = 3.0 * (x1 * x1);
	double t_2 = (t_1 - fma(x2, -2.0, x1)) / fma(x1, x1, 1.0);
	double t_3 = (t_1 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0);
	double t_4 = (fma(x2, -2.0, x1) - t_1) / fma(x1, x1, 1.0);
	double tmp;
	if (x1 <= -7.6e+153) {
		tmp = 6.0 + ((x1 * -17.0) + ((3.0 * (pow(x1, 2.0) * (3.0 - (x2 * -2.0)))) + (-6.0 * x2)));
	} else if (x1 <= -2e-22) {
		tmp = x1 + fma(3.0, t_3, ((t_1 * t_2) + (fma(x1, x1, 1.0) * (x1 + (x1 * ((2.0 * (t_4 * (t_4 - -3.0))) + (x1 * fma(t_2, 4.0, -6.0))))))));
	} else if (x1 <= 1e+104) {
		tmp = x1 + fma(3.0, t_3, (x1 + fma(fma(x1, x1, 1.0), fma(x1, (x1 * fma(t_0, 4.0, -6.0)), ((x1 * (2.0 * t_0)) * (-3.0 + t_0))), fma(t_1, t_0, pow(x1, 3.0)))));
	} else {
		tmp = x1 + ((x1 - (4.0 * (x1 * (x2 * (3.0 - (x2 * 2.0)))))) + (3.0 * fma(x2, -2.0, ((pow(x1, 2.0) * (x1 + (3.0 + (x2 * 2.0)))) - x1))));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(fma(x1, Float64(x1 * 3.0), Float64(x2 * 2.0)) - x1) / fma(x1, x1, 1.0))
	t_1 = Float64(3.0 * Float64(x1 * x1))
	t_2 = Float64(Float64(t_1 - fma(x2, -2.0, x1)) / fma(x1, x1, 1.0))
	t_3 = Float64(Float64(t_1 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0))
	t_4 = Float64(Float64(fma(x2, -2.0, x1) - t_1) / fma(x1, x1, 1.0))
	tmp = 0.0
	if (x1 <= -7.6e+153)
		tmp = Float64(6.0 + Float64(Float64(x1 * -17.0) + Float64(Float64(3.0 * Float64((x1 ^ 2.0) * Float64(3.0 - Float64(x2 * -2.0)))) + Float64(-6.0 * x2))));
	elseif (x1 <= -2e-22)
		tmp = Float64(x1 + fma(3.0, t_3, Float64(Float64(t_1 * t_2) + Float64(fma(x1, x1, 1.0) * Float64(x1 + Float64(x1 * Float64(Float64(2.0 * Float64(t_4 * Float64(t_4 - -3.0))) + Float64(x1 * fma(t_2, 4.0, -6.0)))))))));
	elseif (x1 <= 1e+104)
		tmp = Float64(x1 + fma(3.0, t_3, Float64(x1 + fma(fma(x1, x1, 1.0), fma(x1, Float64(x1 * fma(t_0, 4.0, -6.0)), Float64(Float64(x1 * Float64(2.0 * t_0)) * Float64(-3.0 + t_0))), fma(t_1, t_0, (x1 ^ 3.0))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 - Float64(4.0 * Float64(x1 * Float64(x2 * Float64(3.0 - Float64(x2 * 2.0)))))) + Float64(3.0 * fma(x2, -2.0, Float64(Float64((x1 ^ 2.0) * Float64(x1 + Float64(3.0 + Float64(x2 * 2.0)))) - x1)))));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision] + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 - N[(x2 * -2.0 + x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$1 - N[(2.0 * x2 + x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x2 * -2.0 + x1), $MachinePrecision] - t$95$1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -7.6e+153], N[(6.0 + N[(N[(x1 * -17.0), $MachinePrecision] + N[(N[(3.0 * N[(N[Power[x1, 2.0], $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-6.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2e-22], N[(x1 + N[(3.0 * t$95$3 + N[(N[(t$95$1 * t$95$2), $MachinePrecision] + N[(N[(x1 * x1 + 1.0), $MachinePrecision] * N[(x1 + N[(x1 * N[(N[(2.0 * N[(t$95$4 * N[(t$95$4 - -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(t$95$2 * 4.0 + -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1e+104], N[(x1 + N[(3.0 * t$95$3 + N[(x1 + N[(N[(x1 * x1 + 1.0), $MachinePrecision] * N[(x1 * N[(x1 * N[(t$95$0 * 4.0 + -6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(2.0 * t$95$0), $MachinePrecision]), $MachinePrecision] * N[(-3.0 + t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * t$95$0 + N[Power[x1, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 - N[(4.0 * N[(x1 * N[(x2 * N[(3.0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0 + N[(N[(N[Power[x1, 2.0], $MachinePrecision] * N[(x1 + N[(3.0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -7.59999999999999933e153

   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%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x2 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{\left(6 + -16 \cdot x1\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   6. Step-by-step derivation

      1. *-commutative 0.0%

         \[\leadsto x1 + \left(\left(\left(6 + \color{blue}{x1 \cdot -16}\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   7. Simplified 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{\left(6 + x1 \cdot -16\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   8. Taylor expanded in x1 around 0 69.6%

      \[\leadsto \color{blue}{6 + \left(-17 \cdot x1 + \left(-6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right)} \]

   if -7.59999999999999933e153 < x1 < -2.0000000000000001e-22

   1. Initial program 62.3%

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

   3. Simplified 99.6%

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

   if -2.0000000000000001e-22 < x1 < 1e104

   1. Initial program 98.7%

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

   3. Simplified 99.0%

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

   if 1e104 < x1

   1. Initial program 24.5%

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

   3. Taylor expanded in x1 around 0 1.3%

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

   4. Taylor expanded in x1 around 0 71.4%

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

      1. *-commutative 71.4%

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

      2. fma-def 73.5%

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

      3. +-commutative 73.5%

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

      4. mul-1-neg 73.5%

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

      5. unsub-neg 73.5%

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

      6. +-commutative 73.5%

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

      7. unpow3 73.5%

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

      8. unpow2 73.5%

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

      9. distribute-lft-out 95.9%

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

      10. cancel-sign-sub-inv 95.9%

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

      11. metadata-eval 95.9%

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

   6. Simplified 95.9%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.6 \cdot 10^{+153}:\\ \;\;\;\;6 + \left(x1 \cdot -17 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right) + -6 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq -2 \cdot 10^{-22}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{3 \cdot \left(x1 \cdot x1\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \left(3 \cdot \left(x1 \cdot x1\right)\right) \cdot \frac{3 \cdot \left(x1 \cdot x1\right) - \mathsf{fma}\left(x2, -2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} + \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + x1 \cdot \left(2 \cdot \left(\frac{\mathsf{fma}\left(x2, -2, x1\right) - 3 \cdot \left(x1 \cdot x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(\frac{\mathsf{fma}\left(x2, -2, x1\right) - 3 \cdot \left(x1 \cdot 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)\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{+104}:\\ \;\;\;\;x1 + \mathsf{fma}\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, x2 \cdot 2\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, x2 \cdot 2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right) \cdot \left(-3 + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, x2 \cdot 2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right), \mathsf{fma}\left(3 \cdot \left(x1 \cdot x1\right), \frac{\mathsf{fma}\left(x1, x1 \cdot 3, x2 \cdot 2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, {x1}^{3}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\right)\right) + 3 \cdot \mathsf{fma}\left(x2, -2, {x1}^{2} \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right) - x1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x2 \cdot 2 + t\_0\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{x1 - t\_1}{t\_2}\\ t_4 := 3 \cdot \left(x1 \cdot x1\right)\\ t_5 := \frac{t\_4 - \mathsf{fma}\left(x2, -2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\\ t_6 := \frac{\mathsf{fma}\left(x2, -2, x1\right) - t\_4}{\mathsf{fma}\left(x1, x1, 1\right)}\\ \mathbf{if}\;x1 \leq -7.6 \cdot 10^{+153}:\\ \;\;\;\;6 + \left(x1 \cdot -17 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right) + -6 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq -1.15 \cdot 10^{-175}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{t\_4 - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, t\_4 \cdot t\_5 + \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + x1 \cdot \left(2 \cdot \left(t\_6 \cdot \left(t\_6 - -3\right)\right) + x1 \cdot \mathsf{fma}\left(t\_5, 4, -6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+105}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(\left(\left(x1 \cdot 2\right) \cdot \frac{t\_1 - x1}{t\_2}\right) \cdot \left(3 + t\_3\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_3\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + 3 \cdot t\_0\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\right)\right) + 3 \cdot \mathsf{fma}\left(x2, -2, {x1}^{2} \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right) - x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x2 2.0) t_0))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (/ (- x1 t_1) t_2))
        (t_4 (* 3.0 (* x1 x1)))
        (t_5 (/ (- t_4 (fma x2 -2.0 x1)) (fma x1 x1 1.0)))
        (t_6 (/ (- (fma x2 -2.0 x1) t_4) (fma x1 x1 1.0))))
   (if (<= x1 -7.6e+153)
     (+
      6.0
      (+
       (* x1 -17.0)
       (+ (* 3.0 (* (pow x1 2.0) (- 3.0 (* x2 -2.0)))) (* -6.0 x2))))
     (if (<= x1 -1.15e-175)
       (+
        x1
        (fma
         3.0
         (/ (- t_4 (fma 2.0 x2 x1)) (fma x1 x1 1.0))
         (+
          (* t_4 t_5)
          (*
           (fma x1 x1 1.0)
           (+
            x1
            (*
             x1
             (+ (* 2.0 (* t_6 (- t_6 -3.0))) (* x1 (fma t_5 4.0 -6.0)))))))))
       (if (<= x1 2e+105)
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               (+
                (* (* (* x1 2.0) (/ (- t_1 x1) t_2)) (+ 3.0 t_3))
                (* (* x1 x1) (+ 6.0 (* 4.0 t_3))))
               (- -1.0 (* x1 x1)))
              (* 3.0 t_0))
             (* x1 (* x1 x1))))
           (* 3.0 (- (* x2 -2.0) x1))))
         (+
          x1
          (+
           (- x1 (* 4.0 (* x1 (* x2 (- 3.0 (* x2 2.0))))))
           (*
            3.0
            (fma
             x2
             -2.0
             (- (* (pow x1 2.0) (+ x1 (+ 3.0 (* x2 2.0)))) x1))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x2 * 2.0) + t_0;
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = (x1 - t_1) / t_2;
	double t_4 = 3.0 * (x1 * x1);
	double t_5 = (t_4 - fma(x2, -2.0, x1)) / fma(x1, x1, 1.0);
	double t_6 = (fma(x2, -2.0, x1) - t_4) / fma(x1, x1, 1.0);
	double tmp;
	if (x1 <= -7.6e+153) {
		tmp = 6.0 + ((x1 * -17.0) + ((3.0 * (pow(x1, 2.0) * (3.0 - (x2 * -2.0)))) + (-6.0 * x2)));
	} else if (x1 <= -1.15e-175) {
		tmp = x1 + fma(3.0, ((t_4 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), ((t_4 * t_5) + (fma(x1, x1, 1.0) * (x1 + (x1 * ((2.0 * (t_6 * (t_6 - -3.0))) + (x1 * fma(t_5, 4.0, -6.0))))))));
	} else if (x1 <= 2e+105) {
		tmp = x1 + ((x1 + (((((((x1 * 2.0) * ((t_1 - x1) / t_2)) * (3.0 + t_3)) + ((x1 * x1) * (6.0 + (4.0 * t_3)))) * (-1.0 - (x1 * x1))) + (3.0 * t_0)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = x1 + ((x1 - (4.0 * (x1 * (x2 * (3.0 - (x2 * 2.0)))))) + (3.0 * fma(x2, -2.0, ((pow(x1, 2.0) * (x1 + (3.0 + (x2 * 2.0)))) - x1))));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x2 * 2.0) + t_0)
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(x1 - t_1) / t_2)
	t_4 = Float64(3.0 * Float64(x1 * x1))
	t_5 = Float64(Float64(t_4 - fma(x2, -2.0, x1)) / fma(x1, x1, 1.0))
	t_6 = Float64(Float64(fma(x2, -2.0, x1) - t_4) / fma(x1, x1, 1.0))
	tmp = 0.0
	if (x1 <= -7.6e+153)
		tmp = Float64(6.0 + Float64(Float64(x1 * -17.0) + Float64(Float64(3.0 * Float64((x1 ^ 2.0) * Float64(3.0 - Float64(x2 * -2.0)))) + Float64(-6.0 * x2))));
	elseif (x1 <= -1.15e-175)
		tmp = Float64(x1 + fma(3.0, Float64(Float64(t_4 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), Float64(Float64(t_4 * t_5) + Float64(fma(x1, x1, 1.0) * Float64(x1 + Float64(x1 * Float64(Float64(2.0 * Float64(t_6 * Float64(t_6 - -3.0))) + Float64(x1 * fma(t_5, 4.0, -6.0)))))))));
	elseif (x1 <= 2e+105)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(t_1 - x1) / t_2)) * Float64(3.0 + t_3)) + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_3)))) * Float64(-1.0 - Float64(x1 * x1))) + Float64(3.0 * t_0)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 - Float64(4.0 * Float64(x1 * Float64(x2 * Float64(3.0 - Float64(x2 * 2.0)))))) + Float64(3.0 * fma(x2, -2.0, Float64(Float64((x1 ^ 2.0) * Float64(x1 + Float64(3.0 + Float64(x2 * 2.0)))) - x1)))));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 - t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$4 - N[(x2 * -2.0 + x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(x2 * -2.0 + x1), $MachinePrecision] - t$95$4), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -7.6e+153], N[(6.0 + N[(N[(x1 * -17.0), $MachinePrecision] + N[(N[(3.0 * N[(N[Power[x1, 2.0], $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-6.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.15e-175], N[(x1 + N[(3.0 * N[(N[(t$95$4 - N[(2.0 * x2 + x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$4 * t$95$5), $MachinePrecision] + N[(N[(x1 * x1 + 1.0), $MachinePrecision] * N[(x1 + N[(x1 * N[(N[(2.0 * N[(t$95$6 * N[(t$95$6 - -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(t$95$5 * 4.0 + -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+105], N[(x1 + N[(N[(x1 + N[(N[(N[(N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(t$95$1 - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] * N[(3.0 + t$95$3), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 - N[(4.0 * N[(x1 * N[(x2 * N[(3.0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0 + N[(N[(N[Power[x1, 2.0], $MachinePrecision] * N[(x1 + N[(3.0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -7.59999999999999933e153

   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%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x2 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{\left(6 + -16 \cdot x1\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   6. Step-by-step derivation

      1. *-commutative 0.0%

         \[\leadsto x1 + \left(\left(\left(6 + \color{blue}{x1 \cdot -16}\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   7. Simplified 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{\left(6 + x1 \cdot -16\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   8. Taylor expanded in x1 around 0 69.6%

      \[\leadsto \color{blue}{6 + \left(-17 \cdot x1 + \left(-6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right)} \]

   if -7.59999999999999933e153 < x1 < -1.15e-175

   1. Initial program 79.9%

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

   3. Simplified 99.8%

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

   if -1.15e-175 < x1 < 1.9999999999999999e105

   1. Initial program 98.5%

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

   3. Taylor expanded in x1 around inf 96.7%

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

   4. Taylor expanded in x1 around 0 98.5%

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

      1. mul-1-neg 98.5%

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

      2. unsub-neg 98.5%

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

      3. *-commutative 98.5%

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

   6. Simplified 98.5%

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

   if 1.9999999999999999e105 < x1

   1. Initial program 24.5%

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

   3. Taylor expanded in x1 around 0 1.3%

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

   4. Taylor expanded in x1 around 0 71.4%

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

      1. *-commutative 71.4%

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

      2. fma-def 73.5%

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

      3. +-commutative 73.5%

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

      4. mul-1-neg 73.5%

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

      5. unsub-neg 73.5%

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

      6. +-commutative 73.5%

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

      7. unpow3 73.5%

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

      8. unpow2 73.5%

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

      9. distribute-lft-out 95.9%

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

      10. cancel-sign-sub-inv 95.9%

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

      11. metadata-eval 95.9%

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

   6. Simplified 95.9%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.6 \cdot 10^{+153}:\\ \;\;\;\;6 + \left(x1 \cdot -17 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right) + -6 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq -1.15 \cdot 10^{-175}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{3 \cdot \left(x1 \cdot x1\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \left(3 \cdot \left(x1 \cdot x1\right)\right) \cdot \frac{3 \cdot \left(x1 \cdot x1\right) - \mathsf{fma}\left(x2, -2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} + \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + x1 \cdot \left(2 \cdot \left(\frac{\mathsf{fma}\left(x2, -2, x1\right) - 3 \cdot \left(x1 \cdot x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(\frac{\mathsf{fma}\left(x2, -2, x1\right) - 3 \cdot \left(x1 \cdot 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)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+105}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{x1 - \left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1}\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\right)\right) + 3 \cdot \mathsf{fma}\left(x2, -2, {x1}^{2} \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right) - x1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x2 \cdot 2 + t\_1\\ t_3 := x1 \cdot x1 + 1\\ t_4 := \frac{t\_2 - x1}{t\_3}\\ t_5 := \frac{x1 - t\_2}{t\_3}\\ t_6 := \left(\left(\left(x1 \cdot 2\right) \cdot t\_4\right) \cdot \left(3 + t\_5\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_5\right)\right) \cdot \left(-1 - x1 \cdot x1\right)\\ \mathbf{if}\;x1 + \left(3 \cdot \frac{\left(t\_1 - x2 \cdot 2\right) - x1}{t\_3} + \left(x1 + \left(t\_0 + \left(t\_6 + t\_1 \cdot t\_4\right)\right)\right)\right) \leq \infty:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t\_6 + 3 \cdot t\_1\right) + t\_0\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;6 + \left(x1 \cdot -17 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right) + -6 \cdot x2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ (* x2 2.0) t_1))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (/ (- t_2 x1) t_3))
        (t_5 (/ (- x1 t_2) t_3))
        (t_6
         (*
          (+
           (* (* (* x1 2.0) t_4) (+ 3.0 t_5))
           (* (* x1 x1) (+ 6.0 (* 4.0 t_5))))
          (- -1.0 (* x1 x1)))))
   (if (<=
        (+
         x1
         (+
          (* 3.0 (/ (- (- t_1 (* x2 2.0)) x1) t_3))
          (+ x1 (+ t_0 (+ t_6 (* t_1 t_4))))))
        INFINITY)
     (+ x1 (+ (+ x1 (+ (+ t_6 (* 3.0 t_1)) t_0)) (* 3.0 (- (* x2 -2.0) x1))))
     (+
      6.0
      (+
       (* x1 -17.0)
       (+ (* 3.0 (* (pow x1 2.0) (- 3.0 (* x2 -2.0)))) (* -6.0 x2)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x2 * 2.0) + t_1;
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = (t_2 - x1) / t_3;
	double t_5 = (x1 - t_2) / t_3;
	double t_6 = ((((x1 * 2.0) * t_4) * (3.0 + t_5)) + ((x1 * x1) * (6.0 + (4.0 * t_5)))) * (-1.0 - (x1 * x1));
	double tmp;
	if ((x1 + ((3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_3)) + (x1 + (t_0 + (t_6 + (t_1 * t_4)))))) <= ((double) INFINITY)) {
		tmp = x1 + ((x1 + ((t_6 + (3.0 * t_1)) + t_0)) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = 6.0 + ((x1 * -17.0) + ((3.0 * (pow(x1, 2.0) * (3.0 - (x2 * -2.0)))) + (-6.0 * x2)));
	}
	return tmp;
}

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x2 * 2.0) + t_1;
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = (t_2 - x1) / t_3;
	double t_5 = (x1 - t_2) / t_3;
	double t_6 = ((((x1 * 2.0) * t_4) * (3.0 + t_5)) + ((x1 * x1) * (6.0 + (4.0 * t_5)))) * (-1.0 - (x1 * x1));
	double tmp;
	if ((x1 + ((3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_3)) + (x1 + (t_0 + (t_6 + (t_1 * t_4)))))) <= Double.POSITIVE_INFINITY) {
		tmp = x1 + ((x1 + ((t_6 + (3.0 * t_1)) + t_0)) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = 6.0 + ((x1 * -17.0) + ((3.0 * (Math.pow(x1, 2.0) * (3.0 - (x2 * -2.0)))) + (-6.0 * x2)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = x1 * (x1 * 3.0)
	t_2 = (x2 * 2.0) + t_1
	t_3 = (x1 * x1) + 1.0
	t_4 = (t_2 - x1) / t_3
	t_5 = (x1 - t_2) / t_3
	t_6 = ((((x1 * 2.0) * t_4) * (3.0 + t_5)) + ((x1 * x1) * (6.0 + (4.0 * t_5)))) * (-1.0 - (x1 * x1))
	tmp = 0
	if (x1 + ((3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_3)) + (x1 + (t_0 + (t_6 + (t_1 * t_4)))))) <= math.inf:
		tmp = x1 + ((x1 + ((t_6 + (3.0 * t_1)) + t_0)) + (3.0 * ((x2 * -2.0) - x1)))
	else:
		tmp = 6.0 + ((x1 * -17.0) + ((3.0 * (math.pow(x1, 2.0) * (3.0 - (x2 * -2.0)))) + (-6.0 * x2)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(x2 * 2.0) + t_1)
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(Float64(t_2 - x1) / t_3)
	t_5 = Float64(Float64(x1 - t_2) / t_3)
	t_6 = Float64(Float64(Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(3.0 + t_5)) + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_5)))) * Float64(-1.0 - Float64(x1 * x1)))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(x2 * 2.0)) - x1) / t_3)) + Float64(x1 + Float64(t_0 + Float64(t_6 + Float64(t_1 * t_4)))))) <= Inf)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(t_6 + Float64(3.0 * t_1)) + t_0)) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	else
		tmp = Float64(6.0 + Float64(Float64(x1 * -17.0) + Float64(Float64(3.0 * Float64((x1 ^ 2.0) * Float64(3.0 - Float64(x2 * -2.0)))) + Float64(-6.0 * x2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = x1 * (x1 * 3.0);
	t_2 = (x2 * 2.0) + t_1;
	t_3 = (x1 * x1) + 1.0;
	t_4 = (t_2 - x1) / t_3;
	t_5 = (x1 - t_2) / t_3;
	t_6 = ((((x1 * 2.0) * t_4) * (3.0 + t_5)) + ((x1 * x1) * (6.0 + (4.0 * t_5)))) * (-1.0 - (x1 * x1));
	tmp = 0.0;
	if ((x1 + ((3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_3)) + (x1 + (t_0 + (t_6 + (t_1 * t_4)))))) <= Inf)
		tmp = x1 + ((x1 + ((t_6 + (3.0 * t_1)) + t_0)) + (3.0 * ((x2 * -2.0) - x1)));
	else
		tmp = 6.0 + ((x1 * -17.0) + ((3.0 * ((x1 ^ 2.0) * (3.0 - (x2 * -2.0)))) + (-6.0 * x2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x2 * 2.0), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$2 - x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 - t$95$2), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(3.0 + t$95$5), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$1 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$0 + N[(t$95$6 + N[(t$95$1 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(N[(x1 + N[(N[(t$95$6 + N[(3.0 * t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 + N[(N[(x1 * -17.0), $MachinePrecision] + N[(N[(3.0 * N[(N[Power[x1, 2.0], $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-6.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around inf 98.2%

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

   4. Taylor expanded in x1 around 0 99.5%

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

      1. mul-1-neg 99.5%

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

      2. unsub-neg 99.5%

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

      3. *-commutative 99.5%

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

   6. Simplified 99.5%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around 0 1.8%

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

   5. Taylor expanded in x2 around 0 0.9%

      \[\leadsto x1 + \left(\left(\color{blue}{\left(6 + -16 \cdot x1\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   6. Step-by-step derivation

      1. *-commutative 0.9%

         \[\leadsto x1 + \left(\left(\left(6 + \color{blue}{x1 \cdot -16}\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   7. Simplified 0.9%

      \[\leadsto x1 + \left(\left(\color{blue}{\left(6 + x1 \cdot -16\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   8. Taylor expanded in x1 around 0 60.6%

      \[\leadsto \color{blue}{6 + \left(-17 \cdot x1 + \left(-6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{x1 - \left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1}\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1}\right)\right)\right)\right) \leq \infty:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{x1 - \left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1}\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;6 + \left(x1 \cdot -17 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right) + -6 \cdot x2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x2 \cdot 2 + t\_0\\ t_3 := \frac{x1 - t\_2}{t\_1}\\ \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;6 + \left(x1 \cdot -17 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right) + -6 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq -1 \cdot 10^{+108}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 3 \cdot \frac{\left(t\_0 - x2 \cdot 2\right) - x1}{t\_1}\right)\\ \mathbf{elif}\;x1 \leq 3 \cdot 10^{+106}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(\left(\left(x1 \cdot 2\right) \cdot \frac{t\_2 - x1}{t\_1}\right) \cdot \left(3 + t\_3\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_3\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + 3 \cdot t\_0\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\right)\right) + 3 \cdot \mathsf{fma}\left(x2, -2, {x1}^{2} \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right) - x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (+ (* x2 2.0) t_0))
        (t_3 (/ (- x1 t_2) t_1)))
   (if (<= x1 -1.35e+154)
     (+
      6.0
      (+
       (* x1 -17.0)
       (+ (* 3.0 (* (pow x1 2.0) (- 3.0 (* x2 -2.0)))) (* -6.0 x2))))
     (if (<= x1 -1e+108)
       (+
        x1
        (+
         (+ x1 (* 6.0 (pow x1 4.0)))
         (* 3.0 (/ (- (- t_0 (* x2 2.0)) x1) t_1))))
       (if (<= x1 3e+106)
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               (+
                (* (* (* x1 2.0) (/ (- t_2 x1) t_1)) (+ 3.0 t_3))
                (* (* x1 x1) (+ 6.0 (* 4.0 t_3))))
               (- -1.0 (* x1 x1)))
              (* 3.0 t_0))
             (* x1 (* x1 x1))))
           (* 3.0 (- (* x2 -2.0) x1))))
         (+
          x1
          (+
           (- x1 (* 4.0 (* x1 (* x2 (- 3.0 (* x2 2.0))))))
           (*
            3.0
            (fma
             x2
             -2.0
             (- (* (pow x1 2.0) (+ x1 (+ 3.0 (* x2 2.0)))) x1))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = (x2 * 2.0) + t_0;
	double t_3 = (x1 - t_2) / t_1;
	double tmp;
	if (x1 <= -1.35e+154) {
		tmp = 6.0 + ((x1 * -17.0) + ((3.0 * (pow(x1, 2.0) * (3.0 - (x2 * -2.0)))) + (-6.0 * x2)));
	} else if (x1 <= -1e+108) {
		tmp = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + (3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)));
	} else if (x1 <= 3e+106) {
		tmp = x1 + ((x1 + (((((((x1 * 2.0) * ((t_2 - x1) / t_1)) * (3.0 + t_3)) + ((x1 * x1) * (6.0 + (4.0 * t_3)))) * (-1.0 - (x1 * x1))) + (3.0 * t_0)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = x1 + ((x1 - (4.0 * (x1 * (x2 * (3.0 - (x2 * 2.0)))))) + (3.0 * fma(x2, -2.0, ((pow(x1, 2.0) * (x1 + (3.0 + (x2 * 2.0)))) - x1))));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(x2 * 2.0) + t_0)
	t_3 = Float64(Float64(x1 - t_2) / t_1)
	tmp = 0.0
	if (x1 <= -1.35e+154)
		tmp = Float64(6.0 + Float64(Float64(x1 * -17.0) + Float64(Float64(3.0 * Float64((x1 ^ 2.0) * Float64(3.0 - Float64(x2 * -2.0)))) + Float64(-6.0 * x2))));
	elseif (x1 <= -1e+108)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_1))));
	elseif (x1 <= 3e+106)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(t_2 - x1) / t_1)) * Float64(3.0 + t_3)) + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_3)))) * Float64(-1.0 - Float64(x1 * x1))) + Float64(3.0 * t_0)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 - Float64(4.0 * Float64(x1 * Float64(x2 * Float64(3.0 - Float64(x2 * 2.0)))))) + Float64(3.0 * fma(x2, -2.0, Float64(Float64((x1 ^ 2.0) * Float64(x1 + Float64(3.0 + Float64(x2 * 2.0)))) - x1)))));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 - t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[x1, -1.35e+154], N[(6.0 + N[(N[(x1 * -17.0), $MachinePrecision] + N[(N[(3.0 * N[(N[Power[x1, 2.0], $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-6.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1e+108], N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3e+106], N[(x1 + N[(N[(x1 + N[(N[(N[(N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(t$95$2 - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] * N[(3.0 + t$95$3), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 - N[(4.0 * N[(x1 * N[(x2 * N[(3.0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0 + N[(N[(N[Power[x1, 2.0], $MachinePrecision] * N[(x1 + N[(3.0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.35000000000000003e154

   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%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x2 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{\left(6 + -16 \cdot x1\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   6. Step-by-step derivation

      1. *-commutative 0.0%

         \[\leadsto x1 + \left(\left(\left(6 + \color{blue}{x1 \cdot -16}\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   7. Simplified 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{\left(6 + x1 \cdot -16\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   8. Taylor expanded in x1 around 0 69.6%

      \[\leadsto \color{blue}{6 + \left(-17 \cdot x1 + \left(-6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right)} \]

   if -1.35000000000000003e154 < x1 < -1e108

   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 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -1e108 < x1 < 3.0000000000000001e106

   1. Initial program 98.8%

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

   3. Taylor expanded in x1 around inf 97.5%

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

   4. Taylor expanded in x1 around 0 98.9%

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

      1. mul-1-neg 98.9%

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

      2. unsub-neg 98.9%

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

      3. *-commutative 98.9%

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

   6. Simplified 98.9%

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

   if 3.0000000000000001e106 < x1

   1. Initial program 24.5%

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

   3. Taylor expanded in x1 around 0 1.3%

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

   4. Taylor expanded in x1 around 0 71.4%

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

      1. *-commutative 71.4%

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

      2. fma-def 73.5%

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

      3. +-commutative 73.5%

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

      4. mul-1-neg 73.5%

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

      5. unsub-neg 73.5%

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

      6. +-commutative 73.5%

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

      7. unpow3 73.5%

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

      8. unpow2 73.5%

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

      9. distribute-lft-out 95.9%

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

      10. cancel-sign-sub-inv 95.9%

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

      11. metadata-eval 95.9%

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

   6. Simplified 95.9%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;6 + \left(x1 \cdot -17 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right) + -6 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq -1 \cdot 10^{+108}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 3 \cdot 10^{+106}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{x1 - \left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1}\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\right)\right) + 3 \cdot \mathsf{fma}\left(x2, -2, {x1}^{2} \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right) - x1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := 3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right)\\ t_3 := x2 \cdot 2 + t\_0\\ t_4 := \frac{x1 - t\_3}{t\_1}\\ t_5 := 4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\\ t_6 := x1 \cdot \left(-1 - t\_5\right)\\ \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;6 + \left(x1 \cdot -17 + \left(t\_2 + -6 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 3 \cdot \frac{\left(t\_0 - x2 \cdot 2\right) - x1}{t\_1}\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(\left(\left(x1 \cdot 2\right) \cdot \frac{t\_3 - x1}{t\_1}\right) \cdot \left(3 + t\_4\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_4\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + 3 \cdot t\_0\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 1.6 \cdot 10^{+181}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;x1 \leq 4.8 \cdot 10^{+203}:\\ \;\;\;\;\frac{{x1}^{2} - {\left(-6 \cdot x2\right)}^{2}}{x1 - -6 \cdot x2}\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{+233}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(-6 \cdot x2 + \left(t\_2 - x1 \cdot \left(2 + t\_5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* 3.0 (* (pow x1 2.0) (- 3.0 (* x2 -2.0)))))
        (t_3 (+ (* x2 2.0) t_0))
        (t_4 (/ (- x1 t_3) t_1))
        (t_5 (* 4.0 (* x2 (- 3.0 (* x2 2.0)))))
        (t_6 (* x1 (- -1.0 t_5))))
   (if (<= x1 -1.35e+154)
     (+ 6.0 (+ (* x1 -17.0) (+ t_2 (* -6.0 x2))))
     (if (<= x1 -5.5e+102)
       (+
        x1
        (+
         (+ x1 (* 6.0 (pow x1 4.0)))
         (* 3.0 (/ (- (- t_0 (* x2 2.0)) x1) t_1))))
       (if (<= x1 1.35e+154)
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               (+
                (* (* (* x1 2.0) (/ (- t_3 x1) t_1)) (+ 3.0 t_4))
                (* (* x1 x1) (+ 6.0 (* 4.0 t_4))))
               (- -1.0 (* x1 x1)))
              (* 3.0 t_0))
             (* x1 (* x1 x1))))
           (* 3.0 (- (* x2 -2.0) x1))))
         (if (<= x1 1.6e+181)
           t_6
           (if (<= x1 4.8e+203)
             (/ (- (pow x1 2.0) (pow (* -6.0 x2) 2.0)) (- x1 (* -6.0 x2)))
             (if (<= x1 3.9e+233)
               t_6
               (+ x1 (+ (* -6.0 x2) (- t_2 (* x1 (+ 2.0 t_5)))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = 3.0 * (pow(x1, 2.0) * (3.0 - (x2 * -2.0)));
	double t_3 = (x2 * 2.0) + t_0;
	double t_4 = (x1 - t_3) / t_1;
	double t_5 = 4.0 * (x2 * (3.0 - (x2 * 2.0)));
	double t_6 = x1 * (-1.0 - t_5);
	double tmp;
	if (x1 <= -1.35e+154) {
		tmp = 6.0 + ((x1 * -17.0) + (t_2 + (-6.0 * x2)));
	} else if (x1 <= -5.5e+102) {
		tmp = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + (3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 + (((((((x1 * 2.0) * ((t_3 - x1) / t_1)) * (3.0 + t_4)) + ((x1 * x1) * (6.0 + (4.0 * t_4)))) * (-1.0 - (x1 * x1))) + (3.0 * t_0)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else if (x1 <= 1.6e+181) {
		tmp = t_6;
	} else if (x1 <= 4.8e+203) {
		tmp = (pow(x1, 2.0) - pow((-6.0 * x2), 2.0)) / (x1 - (-6.0 * x2));
	} else if (x1 <= 3.9e+233) {
		tmp = t_6;
	} else {
		tmp = x1 + ((-6.0 * x2) + (t_2 - (x1 * (2.0 + 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) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = 3.0d0 * ((x1 ** 2.0d0) * (3.0d0 - (x2 * (-2.0d0))))
    t_3 = (x2 * 2.0d0) + t_0
    t_4 = (x1 - t_3) / t_1
    t_5 = 4.0d0 * (x2 * (3.0d0 - (x2 * 2.0d0)))
    t_6 = x1 * ((-1.0d0) - t_5)
    if (x1 <= (-1.35d+154)) then
        tmp = 6.0d0 + ((x1 * (-17.0d0)) + (t_2 + ((-6.0d0) * x2)))
    else if (x1 <= (-5.5d+102)) then
        tmp = x1 + ((x1 + (6.0d0 * (x1 ** 4.0d0))) + (3.0d0 * (((t_0 - (x2 * 2.0d0)) - x1) / t_1)))
    else if (x1 <= 1.35d+154) then
        tmp = x1 + ((x1 + (((((((x1 * 2.0d0) * ((t_3 - x1) / t_1)) * (3.0d0 + t_4)) + ((x1 * x1) * (6.0d0 + (4.0d0 * t_4)))) * ((-1.0d0) - (x1 * x1))) + (3.0d0 * t_0)) + (x1 * (x1 * x1)))) + (3.0d0 * ((x2 * (-2.0d0)) - x1)))
    else if (x1 <= 1.6d+181) then
        tmp = t_6
    else if (x1 <= 4.8d+203) then
        tmp = ((x1 ** 2.0d0) - (((-6.0d0) * x2) ** 2.0d0)) / (x1 - ((-6.0d0) * x2))
    else if (x1 <= 3.9d+233) then
        tmp = t_6
    else
        tmp = x1 + (((-6.0d0) * x2) + (t_2 - (x1 * (2.0d0 + t_5))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = 3.0 * (Math.pow(x1, 2.0) * (3.0 - (x2 * -2.0)));
	double t_3 = (x2 * 2.0) + t_0;
	double t_4 = (x1 - t_3) / t_1;
	double t_5 = 4.0 * (x2 * (3.0 - (x2 * 2.0)));
	double t_6 = x1 * (-1.0 - t_5);
	double tmp;
	if (x1 <= -1.35e+154) {
		tmp = 6.0 + ((x1 * -17.0) + (t_2 + (-6.0 * x2)));
	} else if (x1 <= -5.5e+102) {
		tmp = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + (3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 + (((((((x1 * 2.0) * ((t_3 - x1) / t_1)) * (3.0 + t_4)) + ((x1 * x1) * (6.0 + (4.0 * t_4)))) * (-1.0 - (x1 * x1))) + (3.0 * t_0)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else if (x1 <= 1.6e+181) {
		tmp = t_6;
	} else if (x1 <= 4.8e+203) {
		tmp = (Math.pow(x1, 2.0) - Math.pow((-6.0 * x2), 2.0)) / (x1 - (-6.0 * x2));
	} else if (x1 <= 3.9e+233) {
		tmp = t_6;
	} else {
		tmp = x1 + ((-6.0 * x2) + (t_2 - (x1 * (2.0 + t_5))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = 3.0 * (math.pow(x1, 2.0) * (3.0 - (x2 * -2.0)))
	t_3 = (x2 * 2.0) + t_0
	t_4 = (x1 - t_3) / t_1
	t_5 = 4.0 * (x2 * (3.0 - (x2 * 2.0)))
	t_6 = x1 * (-1.0 - t_5)
	tmp = 0
	if x1 <= -1.35e+154:
		tmp = 6.0 + ((x1 * -17.0) + (t_2 + (-6.0 * x2)))
	elif x1 <= -5.5e+102:
		tmp = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + (3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)))
	elif x1 <= 1.35e+154:
		tmp = x1 + ((x1 + (((((((x1 * 2.0) * ((t_3 - x1) / t_1)) * (3.0 + t_4)) + ((x1 * x1) * (6.0 + (4.0 * t_4)))) * (-1.0 - (x1 * x1))) + (3.0 * t_0)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)))
	elif x1 <= 1.6e+181:
		tmp = t_6
	elif x1 <= 4.8e+203:
		tmp = (math.pow(x1, 2.0) - math.pow((-6.0 * x2), 2.0)) / (x1 - (-6.0 * x2))
	elif x1 <= 3.9e+233:
		tmp = t_6
	else:
		tmp = x1 + ((-6.0 * x2) + (t_2 - (x1 * (2.0 + t_5))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(3.0 * Float64((x1 ^ 2.0) * Float64(3.0 - Float64(x2 * -2.0))))
	t_3 = Float64(Float64(x2 * 2.0) + t_0)
	t_4 = Float64(Float64(x1 - t_3) / t_1)
	t_5 = Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(x2 * 2.0))))
	t_6 = Float64(x1 * Float64(-1.0 - t_5))
	tmp = 0.0
	if (x1 <= -1.35e+154)
		tmp = Float64(6.0 + Float64(Float64(x1 * -17.0) + Float64(t_2 + Float64(-6.0 * x2))));
	elseif (x1 <= -5.5e+102)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_1))));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(t_3 - x1) / t_1)) * Float64(3.0 + t_4)) + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_4)))) * Float64(-1.0 - Float64(x1 * x1))) + Float64(3.0 * t_0)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	elseif (x1 <= 1.6e+181)
		tmp = t_6;
	elseif (x1 <= 4.8e+203)
		tmp = Float64(Float64((x1 ^ 2.0) - (Float64(-6.0 * x2) ^ 2.0)) / Float64(x1 - Float64(-6.0 * x2)));
	elseif (x1 <= 3.9e+233)
		tmp = t_6;
	else
		tmp = Float64(x1 + Float64(Float64(-6.0 * x2) + Float64(t_2 - Float64(x1 * Float64(2.0 + t_5)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = 3.0 * ((x1 ^ 2.0) * (3.0 - (x2 * -2.0)));
	t_3 = (x2 * 2.0) + t_0;
	t_4 = (x1 - t_3) / t_1;
	t_5 = 4.0 * (x2 * (3.0 - (x2 * 2.0)));
	t_6 = x1 * (-1.0 - t_5);
	tmp = 0.0;
	if (x1 <= -1.35e+154)
		tmp = 6.0 + ((x1 * -17.0) + (t_2 + (-6.0 * x2)));
	elseif (x1 <= -5.5e+102)
		tmp = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + (3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)));
	elseif (x1 <= 1.35e+154)
		tmp = x1 + ((x1 + (((((((x1 * 2.0) * ((t_3 - x1) / t_1)) * (3.0 + t_4)) + ((x1 * x1) * (6.0 + (4.0 * t_4)))) * (-1.0 - (x1 * x1))) + (3.0 * t_0)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)));
	elseif (x1 <= 1.6e+181)
		tmp = t_6;
	elseif (x1 <= 4.8e+203)
		tmp = ((x1 ^ 2.0) - ((-6.0 * x2) ^ 2.0)) / (x1 - (-6.0 * x2));
	elseif (x1 <= 3.9e+233)
		tmp = t_6;
	else
		tmp = x1 + ((-6.0 * x2) + (t_2 - (x1 * (2.0 + t_5))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 * N[(N[Power[x1, 2.0], $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 - t$95$3), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(4.0 * N[(x2 * N[(3.0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(x1 * N[(-1.0 - t$95$5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.35e+154], N[(6.0 + N[(N[(x1 * -17.0), $MachinePrecision] + N[(t$95$2 + N[(-6.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5.5e+102], N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(N[(x1 + N[(N[(N[(N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(t$95$3 - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] * N[(3.0 + t$95$4), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.6e+181], t$95$6, If[LessEqual[x1, 4.8e+203], N[(N[(N[Power[x1, 2.0], $MachinePrecision] - N[Power[N[(-6.0 * x2), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(-6.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.9e+233], t$95$6, N[(x1 + N[(N[(-6.0 * x2), $MachinePrecision] + N[(t$95$2 - N[(x1 * N[(2.0 + t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x1 < -1.35000000000000003e154

   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%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x2 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{\left(6 + -16 \cdot x1\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   6. Step-by-step derivation

      1. *-commutative 0.0%

         \[\leadsto x1 + \left(\left(\left(6 + \color{blue}{x1 \cdot -16}\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   7. Simplified 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{\left(6 + x1 \cdot -16\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   8. Taylor expanded in x1 around 0 69.6%

      \[\leadsto \color{blue}{6 + \left(-17 \cdot x1 + \left(-6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right)} \]

   if -1.35000000000000003e154 < x1 < -5.49999999999999981e102

   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 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -5.49999999999999981e102 < x1 < 1.35000000000000003e154

   1. Initial program 98.9%

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

   3. Taylor expanded in x1 around inf 97.6%

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

   4. Taylor expanded in x1 around 0 98.9%

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

      1. mul-1-neg 98.9%

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

      2. unsub-neg 98.9%

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

      3. *-commutative 98.9%

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

   6. Simplified 98.9%

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

   if 1.35000000000000003e154 < x1 < 1.6e181 or 4.8000000000000002e203 < x1 < 3.8999999999999999e233

   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 0 0.0%

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

   4. Taylor expanded in x1 around 0 92.3%

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

      1. fma-def 100.0%

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

      2. fma-neg 100.0%

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

      3. fma-neg 100.0%

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

      4. metadata-eval 100.0%

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

      5. metadata-eval 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x1 around inf 100.0%

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

   if 1.6e181 < x1 < 4.8000000000000002e203

   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 0 0.0%

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

   4. Taylor expanded in x1 around 0 5.4%

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

      1. *-commutative 5.4%

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

   6. Simplified 5.4%

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

      1. flip-+ 100.0%

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

      2. pow2 100.0%

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

      3. pow2 100.0%

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

   8. Applied egg-rr 100.0%

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

   if 3.8999999999999999e233 < 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 0 0.0%

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

   4. Taylor expanded in x1 around 0 88.2%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;6 + \left(x1 \cdot -17 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right) + -6 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{x1 - \left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1}\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 1.6 \cdot 10^{+181}:\\ \;\;\;\;x1 \cdot \left(-1 - 4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.8 \cdot 10^{+203}:\\ \;\;\;\;\frac{{x1}^{2} - {\left(-6 \cdot x2\right)}^{2}}{x1 - -6 \cdot x2}\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{+233}:\\ \;\;\;\;x1 \cdot \left(-1 - 4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(-6 \cdot x2 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right) - x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x2 \cdot 2 + t\_0\\ t_3 := 3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right)\\ t_4 := \frac{x1 - t\_2}{t\_1}\\ t_5 := 4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\\ \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;6 + \left(x1 \cdot -17 + \left(t\_3 + -6 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 3 \cdot \frac{\left(t\_0 - x2 \cdot 2\right) - x1}{t\_1}\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(\left(\left(x1 \cdot 2\right) \cdot \frac{t\_2 - x1}{t\_1}\right) \cdot \left(3 + t\_4\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_4\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + 3 \cdot t\_0\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 1.95 \cdot 10^{+188}:\\ \;\;\;\;x1 \cdot \left(-1 - t\_5\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(-6 \cdot x2 + \left(t\_3 - x1 \cdot \left(2 + t\_5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (+ (* x2 2.0) t_0))
        (t_3 (* 3.0 (* (pow x1 2.0) (- 3.0 (* x2 -2.0)))))
        (t_4 (/ (- x1 t_2) t_1))
        (t_5 (* 4.0 (* x2 (- 3.0 (* x2 2.0))))))
   (if (<= x1 -1.35e+154)
     (+ 6.0 (+ (* x1 -17.0) (+ t_3 (* -6.0 x2))))
     (if (<= x1 -5.5e+102)
       (+
        x1
        (+
         (+ x1 (* 6.0 (pow x1 4.0)))
         (* 3.0 (/ (- (- t_0 (* x2 2.0)) x1) t_1))))
       (if (<= x1 1.35e+154)
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               (+
                (* (* (* x1 2.0) (/ (- t_2 x1) t_1)) (+ 3.0 t_4))
                (* (* x1 x1) (+ 6.0 (* 4.0 t_4))))
               (- -1.0 (* x1 x1)))
              (* 3.0 t_0))
             (* x1 (* x1 x1))))
           (* 3.0 (- (* x2 -2.0) x1))))
         (if (<= x1 1.95e+188)
           (* x1 (- -1.0 t_5))
           (+ x1 (+ (* -6.0 x2) (- t_3 (* x1 (+ 2.0 t_5)))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = (x2 * 2.0) + t_0;
	double t_3 = 3.0 * (pow(x1, 2.0) * (3.0 - (x2 * -2.0)));
	double t_4 = (x1 - t_2) / t_1;
	double t_5 = 4.0 * (x2 * (3.0 - (x2 * 2.0)));
	double tmp;
	if (x1 <= -1.35e+154) {
		tmp = 6.0 + ((x1 * -17.0) + (t_3 + (-6.0 * x2)));
	} else if (x1 <= -5.5e+102) {
		tmp = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + (3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 + (((((((x1 * 2.0) * ((t_2 - x1) / t_1)) * (3.0 + t_4)) + ((x1 * x1) * (6.0 + (4.0 * t_4)))) * (-1.0 - (x1 * x1))) + (3.0 * t_0)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else if (x1 <= 1.95e+188) {
		tmp = x1 * (-1.0 - t_5);
	} else {
		tmp = x1 + ((-6.0 * x2) + (t_3 - (x1 * (2.0 + 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) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = (x2 * 2.0d0) + t_0
    t_3 = 3.0d0 * ((x1 ** 2.0d0) * (3.0d0 - (x2 * (-2.0d0))))
    t_4 = (x1 - t_2) / t_1
    t_5 = 4.0d0 * (x2 * (3.0d0 - (x2 * 2.0d0)))
    if (x1 <= (-1.35d+154)) then
        tmp = 6.0d0 + ((x1 * (-17.0d0)) + (t_3 + ((-6.0d0) * x2)))
    else if (x1 <= (-5.5d+102)) then
        tmp = x1 + ((x1 + (6.0d0 * (x1 ** 4.0d0))) + (3.0d0 * (((t_0 - (x2 * 2.0d0)) - x1) / t_1)))
    else if (x1 <= 1.35d+154) then
        tmp = x1 + ((x1 + (((((((x1 * 2.0d0) * ((t_2 - x1) / t_1)) * (3.0d0 + t_4)) + ((x1 * x1) * (6.0d0 + (4.0d0 * t_4)))) * ((-1.0d0) - (x1 * x1))) + (3.0d0 * t_0)) + (x1 * (x1 * x1)))) + (3.0d0 * ((x2 * (-2.0d0)) - x1)))
    else if (x1 <= 1.95d+188) then
        tmp = x1 * ((-1.0d0) - t_5)
    else
        tmp = x1 + (((-6.0d0) * x2) + (t_3 - (x1 * (2.0d0 + t_5))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = (x2 * 2.0) + t_0;
	double t_3 = 3.0 * (Math.pow(x1, 2.0) * (3.0 - (x2 * -2.0)));
	double t_4 = (x1 - t_2) / t_1;
	double t_5 = 4.0 * (x2 * (3.0 - (x2 * 2.0)));
	double tmp;
	if (x1 <= -1.35e+154) {
		tmp = 6.0 + ((x1 * -17.0) + (t_3 + (-6.0 * x2)));
	} else if (x1 <= -5.5e+102) {
		tmp = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + (3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 + (((((((x1 * 2.0) * ((t_2 - x1) / t_1)) * (3.0 + t_4)) + ((x1 * x1) * (6.0 + (4.0 * t_4)))) * (-1.0 - (x1 * x1))) + (3.0 * t_0)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else if (x1 <= 1.95e+188) {
		tmp = x1 * (-1.0 - t_5);
	} else {
		tmp = x1 + ((-6.0 * x2) + (t_3 - (x1 * (2.0 + t_5))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = (x2 * 2.0) + t_0
	t_3 = 3.0 * (math.pow(x1, 2.0) * (3.0 - (x2 * -2.0)))
	t_4 = (x1 - t_2) / t_1
	t_5 = 4.0 * (x2 * (3.0 - (x2 * 2.0)))
	tmp = 0
	if x1 <= -1.35e+154:
		tmp = 6.0 + ((x1 * -17.0) + (t_3 + (-6.0 * x2)))
	elif x1 <= -5.5e+102:
		tmp = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + (3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)))
	elif x1 <= 1.35e+154:
		tmp = x1 + ((x1 + (((((((x1 * 2.0) * ((t_2 - x1) / t_1)) * (3.0 + t_4)) + ((x1 * x1) * (6.0 + (4.0 * t_4)))) * (-1.0 - (x1 * x1))) + (3.0 * t_0)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)))
	elif x1 <= 1.95e+188:
		tmp = x1 * (-1.0 - t_5)
	else:
		tmp = x1 + ((-6.0 * x2) + (t_3 - (x1 * (2.0 + t_5))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(x2 * 2.0) + t_0)
	t_3 = Float64(3.0 * Float64((x1 ^ 2.0) * Float64(3.0 - Float64(x2 * -2.0))))
	t_4 = Float64(Float64(x1 - t_2) / t_1)
	t_5 = Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(x2 * 2.0))))
	tmp = 0.0
	if (x1 <= -1.35e+154)
		tmp = Float64(6.0 + Float64(Float64(x1 * -17.0) + Float64(t_3 + Float64(-6.0 * x2))));
	elseif (x1 <= -5.5e+102)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_1))));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(t_2 - x1) / t_1)) * Float64(3.0 + t_4)) + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_4)))) * Float64(-1.0 - Float64(x1 * x1))) + Float64(3.0 * t_0)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	elseif (x1 <= 1.95e+188)
		tmp = Float64(x1 * Float64(-1.0 - t_5));
	else
		tmp = Float64(x1 + Float64(Float64(-6.0 * x2) + Float64(t_3 - Float64(x1 * Float64(2.0 + t_5)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = (x2 * 2.0) + t_0;
	t_3 = 3.0 * ((x1 ^ 2.0) * (3.0 - (x2 * -2.0)));
	t_4 = (x1 - t_2) / t_1;
	t_5 = 4.0 * (x2 * (3.0 - (x2 * 2.0)));
	tmp = 0.0;
	if (x1 <= -1.35e+154)
		tmp = 6.0 + ((x1 * -17.0) + (t_3 + (-6.0 * x2)));
	elseif (x1 <= -5.5e+102)
		tmp = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + (3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)));
	elseif (x1 <= 1.35e+154)
		tmp = x1 + ((x1 + (((((((x1 * 2.0) * ((t_2 - x1) / t_1)) * (3.0 + t_4)) + ((x1 * x1) * (6.0 + (4.0 * t_4)))) * (-1.0 - (x1 * x1))) + (3.0 * t_0)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)));
	elseif (x1 <= 1.95e+188)
		tmp = x1 * (-1.0 - t_5);
	else
		tmp = x1 + ((-6.0 * x2) + (t_3 - (x1 * (2.0 + t_5))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[Power[x1, 2.0], $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 - t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(4.0 * N[(x2 * N[(3.0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.35e+154], N[(6.0 + N[(N[(x1 * -17.0), $MachinePrecision] + N[(t$95$3 + N[(-6.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5.5e+102], N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(N[(x1 + N[(N[(N[(N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(t$95$2 - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] * N[(3.0 + t$95$4), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.95e+188], N[(x1 * N[(-1.0 - t$95$5), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(-6.0 * x2), $MachinePrecision] + N[(t$95$3 - N[(x1 * N[(2.0 + t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -1.35000000000000003e154

   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%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x2 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{\left(6 + -16 \cdot x1\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   6. Step-by-step derivation

      1. *-commutative 0.0%

         \[\leadsto x1 + \left(\left(\left(6 + \color{blue}{x1 \cdot -16}\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   7. Simplified 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{\left(6 + x1 \cdot -16\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   8. Taylor expanded in x1 around 0 69.6%

      \[\leadsto \color{blue}{6 + \left(-17 \cdot x1 + \left(-6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right)} \]

   if -1.35000000000000003e154 < x1 < -5.49999999999999981e102

   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 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -5.49999999999999981e102 < x1 < 1.35000000000000003e154

   1. Initial program 98.9%

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

   3. Taylor expanded in x1 around inf 97.6%

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

   4. Taylor expanded in x1 around 0 98.9%

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

      1. mul-1-neg 98.9%

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

      2. unsub-neg 98.9%

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

      3. *-commutative 98.9%

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

   6. Simplified 98.9%

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

   if 1.35000000000000003e154 < x1 < 1.95e188

   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 0 0.0%

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

   4. Taylor expanded in x1 around 0 75.7%

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

      1. fma-def 88.2%

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

      2. fma-neg 88.2%

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

      3. fma-neg 88.2%

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

      4. metadata-eval 88.2%

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

      5. metadata-eval 88.2%

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

   6. Simplified 88.2%

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

   7. Taylor expanded in x1 around inf 88.2%

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

   if 1.95e188 < 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 0 0.0%

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

   4. Taylor expanded in x1 around 0 79.3%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;6 + \left(x1 \cdot -17 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right) + -6 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{x1 - \left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1}\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 1.95 \cdot 10^{+188}:\\ \;\;\;\;x1 \cdot \left(-1 - 4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(-6 \cdot x2 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right) - x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 91.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 6 + \left(x1 \cdot -17 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right) + -6 \cdot x2\right)\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := x2 \cdot 2 + t\_0\\ t_4 := \frac{x1 - t\_3}{t\_2}\\ \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -1 \cdot 10^{+108}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 3 \cdot \frac{\left(t\_0 - x2 \cdot 2\right) - x1}{t\_2}\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(\left(\left(x1 \cdot 2\right) \cdot \frac{t\_3 - x1}{t\_2}\right) \cdot \left(3 + t\_4\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_4\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + 3 \cdot t\_0\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 1.32 \cdot 10^{+188}:\\ \;\;\;\;x1 \cdot \left(-1 - 4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1
         (+
          6.0
          (+
           (* x1 -17.0)
           (+ (* 3.0 (* (pow x1 2.0) (- 3.0 (* x2 -2.0)))) (* -6.0 x2)))))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (+ (* x2 2.0) t_0))
        (t_4 (/ (- x1 t_3) t_2)))
   (if (<= x1 -1.35e+154)
     t_1
     (if (<= x1 -1e+108)
       (+
        x1
        (+
         (+ x1 (* 6.0 (pow x1 4.0)))
         (* 3.0 (/ (- (- t_0 (* x2 2.0)) x1) t_2))))
       (if (<= x1 1.35e+154)
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               (+
                (* (* (* x1 2.0) (/ (- t_3 x1) t_2)) (+ 3.0 t_4))
                (* (* x1 x1) (+ 6.0 (* 4.0 t_4))))
               (- -1.0 (* x1 x1)))
              (* 3.0 t_0))
             (* x1 (* x1 x1))))
           (* 3.0 (- (* x2 -2.0) x1))))
         (if (<= x1 1.32e+188)
           (* x1 (- -1.0 (* 4.0 (* x2 (- 3.0 (* x2 2.0))))))
           t_1))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 6.0 + ((x1 * -17.0) + ((3.0 * (pow(x1, 2.0) * (3.0 - (x2 * -2.0)))) + (-6.0 * x2)));
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = (x2 * 2.0) + t_0;
	double t_4 = (x1 - t_3) / t_2;
	double tmp;
	if (x1 <= -1.35e+154) {
		tmp = t_1;
	} else if (x1 <= -1e+108) {
		tmp = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + (3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_2)));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 + (((((((x1 * 2.0) * ((t_3 - x1) / t_2)) * (3.0 + t_4)) + ((x1 * x1) * (6.0 + (4.0 * t_4)))) * (-1.0 - (x1 * x1))) + (3.0 * t_0)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else if (x1 <= 1.32e+188) {
		tmp = x1 * (-1.0 - (4.0 * (x2 * (3.0 - (x2 * 2.0)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = 6.0d0 + ((x1 * (-17.0d0)) + ((3.0d0 * ((x1 ** 2.0d0) * (3.0d0 - (x2 * (-2.0d0))))) + ((-6.0d0) * x2)))
    t_2 = (x1 * x1) + 1.0d0
    t_3 = (x2 * 2.0d0) + t_0
    t_4 = (x1 - t_3) / t_2
    if (x1 <= (-1.35d+154)) then
        tmp = t_1
    else if (x1 <= (-1d+108)) then
        tmp = x1 + ((x1 + (6.0d0 * (x1 ** 4.0d0))) + (3.0d0 * (((t_0 - (x2 * 2.0d0)) - x1) / t_2)))
    else if (x1 <= 1.35d+154) then
        tmp = x1 + ((x1 + (((((((x1 * 2.0d0) * ((t_3 - x1) / t_2)) * (3.0d0 + t_4)) + ((x1 * x1) * (6.0d0 + (4.0d0 * t_4)))) * ((-1.0d0) - (x1 * x1))) + (3.0d0 * t_0)) + (x1 * (x1 * x1)))) + (3.0d0 * ((x2 * (-2.0d0)) - x1)))
    else if (x1 <= 1.32d+188) then
        tmp = x1 * ((-1.0d0) - (4.0d0 * (x2 * (3.0d0 - (x2 * 2.0d0)))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 6.0 + ((x1 * -17.0) + ((3.0 * (Math.pow(x1, 2.0) * (3.0 - (x2 * -2.0)))) + (-6.0 * x2)));
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = (x2 * 2.0) + t_0;
	double t_4 = (x1 - t_3) / t_2;
	double tmp;
	if (x1 <= -1.35e+154) {
		tmp = t_1;
	} else if (x1 <= -1e+108) {
		tmp = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + (3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_2)));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 + (((((((x1 * 2.0) * ((t_3 - x1) / t_2)) * (3.0 + t_4)) + ((x1 * x1) * (6.0 + (4.0 * t_4)))) * (-1.0 - (x1 * x1))) + (3.0 * t_0)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else if (x1 <= 1.32e+188) {
		tmp = x1 * (-1.0 - (4.0 * (x2 * (3.0 - (x2 * 2.0)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = 6.0 + ((x1 * -17.0) + ((3.0 * (math.pow(x1, 2.0) * (3.0 - (x2 * -2.0)))) + (-6.0 * x2)))
	t_2 = (x1 * x1) + 1.0
	t_3 = (x2 * 2.0) + t_0
	t_4 = (x1 - t_3) / t_2
	tmp = 0
	if x1 <= -1.35e+154:
		tmp = t_1
	elif x1 <= -1e+108:
		tmp = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + (3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_2)))
	elif x1 <= 1.35e+154:
		tmp = x1 + ((x1 + (((((((x1 * 2.0) * ((t_3 - x1) / t_2)) * (3.0 + t_4)) + ((x1 * x1) * (6.0 + (4.0 * t_4)))) * (-1.0 - (x1 * x1))) + (3.0 * t_0)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)))
	elif x1 <= 1.32e+188:
		tmp = x1 * (-1.0 - (4.0 * (x2 * (3.0 - (x2 * 2.0)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(6.0 + Float64(Float64(x1 * -17.0) + Float64(Float64(3.0 * Float64((x1 ^ 2.0) * Float64(3.0 - Float64(x2 * -2.0)))) + Float64(-6.0 * x2))))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(x2 * 2.0) + t_0)
	t_4 = Float64(Float64(x1 - t_3) / t_2)
	tmp = 0.0
	if (x1 <= -1.35e+154)
		tmp = t_1;
	elseif (x1 <= -1e+108)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_2))));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(t_3 - x1) / t_2)) * Float64(3.0 + t_4)) + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_4)))) * Float64(-1.0 - Float64(x1 * x1))) + Float64(3.0 * t_0)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	elseif (x1 <= 1.32e+188)
		tmp = Float64(x1 * Float64(-1.0 - Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(x2 * 2.0))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = 6.0 + ((x1 * -17.0) + ((3.0 * ((x1 ^ 2.0) * (3.0 - (x2 * -2.0)))) + (-6.0 * x2)));
	t_2 = (x1 * x1) + 1.0;
	t_3 = (x2 * 2.0) + t_0;
	t_4 = (x1 - t_3) / t_2;
	tmp = 0.0;
	if (x1 <= -1.35e+154)
		tmp = t_1;
	elseif (x1 <= -1e+108)
		tmp = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + (3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_2)));
	elseif (x1 <= 1.35e+154)
		tmp = x1 + ((x1 + (((((((x1 * 2.0) * ((t_3 - x1) / t_2)) * (3.0 + t_4)) + ((x1 * x1) * (6.0 + (4.0 * t_4)))) * (-1.0 - (x1 * x1))) + (3.0 * t_0)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)));
	elseif (x1 <= 1.32e+188)
		tmp = x1 * (-1.0 - (4.0 * (x2 * (3.0 - (x2 * 2.0)))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 + N[(N[(x1 * -17.0), $MachinePrecision] + N[(N[(3.0 * N[(N[Power[x1, 2.0], $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-6.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 - t$95$3), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[x1, -1.35e+154], t$95$1, If[LessEqual[x1, -1e+108], N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(N[(x1 + N[(N[(N[(N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(t$95$3 - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] * N[(3.0 + t$95$4), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.32e+188], N[(x1 * N[(-1.0 - N[(4.0 * N[(x2 * N[(3.0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.35000000000000003e154 or 1.3200000000000001e188 < 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%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x2 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{\left(6 + -16 \cdot x1\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   6. Step-by-step derivation

      1. *-commutative 0.0%

         \[\leadsto x1 + \left(\left(\left(6 + \color{blue}{x1 \cdot -16}\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   7. Simplified 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{\left(6 + x1 \cdot -16\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   8. Taylor expanded in x1 around 0 73.1%

      \[\leadsto \color{blue}{6 + \left(-17 \cdot x1 + \left(-6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right)} \]

   if -1.35000000000000003e154 < x1 < -1e108

   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 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -1e108 < x1 < 1.35000000000000003e154

   1. Initial program 98.9%

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

   3. Taylor expanded in x1 around inf 97.6%

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

   4. Taylor expanded in x1 around 0 98.9%

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

      1. mul-1-neg 98.9%

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

      2. unsub-neg 98.9%

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

      3. *-commutative 98.9%

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

   6. Simplified 98.9%

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

   if 1.35000000000000003e154 < x1 < 1.3200000000000001e188

   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 0 0.0%

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

   4. Taylor expanded in x1 around 0 75.7%

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

      1. fma-def 88.2%

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

      2. fma-neg 88.2%

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

      3. fma-neg 88.2%

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

      4. metadata-eval 88.2%

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

      5. metadata-eval 88.2%

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

   6. Simplified 88.2%

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

   7. Taylor expanded in x1 around inf 88.2%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;6 + \left(x1 \cdot -17 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right) + -6 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq -1 \cdot 10^{+108}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{x1 - \left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1}\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 1.32 \cdot 10^{+188}:\\ \;\;\;\;x1 \cdot \left(-1 - 4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;6 + \left(x1 \cdot -17 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right) + -6 \cdot x2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x2 \cdot \left(3 - x2 \cdot 2\right)\\ t_3 := x1 \cdot x1 + 1\\ t_4 := 3 \cdot \frac{\left(t\_1 - x2 \cdot 2\right) - x1}{t\_3}\\ t_5 := x1 + \left(t\_4 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_1 + t\_3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x2 \cdot 2 + t\_1\right) - x1}{t\_3} - 6\right) + \frac{1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right)\right)\right)\right)\right)\right)\\ t_6 := x1 + \left(\left(x1 - 4 \cdot \left(x1 \cdot t\_2\right)\right) + t\_4\right)\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -125:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x1 \leq -3.25 \cdot 10^{-196}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{-176}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 2.4 \cdot 10^{+45}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot t\_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (- (* x1 -2.0) (* x2 (- 6.0 (* x1 -12.0))))))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (* x2 (- 3.0 (* x2 2.0))))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (* 3.0 (/ (- (- t_1 (* x2 2.0)) x1) t_3)))
        (t_5
         (+
          x1
          (+
           t_4
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* 3.0 t_1)
              (*
               t_3
               (+
                (* (* x1 x1) (- (* 4.0 (/ (- (+ (* x2 2.0) t_1) x1) t_3)) 6.0))
                (* (/ 1.0 x1) (* (* x1 2.0) (- (/ 1.0 x1) 3.0)))))))))))
        (t_6 (+ x1 (+ (- x1 (* 4.0 (* x1 t_2))) t_4))))
   (if (<= x1 -5.6e+102)
     t_0
     (if (<= x1 -125.0)
       t_5
       (if (<= x1 -3.25e-196)
         t_6
         (if (<= x1 4e-176)
           t_0
           (if (<= x1 2.4e+45)
             t_6
             (if (<= x1 1.35e+154)
               t_5
               (+ x1 (* x1 (- 1.0 (* 4.0 t_2))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = x2 * (3.0 - (x2 * 2.0));
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = 3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_3);
	double t_5 = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_3 * (((x1 * x1) * ((4.0 * ((((x2 * 2.0) + t_1) - x1) / t_3)) - 6.0)) + ((1.0 / x1) * ((x1 * 2.0) * ((1.0 / x1) - 3.0)))))))));
	double t_6 = x1 + ((x1 - (4.0 * (x1 * t_2))) + t_4);
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_0;
	} else if (x1 <= -125.0) {
		tmp = t_5;
	} else if (x1 <= -3.25e-196) {
		tmp = t_6;
	} else if (x1 <= 4e-176) {
		tmp = t_0;
	} else if (x1 <= 2.4e+45) {
		tmp = t_6;
	} else if (x1 <= 1.35e+154) {
		tmp = t_5;
	} else {
		tmp = x1 + (x1 * (1.0 - (4.0 * 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 * (-2.0d0)) - (x2 * (6.0d0 - (x1 * (-12.0d0)))))
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = x2 * (3.0d0 - (x2 * 2.0d0))
    t_3 = (x1 * x1) + 1.0d0
    t_4 = 3.0d0 * (((t_1 - (x2 * 2.0d0)) - x1) / t_3)
    t_5 = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_1) + (t_3 * (((x1 * x1) * ((4.0d0 * ((((x2 * 2.0d0) + t_1) - x1) / t_3)) - 6.0d0)) + ((1.0d0 / x1) * ((x1 * 2.0d0) * ((1.0d0 / x1) - 3.0d0)))))))))
    t_6 = x1 + ((x1 - (4.0d0 * (x1 * t_2))) + t_4)
    if (x1 <= (-5.6d+102)) then
        tmp = t_0
    else if (x1 <= (-125.0d0)) then
        tmp = t_5
    else if (x1 <= (-3.25d-196)) then
        tmp = t_6
    else if (x1 <= 4d-176) then
        tmp = t_0
    else if (x1 <= 2.4d+45) then
        tmp = t_6
    else if (x1 <= 1.35d+154) then
        tmp = t_5
    else
        tmp = x1 + (x1 * (1.0d0 - (4.0d0 * t_2)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = x2 * (3.0 - (x2 * 2.0));
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = 3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_3);
	double t_5 = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_3 * (((x1 * x1) * ((4.0 * ((((x2 * 2.0) + t_1) - x1) / t_3)) - 6.0)) + ((1.0 / x1) * ((x1 * 2.0) * ((1.0 / x1) - 3.0)))))))));
	double t_6 = x1 + ((x1 - (4.0 * (x1 * t_2))) + t_4);
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_0;
	} else if (x1 <= -125.0) {
		tmp = t_5;
	} else if (x1 <= -3.25e-196) {
		tmp = t_6;
	} else if (x1 <= 4e-176) {
		tmp = t_0;
	} else if (x1 <= 2.4e+45) {
		tmp = t_6;
	} else if (x1 <= 1.35e+154) {
		tmp = t_5;
	} else {
		tmp = x1 + (x1 * (1.0 - (4.0 * t_2)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))))
	t_1 = x1 * (x1 * 3.0)
	t_2 = x2 * (3.0 - (x2 * 2.0))
	t_3 = (x1 * x1) + 1.0
	t_4 = 3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_3)
	t_5 = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_3 * (((x1 * x1) * ((4.0 * ((((x2 * 2.0) + t_1) - x1) / t_3)) - 6.0)) + ((1.0 / x1) * ((x1 * 2.0) * ((1.0 / x1) - 3.0)))))))))
	t_6 = x1 + ((x1 - (4.0 * (x1 * t_2))) + t_4)
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = t_0
	elif x1 <= -125.0:
		tmp = t_5
	elif x1 <= -3.25e-196:
		tmp = t_6
	elif x1 <= 4e-176:
		tmp = t_0
	elif x1 <= 2.4e+45:
		tmp = t_6
	elif x1 <= 1.35e+154:
		tmp = t_5
	else:
		tmp = x1 + (x1 * (1.0 - (4.0 * t_2)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x1 * -2.0) - Float64(x2 * Float64(6.0 - Float64(x1 * -12.0)))))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(x2 * Float64(3.0 - Float64(x2 * 2.0)))
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(x2 * 2.0)) - x1) / t_3))
	t_5 = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_1) + Float64(t_3 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(Float64(Float64(Float64(x2 * 2.0) + t_1) - x1) / t_3)) - 6.0)) + Float64(Float64(1.0 / x1) * Float64(Float64(x1 * 2.0) * Float64(Float64(1.0 / x1) - 3.0))))))))))
	t_6 = Float64(x1 + Float64(Float64(x1 - Float64(4.0 * Float64(x1 * t_2))) + t_4))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = t_0;
	elseif (x1 <= -125.0)
		tmp = t_5;
	elseif (x1 <= -3.25e-196)
		tmp = t_6;
	elseif (x1 <= 4e-176)
		tmp = t_0;
	elseif (x1 <= 2.4e+45)
		tmp = t_6;
	elseif (x1 <= 1.35e+154)
		tmp = t_5;
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 - Float64(4.0 * t_2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))));
	t_1 = x1 * (x1 * 3.0);
	t_2 = x2 * (3.0 - (x2 * 2.0));
	t_3 = (x1 * x1) + 1.0;
	t_4 = 3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_3);
	t_5 = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_3 * (((x1 * x1) * ((4.0 * ((((x2 * 2.0) + t_1) - x1) / t_3)) - 6.0)) + ((1.0 / x1) * ((x1 * 2.0) * ((1.0 / x1) - 3.0)))))))));
	t_6 = x1 + ((x1 - (4.0 * (x1 * t_2))) + t_4);
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = t_0;
	elseif (x1 <= -125.0)
		tmp = t_5;
	elseif (x1 <= -3.25e-196)
		tmp = t_6;
	elseif (x1 <= 4e-176)
		tmp = t_0;
	elseif (x1 <= 2.4e+45)
		tmp = t_6;
	elseif (x1 <= 1.35e+154)
		tmp = t_5;
	else
		tmp = x1 + (x1 * (1.0 - (4.0 * t_2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] - N[(x2 * N[(6.0 - N[(x1 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x2 * N[(3.0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(N[(N[(t$95$1 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(t$95$4 + 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[(N[(4.0 * N[(N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$1), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 / x1), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(1.0 / x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(x1 + N[(N[(x1 - N[(4.0 * N[(x1 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], t$95$0, If[LessEqual[x1, -125.0], t$95$5, If[LessEqual[x1, -3.25e-196], t$95$6, If[LessEqual[x1, 4e-176], t$95$0, If[LessEqual[x1, 2.4e+45], t$95$6, If[LessEqual[x1, 1.35e+154], t$95$5, N[(x1 + N[(x1 * N[(1.0 - N[(4.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.60000000000000037e102 or -3.2500000000000002e-196 < x1 < 4e-176

   1. Initial program 53.8%

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

   3. Taylor expanded in x1 around 0 39.5%

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

   4. Taylor expanded in x1 around 0 40.6%

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

      1. fma-def 41.8%

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

      2. fma-neg 41.8%

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

      3. fma-neg 41.8%

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

      4. metadata-eval 41.8%

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

      5. metadata-eval 41.8%

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

   6. Simplified 41.8%

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

   7. Taylor expanded in x2 around 0 60.7%

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

   if -5.60000000000000037e102 < x1 < -125 or 2.39999999999999989e45 < x1 < 1.35000000000000003e154

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around inf 88.2%

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

   4. Taylor expanded in x1 around inf 88.2%

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

   5. Taylor expanded in x1 around inf 88.2%

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

   if -125 < x1 < -3.2500000000000002e-196 or 4e-176 < x1 < 2.39999999999999989e45

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 91.8%

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

   if 1.35000000000000003e154 < 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 0 0.0%

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

   4. Taylor expanded in x1 around inf 52.8%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \mathbf{elif}\;x1 \leq -125:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 6\right) + \frac{1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3.25 \cdot 10^{-196}:\\ \;\;\;\;x1 + \left(\left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{-176}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \mathbf{elif}\;x1 \leq 2.4 \cdot 10^{+45}:\\ \;\;\;\;x1 + \left(\left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 6\right) + \frac{1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x2 \cdot \left(3 - x2 \cdot 2\right)\\ t_3 := x1 \cdot x1 + 1\\ t_4 := 3 \cdot \frac{\left(t\_1 - x2 \cdot 2\right) - x1}{t\_3}\\ t_5 := x1 + \left(t\_4 - \left(\left(\left(\left(6 \cdot \left(x1 \cdot x1\right) + \left(\frac{\left(x2 \cdot 2 + t\_1\right) - x1}{t\_3} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 + \frac{-1}{x1}\right)\right)\right) \cdot \left(-1 - x1 \cdot x1\right) - 3 \cdot t\_1\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ t_6 := x1 + \left(\left(x1 - 4 \cdot \left(x1 \cdot t\_2\right)\right) + t\_4\right)\\ \mathbf{if}\;x1 \leq -3.5 \cdot 10^{+96}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -1.35 \cdot 10^{+19}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x1 \leq -3.2 \cdot 10^{-202}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;x1 \leq 9.5 \cdot 10^{-174}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 2.4 \cdot 10^{+45}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot t\_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (- (* x1 -2.0) (* x2 (- 6.0 (* x1 -12.0))))))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (* x2 (- 3.0 (* x2 2.0))))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (* 3.0 (/ (- (- t_1 (* x2 2.0)) x1) t_3)))
        (t_5
         (+
          x1
          (-
           t_4
           (-
            (-
             (-
              (*
               (+
                (* 6.0 (* x1 x1))
                (*
                 (- (/ (- (+ (* x2 2.0) t_1) x1) t_3) 3.0)
                 (* (* x1 2.0) (+ 3.0 (/ -1.0 x1)))))
               (- -1.0 (* x1 x1)))
              (* 3.0 t_1))
             (* x1 (* x1 x1)))
            x1))))
        (t_6 (+ x1 (+ (- x1 (* 4.0 (* x1 t_2))) t_4))))
   (if (<= x1 -3.5e+96)
     t_0
     (if (<= x1 -1.35e+19)
       t_5
       (if (<= x1 -3.2e-202)
         t_6
         (if (<= x1 9.5e-174)
           t_0
           (if (<= x1 2.4e+45)
             t_6
             (if (<= x1 1.35e+154)
               t_5
               (+ x1 (* x1 (- 1.0 (* 4.0 t_2))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = x2 * (3.0 - (x2 * 2.0));
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = 3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_3);
	double t_5 = x1 + (t_4 - ((((((6.0 * (x1 * x1)) + ((((((x2 * 2.0) + t_1) - x1) / t_3) - 3.0) * ((x1 * 2.0) * (3.0 + (-1.0 / x1))))) * (-1.0 - (x1 * x1))) - (3.0 * t_1)) - (x1 * (x1 * x1))) - x1));
	double t_6 = x1 + ((x1 - (4.0 * (x1 * t_2))) + t_4);
	double tmp;
	if (x1 <= -3.5e+96) {
		tmp = t_0;
	} else if (x1 <= -1.35e+19) {
		tmp = t_5;
	} else if (x1 <= -3.2e-202) {
		tmp = t_6;
	} else if (x1 <= 9.5e-174) {
		tmp = t_0;
	} else if (x1 <= 2.4e+45) {
		tmp = t_6;
	} else if (x1 <= 1.35e+154) {
		tmp = t_5;
	} else {
		tmp = x1 + (x1 * (1.0 - (4.0 * 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 * (-2.0d0)) - (x2 * (6.0d0 - (x1 * (-12.0d0)))))
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = x2 * (3.0d0 - (x2 * 2.0d0))
    t_3 = (x1 * x1) + 1.0d0
    t_4 = 3.0d0 * (((t_1 - (x2 * 2.0d0)) - x1) / t_3)
    t_5 = x1 + (t_4 - ((((((6.0d0 * (x1 * x1)) + ((((((x2 * 2.0d0) + t_1) - x1) / t_3) - 3.0d0) * ((x1 * 2.0d0) * (3.0d0 + ((-1.0d0) / x1))))) * ((-1.0d0) - (x1 * x1))) - (3.0d0 * t_1)) - (x1 * (x1 * x1))) - x1))
    t_6 = x1 + ((x1 - (4.0d0 * (x1 * t_2))) + t_4)
    if (x1 <= (-3.5d+96)) then
        tmp = t_0
    else if (x1 <= (-1.35d+19)) then
        tmp = t_5
    else if (x1 <= (-3.2d-202)) then
        tmp = t_6
    else if (x1 <= 9.5d-174) then
        tmp = t_0
    else if (x1 <= 2.4d+45) then
        tmp = t_6
    else if (x1 <= 1.35d+154) then
        tmp = t_5
    else
        tmp = x1 + (x1 * (1.0d0 - (4.0d0 * t_2)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = x2 * (3.0 - (x2 * 2.0));
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = 3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_3);
	double t_5 = x1 + (t_4 - ((((((6.0 * (x1 * x1)) + ((((((x2 * 2.0) + t_1) - x1) / t_3) - 3.0) * ((x1 * 2.0) * (3.0 + (-1.0 / x1))))) * (-1.0 - (x1 * x1))) - (3.0 * t_1)) - (x1 * (x1 * x1))) - x1));
	double t_6 = x1 + ((x1 - (4.0 * (x1 * t_2))) + t_4);
	double tmp;
	if (x1 <= -3.5e+96) {
		tmp = t_0;
	} else if (x1 <= -1.35e+19) {
		tmp = t_5;
	} else if (x1 <= -3.2e-202) {
		tmp = t_6;
	} else if (x1 <= 9.5e-174) {
		tmp = t_0;
	} else if (x1 <= 2.4e+45) {
		tmp = t_6;
	} else if (x1 <= 1.35e+154) {
		tmp = t_5;
	} else {
		tmp = x1 + (x1 * (1.0 - (4.0 * t_2)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))))
	t_1 = x1 * (x1 * 3.0)
	t_2 = x2 * (3.0 - (x2 * 2.0))
	t_3 = (x1 * x1) + 1.0
	t_4 = 3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_3)
	t_5 = x1 + (t_4 - ((((((6.0 * (x1 * x1)) + ((((((x2 * 2.0) + t_1) - x1) / t_3) - 3.0) * ((x1 * 2.0) * (3.0 + (-1.0 / x1))))) * (-1.0 - (x1 * x1))) - (3.0 * t_1)) - (x1 * (x1 * x1))) - x1))
	t_6 = x1 + ((x1 - (4.0 * (x1 * t_2))) + t_4)
	tmp = 0
	if x1 <= -3.5e+96:
		tmp = t_0
	elif x1 <= -1.35e+19:
		tmp = t_5
	elif x1 <= -3.2e-202:
		tmp = t_6
	elif x1 <= 9.5e-174:
		tmp = t_0
	elif x1 <= 2.4e+45:
		tmp = t_6
	elif x1 <= 1.35e+154:
		tmp = t_5
	else:
		tmp = x1 + (x1 * (1.0 - (4.0 * t_2)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x1 * -2.0) - Float64(x2 * Float64(6.0 - Float64(x1 * -12.0)))))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(x2 * Float64(3.0 - Float64(x2 * 2.0)))
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(x2 * 2.0)) - x1) / t_3))
	t_5 = Float64(x1 + Float64(t_4 - Float64(Float64(Float64(Float64(Float64(Float64(6.0 * Float64(x1 * x1)) + Float64(Float64(Float64(Float64(Float64(Float64(x2 * 2.0) + t_1) - x1) / t_3) - 3.0) * Float64(Float64(x1 * 2.0) * Float64(3.0 + Float64(-1.0 / x1))))) * Float64(-1.0 - Float64(x1 * x1))) - Float64(3.0 * t_1)) - Float64(x1 * Float64(x1 * x1))) - x1)))
	t_6 = Float64(x1 + Float64(Float64(x1 - Float64(4.0 * Float64(x1 * t_2))) + t_4))
	tmp = 0.0
	if (x1 <= -3.5e+96)
		tmp = t_0;
	elseif (x1 <= -1.35e+19)
		tmp = t_5;
	elseif (x1 <= -3.2e-202)
		tmp = t_6;
	elseif (x1 <= 9.5e-174)
		tmp = t_0;
	elseif (x1 <= 2.4e+45)
		tmp = t_6;
	elseif (x1 <= 1.35e+154)
		tmp = t_5;
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 - Float64(4.0 * t_2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))));
	t_1 = x1 * (x1 * 3.0);
	t_2 = x2 * (3.0 - (x2 * 2.0));
	t_3 = (x1 * x1) + 1.0;
	t_4 = 3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_3);
	t_5 = x1 + (t_4 - ((((((6.0 * (x1 * x1)) + ((((((x2 * 2.0) + t_1) - x1) / t_3) - 3.0) * ((x1 * 2.0) * (3.0 + (-1.0 / x1))))) * (-1.0 - (x1 * x1))) - (3.0 * t_1)) - (x1 * (x1 * x1))) - x1));
	t_6 = x1 + ((x1 - (4.0 * (x1 * t_2))) + t_4);
	tmp = 0.0;
	if (x1 <= -3.5e+96)
		tmp = t_0;
	elseif (x1 <= -1.35e+19)
		tmp = t_5;
	elseif (x1 <= -3.2e-202)
		tmp = t_6;
	elseif (x1 <= 9.5e-174)
		tmp = t_0;
	elseif (x1 <= 2.4e+45)
		tmp = t_6;
	elseif (x1 <= 1.35e+154)
		tmp = t_5;
	else
		tmp = x1 + (x1 * (1.0 - (4.0 * t_2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] - N[(x2 * N[(6.0 - N[(x1 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x2 * N[(3.0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(N[(N[(t$95$1 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(t$95$4 - N[(N[(N[(N[(N[(N[(6.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$1), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision] - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(3.0 + N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(x1 + N[(N[(x1 - N[(4.0 * N[(x1 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3.5e+96], t$95$0, If[LessEqual[x1, -1.35e+19], t$95$5, If[LessEqual[x1, -3.2e-202], t$95$6, If[LessEqual[x1, 9.5e-174], t$95$0, If[LessEqual[x1, 2.4e+45], t$95$6, If[LessEqual[x1, 1.35e+154], t$95$5, N[(x1 + N[(x1 * N[(1.0 - N[(4.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -3.4999999999999999e96 or -3.2000000000000001e-202 < x1 < 9.50000000000000075e-174

   1. Initial program 54.9%

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

   3. Taylor expanded in x1 around 0 39.7%

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

   4. Taylor expanded in x1 around 0 40.8%

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

      1. fma-def 42.0%

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

      2. fma-neg 42.0%

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

      3. fma-neg 42.0%

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

      4. metadata-eval 42.0%

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

      5. metadata-eval 42.0%

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

   6. Simplified 42.0%

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

   7. Taylor expanded in x2 around 0 60.5%

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

   if -3.4999999999999999e96 < x1 < -1.35e19 or 2.39999999999999989e45 < x1 < 1.35000000000000003e154

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around inf 88.7%

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

   4. Taylor expanded in x1 around inf 88.7%

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

   5. Taylor expanded in x1 around inf 84.4%

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

   if -1.35e19 < x1 < -3.2000000000000001e-202 or 9.50000000000000075e-174 < x1 < 2.39999999999999989e45

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 89.7%

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

   if 1.35000000000000003e154 < 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 0 0.0%

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

   4. Taylor expanded in x1 around inf 52.8%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.5 \cdot 10^{+96}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \mathbf{elif}\;x1 \leq -1.35 \cdot 10^{+19}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} - \left(\left(\left(\left(6 \cdot \left(x1 \cdot x1\right) + \left(\frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 + \frac{-1}{x1}\right)\right)\right) \cdot \left(-1 - x1 \cdot x1\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq -3.2 \cdot 10^{-202}:\\ \;\;\;\;x1 + \left(\left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 9.5 \cdot 10^{-174}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \mathbf{elif}\;x1 \leq 2.4 \cdot 10^{+45}:\\ \;\;\;\;x1 + \left(\left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} - \left(\left(\left(\left(6 \cdot \left(x1 \cdot x1\right) + \left(\frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 + \frac{-1}{x1}\right)\right)\right) \cdot \left(-1 - x1 \cdot x1\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 79.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x2 \cdot 2 + t\_0\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{x1 - t\_1}{t\_2}\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(\left(\left(x1 \cdot 2\right) \cdot \frac{t\_1 - x1}{t\_2}\right) \cdot \left(3 + t\_3\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_3\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + 3 \cdot t\_0\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x2 2.0) t_0))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (/ (- x1 t_1) t_2)))
   (if (<= x1 -5.6e+102)
     (+ x1 (- (* x1 -2.0) (* x2 (- 6.0 (* x1 -12.0)))))
     (if (<= x1 1.35e+154)
       (+
        x1
        (+
         (+
          x1
          (+
           (+
            (*
             (+
              (* (* (* x1 2.0) (/ (- t_1 x1) t_2)) (+ 3.0 t_3))
              (* (* x1 x1) (+ 6.0 (* 4.0 t_3))))
             (- -1.0 (* x1 x1)))
            (* 3.0 t_0))
           (* x1 (* x1 x1))))
         (* 3.0 (- (* x2 -2.0) x1))))
       (+ x1 (* x1 (- 1.0 (* 4.0 (* x2 (- 3.0 (* x2 2.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x2 * 2.0) + t_0;
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = (x1 - t_1) / t_2;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 + (((((((x1 * 2.0) * ((t_1 - x1) / t_2)) * (3.0 + t_3)) + ((x1 * x1) * (6.0 + (4.0 * t_3)))) * (-1.0 - (x1 * x1))) + (3.0 * t_0)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (x2 * 2.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x2 * 2.0d0) + t_0
    t_2 = (x1 * x1) + 1.0d0
    t_3 = (x1 - t_1) / t_2
    if (x1 <= (-5.6d+102)) then
        tmp = x1 + ((x1 * (-2.0d0)) - (x2 * (6.0d0 - (x1 * (-12.0d0)))))
    else if (x1 <= 1.35d+154) then
        tmp = x1 + ((x1 + (((((((x1 * 2.0d0) * ((t_1 - x1) / t_2)) * (3.0d0 + t_3)) + ((x1 * x1) * (6.0d0 + (4.0d0 * t_3)))) * ((-1.0d0) - (x1 * x1))) + (3.0d0 * t_0)) + (x1 * (x1 * x1)))) + (3.0d0 * ((x2 * (-2.0d0)) - x1)))
    else
        tmp = x1 + (x1 * (1.0d0 - (4.0d0 * (x2 * (3.0d0 - (x2 * 2.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x2 * 2.0) + t_0;
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = (x1 - t_1) / t_2;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 + (((((((x1 * 2.0) * ((t_1 - x1) / t_2)) * (3.0 + t_3)) + ((x1 * x1) * (6.0 + (4.0 * t_3)))) * (-1.0 - (x1 * x1))) + (3.0 * t_0)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (x2 * 2.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x2 * 2.0) + t_0
	t_2 = (x1 * x1) + 1.0
	t_3 = (x1 - t_1) / t_2
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))))
	elif x1 <= 1.35e+154:
		tmp = x1 + ((x1 + (((((((x1 * 2.0) * ((t_1 - x1) / t_2)) * (3.0 + t_3)) + ((x1 * x1) * (6.0 + (4.0 * t_3)))) * (-1.0 - (x1 * x1))) + (3.0 * t_0)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)))
	else:
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (x2 * 2.0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x2 * 2.0) + t_0)
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(x1 - t_1) / t_2)
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(Float64(x1 * -2.0) - Float64(x2 * Float64(6.0 - Float64(x1 * -12.0)))));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(t_1 - x1) / t_2)) * Float64(3.0 + t_3)) + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_3)))) * Float64(-1.0 - Float64(x1 * x1))) + Float64(3.0 * t_0)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 - Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(x2 * 2.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x2 * 2.0) + t_0;
	t_2 = (x1 * x1) + 1.0;
	t_3 = (x1 - t_1) / t_2;
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))));
	elseif (x1 <= 1.35e+154)
		tmp = x1 + ((x1 + (((((((x1 * 2.0) * ((t_1 - x1) / t_2)) * (3.0 + t_3)) + ((x1 * x1) * (6.0 + (4.0 * t_3)))) * (-1.0 - (x1 * x1))) + (3.0 * t_0)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)));
	else
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (x2 * 2.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 - t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] - N[(x2 * N[(6.0 - N[(x1 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(N[(x1 + N[(N[(N[(N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(t$95$1 - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] * N[(3.0 + t$95$3), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * N[(1.0 - N[(4.0 * N[(x2 * N[(3.0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.1%

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

   4. Taylor expanded in x1 around 0 2.5%

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

      1. fma-def 2.5%

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

      2. fma-neg 2.5%

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

      3. fma-neg 2.5%

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

      4. metadata-eval 2.5%

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

      5. metadata-eval 2.5%

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

   6. Simplified 2.5%

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

   7. Taylor expanded in x2 around 0 28.5%

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

   if -5.60000000000000037e102 < x1 < 1.35000000000000003e154

   1. Initial program 98.9%

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

   3. Taylor expanded in x1 around inf 97.6%

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

   4. Taylor expanded in x1 around 0 98.9%

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

      1. mul-1-neg 98.9%

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

      2. unsub-neg 98.9%

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

      3. *-commutative 98.9%

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

   6. Simplified 98.9%

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

   if 1.35000000000000003e154 < 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 0 0.0%

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

   4. Taylor expanded in x1 around inf 52.8%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{x1 - \left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1}\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 77.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(x2 \cdot 2 + t\_0\right) - x1}{t\_1}\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 + \left(x2 \cdot 2 - t\_0\right)}{t\_1} - \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_0 - \left(\left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + 6 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ (* x2 2.0) t_0) x1) t_1)))
   (if (<= x1 -5.6e+102)
     (+ x1 (- (* x1 -2.0) (* x2 (- 6.0 (* x1 -12.0)))))
     (if (<= x1 1.35e+154)
       (-
        x1
        (-
         (* 3.0 (/ (+ x1 (- (* x2 2.0) t_0)) t_1))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (-
            (* 3.0 t_0)
            (*
             (+ (* (* (* x1 2.0) t_2) (- t_2 3.0)) (* 6.0 (* x1 x1)))
             (- -1.0 (* x1 x1))))))))
       (+ x1 (* x1 (- 1.0 (* 4.0 (* x2 (- 3.0 (* x2 2.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = (((x2 * 2.0) + t_0) - x1) / t_1;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 - ((3.0 * ((x1 + ((x2 * 2.0) - t_0)) / t_1)) - (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) - (((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + (6.0 * (x1 * x1))) * (-1.0 - (x1 * x1)))))));
	} else {
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (x2 * 2.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = (((x2 * 2.0d0) + t_0) - x1) / t_1
    if (x1 <= (-5.6d+102)) then
        tmp = x1 + ((x1 * (-2.0d0)) - (x2 * (6.0d0 - (x1 * (-12.0d0)))))
    else if (x1 <= 1.35d+154) then
        tmp = x1 - ((3.0d0 * ((x1 + ((x2 * 2.0d0) - t_0)) / t_1)) - (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_0) - (((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + (6.0d0 * (x1 * x1))) * ((-1.0d0) - (x1 * x1)))))))
    else
        tmp = x1 + (x1 * (1.0d0 - (4.0d0 * (x2 * (3.0d0 - (x2 * 2.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = (((x2 * 2.0) + t_0) - x1) / t_1;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 - ((3.0 * ((x1 + ((x2 * 2.0) - t_0)) / t_1)) - (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) - (((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + (6.0 * (x1 * x1))) * (-1.0 - (x1 * x1)))))));
	} else {
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (x2 * 2.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = (((x2 * 2.0) + t_0) - x1) / t_1
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))))
	elif x1 <= 1.35e+154:
		tmp = x1 - ((3.0 * ((x1 + ((x2 * 2.0) - t_0)) / t_1)) - (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) - (((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + (6.0 * (x1 * x1))) * (-1.0 - (x1 * x1)))))))
	else:
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (x2 * 2.0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(Float64(x2 * 2.0) + t_0) - x1) / t_1)
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(Float64(x1 * -2.0) - Float64(x2 * Float64(6.0 - Float64(x1 * -12.0)))));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(Float64(x1 + Float64(Float64(x2 * 2.0) - t_0)) / t_1)) - Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_0) - Float64(Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(6.0 * Float64(x1 * x1))) * Float64(-1.0 - Float64(x1 * x1))))))));
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 - Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(x2 * 2.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = (((x2 * 2.0) + t_0) - x1) / t_1;
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))));
	elseif (x1 <= 1.35e+154)
		tmp = x1 - ((3.0 * ((x1 + ((x2 * 2.0) - t_0)) / t_1)) - (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) - (((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + (6.0 * (x1 * x1))) * (-1.0 - (x1 * x1)))))));
	else
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (x2 * 2.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] - N[(x2 * N[(6.0 - N[(x1 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 - N[(N[(3.0 * N[(N[(x1 + N[(N[(x2 * 2.0), $MachinePrecision] - t$95$0), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$0), $MachinePrecision] - N[(N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(6.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * N[(1.0 - N[(4.0 * N[(x2 * N[(3.0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.1%

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

   4. Taylor expanded in x1 around 0 2.5%

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

      1. fma-def 2.5%

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

      2. fma-neg 2.5%

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

      3. fma-neg 2.5%

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

      4. metadata-eval 2.5%

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

      5. metadata-eval 2.5%

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

   6. Simplified 2.5%

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

   7. Taylor expanded in x2 around 0 28.5%

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

   if -5.60000000000000037e102 < x1 < 1.35000000000000003e154

   1. Initial program 98.9%

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

   3. Taylor expanded in x1 around inf 97.6%

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

   4. Taylor expanded in x1 around inf 94.9%

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

   if 1.35000000000000003e154 < 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 0 0.0%

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

   4. Taylor expanded in x1 around inf 52.8%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 + \left(x2 \cdot 2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} - \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) - \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 3\right) + 6 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.8% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ t_1 := x2 \cdot \left(3 - x2 \cdot 2\right)\\ \mathbf{if}\;x1 \leq -7 \cdot 10^{+47}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -2.9 \cdot 10^{-200}:\\ \;\;\;\;-6 \cdot x2 - x1 \cdot \left(4 \cdot t\_1 - -1\right)\\ \mathbf{elif}\;x1 \leq 2.2 \cdot 10^{-170}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 - 4 \cdot \left(x1 \cdot t\_1\right)\right) - 3 \cdot \frac{x1 - x2 \cdot -2}{x1 \cdot x1 + 1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (- (* x1 -2.0) (* x2 (- 6.0 (* x1 -12.0))))))
        (t_1 (* x2 (- 3.0 (* x2 2.0)))))
   (if (<= x1 -7e+47)
     t_0
     (if (<= x1 -2.9e-200)
       (- (* -6.0 x2) (* x1 (- (* 4.0 t_1) -1.0)))
       (if (<= x1 2.2e-170)
         t_0
         (+
          x1
          (-
           (- x1 (* 4.0 (* x1 t_1)))
           (* 3.0 (/ (- x1 (* x2 -2.0)) (+ (* x1 x1) 1.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))));
	double t_1 = x2 * (3.0 - (x2 * 2.0));
	double tmp;
	if (x1 <= -7e+47) {
		tmp = t_0;
	} else if (x1 <= -2.9e-200) {
		tmp = (-6.0 * x2) - (x1 * ((4.0 * t_1) - -1.0));
	} else if (x1 <= 2.2e-170) {
		tmp = t_0;
	} else {
		tmp = x1 + ((x1 - (4.0 * (x1 * t_1))) - (3.0 * ((x1 - (x2 * -2.0)) / ((x1 * x1) + 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 = x1 + ((x1 * (-2.0d0)) - (x2 * (6.0d0 - (x1 * (-12.0d0)))))
    t_1 = x2 * (3.0d0 - (x2 * 2.0d0))
    if (x1 <= (-7d+47)) then
        tmp = t_0
    else if (x1 <= (-2.9d-200)) then
        tmp = ((-6.0d0) * x2) - (x1 * ((4.0d0 * t_1) - (-1.0d0)))
    else if (x1 <= 2.2d-170) then
        tmp = t_0
    else
        tmp = x1 + ((x1 - (4.0d0 * (x1 * t_1))) - (3.0d0 * ((x1 - (x2 * (-2.0d0))) / ((x1 * x1) + 1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))));
	double t_1 = x2 * (3.0 - (x2 * 2.0));
	double tmp;
	if (x1 <= -7e+47) {
		tmp = t_0;
	} else if (x1 <= -2.9e-200) {
		tmp = (-6.0 * x2) - (x1 * ((4.0 * t_1) - -1.0));
	} else if (x1 <= 2.2e-170) {
		tmp = t_0;
	} else {
		tmp = x1 + ((x1 - (4.0 * (x1 * t_1))) - (3.0 * ((x1 - (x2 * -2.0)) / ((x1 * x1) + 1.0))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))))
	t_1 = x2 * (3.0 - (x2 * 2.0))
	tmp = 0
	if x1 <= -7e+47:
		tmp = t_0
	elif x1 <= -2.9e-200:
		tmp = (-6.0 * x2) - (x1 * ((4.0 * t_1) - -1.0))
	elif x1 <= 2.2e-170:
		tmp = t_0
	else:
		tmp = x1 + ((x1 - (4.0 * (x1 * t_1))) - (3.0 * ((x1 - (x2 * -2.0)) / ((x1 * x1) + 1.0))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x1 * -2.0) - Float64(x2 * Float64(6.0 - Float64(x1 * -12.0)))))
	t_1 = Float64(x2 * Float64(3.0 - Float64(x2 * 2.0)))
	tmp = 0.0
	if (x1 <= -7e+47)
		tmp = t_0;
	elseif (x1 <= -2.9e-200)
		tmp = Float64(Float64(-6.0 * x2) - Float64(x1 * Float64(Float64(4.0 * t_1) - -1.0)));
	elseif (x1 <= 2.2e-170)
		tmp = t_0;
	else
		tmp = Float64(x1 + Float64(Float64(x1 - Float64(4.0 * Float64(x1 * t_1))) - Float64(3.0 * Float64(Float64(x1 - Float64(x2 * -2.0)) / Float64(Float64(x1 * x1) + 1.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))));
	t_1 = x2 * (3.0 - (x2 * 2.0));
	tmp = 0.0;
	if (x1 <= -7e+47)
		tmp = t_0;
	elseif (x1 <= -2.9e-200)
		tmp = (-6.0 * x2) - (x1 * ((4.0 * t_1) - -1.0));
	elseif (x1 <= 2.2e-170)
		tmp = t_0;
	else
		tmp = x1 + ((x1 - (4.0 * (x1 * t_1))) - (3.0 * ((x1 - (x2 * -2.0)) / ((x1 * x1) + 1.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] - N[(x2 * N[(6.0 - N[(x1 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x2 * N[(3.0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -7e+47], t$95$0, If[LessEqual[x1, -2.9e-200], N[(N[(-6.0 * x2), $MachinePrecision] - N[(x1 * N[(N[(4.0 * t$95$1), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.2e-170], t$95$0, N[(x1 + N[(N[(x1 - N[(4.0 * N[(x1 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * N[(N[(x1 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -7.00000000000000031e47 or -2.9e-200 < x1 < 2.20000000000000015e-170

   1. Initial program 60.9%

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

   3. Taylor expanded in x1 around 0 34.4%

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

   4. Taylor expanded in x1 around 0 35.7%

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

      1. fma-def 36.7%

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

      2. fma-neg 36.7%

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

      3. fma-neg 36.7%

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

      4. metadata-eval 36.7%

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

      5. metadata-eval 36.7%

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

   6. Simplified 36.7%

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

   7. Taylor expanded in x2 around 0 53.9%

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

   if -7.00000000000000031e47 < x1 < -2.9e-200

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 87.9%

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

   4. Taylor expanded in x1 around 0 88.1%

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

      1. fma-def 88.1%

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

      2. fma-neg 88.1%

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

      3. fma-neg 88.1%

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

      4. metadata-eval 88.1%

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

      5. metadata-eval 88.1%

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

   6. Simplified 88.1%

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

   7. Taylor expanded in x1 around 0 88.1%

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

   if 2.20000000000000015e-170 < x1

   1. Initial program 62.3%

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

   3. Taylor expanded in x1 around 0 28.4%

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

   4. Taylor expanded in x1 around 0 46.8%

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

      1. *-commutative 46.8%

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

   6. Simplified 46.8%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7 \cdot 10^{+47}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \mathbf{elif}\;x1 \leq -2.9 \cdot 10^{-200}:\\ \;\;\;\;-6 \cdot x2 - x1 \cdot \left(4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq 2.2 \cdot 10^{-170}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\right)\right) - 3 \cdot \frac{x1 - x2 \cdot -2}{x1 \cdot x1 + 1}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.1% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -7 \cdot 10^{+47} \lor \neg \left(x1 \leq -1.9 \cdot 10^{-200}\right) \land x1 \leq 6.6 \cdot 10^{-177}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot x2 - x1 \cdot \left(4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right) - -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -7e+47) (and (not (<= x1 -1.9e-200)) (<= x1 6.6e-177)))
   (+ x1 (- (* x1 -2.0) (* x2 (- 6.0 (* x1 -12.0)))))
   (- (* -6.0 x2) (* x1 (- (* 4.0 (* x2 (- 3.0 (* x2 2.0)))) -1.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -7e+47) || (!(x1 <= -1.9e-200) && (x1 <= 6.6e-177))) {
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))));
	} else {
		tmp = (-6.0 * x2) - (x1 * ((4.0 * (x2 * (3.0 - (x2 * 2.0)))) - -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 <= (-7d+47)) .or. (.not. (x1 <= (-1.9d-200))) .and. (x1 <= 6.6d-177)) then
        tmp = x1 + ((x1 * (-2.0d0)) - (x2 * (6.0d0 - (x1 * (-12.0d0)))))
    else
        tmp = ((-6.0d0) * x2) - (x1 * ((4.0d0 * (x2 * (3.0d0 - (x2 * 2.0d0)))) - (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -7e+47) || (!(x1 <= -1.9e-200) && (x1 <= 6.6e-177))) {
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))));
	} else {
		tmp = (-6.0 * x2) - (x1 * ((4.0 * (x2 * (3.0 - (x2 * 2.0)))) - -1.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -7e+47) or (not (x1 <= -1.9e-200) and (x1 <= 6.6e-177)):
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))))
	else:
		tmp = (-6.0 * x2) - (x1 * ((4.0 * (x2 * (3.0 - (x2 * 2.0)))) - -1.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -7e+47) || (!(x1 <= -1.9e-200) && (x1 <= 6.6e-177)))
		tmp = Float64(x1 + Float64(Float64(x1 * -2.0) - Float64(x2 * Float64(6.0 - Float64(x1 * -12.0)))));
	else
		tmp = Float64(Float64(-6.0 * x2) - Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(x2 * 2.0)))) - -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -7e+47) || (~((x1 <= -1.9e-200)) && (x1 <= 6.6e-177)))
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))));
	else
		tmp = (-6.0 * x2) - (x1 * ((4.0 * (x2 * (3.0 - (x2 * 2.0)))) - -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -7e+47], And[N[Not[LessEqual[x1, -1.9e-200]], $MachinePrecision], LessEqual[x1, 6.6e-177]]], N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] - N[(x2 * N[(6.0 - N[(x1 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-6.0 * x2), $MachinePrecision] - N[(x1 * N[(N[(4.0 * N[(x2 * N[(3.0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -7.00000000000000031e47 or -1.9e-200 < x1 < 6.5999999999999999e-177

   1. Initial program 60.9%

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

   3. Taylor expanded in x1 around 0 34.4%

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

   4. Taylor expanded in x1 around 0 35.7%

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

      1. fma-def 36.7%

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

      2. fma-neg 36.7%

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

      3. fma-neg 36.7%

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

      4. metadata-eval 36.7%

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

      5. metadata-eval 36.7%

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

   6. Simplified 36.7%

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

   7. Taylor expanded in x2 around 0 53.9%

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

   if -7.00000000000000031e47 < x1 < -1.9e-200 or 6.5999999999999999e-177 < x1

   1. Initial program 75.3%

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

   3. Taylor expanded in x1 around 0 49.4%

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

   4. Taylor expanded in x1 around 0 59.9%

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

      1. fma-def 60.6%

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

      2. fma-neg 60.6%

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

      3. fma-neg 60.6%

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

      4. metadata-eval 60.6%

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

      5. metadata-eval 60.6%

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

   6. Simplified 60.6%

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

   7. Taylor expanded in x1 around 0 59.9%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7 \cdot 10^{+47} \lor \neg \left(x1 \leq -1.9 \cdot 10^{-200}\right) \land x1 \leq 6.6 \cdot 10^{-177}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot x2 - x1 \cdot \left(4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right) - -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 53.2% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ t_1 := 4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\\ \mathbf{if}\;x1 \leq -7 \cdot 10^{+47}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -1.15 \cdot 10^{-145}:\\ \;\;\;\;x1 \cdot \left(-1 - t\_1\right)\\ \mathbf{elif}\;x1 \leq 1.45 \cdot 10^{-20}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (- (* x1 -2.0) (* x2 (- 6.0 (* x1 -12.0))))))
        (t_1 (* 4.0 (* x2 (- 3.0 (* x2 2.0))))))
   (if (<= x1 -7e+47)
     t_0
     (if (<= x1 -1.15e-145)
       (* x1 (- -1.0 t_1))
       (if (<= x1 1.45e-20) t_0 (+ x1 (* x1 (- 1.0 t_1))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))));
	double t_1 = 4.0 * (x2 * (3.0 - (x2 * 2.0)));
	double tmp;
	if (x1 <= -7e+47) {
		tmp = t_0;
	} else if (x1 <= -1.15e-145) {
		tmp = x1 * (-1.0 - t_1);
	} else if (x1 <= 1.45e-20) {
		tmp = t_0;
	} else {
		tmp = x1 + (x1 * (1.0 - 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) :: tmp
    t_0 = x1 + ((x1 * (-2.0d0)) - (x2 * (6.0d0 - (x1 * (-12.0d0)))))
    t_1 = 4.0d0 * (x2 * (3.0d0 - (x2 * 2.0d0)))
    if (x1 <= (-7d+47)) then
        tmp = t_0
    else if (x1 <= (-1.15d-145)) then
        tmp = x1 * ((-1.0d0) - t_1)
    else if (x1 <= 1.45d-20) then
        tmp = t_0
    else
        tmp = x1 + (x1 * (1.0d0 - t_1))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))));
	double t_1 = 4.0 * (x2 * (3.0 - (x2 * 2.0)));
	double tmp;
	if (x1 <= -7e+47) {
		tmp = t_0;
	} else if (x1 <= -1.15e-145) {
		tmp = x1 * (-1.0 - t_1);
	} else if (x1 <= 1.45e-20) {
		tmp = t_0;
	} else {
		tmp = x1 + (x1 * (1.0 - t_1));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))))
	t_1 = 4.0 * (x2 * (3.0 - (x2 * 2.0)))
	tmp = 0
	if x1 <= -7e+47:
		tmp = t_0
	elif x1 <= -1.15e-145:
		tmp = x1 * (-1.0 - t_1)
	elif x1 <= 1.45e-20:
		tmp = t_0
	else:
		tmp = x1 + (x1 * (1.0 - t_1))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x1 * -2.0) - Float64(x2 * Float64(6.0 - Float64(x1 * -12.0)))))
	t_1 = Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(x2 * 2.0))))
	tmp = 0.0
	if (x1 <= -7e+47)
		tmp = t_0;
	elseif (x1 <= -1.15e-145)
		tmp = Float64(x1 * Float64(-1.0 - t_1));
	elseif (x1 <= 1.45e-20)
		tmp = t_0;
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 - t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))));
	t_1 = 4.0 * (x2 * (3.0 - (x2 * 2.0)));
	tmp = 0.0;
	if (x1 <= -7e+47)
		tmp = t_0;
	elseif (x1 <= -1.15e-145)
		tmp = x1 * (-1.0 - t_1);
	elseif (x1 <= 1.45e-20)
		tmp = t_0;
	else
		tmp = x1 + (x1 * (1.0 - t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] - N[(x2 * N[(6.0 - N[(x1 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(4.0 * N[(x2 * N[(3.0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -7e+47], t$95$0, If[LessEqual[x1, -1.15e-145], N[(x1 * N[(-1.0 - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.45e-20], t$95$0, N[(x1 + N[(x1 * N[(1.0 - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -7.00000000000000031e47 or -1.15000000000000004e-145 < x1 < 1.45e-20

   1. Initial program 68.7%

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

   3. Taylor expanded in x1 around 0 46.0%

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

   4. Taylor expanded in x1 around 0 47.2%

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

      1. fma-def 48.0%

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

      2. fma-neg 48.0%

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

      3. fma-neg 48.0%

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

      4. metadata-eval 48.0%

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

      5. metadata-eval 48.0%

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

   6. Simplified 48.0%

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

   7. Taylor expanded in x2 around 0 57.6%

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

   if -7.00000000000000031e47 < x1 < -1.15000000000000004e-145

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 87.7%

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

   4. Taylor expanded in x1 around 0 87.8%

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

      1. fma-def 87.9%

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

      2. fma-neg 87.9%

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

      3. fma-neg 87.9%

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

      4. metadata-eval 87.9%

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

      5. metadata-eval 87.9%

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

   6. Simplified 87.9%

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

   7. Taylor expanded in x1 around inf 68.2%

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

   if 1.45e-20 < x1

   1. Initial program 54.6%

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

   3. Taylor expanded in x1 around 0 14.8%

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

   4. Taylor expanded in x1 around inf 37.1%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7 \cdot 10^{+47}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \mathbf{elif}\;x1 \leq -1.15 \cdot 10^{-145}:\\ \;\;\;\;x1 \cdot \left(-1 - 4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.45 \cdot 10^{-20}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 53.7% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -7 \cdot 10^{+47} \lor \neg \left(x1 \leq -2.05 \cdot 10^{-145}\right) \land x1 \leq 3.8 \cdot 10^{-95}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(-1 - 4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -7e+47) (and (not (<= x1 -2.05e-145)) (<= x1 3.8e-95)))
   (+ x1 (- (* x1 -2.0) (* x2 (- 6.0 (* x1 -12.0)))))
   (* x1 (- -1.0 (* 4.0 (* x2 (- 3.0 (* x2 2.0))))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -7e+47) || (!(x1 <= -2.05e-145) && (x1 <= 3.8e-95))) {
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))));
	} else {
		tmp = x1 * (-1.0 - (4.0 * (x2 * (3.0 - (x2 * 2.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-7d+47)) .or. (.not. (x1 <= (-2.05d-145))) .and. (x1 <= 3.8d-95)) then
        tmp = x1 + ((x1 * (-2.0d0)) - (x2 * (6.0d0 - (x1 * (-12.0d0)))))
    else
        tmp = x1 * ((-1.0d0) - (4.0d0 * (x2 * (3.0d0 - (x2 * 2.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -7e+47) || (!(x1 <= -2.05e-145) && (x1 <= 3.8e-95))) {
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))));
	} else {
		tmp = x1 * (-1.0 - (4.0 * (x2 * (3.0 - (x2 * 2.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -7e+47) or (not (x1 <= -2.05e-145) and (x1 <= 3.8e-95)):
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))))
	else:
		tmp = x1 * (-1.0 - (4.0 * (x2 * (3.0 - (x2 * 2.0)))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -7e+47) || (!(x1 <= -2.05e-145) && (x1 <= 3.8e-95)))
		tmp = Float64(x1 + Float64(Float64(x1 * -2.0) - Float64(x2 * Float64(6.0 - Float64(x1 * -12.0)))));
	else
		tmp = Float64(x1 * Float64(-1.0 - Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(x2 * 2.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -7e+47) || (~((x1 <= -2.05e-145)) && (x1 <= 3.8e-95)))
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - (x1 * -12.0))));
	else
		tmp = x1 * (-1.0 - (4.0 * (x2 * (3.0 - (x2 * 2.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -7e+47], And[N[Not[LessEqual[x1, -2.05e-145]], $MachinePrecision], LessEqual[x1, 3.8e-95]]], N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] - N[(x2 * N[(6.0 - N[(x1 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 * N[(-1.0 - N[(4.0 * N[(x2 * N[(3.0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -7.00000000000000031e47 or -2.0499999999999999e-145 < x1 < 3.7999999999999997e-95

   1. Initial program 66.7%

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

   3. Taylor expanded in x1 around 0 42.5%

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

   4. Taylor expanded in x1 around 0 43.7%

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

      1. fma-def 44.6%

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

      2. fma-neg 44.6%

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

      3. fma-neg 44.6%

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

      4. metadata-eval 44.6%

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

      5. metadata-eval 44.6%

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

   6. Simplified 44.6%

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

   7. Taylor expanded in x2 around 0 57.2%

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

   if -7.00000000000000031e47 < x1 < -2.0499999999999999e-145 or 3.7999999999999997e-95 < x1

   1. Initial program 72.1%

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

   3. Taylor expanded in x1 around 0 44.1%

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

   4. Taylor expanded in x1 around 0 55.9%

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

      1. fma-def 56.7%

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

      2. fma-neg 56.7%

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

      3. fma-neg 56.7%

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

      4. metadata-eval 56.7%

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

      5. metadata-eval 56.7%

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

   6. Simplified 56.7%

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

   7. Taylor expanded in x1 around inf 48.7%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7 \cdot 10^{+47} \lor \neg \left(x1 \leq -2.05 \cdot 10^{-145}\right) \land x1 \leq 3.8 \cdot 10^{-95}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(-1 - 4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 46.6% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -6 \cdot 10^{-153} \lor \neg \left(x1 \leq 3.9 \cdot 10^{-116}\right):\\ \;\;\;\;x1 \cdot \left(-1 - 4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot x2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -6e-153) (not (<= x1 3.9e-116)))
   (* x1 (- -1.0 (* 4.0 (* x2 (- 3.0 (* x2 2.0))))))
   (* -6.0 x2)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -6e-153) || !(x1 <= 3.9e-116)) {
		tmp = x1 * (-1.0 - (4.0 * (x2 * (3.0 - (x2 * 2.0)))));
	} else {
		tmp = -6.0 * x2;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-6d-153)) .or. (.not. (x1 <= 3.9d-116))) then
        tmp = x1 * ((-1.0d0) - (4.0d0 * (x2 * (3.0d0 - (x2 * 2.0d0)))))
    else
        tmp = (-6.0d0) * x2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -6e-153) || !(x1 <= 3.9e-116)) {
		tmp = x1 * (-1.0 - (4.0 * (x2 * (3.0 - (x2 * 2.0)))));
	} else {
		tmp = -6.0 * x2;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -6e-153) or not (x1 <= 3.9e-116):
		tmp = x1 * (-1.0 - (4.0 * (x2 * (3.0 - (x2 * 2.0)))))
	else:
		tmp = -6.0 * x2
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -6e-153) || !(x1 <= 3.9e-116))
		tmp = Float64(x1 * Float64(-1.0 - Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(x2 * 2.0))))));
	else
		tmp = Float64(-6.0 * x2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -6e-153) || ~((x1 <= 3.9e-116)))
		tmp = x1 * (-1.0 - (4.0 * (x2 * (3.0 - (x2 * 2.0)))));
	else
		tmp = -6.0 * x2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -6e-153], N[Not[LessEqual[x1, 3.9e-116]], $MachinePrecision]], N[(x1 * N[(-1.0 - N[(4.0 * N[(x2 * N[(3.0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-6.0 * x2), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -6e-153 or 3.9000000000000001e-116 < x1

   1. Initial program 60.6%

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

   3. Taylor expanded in x1 around 0 33.2%

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

   4. Taylor expanded in x1 around 0 42.0%

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

      1. fma-def 42.6%

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

      2. fma-neg 42.6%

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

      3. fma-neg 42.6%

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

      4. metadata-eval 42.6%

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

      5. metadata-eval 42.6%

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

   6. Simplified 42.6%

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

   7. Taylor expanded in x1 around inf 36.1%

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

   if -6e-153 < x1 < 3.9000000000000001e-116

   1. Initial program 98.0%

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

   3. Taylor expanded in x1 around 0 75.9%

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

   4. Taylor expanded in x1 around 0 76.1%

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

      1. *-commutative 76.1%

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

   6. Simplified 76.1%

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

   7. Taylor expanded in x1 around 0 76.3%

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

      1. *-commutative 76.3%

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

   9. Simplified 76.3%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6 \cdot 10^{-153} \lor \neg \left(x1 \leq 3.9 \cdot 10^{-116}\right):\\ \;\;\;\;x1 \cdot \left(-1 - 4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot x2\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 30.9% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -1.35 \cdot 10^{-120}:\\ \;\;\;\;-6 \cdot x2\\ \mathbf{elif}\;x2 \leq 4.4 \cdot 10^{-251}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x1 + -6 \cdot x2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 -1.35e-120)
   (* -6.0 x2)
   (if (<= x2 4.4e-251) (- x1) (+ x1 (* -6.0 x2)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= -1.35e-120) {
		tmp = -6.0 * x2;
	} else if (x2 <= 4.4e-251) {
		tmp = -x1;
	} else {
		tmp = x1 + (-6.0 * x2);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x2 <= (-1.35d-120)) then
        tmp = (-6.0d0) * x2
    else if (x2 <= 4.4d-251) then
        tmp = -x1
    else
        tmp = x1 + ((-6.0d0) * x2)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x2 <= -1.35e-120) {
		tmp = -6.0 * x2;
	} else if (x2 <= 4.4e-251) {
		tmp = -x1;
	} else {
		tmp = x1 + (-6.0 * x2);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= -1.35e-120:
		tmp = -6.0 * x2
	elif x2 <= 4.4e-251:
		tmp = -x1
	else:
		tmp = x1 + (-6.0 * x2)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= -1.35e-120)
		tmp = Float64(-6.0 * x2);
	elseif (x2 <= 4.4e-251)
		tmp = Float64(-x1);
	else
		tmp = Float64(x1 + Float64(-6.0 * x2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= -1.35e-120)
		tmp = -6.0 * x2;
	elseif (x2 <= 4.4e-251)
		tmp = -x1;
	else
		tmp = x1 + (-6.0 * x2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, -1.35e-120], N[(-6.0 * x2), $MachinePrecision], If[LessEqual[x2, 4.4e-251], (-x1), N[(x1 + N[(-6.0 * x2), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -1.3499999999999999e-120

   1. Initial program 68.4%

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

   3. Taylor expanded in x1 around 0 45.3%

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

   4. Taylor expanded in x1 around 0 29.0%

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

      1. *-commutative 29.0%

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

   6. Simplified 29.0%

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

   7. Taylor expanded in x1 around 0 29.1%

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

      1. *-commutative 29.1%

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

   9. Simplified 29.1%

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

   if -1.3499999999999999e-120 < x2 < 4.4e-251

   1. Initial program 70.3%

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

   3. Taylor expanded in x1 around 0 38.9%

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

   4. Taylor expanded in x1 around 0 38.8%

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

      1. fma-def 38.8%

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

      2. fma-neg 38.8%

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

      3. fma-neg 38.8%

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

      4. metadata-eval 38.8%

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

      5. metadata-eval 38.8%

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

   6. Simplified 38.8%

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

   7. Taylor expanded in x2 around 0 34.9%

      \[\leadsto \color{blue}{x1 + -2 \cdot x1} \]
   8. Step-by-step derivation

      1. distribute-rgt1-in 34.9%

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

      2. metadata-eval 34.9%

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

      3. mul-1-neg 34.9%

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

   9. Simplified 34.9%

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

   if 4.4e-251 < x2

   1. Initial program 70.1%

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

   3. Taylor expanded in x1 around 0 43.9%

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

   4. Taylor expanded in x1 around 0 28.8%

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

      1. *-commutative 28.8%

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

   6. Simplified 28.8%

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

4. Final simplification 30.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.35 \cdot 10^{-120}:\\ \;\;\;\;-6 \cdot x2\\ \mathbf{elif}\;x2 \leq 4.4 \cdot 10^{-251}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x1 + -6 \cdot x2\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.6% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -2.5 \cdot 10^{-120} \lor \neg \left(x2 \leq 4.4 \cdot 10^{-251}\right):\\ \;\;\;\;-6 \cdot x2\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -2.5e-120) (not (<= x2 4.4e-251))) (* -6.0 x2) (- x1)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -2.5e-120) || !(x2 <= 4.4e-251)) {
		tmp = -6.0 * x2;
	} else {
		tmp = -x1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-2.5d-120)) .or. (.not. (x2 <= 4.4d-251))) then
        tmp = (-6.0d0) * x2
    else
        tmp = -x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -2.5e-120) || !(x2 <= 4.4e-251)) {
		tmp = -6.0 * x2;
	} else {
		tmp = -x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -2.5e-120) or not (x2 <= 4.4e-251):
		tmp = -6.0 * x2
	else:
		tmp = -x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -2.5e-120) || !(x2 <= 4.4e-251))
		tmp = Float64(-6.0 * x2);
	else
		tmp = Float64(-x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -2.5e-120) || ~((x2 <= 4.4e-251)))
		tmp = -6.0 * x2;
	else
		tmp = -x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -2.5e-120], N[Not[LessEqual[x2, 4.4e-251]], $MachinePrecision]], N[(-6.0 * x2), $MachinePrecision], (-x1)]

Derivation

1. Split input into 2 regimes

2. if x2 < -2.50000000000000003e-120 or 4.4e-251 < x2

   1. Initial program 69.4%

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

   3. Taylor expanded in x1 around 0 44.5%

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

   4. Taylor expanded in x1 around 0 28.9%

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

      1. *-commutative 28.9%

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

   6. Simplified 28.9%

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

   7. Taylor expanded in x1 around 0 28.5%

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

      1. *-commutative 28.5%

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

   9. Simplified 28.5%

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

   if -2.50000000000000003e-120 < x2 < 4.4e-251

   1. Initial program 70.3%

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

   3. Taylor expanded in x1 around 0 38.9%

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

   4. Taylor expanded in x1 around 0 38.8%

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

      1. fma-def 38.8%

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

      2. fma-neg 38.8%

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

      3. fma-neg 38.8%

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

      4. metadata-eval 38.8%

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

      5. metadata-eval 38.8%

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

   6. Simplified 38.8%

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

   7. Taylor expanded in x2 around 0 34.9%

      \[\leadsto \color{blue}{x1 + -2 \cdot x1} \]
   8. Step-by-step derivation

      1. distribute-rgt1-in 34.9%

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

      2. metadata-eval 34.9%

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

      3. mul-1-neg 34.9%

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

   9. Simplified 34.9%

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

4. Final simplification 29.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -2.5 \cdot 10^{-120} \lor \neg \left(x2 \leq 4.4 \cdot 10^{-251}\right):\\ \;\;\;\;-6 \cdot x2\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 14.0% 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 69.5%

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

3. Taylor expanded in x1 around 0 43.4%

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

4. Taylor expanded in x1 around 0 50.1%

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

   1. fma-def 51.0%

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

   2. fma-neg 51.0%

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

   3. fma-neg 51.0%

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

   4. metadata-eval 51.0%

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

   5. metadata-eval 51.0%

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

6. Simplified 51.0%

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

7. Taylor expanded in x2 around 0 11.4%

   \[\leadsto \color{blue}{x1 + -2 \cdot x1} \]
8. Step-by-step derivation

   1. distribute-rgt1-in 11.4%

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

   2. metadata-eval 11.4%

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

   3. mul-1-neg 11.4%

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

9. Simplified 11.4%

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

10. Final simplification 11.4%

    \[\leadsto -x1 \]
11. Add Preprocessing

Alternative 20: 3.3% accurate, 127.0× speedup

Math

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

FPCore

(FPCore (x1 x2) :precision binary64 x1)

C

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

Fortran

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

Java

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

Python

def code(x1, x2):
	return x1

Julia

function code(x1, x2)
	return x1
end

MATLAB

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

Wolfram

code[x1_, x2_] := x1

Derivation

1. Initial program 69.5%

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

3. Taylor expanded in x1 around 0 43.4%

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

4. Taylor expanded in x1 around 0 24.5%

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

   1. *-commutative 24.5%

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

6. Simplified 24.5%

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

7. Taylor expanded in x1 around inf 3.3%

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

8. Final simplification 3.3%

   \[\leadsto x1 \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024027 
(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))))))