Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 68.0% → 99.2%

Time: 1.8min

Alternatives: 28

Speedup: 3.2×

• 47.1% of points produce a very large (infinite) output. You may want to add a precondition.

• could not determine a ground truth

  1. x1 = -4.541628305545041e-252
  2. x2 = -1.0219504094978108e-161

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: 68.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 \cdot \left(x1 \cdot x1\right)\\ t_1 := \frac{t\_0 - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\\ t_2 := x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ t_3 := \frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\\ t_4 := \frac{t\_0 - \mathsf{fma}\left(x2, -2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\\ \mathbf{if}\;x1 \leq -4 \cdot 10^{+154}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq -1.7 \cdot 10^{-80}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, t\_1, t\_0 \cdot t\_4 + \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + x1 \cdot \left(2 \cdot \left(t\_4 \cdot \left(t\_4 + -3\right)\right) + x1 \cdot \mathsf{fma}\left(t\_4, 4, -6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+152}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, t\_1, x1 + \mathsf{fma}\left(\mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot \mathsf{fma}\left(t\_3, 4, -6\right), \left(x1 \cdot \left(2 \cdot t\_3\right)\right) \cdot \left(-3 + t\_3\right)\right), \mathsf{fma}\left(t\_0, t\_3, {x1}^{3}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 3.0 (* x1 x1)))
        (t_1 (/ (- t_0 (fma 2.0 x2 x1)) (fma x1 x1 1.0)))
        (t_2 (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0))))))
        (t_3 (/ (- (fma x1 (* x1 3.0) (* 2.0 x2)) x1) (fma x1 x1 1.0)))
        (t_4 (/ (- t_0 (fma x2 -2.0 x1)) (fma x1 x1 1.0))))
   (if (<= x1 -4e+154)
     t_2
     (if (<= x1 -1.7e-80)
       (+
        x1
        (fma
         3.0
         t_1
         (+
          (* t_0 t_4)
          (*
           (fma x1 x1 1.0)
           (+
            x1
            (*
             x1
             (+ (* 2.0 (* t_4 (+ t_4 -3.0))) (* x1 (fma t_4 4.0 -6.0)))))))))
       (if (<= x1 2e+152)
         (+
          x1
          (fma
           3.0
           t_1
           (+
            x1
            (fma
             (fma x1 x1 1.0)
             (fma
              x1
              (* x1 (fma t_3 4.0 -6.0))
              (* (* x1 (* 2.0 t_3)) (+ -3.0 t_3)))
             (fma t_0 t_3 (pow x1 3.0))))))
         t_2)))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 * (x1 * x1);
	double t_1 = (t_0 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0);
	double t_2 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_3 = (fma(x1, (x1 * 3.0), (2.0 * x2)) - x1) / fma(x1, x1, 1.0);
	double t_4 = (t_0 - fma(x2, -2.0, x1)) / fma(x1, x1, 1.0);
	double tmp;
	if (x1 <= -4e+154) {
		tmp = t_2;
	} else if (x1 <= -1.7e-80) {
		tmp = x1 + fma(3.0, t_1, ((t_0 * t_4) + (fma(x1, x1, 1.0) * (x1 + (x1 * ((2.0 * (t_4 * (t_4 + -3.0))) + (x1 * fma(t_4, 4.0, -6.0))))))));
	} else if (x1 <= 2e+152) {
		tmp = x1 + fma(3.0, t_1, (x1 + fma(fma(x1, x1, 1.0), fma(x1, (x1 * fma(t_3, 4.0, -6.0)), ((x1 * (2.0 * t_3)) * (-3.0 + t_3))), fma(t_0, t_3, pow(x1, 3.0)))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(3.0 * Float64(x1 * x1))
	t_1 = Float64(Float64(t_0 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0))
	t_2 = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))))
	t_3 = Float64(Float64(fma(x1, Float64(x1 * 3.0), Float64(2.0 * x2)) - x1) / fma(x1, x1, 1.0))
	t_4 = Float64(Float64(t_0 - fma(x2, -2.0, x1)) / fma(x1, x1, 1.0))
	tmp = 0.0
	if (x1 <= -4e+154)
		tmp = t_2;
	elseif (x1 <= -1.7e-80)
		tmp = Float64(x1 + fma(3.0, t_1, Float64(Float64(t_0 * t_4) + 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_4, 4.0, -6.0)))))))));
	elseif (x1 <= 2e+152)
		tmp = Float64(x1 + fma(3.0, t_1, Float64(x1 + fma(fma(x1, x1, 1.0), fma(x1, Float64(x1 * fma(t_3, 4.0, -6.0)), Float64(Float64(x1 * Float64(2.0 * t_3)) * Float64(-3.0 + t_3))), fma(t_0, t_3, (x1 ^ 3.0))))));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(t$95$0 - N[(2.0 * x2 + x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision] + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$0 - N[(x2 * -2.0 + x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4e+154], t$95$2, If[LessEqual[x1, -1.7e-80], N[(x1 + N[(3.0 * t$95$1 + N[(N[(t$95$0 * t$95$4), $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$4 * 4.0 + -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+152], N[(x1 + N[(3.0 * t$95$1 + N[(x1 + N[(N[(x1 * x1 + 1.0), $MachinePrecision] * N[(x1 * N[(x1 * N[(t$95$3 * 4.0 + -6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(2.0 * t$95$3), $MachinePrecision]), $MachinePrecision] * N[(-3.0 + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$3 + N[Power[x1, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4.00000000000000015e154 or 2.0000000000000001e152 < 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 73.1%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -4.00000000000000015e154 < x1 < -1.7e-80

   1. Initial program 76.3%

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

   3. Simplified 99.7%

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

   if -1.7e-80 < x1 < 2.0000000000000001e152

   1. Initial program 99.5%

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

   3. Simplified 99.7%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.7 \cdot 10^{-80}:\\ \;\;\;\;x1 + \mathsf{fma}\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{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)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+152}:\\ \;\;\;\;x1 + \mathsf{fma}\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(-3 + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\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, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, {x1}^{3}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 3 \cdot \left(x1 \cdot x1\right)\\ t_2 := x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ t_3 := \frac{\mathsf{fma}\left(x1 \cdot 3, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\\ t_4 := \frac{t\_1 - \mathsf{fma}\left(x2, -2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\\ \mathbf{if}\;x1 \leq -4 \cdot 10^{+154}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq -1.05 \cdot 10^{-99}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{t\_1 - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, t\_1 \cdot t\_4 + \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + x1 \cdot \left(2 \cdot \left(t\_4 \cdot \left(t\_4 + -3\right)\right) + x1 \cdot \mathsf{fma}\left(t\_4, 4, -6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(\left(\mathsf{fma}\left(\mathsf{fma}\left(t\_3 \cdot \left(x1 \cdot 2\right), -3 + t\_3, \left(x1 \cdot x1\right) \cdot \mathsf{fma}\left(4, t\_3, -6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), t\_3 \cdot t\_0\right) + x1 \cdot \left(x1 \cdot x1\right)\right) + \left(x1 + 3 \cdot \frac{t\_0 - \left(x1 + 2 \cdot x2\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (* 3.0 (* x1 x1)))
        (t_2 (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0))))))
        (t_3 (/ (- (fma (* x1 3.0) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0)))
        (t_4 (/ (- t_1 (fma x2 -2.0 x1)) (fma x1 x1 1.0))))
   (if (<= x1 -4e+154)
     t_2
     (if (<= x1 -1.05e-99)
       (+
        x1
        (fma
         3.0
         (/ (- t_1 (fma 2.0 x2 x1)) (fma x1 x1 1.0))
         (+
          (* t_1 t_4)
          (*
           (fma x1 x1 1.0)
           (+
            x1
            (*
             x1
             (+ (* 2.0 (* t_4 (+ t_4 -3.0))) (* x1 (fma t_4 4.0 -6.0)))))))))
       (if (<= x1 2e+152)
         (+
          x1
          (+
           (+
            (fma
             (fma
              (* t_3 (* x1 2.0))
              (+ -3.0 t_3)
              (* (* x1 x1) (fma 4.0 t_3 -6.0)))
             (fma x1 x1 1.0)
             (* t_3 t_0))
            (* x1 (* x1 x1)))
           (+ x1 (* 3.0 (/ (- t_0 (+ x1 (* 2.0 x2))) (fma x1 x1 1.0))))))
         t_2)))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 3.0 * (x1 * x1);
	double t_2 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_3 = (fma((x1 * 3.0), x1, (2.0 * x2)) - x1) / fma(x1, x1, 1.0);
	double t_4 = (t_1 - fma(x2, -2.0, x1)) / fma(x1, x1, 1.0);
	double tmp;
	if (x1 <= -4e+154) {
		tmp = t_2;
	} else if (x1 <= -1.05e-99) {
		tmp = x1 + fma(3.0, ((t_1 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), ((t_1 * t_4) + (fma(x1, x1, 1.0) * (x1 + (x1 * ((2.0 * (t_4 * (t_4 + -3.0))) + (x1 * fma(t_4, 4.0, -6.0))))))));
	} else if (x1 <= 2e+152) {
		tmp = x1 + ((fma(fma((t_3 * (x1 * 2.0)), (-3.0 + t_3), ((x1 * x1) * fma(4.0, t_3, -6.0))), fma(x1, x1, 1.0), (t_3 * t_0)) + (x1 * (x1 * x1))) + (x1 + (3.0 * ((t_0 - (x1 + (2.0 * x2))) / fma(x1, x1, 1.0)))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(3.0 * Float64(x1 * x1))
	t_2 = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))))
	t_3 = Float64(Float64(fma(Float64(x1 * 3.0), x1, Float64(2.0 * x2)) - x1) / fma(x1, x1, 1.0))
	t_4 = Float64(Float64(t_1 - fma(x2, -2.0, x1)) / fma(x1, x1, 1.0))
	tmp = 0.0
	if (x1 <= -4e+154)
		tmp = t_2;
	elseif (x1 <= -1.05e-99)
		tmp = Float64(x1 + fma(3.0, Float64(Float64(t_1 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), Float64(Float64(t_1 * t_4) + 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_4, 4.0, -6.0)))))))));
	elseif (x1 <= 2e+152)
		tmp = Float64(x1 + Float64(Float64(fma(fma(Float64(t_3 * Float64(x1 * 2.0)), Float64(-3.0 + t_3), Float64(Float64(x1 * x1) * fma(4.0, t_3, -6.0))), fma(x1, x1, 1.0), Float64(t_3 * t_0)) + Float64(x1 * Float64(x1 * x1))) + Float64(x1 + Float64(3.0 * Float64(Float64(t_0 - Float64(x1 + Float64(2.0 * x2))) / fma(x1, x1, 1.0))))));
	else
		tmp = t_2;
	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[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(x1 * 3.0), $MachinePrecision] * x1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$1 - N[(x2 * -2.0 + x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4e+154], t$95$2, If[LessEqual[x1, -1.05e-99], N[(x1 + N[(3.0 * N[(N[(t$95$1 - N[(2.0 * x2 + x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * t$95$4), $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$4 * 4.0 + -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+152], N[(x1 + N[(N[(N[(N[(N[(t$95$3 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(-3.0 + t$95$3), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(4.0 * t$95$3 + -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x1 * x1 + 1.0), $MachinePrecision] + N[(t$95$3 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(3.0 * N[(N[(t$95$0 - N[(x1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4.00000000000000015e154 or 2.0000000000000001e152 < 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 73.1%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -4.00000000000000015e154 < x1 < -1.04999999999999992e-99

   1. Initial program 78.3%

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

   3. Simplified 99.7%

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

   if -1.04999999999999992e-99 < x1 < 2.0000000000000001e152

   1. Initial program 99.6%

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

   3. Simplified 99.6%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.05 \cdot 10^{-99}:\\ \;\;\;\;x1 + \mathsf{fma}\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{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)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(x1 \cdot 3, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(x1 \cdot 2\right), -3 + \frac{\mathsf{fma}\left(x1 \cdot 3, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, \left(x1 \cdot x1\right) \cdot \mathsf{fma}\left(4, \frac{\mathsf{fma}\left(x1 \cdot 3, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, -6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \frac{\mathsf{fma}\left(x1 \cdot 3, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right) + \left(x1 + 3 \cdot \frac{x1 \cdot \left(x1 \cdot 3\right) - \left(x1 + 2 \cdot x2\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 3 \cdot \left(x1 \cdot x1\right)\\ t_2 := x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ t_3 := 1 + x1 \cdot x1\\ t_4 := \frac{\left(2 \cdot x2 + t\_0\right) - x1}{t\_3}\\ t_5 := \frac{t\_1 - \mathsf{fma}\left(x2, -2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\\ \mathbf{if}\;x1 \leq -4 \cdot 10^{+154}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq -4.9 \cdot 10^{-100}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{t\_1 - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, t\_1 \cdot t\_5 + \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + x1 \cdot \left(2 \cdot \left(t\_5 \cdot \left(t\_5 + -3\right)\right) + x1 \cdot \mathsf{fma}\left(t\_5, 4, -6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t\_3 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_4\right) \cdot \left(t\_4 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_4 - 6\right)\right) + t\_0 \cdot t\_4\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_3}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (* 3.0 (* x1 x1)))
        (t_2 (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0))))))
        (t_3 (+ 1.0 (* x1 x1)))
        (t_4 (/ (- (+ (* 2.0 x2) t_0) x1) t_3))
        (t_5 (/ (- t_1 (fma x2 -2.0 x1)) (fma x1 x1 1.0))))
   (if (<= x1 -4e+154)
     t_2
     (if (<= x1 -4.9e-100)
       (+
        x1
        (fma
         3.0
         (/ (- t_1 (fma 2.0 x2 x1)) (fma x1 x1 1.0))
         (+
          (* t_1 t_5)
          (*
           (fma x1 x1 1.0)
           (+
            x1
            (*
             x1
             (+ (* 2.0 (* t_5 (+ t_5 -3.0))) (* x1 (fma t_5 4.0 -6.0)))))))))
       (if (<= x1 2e+152)
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               t_3
               (+
                (* (* (* x1 2.0) t_4) (- t_4 3.0))
                (* (* x1 x1) (- (* 4.0 t_4) 6.0))))
              (* t_0 t_4))
             (* x1 (* x1 x1))))
           (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_3))))
         t_2)))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 3.0 * (x1 * x1);
	double t_2 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_3 = 1.0 + (x1 * x1);
	double t_4 = (((2.0 * x2) + t_0) - x1) / t_3;
	double t_5 = (t_1 - fma(x2, -2.0, x1)) / fma(x1, x1, 1.0);
	double tmp;
	if (x1 <= -4e+154) {
		tmp = t_2;
	} else if (x1 <= -4.9e-100) {
		tmp = x1 + fma(3.0, ((t_1 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), ((t_1 * t_5) + (fma(x1, x1, 1.0) * (x1 + (x1 * ((2.0 * (t_5 * (t_5 + -3.0))) + (x1 * fma(t_5, 4.0, -6.0))))))));
	} else if (x1 <= 2e+152) {
		tmp = x1 + ((x1 + (((t_3 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((4.0 * t_4) - 6.0)))) + (t_0 * t_4)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(3.0 * Float64(x1 * x1))
	t_2 = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))))
	t_3 = Float64(1.0 + Float64(x1 * x1))
	t_4 = Float64(Float64(Float64(Float64(2.0 * x2) + t_0) - x1) / t_3)
	t_5 = Float64(Float64(t_1 - fma(x2, -2.0, x1)) / fma(x1, x1, 1.0))
	tmp = 0.0
	if (x1 <= -4e+154)
		tmp = t_2;
	elseif (x1 <= -4.9e-100)
		tmp = Float64(x1 + fma(3.0, Float64(Float64(t_1 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), Float64(Float64(t_1 * t_5) + Float64(fma(x1, x1, 1.0) * Float64(x1 + Float64(x1 * Float64(Float64(2.0 * Float64(t_5 * Float64(t_5 + -3.0))) + Float64(x1 * fma(t_5, 4.0, -6.0)))))))));
	elseif (x1 <= 2e+152)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_3 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(t_4 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_4) - 6.0)))) + Float64(t_0 * t_4)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_3))));
	else
		tmp = t_2;
	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[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(N[(2.0 * x2), $MachinePrecision] + t$95$0), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$1 - N[(x2 * -2.0 + x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4e+154], t$95$2, If[LessEqual[x1, -4.9e-100], N[(x1 + N[(3.0 * N[(N[(t$95$1 - N[(2.0 * x2 + x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * t$95$5), $MachinePrecision] + N[(N[(x1 * x1 + 1.0), $MachinePrecision] * N[(x1 + N[(x1 * N[(N[(2.0 * N[(t$95$5 * N[(t$95$5 + -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+152], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$3 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$4), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4.00000000000000015e154 or 2.0000000000000001e152 < 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 73.1%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -4.00000000000000015e154 < x1 < -4.9000000000000003e-100

   1. Initial program 78.3%

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

   3. Simplified 99.7%

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

   if -4.9000000000000003e-100 < x1 < 2.0000000000000001e152

   1. Initial program 99.6%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -4.9 \cdot 10^{-100}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{3 \cdot \left(x1 \cdot x1\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \left(3 \cdot \left(x1 \cdot x1\right)\right) \cdot \frac{3 \cdot \left(x1 \cdot x1\right) - \mathsf{fma}\left(x2, -2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} + \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + x1 \cdot \left(2 \cdot \left(\frac{3 \cdot \left(x1 \cdot x1\right) - \mathsf{fma}\left(x2, -2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(\frac{3 \cdot \left(x1 \cdot x1\right) - \mathsf{fma}\left(x2, -2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} + -3\right)\right) + x1 \cdot \mathsf{fma}\left(\frac{3 \cdot \left(x1 \cdot x1\right) - \mathsf{fma}\left(x2, -2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, 4, -6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(1 + x1 \cdot x1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(\frac{\left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(2 \cdot x2 - 3\right)\\ t_1 := x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := 1 + x1 \cdot x1\\ t_4 := \frac{\left(2 \cdot x2 + t\_2\right) - x1}{t\_3}\\ t_5 := 3 \cdot \frac{\left(t\_2 - 2 \cdot x2\right) - x1}{t\_3}\\ \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(t\_5 + \left(x1 + x1 \cdot \left(t\_0 + x1 \cdot \left(\left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(t\_0 + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 6\right)\right)\right) - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t\_3 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_4\right) \cdot \left(t\_4 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_4 - 6\right)\right) + t\_2 \cdot t\_4\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + t\_5\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 6.0 (- (* 2.0 x2) 3.0)))
        (t_1 (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0))))))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (+ 1.0 (* x1 x1)))
        (t_4 (/ (- (+ (* 2.0 x2) t_2) x1) t_3))
        (t_5 (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_3))))
   (if (<= x1 -4.5e+153)
     t_1
     (if (<= x1 -5e+102)
       (+
        x1
        (+
         t_5
         (+
          x1
          (*
           x1
           (+
            t_0
            (*
             x1
             (-
              (+
               (* x2 6.0)
               (+
                (* x2 8.0)
                (* x1 (- (+ t_0 (* 6.0 (+ 3.0 (* x2 -2.0)))) 6.0))))
              12.0)))))))
       (if (<= x1 2e+152)
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               t_3
               (+
                (* (* (* x1 2.0) t_4) (- t_4 3.0))
                (* (* x1 x1) (- (* 4.0 t_4) 6.0))))
              (* t_2 t_4))
             (* x1 (* x1 x1))))
           t_5))
         t_1)))))

C

double code(double x1, double x2) {
	double t_0 = 6.0 * ((2.0 * x2) - 3.0);
	double t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 1.0 + (x1 * x1);
	double t_4 = (((2.0 * x2) + t_2) - x1) / t_3;
	double t_5 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_3);
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = t_1;
	} else if (x1 <= -5e+102) {
		tmp = x1 + (t_5 + (x1 + (x1 * (t_0 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_0 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))));
	} else if (x1 <= 2e+152) {
		tmp = x1 + ((x1 + (((t_3 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((4.0 * t_4) - 6.0)))) + (t_2 * t_4)) + (x1 * (x1 * x1)))) + t_5);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = 6.0d0 * ((2.0d0 * x2) - 3.0d0)
    t_1 = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = 1.0d0 + (x1 * x1)
    t_4 = (((2.0d0 * x2) + t_2) - x1) / t_3
    t_5 = 3.0d0 * (((t_2 - (2.0d0 * x2)) - x1) / t_3)
    if (x1 <= (-4.5d+153)) then
        tmp = t_1
    else if (x1 <= (-5d+102)) then
        tmp = x1 + (t_5 + (x1 + (x1 * (t_0 + (x1 * (((x2 * 6.0d0) + ((x2 * 8.0d0) + (x1 * ((t_0 + (6.0d0 * (3.0d0 + (x2 * (-2.0d0))))) - 6.0d0)))) - 12.0d0))))))
    else if (x1 <= 2d+152) then
        tmp = x1 + ((x1 + (((t_3 * ((((x1 * 2.0d0) * t_4) * (t_4 - 3.0d0)) + ((x1 * x1) * ((4.0d0 * t_4) - 6.0d0)))) + (t_2 * t_4)) + (x1 * (x1 * x1)))) + t_5)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 6.0 * ((2.0 * x2) - 3.0);
	double t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 1.0 + (x1 * x1);
	double t_4 = (((2.0 * x2) + t_2) - x1) / t_3;
	double t_5 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_3);
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = t_1;
	} else if (x1 <= -5e+102) {
		tmp = x1 + (t_5 + (x1 + (x1 * (t_0 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_0 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))));
	} else if (x1 <= 2e+152) {
		tmp = x1 + ((x1 + (((t_3 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((4.0 * t_4) - 6.0)))) + (t_2 * t_4)) + (x1 * (x1 * x1)))) + t_5);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 6.0 * ((2.0 * x2) - 3.0)
	t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	t_2 = x1 * (x1 * 3.0)
	t_3 = 1.0 + (x1 * x1)
	t_4 = (((2.0 * x2) + t_2) - x1) / t_3
	t_5 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_3)
	tmp = 0
	if x1 <= -4.5e+153:
		tmp = t_1
	elif x1 <= -5e+102:
		tmp = x1 + (t_5 + (x1 + (x1 * (t_0 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_0 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))))
	elif x1 <= 2e+152:
		tmp = x1 + ((x1 + (((t_3 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((4.0 * t_4) - 6.0)))) + (t_2 * t_4)) + (x1 * (x1 * x1)))) + t_5)
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(6.0 * Float64(Float64(2.0 * x2) - 3.0))
	t_1 = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(1.0 + Float64(x1 * x1))
	t_4 = Float64(Float64(Float64(Float64(2.0 * x2) + t_2) - x1) / t_3)
	t_5 = Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_3))
	tmp = 0.0
	if (x1 <= -4.5e+153)
		tmp = t_1;
	elseif (x1 <= -5e+102)
		tmp = Float64(x1 + Float64(t_5 + Float64(x1 + Float64(x1 * Float64(t_0 + Float64(x1 * Float64(Float64(Float64(x2 * 6.0) + Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_0 + Float64(6.0 * Float64(3.0 + Float64(x2 * -2.0)))) - 6.0)))) - 12.0)))))));
	elseif (x1 <= 2e+152)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_3 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(t_4 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_4) - 6.0)))) + Float64(t_2 * t_4)) + Float64(x1 * Float64(x1 * x1)))) + t_5));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 6.0 * ((2.0 * x2) - 3.0);
	t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	t_2 = x1 * (x1 * 3.0);
	t_3 = 1.0 + (x1 * x1);
	t_4 = (((2.0 * x2) + t_2) - x1) / t_3;
	t_5 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_3);
	tmp = 0.0;
	if (x1 <= -4.5e+153)
		tmp = t_1;
	elseif (x1 <= -5e+102)
		tmp = x1 + (t_5 + (x1 + (x1 * (t_0 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_0 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))));
	elseif (x1 <= 2e+152)
		tmp = x1 + ((x1 + (((t_3 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((4.0 * t_4) - 6.0)))) + (t_2 * t_4)) + (x1 * (x1 * x1)))) + t_5);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(6.0 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(N[(2.0 * x2), $MachinePrecision] + t$95$2), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.5e+153], t$95$1, If[LessEqual[x1, -5e+102], N[(x1 + N[(t$95$5 + N[(x1 + N[(x1 * N[(t$95$0 + N[(x1 * N[(N[(N[(x2 * 6.0), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$0 + N[(6.0 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+152], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$3 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$4), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4.5000000000000001e153 or 2.0000000000000001e152 < 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 73.1%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -4.5000000000000001e153 < x1 < -5e102

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around 0 91.7%

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

   if -5e102 < x1 < 2.0000000000000001e152

   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. Recombined 3 regimes into one program.

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + x1 \cdot \left(6 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(\left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(6 \cdot \left(2 \cdot x2 - 3\right) + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 6\right)\right)\right) - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(1 + x1 \cdot x1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(\frac{\left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := 1 + x1 \cdot x1\\ t_3 := \frac{\left(2 \cdot x2 + t\_1\right) - x1}{t\_2}\\ t_4 := 3 \cdot \frac{\left(t\_1 - 2 \cdot x2\right) - x1}{t\_2}\\ \mathbf{if}\;x1 \leq -4 \cdot 10^{+154}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(t\_4 + \left(x1 + 6 \cdot {x1}^{4}\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t\_2 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_3\right) \cdot \left(t\_3 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_3 - 6\right)\right) + t\_1 \cdot t\_3\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + t\_4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0))))))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ 1.0 (* x1 x1)))
        (t_3 (/ (- (+ (* 2.0 x2) t_1) x1) t_2))
        (t_4 (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2))))
   (if (<= x1 -4e+154)
     t_0
     (if (<= x1 -5e+102)
       (+ x1 (+ t_4 (+ x1 (* 6.0 (pow x1 4.0)))))
       (if (<= x1 2e+152)
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               t_2
               (+
                (* (* (* x1 2.0) t_3) (- t_3 3.0))
                (* (* x1 x1) (- (* 4.0 t_3) 6.0))))
              (* t_1 t_3))
             (* x1 (* x1 x1))))
           t_4))
         t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = 1.0 + (x1 * x1);
	double t_3 = (((2.0 * x2) + t_1) - x1) / t_2;
	double t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double tmp;
	if (x1 <= -4e+154) {
		tmp = t_0;
	} else if (x1 <= -5e+102) {
		tmp = x1 + (t_4 + (x1 + (6.0 * pow(x1, 4.0))));
	} else if (x1 <= 2e+152) {
		tmp = x1 + ((x1 + (((t_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((4.0 * t_3) - 6.0)))) + (t_1 * t_3)) + (x1 * (x1 * x1)))) + t_4);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = 1.0d0 + (x1 * x1)
    t_3 = (((2.0d0 * x2) + t_1) - x1) / t_2
    t_4 = 3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_2)
    if (x1 <= (-4d+154)) then
        tmp = t_0
    else if (x1 <= (-5d+102)) then
        tmp = x1 + (t_4 + (x1 + (6.0d0 * (x1 ** 4.0d0))))
    else if (x1 <= 2d+152) then
        tmp = x1 + ((x1 + (((t_2 * ((((x1 * 2.0d0) * t_3) * (t_3 - 3.0d0)) + ((x1 * x1) * ((4.0d0 * t_3) - 6.0d0)))) + (t_1 * t_3)) + (x1 * (x1 * x1)))) + t_4)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = 1.0 + (x1 * x1);
	double t_3 = (((2.0 * x2) + t_1) - x1) / t_2;
	double t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double tmp;
	if (x1 <= -4e+154) {
		tmp = t_0;
	} else if (x1 <= -5e+102) {
		tmp = x1 + (t_4 + (x1 + (6.0 * Math.pow(x1, 4.0))));
	} else if (x1 <= 2e+152) {
		tmp = x1 + ((x1 + (((t_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((4.0 * t_3) - 6.0)))) + (t_1 * t_3)) + (x1 * (x1 * x1)))) + t_4);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	t_1 = x1 * (x1 * 3.0)
	t_2 = 1.0 + (x1 * x1)
	t_3 = (((2.0 * x2) + t_1) - x1) / t_2
	t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)
	tmp = 0
	if x1 <= -4e+154:
		tmp = t_0
	elif x1 <= -5e+102:
		tmp = x1 + (t_4 + (x1 + (6.0 * math.pow(x1, 4.0))))
	elif x1 <= 2e+152:
		tmp = x1 + ((x1 + (((t_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((4.0 * t_3) - 6.0)))) + (t_1 * t_3)) + (x1 * (x1 * x1)))) + t_4)
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(1.0 + Float64(x1 * x1))
	t_3 = Float64(Float64(Float64(Float64(2.0 * x2) + t_1) - x1) / t_2)
	t_4 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2))
	tmp = 0.0
	if (x1 <= -4e+154)
		tmp = t_0;
	elseif (x1 <= -5e+102)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(6.0 * (x1 ^ 4.0)))));
	elseif (x1 <= 2e+152)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_2 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(t_3 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_3) - 6.0)))) + Float64(t_1 * t_3)) + Float64(x1 * Float64(x1 * x1)))) + t_4));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	t_1 = x1 * (x1 * 3.0);
	t_2 = 1.0 + (x1 * x1);
	t_3 = (((2.0 * x2) + t_1) - x1) / t_2;
	t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	tmp = 0.0;
	if (x1 <= -4e+154)
		tmp = t_0;
	elseif (x1 <= -5e+102)
		tmp = x1 + (t_4 + (x1 + (6.0 * (x1 ^ 4.0))));
	elseif (x1 <= 2e+152)
		tmp = x1 + ((x1 + (((t_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((4.0 * t_3) - 6.0)))) + (t_1 * t_3)) + (x1 * (x1 * x1)))) + t_4);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(2.0 * x2), $MachinePrecision] + t$95$1), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4e+154], t$95$0, If[LessEqual[x1, -5e+102], N[(x1 + N[(t$95$4 + N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+152], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$2 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$3), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4.00000000000000015e154 or 2.0000000000000001e152 < 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 73.1%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -4.00000000000000015e154 < x1 < -5e102

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 100.0%

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

   if -5e102 < x1 < 2.0000000000000001e152

   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. Recombined 3 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + 6 \cdot {x1}^{4}\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(1 + x1 \cdot x1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(\frac{\left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(2 \cdot x2 - 3\right)\\ t_1 := x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := 1 + x1 \cdot x1\\ t_4 := 3 \cdot \frac{\left(t\_2 - 2 \cdot x2\right) - x1}{t\_3}\\ t_5 := \frac{\left(2 \cdot x2 + t\_2\right) - x1}{t\_3}\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -1.02 \cdot 10^{+98}:\\ \;\;\;\;x1 + \left(t\_4 + \left(x1 + x1 \cdot \left(t\_0 + x1 \cdot \left(\left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(t\_0 + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 6\right)\right)\right) - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(t\_4 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_2 \cdot t\_5 + t\_3 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_5\right) \cdot \left(t\_5 - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 6.0 (- (* 2.0 x2) 3.0)))
        (t_1 (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0))))))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (+ 1.0 (* x1 x1)))
        (t_4 (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_3)))
        (t_5 (/ (- (+ (* 2.0 x2) t_2) x1) t_3)))
   (if (<= x1 -5e+153)
     t_1
     (if (<= x1 -1.02e+98)
       (+
        x1
        (+
         t_4
         (+
          x1
          (*
           x1
           (+
            t_0
            (*
             x1
             (-
              (+
               (* x2 6.0)
               (+
                (* x2 8.0)
                (* x1 (- (+ t_0 (* 6.0 (+ 3.0 (* x2 -2.0)))) 6.0))))
              12.0)))))))
       (if (<= x1 2e+152)
         (+
          x1
          (+
           t_4
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* t_2 t_5)
              (*
               t_3
               (+ (* (* (* x1 2.0) t_5) (- t_5 3.0)) (* (* x1 x1) 6.0))))))))
         t_1)))))

C

double code(double x1, double x2) {
	double t_0 = 6.0 * ((2.0 * x2) - 3.0);
	double t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 1.0 + (x1 * x1);
	double t_4 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_3);
	double t_5 = (((2.0 * x2) + t_2) - x1) / t_3;
	double tmp;
	if (x1 <= -5e+153) {
		tmp = t_1;
	} else if (x1 <= -1.02e+98) {
		tmp = x1 + (t_4 + (x1 + (x1 * (t_0 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_0 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))));
	} else if (x1 <= 2e+152) {
		tmp = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_5) + (t_3 * ((((x1 * 2.0) * t_5) * (t_5 - 3.0)) + ((x1 * x1) * 6.0)))))));
	} 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) :: t_5
    real(8) :: tmp
    t_0 = 6.0d0 * ((2.0d0 * x2) - 3.0d0)
    t_1 = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = 1.0d0 + (x1 * x1)
    t_4 = 3.0d0 * (((t_2 - (2.0d0 * x2)) - x1) / t_3)
    t_5 = (((2.0d0 * x2) + t_2) - x1) / t_3
    if (x1 <= (-5d+153)) then
        tmp = t_1
    else if (x1 <= (-1.02d+98)) then
        tmp = x1 + (t_4 + (x1 + (x1 * (t_0 + (x1 * (((x2 * 6.0d0) + ((x2 * 8.0d0) + (x1 * ((t_0 + (6.0d0 * (3.0d0 + (x2 * (-2.0d0))))) - 6.0d0)))) - 12.0d0))))))
    else if (x1 <= 2d+152) then
        tmp = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_5) + (t_3 * ((((x1 * 2.0d0) * t_5) * (t_5 - 3.0d0)) + ((x1 * x1) * 6.0d0)))))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 6.0 * ((2.0 * x2) - 3.0);
	double t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 1.0 + (x1 * x1);
	double t_4 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_3);
	double t_5 = (((2.0 * x2) + t_2) - x1) / t_3;
	double tmp;
	if (x1 <= -5e+153) {
		tmp = t_1;
	} else if (x1 <= -1.02e+98) {
		tmp = x1 + (t_4 + (x1 + (x1 * (t_0 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_0 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))));
	} else if (x1 <= 2e+152) {
		tmp = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_5) + (t_3 * ((((x1 * 2.0) * t_5) * (t_5 - 3.0)) + ((x1 * x1) * 6.0)))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 6.0 * ((2.0 * x2) - 3.0)
	t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	t_2 = x1 * (x1 * 3.0)
	t_3 = 1.0 + (x1 * x1)
	t_4 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_3)
	t_5 = (((2.0 * x2) + t_2) - x1) / t_3
	tmp = 0
	if x1 <= -5e+153:
		tmp = t_1
	elif x1 <= -1.02e+98:
		tmp = x1 + (t_4 + (x1 + (x1 * (t_0 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_0 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))))
	elif x1 <= 2e+152:
		tmp = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_5) + (t_3 * ((((x1 * 2.0) * t_5) * (t_5 - 3.0)) + ((x1 * x1) * 6.0)))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(6.0 * Float64(Float64(2.0 * x2) - 3.0))
	t_1 = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(1.0 + Float64(x1 * x1))
	t_4 = Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_3))
	t_5 = Float64(Float64(Float64(Float64(2.0 * x2) + t_2) - x1) / t_3)
	tmp = 0.0
	if (x1 <= -5e+153)
		tmp = t_1;
	elseif (x1 <= -1.02e+98)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(x1 * Float64(t_0 + Float64(x1 * Float64(Float64(Float64(x2 * 6.0) + Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_0 + Float64(6.0 * Float64(3.0 + Float64(x2 * -2.0)))) - 6.0)))) - 12.0)))))));
	elseif (x1 <= 2e+152)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_2 * t_5) + Float64(t_3 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_5) * Float64(t_5 - 3.0)) + Float64(Float64(x1 * x1) * 6.0))))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 6.0 * ((2.0 * x2) - 3.0);
	t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	t_2 = x1 * (x1 * 3.0);
	t_3 = 1.0 + (x1 * x1);
	t_4 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_3);
	t_5 = (((2.0 * x2) + t_2) - x1) / t_3;
	tmp = 0.0;
	if (x1 <= -5e+153)
		tmp = t_1;
	elseif (x1 <= -1.02e+98)
		tmp = x1 + (t_4 + (x1 + (x1 * (t_0 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_0 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))));
	elseif (x1 <= 2e+152)
		tmp = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_5) + (t_3 * ((((x1 * 2.0) * t_5) * (t_5 - 3.0)) + ((x1 * x1) * 6.0)))))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(6.0 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(N[(2.0 * x2), $MachinePrecision] + t$95$2), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, If[LessEqual[x1, -5e+153], t$95$1, If[LessEqual[x1, -1.02e+98], N[(x1 + N[(t$95$4 + N[(x1 + N[(x1 * N[(t$95$0 + N[(x1 * N[(N[(N[(x2 * 6.0), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$0 + N[(6.0 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+152], N[(x1 + N[(t$95$4 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * t$95$5), $MachinePrecision] + N[(t$95$3 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$5), $MachinePrecision] * N[(t$95$5 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.00000000000000018e153 or 2.0000000000000001e152 < 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 73.1%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -5.00000000000000018e153 < x1 < -1.02000000000000007e98

   1. Initial program 7.7%

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

   3. Taylor expanded in x1 around inf 7.7%

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

   4. Taylor expanded in x1 around 0 92.3%

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

   if -1.02000000000000007e98 < x1 < 2.0000000000000001e152

   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 97.1%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.02 \cdot 10^{+98}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + x1 \cdot \left(6 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(\left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(6 \cdot \left(2 \cdot x2 - 3\right) + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 6\right)\right)\right) - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(\frac{\left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot x2 - 3\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := 1 + x1 \cdot x1\\ t_3 := 6 \cdot t\_0\\ t_4 := \frac{\left(2 \cdot x2 + t\_1\right) - x1}{t\_2}\\ t_5 := x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_2 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_4\right) \cdot \left(t\_4 - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right) + t\_1 \cdot \left(2 \cdot x2 - x1\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{if}\;x1 \leq -4 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -9.2 \cdot 10^{+97}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_1 - 2 \cdot x2\right) - x1}{t\_2} + \left(x1 + x1 \cdot \left(t\_3 + x1 \cdot \left(\left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(t\_3 + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 6\right)\right)\right) - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.12 \cdot 10^{+19}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x1 \leq 2.8 \cdot 10^{-7}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+102}:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot t\_0\right) + x1 \cdot \left(x1 \cdot 3 + 3 \cdot \left(3 - x2 \cdot -2\right)\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* 2.0 x2) 3.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ 1.0 (* x1 x1)))
        (t_3 (* 6.0 t_0))
        (t_4 (/ (- (+ (* 2.0 x2) t_1) x1) t_2))
        (t_5
         (+
          x1
          (+
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* t_2 (+ (* (* (* x1 2.0) t_4) (- t_4 3.0)) (* (* x1 x1) 6.0)))
              (* t_1 (- (* 2.0 x2) x1)))))
           (* 3.0 (* x2 -2.0))))))
   (if (<= x1 -4e+154)
     (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))
     (if (<= x1 -9.2e+97)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2))
         (+
          x1
          (*
           x1
           (+
            t_3
            (*
             x1
             (-
              (+
               (* x2 6.0)
               (+
                (* x2 8.0)
                (* x1 (- (+ t_3 (* 6.0 (+ 3.0 (* x2 -2.0)))) 6.0))))
              12.0)))))))
       (if (<= x1 -1.12e+19)
         t_5
         (if (<= x1 2.8e-7)
           (+
            x1
            (+
             (* x2 -6.0)
             (+
              (* x1 (- (* x1 9.0) 2.0))
              (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 6.0) 12.0)))))))
           (if (<= x1 4e+102)
             t_5
             (+
              x1
              (+
               (* x2 -6.0)
               (*
                x1
                (-
                 (+
                  (* 4.0 (* x2 t_0))
                  (* x1 (+ (* x1 3.0) (* 3.0 (- 3.0 (* x2 -2.0))))))
                 2.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = 1.0 + (x1 * x1);
	double t_3 = 6.0 * t_0;
	double t_4 = (((2.0 * x2) + t_1) - x1) / t_2;
	double t_5 = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_2 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * 6.0))) + (t_1 * ((2.0 * x2) - x1))))) + (3.0 * (x2 * -2.0)));
	double tmp;
	if (x1 <= -4e+154) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -9.2e+97) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + (x1 * (t_3 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_3 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))));
	} else if (x1 <= -1.12e+19) {
		tmp = t_5;
	} else if (x1 <= 2.8e-7) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else if (x1 <= 4e+102) {
		tmp = t_5;
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_0)) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = (2.0d0 * x2) - 3.0d0
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = 1.0d0 + (x1 * x1)
    t_3 = 6.0d0 * t_0
    t_4 = (((2.0d0 * x2) + t_1) - x1) / t_2
    t_5 = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_2 * ((((x1 * 2.0d0) * t_4) * (t_4 - 3.0d0)) + ((x1 * x1) * 6.0d0))) + (t_1 * ((2.0d0 * x2) - x1))))) + (3.0d0 * (x2 * (-2.0d0))))
    if (x1 <= (-4d+154)) then
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    else if (x1 <= (-9.2d+97)) then
        tmp = x1 + ((3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_2)) + (x1 + (x1 * (t_3 + (x1 * (((x2 * 6.0d0) + ((x2 * 8.0d0) + (x1 * ((t_3 + (6.0d0 * (3.0d0 + (x2 * (-2.0d0))))) - 6.0d0)))) - 12.0d0))))))
    else if (x1 <= (-1.12d+19)) then
        tmp = t_5
    else if (x1 <= 2.8d-7) then
        tmp = x1 + ((x2 * (-6.0d0)) + ((x1 * ((x1 * 9.0d0) - 2.0d0)) + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 6.0d0) - 12.0d0))))))
    else if (x1 <= 4d+102) then
        tmp = t_5
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((4.0d0 * (x2 * t_0)) + (x1 * ((x1 * 3.0d0) + (3.0d0 * (3.0d0 - (x2 * (-2.0d0))))))) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = 1.0 + (x1 * x1);
	double t_3 = 6.0 * t_0;
	double t_4 = (((2.0 * x2) + t_1) - x1) / t_2;
	double t_5 = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_2 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * 6.0))) + (t_1 * ((2.0 * x2) - x1))))) + (3.0 * (x2 * -2.0)));
	double tmp;
	if (x1 <= -4e+154) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -9.2e+97) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + (x1 * (t_3 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_3 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))));
	} else if (x1 <= -1.12e+19) {
		tmp = t_5;
	} else if (x1 <= 2.8e-7) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else if (x1 <= 4e+102) {
		tmp = t_5;
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_0)) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (2.0 * x2) - 3.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = 1.0 + (x1 * x1)
	t_3 = 6.0 * t_0
	t_4 = (((2.0 * x2) + t_1) - x1) / t_2
	t_5 = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_2 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * 6.0))) + (t_1 * ((2.0 * x2) - x1))))) + (3.0 * (x2 * -2.0)))
	tmp = 0
	if x1 <= -4e+154:
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	elif x1 <= -9.2e+97:
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + (x1 * (t_3 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_3 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))))
	elif x1 <= -1.12e+19:
		tmp = t_5
	elif x1 <= 2.8e-7:
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))))
	elif x1 <= 4e+102:
		tmp = t_5
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_0)) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(2.0 * x2) - 3.0)
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(1.0 + Float64(x1 * x1))
	t_3 = Float64(6.0 * t_0)
	t_4 = Float64(Float64(Float64(Float64(2.0 * x2) + t_1) - x1) / t_2)
	t_5 = Float64(x1 + Float64(Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_2 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(t_4 - 3.0)) + Float64(Float64(x1 * x1) * 6.0))) + Float64(t_1 * Float64(Float64(2.0 * x2) - x1))))) + Float64(3.0 * Float64(x2 * -2.0))))
	tmp = 0.0
	if (x1 <= -4e+154)
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))));
	elseif (x1 <= -9.2e+97)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2)) + Float64(x1 + Float64(x1 * Float64(t_3 + Float64(x1 * Float64(Float64(Float64(x2 * 6.0) + Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_3 + Float64(6.0 * Float64(3.0 + Float64(x2 * -2.0)))) - 6.0)))) - 12.0)))))));
	elseif (x1 <= -1.12e+19)
		tmp = t_5;
	elseif (x1 <= 2.8e-7)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0)) + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)))))));
	elseif (x1 <= 4e+102)
		tmp = t_5;
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(4.0 * Float64(x2 * t_0)) + Float64(x1 * Float64(Float64(x1 * 3.0) + Float64(3.0 * Float64(3.0 - Float64(x2 * -2.0)))))) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (2.0 * x2) - 3.0;
	t_1 = x1 * (x1 * 3.0);
	t_2 = 1.0 + (x1 * x1);
	t_3 = 6.0 * t_0;
	t_4 = (((2.0 * x2) + t_1) - x1) / t_2;
	t_5 = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_2 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * 6.0))) + (t_1 * ((2.0 * x2) - x1))))) + (3.0 * (x2 * -2.0)));
	tmp = 0.0;
	if (x1 <= -4e+154)
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	elseif (x1 <= -9.2e+97)
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + (x1 * (t_3 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_3 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))));
	elseif (x1 <= -1.12e+19)
		tmp = t_5;
	elseif (x1 <= 2.8e-7)
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	elseif (x1 <= 4e+102)
		tmp = t_5;
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_0)) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(6.0 * t$95$0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(N[(2.0 * x2), $MachinePrecision] + t$95$1), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4e+154], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -9.2e+97], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x1 * N[(t$95$3 + N[(x1 * N[(N[(N[(x2 * 6.0), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$3 + N[(6.0 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.12e+19], t$95$5, If[LessEqual[x1, 2.8e-7], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4e+102], t$95$5, N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(4.0 * N[(x2 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + N[(3.0 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -4.00000000000000015e154

   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 60.0%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -4.00000000000000015e154 < x1 < -9.20000000000000022e97

   1. Initial program 7.7%

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

   3. Taylor expanded in x1 around inf 7.7%

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

   4. Taylor expanded in x1 around 0 92.3%

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

   if -9.20000000000000022e97 < x1 < -1.12e19 or 2.80000000000000019e-7 < x1 < 3.99999999999999991e102

   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 inf 91.2%

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

   4. Taylor expanded in x1 around 0 86.0%

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

      1. +-commutative 86.0%

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

      2. mul-1-neg 86.0%

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

      3. sub-neg 86.0%

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

   6. Simplified 86.0%

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

   7. Taylor expanded in x1 around 0 86.0%

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

      1. *-commutative 86.0%

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

   9. Simplified 86.0%

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

   if -1.12e19 < x1 < 2.80000000000000019e-7

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around 0 87.3%

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

   4. Taylor expanded in x1 around 0 87.6%

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

   5. Taylor expanded in x2 around 0 99.7%

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

   if 3.99999999999999991e102 < x1

   1. Initial program 26.0%

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

   3. Taylor expanded in x1 around 0 12.7%

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

   4. Taylor expanded in x1 around 0 96.0%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -9.2 \cdot 10^{+97}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + x1 \cdot \left(6 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(\left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(6 \cdot \left(2 \cdot x2 - 3\right) + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 6\right)\right)\right) - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.12 \cdot 10^{+19}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(1 + x1 \cdot x1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(\frac{\left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2 - x1\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 2.8 \cdot 10^{-7}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(1 + x1 \cdot x1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(\frac{\left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2 - x1\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(x1 \cdot 3 + 3 \cdot \left(3 - x2 \cdot -2\right)\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 95.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := 1 + x1 \cdot x1\\ t_3 := 3 \cdot \frac{\left(t\_1 - 2 \cdot x2\right) - x1}{t\_2}\\ t_4 := 6 \cdot \left(2 \cdot x2 - 3\right)\\ t_5 := \frac{\left(2 \cdot x2 + t\_1\right) - x1}{t\_2}\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+153}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -1.02 \cdot 10^{+98}:\\ \;\;\;\;x1 + \left(t\_3 + \left(x1 + x1 \cdot \left(t\_4 + x1 \cdot \left(\left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(t\_4 + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 6\right)\right)\right) - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(t\_3 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_2 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_5\right) \cdot \left(t\_5 - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right) + 3 \cdot t\_1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0))))))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ 1.0 (* x1 x1)))
        (t_3 (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2)))
        (t_4 (* 6.0 (- (* 2.0 x2) 3.0)))
        (t_5 (/ (- (+ (* 2.0 x2) t_1) x1) t_2)))
   (if (<= x1 -5e+153)
     t_0
     (if (<= x1 -1.02e+98)
       (+
        x1
        (+
         t_3
         (+
          x1
          (*
           x1
           (+
            t_4
            (*
             x1
             (-
              (+
               (* x2 6.0)
               (+
                (* x2 8.0)
                (* x1 (- (+ t_4 (* 6.0 (+ 3.0 (* x2 -2.0)))) 6.0))))
              12.0)))))))
       (if (<= x1 2e+152)
         (+
          x1
          (+
           t_3
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* t_2 (+ (* (* (* x1 2.0) t_5) (- t_5 3.0)) (* (* x1 x1) 6.0)))
              (* 3.0 t_1))))))
         t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = 1.0 + (x1 * x1);
	double t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double t_4 = 6.0 * ((2.0 * x2) - 3.0);
	double t_5 = (((2.0 * x2) + t_1) - x1) / t_2;
	double tmp;
	if (x1 <= -5e+153) {
		tmp = t_0;
	} else if (x1 <= -1.02e+98) {
		tmp = x1 + (t_3 + (x1 + (x1 * (t_4 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_4 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))));
	} else if (x1 <= 2e+152) {
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * ((((x1 * 2.0) * t_5) * (t_5 - 3.0)) + ((x1 * x1) * 6.0))) + (3.0 * t_1)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = 1.0d0 + (x1 * x1)
    t_3 = 3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_2)
    t_4 = 6.0d0 * ((2.0d0 * x2) - 3.0d0)
    t_5 = (((2.0d0 * x2) + t_1) - x1) / t_2
    if (x1 <= (-5d+153)) then
        tmp = t_0
    else if (x1 <= (-1.02d+98)) then
        tmp = x1 + (t_3 + (x1 + (x1 * (t_4 + (x1 * (((x2 * 6.0d0) + ((x2 * 8.0d0) + (x1 * ((t_4 + (6.0d0 * (3.0d0 + (x2 * (-2.0d0))))) - 6.0d0)))) - 12.0d0))))))
    else if (x1 <= 2d+152) then
        tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * ((((x1 * 2.0d0) * t_5) * (t_5 - 3.0d0)) + ((x1 * x1) * 6.0d0))) + (3.0d0 * t_1)))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = 1.0 + (x1 * x1);
	double t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double t_4 = 6.0 * ((2.0 * x2) - 3.0);
	double t_5 = (((2.0 * x2) + t_1) - x1) / t_2;
	double tmp;
	if (x1 <= -5e+153) {
		tmp = t_0;
	} else if (x1 <= -1.02e+98) {
		tmp = x1 + (t_3 + (x1 + (x1 * (t_4 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_4 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))));
	} else if (x1 <= 2e+152) {
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * ((((x1 * 2.0) * t_5) * (t_5 - 3.0)) + ((x1 * x1) * 6.0))) + (3.0 * t_1)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	t_1 = x1 * (x1 * 3.0)
	t_2 = 1.0 + (x1 * x1)
	t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)
	t_4 = 6.0 * ((2.0 * x2) - 3.0)
	t_5 = (((2.0 * x2) + t_1) - x1) / t_2
	tmp = 0
	if x1 <= -5e+153:
		tmp = t_0
	elif x1 <= -1.02e+98:
		tmp = x1 + (t_3 + (x1 + (x1 * (t_4 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_4 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))))
	elif x1 <= 2e+152:
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * ((((x1 * 2.0) * t_5) * (t_5 - 3.0)) + ((x1 * x1) * 6.0))) + (3.0 * t_1)))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(1.0 + Float64(x1 * x1))
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2))
	t_4 = Float64(6.0 * Float64(Float64(2.0 * x2) - 3.0))
	t_5 = Float64(Float64(Float64(Float64(2.0 * x2) + t_1) - x1) / t_2)
	tmp = 0.0
	if (x1 <= -5e+153)
		tmp = t_0;
	elseif (x1 <= -1.02e+98)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(x1 * Float64(t_4 + Float64(x1 * Float64(Float64(Float64(x2 * 6.0) + Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_4 + Float64(6.0 * Float64(3.0 + Float64(x2 * -2.0)))) - 6.0)))) - 12.0)))))));
	elseif (x1 <= 2e+152)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_2 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_5) * Float64(t_5 - 3.0)) + Float64(Float64(x1 * x1) * 6.0))) + Float64(3.0 * t_1))))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	t_1 = x1 * (x1 * 3.0);
	t_2 = 1.0 + (x1 * x1);
	t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	t_4 = 6.0 * ((2.0 * x2) - 3.0);
	t_5 = (((2.0 * x2) + t_1) - x1) / t_2;
	tmp = 0.0;
	if (x1 <= -5e+153)
		tmp = t_0;
	elseif (x1 <= -1.02e+98)
		tmp = x1 + (t_3 + (x1 + (x1 * (t_4 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_4 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))));
	elseif (x1 <= 2e+152)
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * ((((x1 * 2.0) * t_5) * (t_5 - 3.0)) + ((x1 * x1) * 6.0))) + (3.0 * t_1)))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(6.0 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(N[(2.0 * x2), $MachinePrecision] + t$95$1), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[x1, -5e+153], t$95$0, If[LessEqual[x1, -1.02e+98], N[(x1 + N[(t$95$3 + N[(x1 + N[(x1 * N[(t$95$4 + N[(x1 * N[(N[(N[(x2 * 6.0), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$4 + N[(6.0 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+152], N[(x1 + N[(t$95$3 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$5), $MachinePrecision] * N[(t$95$5 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.00000000000000018e153 or 2.0000000000000001e152 < 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 73.1%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -5.00000000000000018e153 < x1 < -1.02000000000000007e98

   1. Initial program 7.7%

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

   3. Taylor expanded in x1 around inf 7.7%

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

   4. Taylor expanded in x1 around 0 92.3%

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

   if -1.02000000000000007e98 < x1 < 2.0000000000000001e152

   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 97.1%

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

   4. Taylor expanded in x1 around inf 97.0%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.02 \cdot 10^{+98}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + x1 \cdot \left(6 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(\left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(6 \cdot \left(2 \cdot x2 - 3\right) + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 6\right)\right)\right) - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(1 + x1 \cdot x1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(\frac{\left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 1 + x1 \cdot x1\\ t_2 := 3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_1}\\ t_3 := 2 \cdot x2 - 3\\ t_4 := 6 \cdot t\_3\\ \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -4.5 \cdot 10^{+77}:\\ \;\;\;\;x1 + \left(t\_2 + \left(x1 + x1 \cdot \left(t\_4 + x1 \cdot \left(\left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(t\_4 + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 6\right)\right)\right) - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 210000000:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(t\_2 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_0 \cdot \left(2 \cdot x2 - x1\right) + t\_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(2 \cdot x2 + t\_0\right) - x1}{t\_1} - 6\right) + \left(3 \cdot \left(x1 \cdot 2\right)\right) \cdot \frac{-1}{x1}\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot t\_3\right) + x1 \cdot \left(x1 \cdot 3 + 3 \cdot \left(3 - x2 \cdot -2\right)\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ 1.0 (* x1 x1)))
        (t_2 (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1)))
        (t_3 (- (* 2.0 x2) 3.0))
        (t_4 (* 6.0 t_3)))
   (if (<= x1 -4.5e+153)
     (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))
     (if (<= x1 -4.5e+77)
       (+
        x1
        (+
         t_2
         (+
          x1
          (*
           x1
           (+
            t_4
            (*
             x1
             (-
              (+
               (* x2 6.0)
               (+
                (* x2 8.0)
                (* x1 (- (+ t_4 (* 6.0 (+ 3.0 (* x2 -2.0)))) 6.0))))
              12.0)))))))
       (if (<= x1 210000000.0)
         (+
          x1
          (+
           (* x2 -6.0)
           (+
            (* x1 (- (* x1 9.0) 2.0))
            (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 6.0) 12.0)))))))
         (if (<= x1 4e+102)
           (+
            x1
            (+
             t_2
             (+
              x1
              (+
               (* x1 (* x1 x1))
               (+
                (* t_0 (- (* 2.0 x2) x1))
                (*
                 t_1
                 (+
                  (*
                   (* x1 x1)
                   (- (* 4.0 (/ (- (+ (* 2.0 x2) t_0) x1) t_1)) 6.0))
                  (* (* 3.0 (* x1 2.0)) (/ -1.0 x1)))))))))
           (+
            x1
            (+
             (* x2 -6.0)
             (*
              x1
              (-
               (+
                (* 4.0 (* x2 t_3))
                (* x1 (+ (* x1 3.0) (* 3.0 (- 3.0 (* x2 -2.0))))))
               2.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 1.0 + (x1 * x1);
	double t_2 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1);
	double t_3 = (2.0 * x2) - 3.0;
	double t_4 = 6.0 * t_3;
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -4.5e+77) {
		tmp = x1 + (t_2 + (x1 + (x1 * (t_4 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_4 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))));
	} else if (x1 <= 210000000.0) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else if (x1 <= 4e+102) {
		tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((2.0 * x2) - x1)) + (t_1 * (((x1 * x1) * ((4.0 * ((((2.0 * x2) + t_0) - x1) / t_1)) - 6.0)) + ((3.0 * (x1 * 2.0)) * (-1.0 / x1))))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_3)) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = 1.0d0 + (x1 * x1)
    t_2 = 3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)
    t_3 = (2.0d0 * x2) - 3.0d0
    t_4 = 6.0d0 * t_3
    if (x1 <= (-4.5d+153)) then
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    else if (x1 <= (-4.5d+77)) then
        tmp = x1 + (t_2 + (x1 + (x1 * (t_4 + (x1 * (((x2 * 6.0d0) + ((x2 * 8.0d0) + (x1 * ((t_4 + (6.0d0 * (3.0d0 + (x2 * (-2.0d0))))) - 6.0d0)))) - 12.0d0))))))
    else if (x1 <= 210000000.0d0) then
        tmp = x1 + ((x2 * (-6.0d0)) + ((x1 * ((x1 * 9.0d0) - 2.0d0)) + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 6.0d0) - 12.0d0))))))
    else if (x1 <= 4d+102) then
        tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((2.0d0 * x2) - x1)) + (t_1 * (((x1 * x1) * ((4.0d0 * ((((2.0d0 * x2) + t_0) - x1) / t_1)) - 6.0d0)) + ((3.0d0 * (x1 * 2.0d0)) * ((-1.0d0) / x1))))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((4.0d0 * (x2 * t_3)) + (x1 * ((x1 * 3.0d0) + (3.0d0 * (3.0d0 - (x2 * (-2.0d0))))))) - 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 = 1.0 + (x1 * x1);
	double t_2 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1);
	double t_3 = (2.0 * x2) - 3.0;
	double t_4 = 6.0 * t_3;
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -4.5e+77) {
		tmp = x1 + (t_2 + (x1 + (x1 * (t_4 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_4 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))));
	} else if (x1 <= 210000000.0) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else if (x1 <= 4e+102) {
		tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((2.0 * x2) - x1)) + (t_1 * (((x1 * x1) * ((4.0 * ((((2.0 * x2) + t_0) - x1) / t_1)) - 6.0)) + ((3.0 * (x1 * 2.0)) * (-1.0 / x1))))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_3)) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = 1.0 + (x1 * x1)
	t_2 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)
	t_3 = (2.0 * x2) - 3.0
	t_4 = 6.0 * t_3
	tmp = 0
	if x1 <= -4.5e+153:
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	elif x1 <= -4.5e+77:
		tmp = x1 + (t_2 + (x1 + (x1 * (t_4 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_4 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))))
	elif x1 <= 210000000.0:
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))))
	elif x1 <= 4e+102:
		tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((2.0 * x2) - x1)) + (t_1 * (((x1 * x1) * ((4.0 * ((((2.0 * x2) + t_0) - x1) / t_1)) - 6.0)) + ((3.0 * (x1 * 2.0)) * (-1.0 / x1))))))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_3)) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(1.0 + Float64(x1 * x1))
	t_2 = Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1))
	t_3 = Float64(Float64(2.0 * x2) - 3.0)
	t_4 = Float64(6.0 * t_3)
	tmp = 0.0
	if (x1 <= -4.5e+153)
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))));
	elseif (x1 <= -4.5e+77)
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(x1 * Float64(t_4 + Float64(x1 * Float64(Float64(Float64(x2 * 6.0) + Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_4 + Float64(6.0 * Float64(3.0 + Float64(x2 * -2.0)))) - 6.0)))) - 12.0)))))));
	elseif (x1 <= 210000000.0)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0)) + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)))))));
	elseif (x1 <= 4e+102)
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * Float64(Float64(2.0 * x2) - x1)) + Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(Float64(Float64(Float64(2.0 * x2) + t_0) - x1) / t_1)) - 6.0)) + Float64(Float64(3.0 * Float64(x1 * 2.0)) * Float64(-1.0 / x1)))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(4.0 * Float64(x2 * t_3)) + Float64(x1 * Float64(Float64(x1 * 3.0) + Float64(3.0 * Float64(3.0 - Float64(x2 * -2.0)))))) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = 1.0 + (x1 * x1);
	t_2 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1);
	t_3 = (2.0 * x2) - 3.0;
	t_4 = 6.0 * t_3;
	tmp = 0.0;
	if (x1 <= -4.5e+153)
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	elseif (x1 <= -4.5e+77)
		tmp = x1 + (t_2 + (x1 + (x1 * (t_4 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_4 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))));
	elseif (x1 <= 210000000.0)
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	elseif (x1 <= 4e+102)
		tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((2.0 * x2) - x1)) + (t_1 * (((x1 * x1) * ((4.0 * ((((2.0 * x2) + t_0) - x1) / t_1)) - 6.0)) + ((3.0 * (x1 * 2.0)) * (-1.0 / x1))))))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_3)) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))) - 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[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$4 = N[(6.0 * t$95$3), $MachinePrecision]}, If[LessEqual[x1, -4.5e+153], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -4.5e+77], N[(x1 + N[(t$95$2 + N[(x1 + N[(x1 * N[(t$95$4 + N[(x1 * N[(N[(N[(x2 * 6.0), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$4 + N[(6.0 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 210000000.0], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4e+102], N[(x1 + N[(t$95$2 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(N[(N[(N[(2.0 * x2), $MachinePrecision] + t$95$0), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(4.0 * N[(x2 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + N[(3.0 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -4.5000000000000001e153

   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 60.0%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -4.5000000000000001e153 < x1 < -4.50000000000000024e77

   1. Initial program 25.0%

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

   3. Taylor expanded in x1 around inf 25.0%

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

   4. Taylor expanded in x1 around 0 82.4%

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

   if -4.50000000000000024e77 < x1 < 2.1e8

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 82.4%

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

   4. Taylor expanded in x1 around 0 81.5%

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

   5. Taylor expanded in x2 around 0 93.7%

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

   if 2.1e8 < x1 < 3.99999999999999991e102

   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 inf 99.3%

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

   4. Taylor expanded in x1 around 0 97.1%

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

      1. +-commutative 92.5%

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

      2. mul-1-neg 92.5%

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

      3. sub-neg 92.5%

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

   6. Simplified 97.1%

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

   7. Taylor expanded in x1 around inf 97.1%

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

   if 3.99999999999999991e102 < x1

   1. Initial program 26.0%

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

   3. Taylor expanded in x1 around 0 12.7%

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

   4. Taylor expanded in x1 around 0 96.0%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -4.5 \cdot 10^{+77}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + x1 \cdot \left(6 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(\left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(6 \cdot \left(2 \cdot x2 - 3\right) + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 6\right)\right)\right) - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 210000000:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2 - x1\right) + \left(1 + x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} - 6\right) + \left(3 \cdot \left(x1 \cdot 2\right)\right) \cdot \frac{-1}{x1}\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(x1 \cdot 3 + 3 \cdot \left(3 - x2 \cdot -2\right)\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 88.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 1 + x1 \cdot x1\\ t_2 := 3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_1}\\ t_3 := 2 \cdot x2 - 3\\ t_4 := 6 \cdot t\_3\\ \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -6.6 \cdot 10^{+77}:\\ \;\;\;\;x1 + \left(t\_2 + \left(x1 + x1 \cdot \left(t\_4 + x1 \cdot \left(\left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(t\_4 + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 6\right)\right)\right) - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 170000:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(t\_2 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_0 \cdot \left(2 \cdot x2 - x1\right) + t\_1 \cdot \left(\left(x1 \cdot x1\right) \cdot 6 + \left(\frac{\left(2 \cdot x2 + t\_0\right) - x1}{t\_1} - 3\right) \cdot \left(3 \cdot \left(x1 \cdot 2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot t\_3\right) + x1 \cdot \left(x1 \cdot 3 + 3 \cdot \left(3 - x2 \cdot -2\right)\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ 1.0 (* x1 x1)))
        (t_2 (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1)))
        (t_3 (- (* 2.0 x2) 3.0))
        (t_4 (* 6.0 t_3)))
   (if (<= x1 -4.5e+153)
     (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))
     (if (<= x1 -6.6e+77)
       (+
        x1
        (+
         t_2
         (+
          x1
          (*
           x1
           (+
            t_4
            (*
             x1
             (-
              (+
               (* x2 6.0)
               (+
                (* x2 8.0)
                (* x1 (- (+ t_4 (* 6.0 (+ 3.0 (* x2 -2.0)))) 6.0))))
              12.0)))))))
       (if (<= x1 170000.0)
         (+
          x1
          (+
           (* x2 -6.0)
           (+
            (* x1 (- (* x1 9.0) 2.0))
            (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 6.0) 12.0)))))))
         (if (<= x1 4e+102)
           (+
            x1
            (+
             t_2
             (+
              x1
              (+
               (* x1 (* x1 x1))
               (+
                (* t_0 (- (* 2.0 x2) x1))
                (*
                 t_1
                 (+
                  (* (* x1 x1) 6.0)
                  (*
                   (- (/ (- (+ (* 2.0 x2) t_0) x1) t_1) 3.0)
                   (* 3.0 (* x1 2.0))))))))))
           (+
            x1
            (+
             (* x2 -6.0)
             (*
              x1
              (-
               (+
                (* 4.0 (* x2 t_3))
                (* x1 (+ (* x1 3.0) (* 3.0 (- 3.0 (* x2 -2.0))))))
               2.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 1.0 + (x1 * x1);
	double t_2 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1);
	double t_3 = (2.0 * x2) - 3.0;
	double t_4 = 6.0 * t_3;
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -6.6e+77) {
		tmp = x1 + (t_2 + (x1 + (x1 * (t_4 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_4 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))));
	} else if (x1 <= 170000.0) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else if (x1 <= 4e+102) {
		tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((2.0 * x2) - x1)) + (t_1 * (((x1 * x1) * 6.0) + ((((((2.0 * x2) + t_0) - x1) / t_1) - 3.0) * (3.0 * (x1 * 2.0)))))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_3)) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = 1.0d0 + (x1 * x1)
    t_2 = 3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)
    t_3 = (2.0d0 * x2) - 3.0d0
    t_4 = 6.0d0 * t_3
    if (x1 <= (-4.5d+153)) then
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    else if (x1 <= (-6.6d+77)) then
        tmp = x1 + (t_2 + (x1 + (x1 * (t_4 + (x1 * (((x2 * 6.0d0) + ((x2 * 8.0d0) + (x1 * ((t_4 + (6.0d0 * (3.0d0 + (x2 * (-2.0d0))))) - 6.0d0)))) - 12.0d0))))))
    else if (x1 <= 170000.0d0) then
        tmp = x1 + ((x2 * (-6.0d0)) + ((x1 * ((x1 * 9.0d0) - 2.0d0)) + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 6.0d0) - 12.0d0))))))
    else if (x1 <= 4d+102) then
        tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((2.0d0 * x2) - x1)) + (t_1 * (((x1 * x1) * 6.0d0) + ((((((2.0d0 * x2) + t_0) - x1) / t_1) - 3.0d0) * (3.0d0 * (x1 * 2.0d0)))))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((4.0d0 * (x2 * t_3)) + (x1 * ((x1 * 3.0d0) + (3.0d0 * (3.0d0 - (x2 * (-2.0d0))))))) - 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 = 1.0 + (x1 * x1);
	double t_2 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1);
	double t_3 = (2.0 * x2) - 3.0;
	double t_4 = 6.0 * t_3;
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -6.6e+77) {
		tmp = x1 + (t_2 + (x1 + (x1 * (t_4 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_4 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))));
	} else if (x1 <= 170000.0) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else if (x1 <= 4e+102) {
		tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((2.0 * x2) - x1)) + (t_1 * (((x1 * x1) * 6.0) + ((((((2.0 * x2) + t_0) - x1) / t_1) - 3.0) * (3.0 * (x1 * 2.0)))))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_3)) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = 1.0 + (x1 * x1)
	t_2 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)
	t_3 = (2.0 * x2) - 3.0
	t_4 = 6.0 * t_3
	tmp = 0
	if x1 <= -4.5e+153:
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	elif x1 <= -6.6e+77:
		tmp = x1 + (t_2 + (x1 + (x1 * (t_4 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_4 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))))
	elif x1 <= 170000.0:
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))))
	elif x1 <= 4e+102:
		tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((2.0 * x2) - x1)) + (t_1 * (((x1 * x1) * 6.0) + ((((((2.0 * x2) + t_0) - x1) / t_1) - 3.0) * (3.0 * (x1 * 2.0)))))))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_3)) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(1.0 + Float64(x1 * x1))
	t_2 = Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1))
	t_3 = Float64(Float64(2.0 * x2) - 3.0)
	t_4 = Float64(6.0 * t_3)
	tmp = 0.0
	if (x1 <= -4.5e+153)
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))));
	elseif (x1 <= -6.6e+77)
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(x1 * Float64(t_4 + Float64(x1 * Float64(Float64(Float64(x2 * 6.0) + Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_4 + Float64(6.0 * Float64(3.0 + Float64(x2 * -2.0)))) - 6.0)))) - 12.0)))))));
	elseif (x1 <= 170000.0)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0)) + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)))))));
	elseif (x1 <= 4e+102)
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * Float64(Float64(2.0 * x2) - x1)) + Float64(t_1 * Float64(Float64(Float64(x1 * x1) * 6.0) + Float64(Float64(Float64(Float64(Float64(Float64(2.0 * x2) + t_0) - x1) / t_1) - 3.0) * Float64(3.0 * Float64(x1 * 2.0))))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(4.0 * Float64(x2 * t_3)) + Float64(x1 * Float64(Float64(x1 * 3.0) + Float64(3.0 * Float64(3.0 - Float64(x2 * -2.0)))))) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = 1.0 + (x1 * x1);
	t_2 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1);
	t_3 = (2.0 * x2) - 3.0;
	t_4 = 6.0 * t_3;
	tmp = 0.0;
	if (x1 <= -4.5e+153)
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	elseif (x1 <= -6.6e+77)
		tmp = x1 + (t_2 + (x1 + (x1 * (t_4 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_4 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))));
	elseif (x1 <= 170000.0)
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	elseif (x1 <= 4e+102)
		tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((2.0 * x2) - x1)) + (t_1 * (((x1 * x1) * 6.0) + ((((((2.0 * x2) + t_0) - x1) / t_1) - 3.0) * (3.0 * (x1 * 2.0)))))))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_3)) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))) - 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[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$4 = N[(6.0 * t$95$3), $MachinePrecision]}, If[LessEqual[x1, -4.5e+153], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -6.6e+77], N[(x1 + N[(t$95$2 + N[(x1 + N[(x1 * N[(t$95$4 + N[(x1 * N[(N[(N[(x2 * 6.0), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$4 + N[(6.0 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 170000.0], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4e+102], N[(x1 + N[(t$95$2 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision] + N[(N[(N[(N[(N[(N[(2.0 * x2), $MachinePrecision] + t$95$0), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision] - 3.0), $MachinePrecision] * N[(3.0 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(4.0 * N[(x2 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + N[(3.0 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -4.5000000000000001e153

   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 60.0%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -4.5000000000000001e153 < x1 < -6.5999999999999996e77

   1. Initial program 25.0%

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

   3. Taylor expanded in x1 around inf 25.0%

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

   4. Taylor expanded in x1 around 0 82.4%

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

   if -6.5999999999999996e77 < x1 < 1.7e5

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 82.4%

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

   4. Taylor expanded in x1 around 0 81.5%

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

   5. Taylor expanded in x2 around 0 93.7%

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

   if 1.7e5 < x1 < 3.99999999999999991e102

   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 inf 87.6%

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

   4. Taylor expanded in x1 around 0 92.5%

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

      1. +-commutative 92.5%

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

      2. mul-1-neg 92.5%

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

      3. sub-neg 92.5%

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

   6. Simplified 92.5%

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

   7. Taylor expanded in x1 around inf 92.5%

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

   if 3.99999999999999991e102 < x1

   1. Initial program 26.0%

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

   3. Taylor expanded in x1 around 0 12.7%

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

   4. Taylor expanded in x1 around 0 96.0%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -6.6 \cdot 10^{+77}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + x1 \cdot \left(6 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(\left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(6 \cdot \left(2 \cdot x2 - 3\right) + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 6\right)\right)\right) - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 170000:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2 - x1\right) + \left(1 + x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6 + \left(\frac{\left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} - 3\right) \cdot \left(3 \cdot \left(x1 \cdot 2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(x1 \cdot 3 + 3 \cdot \left(3 - x2 \cdot -2\right)\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 94.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot x2 - 3\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := 1 + x1 \cdot x1\\ t_3 := 6 \cdot t\_0\\ t_4 := \frac{\left(2 \cdot x2 + t\_1\right) - x1}{t\_2}\\ \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.02 \cdot 10^{+98}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_1 - 2 \cdot x2\right) - x1}{t\_2} + \left(x1 + x1 \cdot \left(t\_3 + x1 \cdot \left(\left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(t\_3 + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 6\right)\right)\right) - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_2 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_4\right) \cdot \left(t\_4 - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right) + t\_1 \cdot \left(2 \cdot x2 - x1\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot t\_0\right) + x1 \cdot \left(x1 \cdot 3 + 3 \cdot \left(3 - x2 \cdot -2\right)\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* 2.0 x2) 3.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ 1.0 (* x1 x1)))
        (t_3 (* 6.0 t_0))
        (t_4 (/ (- (+ (* 2.0 x2) t_1) x1) t_2)))
   (if (<= x1 -4.5e+153)
     (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))
     (if (<= x1 -1.02e+98)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2))
         (+
          x1
          (*
           x1
           (+
            t_3
            (*
             x1
             (-
              (+
               (* x2 6.0)
               (+
                (* x2 8.0)
                (* x1 (- (+ t_3 (* 6.0 (+ 3.0 (* x2 -2.0)))) 6.0))))
              12.0)))))))
       (if (<= x1 4e+102)
         (+
          x1
          (+
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* t_2 (+ (* (* (* x1 2.0) t_4) (- t_4 3.0)) (* (* x1 x1) 6.0)))
              (* t_1 (- (* 2.0 x2) x1)))))
           (* 3.0 (- (* x2 -2.0) x1))))
         (+
          x1
          (+
           (* x2 -6.0)
           (*
            x1
            (-
             (+
              (* 4.0 (* x2 t_0))
              (* x1 (+ (* x1 3.0) (* 3.0 (- 3.0 (* x2 -2.0))))))
             2.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = 1.0 + (x1 * x1);
	double t_3 = 6.0 * t_0;
	double t_4 = (((2.0 * x2) + t_1) - x1) / t_2;
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -1.02e+98) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + (x1 * (t_3 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_3 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))));
	} else if (x1 <= 4e+102) {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_2 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * 6.0))) + (t_1 * ((2.0 * x2) - x1))))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_0)) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = (2.0d0 * x2) - 3.0d0
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = 1.0d0 + (x1 * x1)
    t_3 = 6.0d0 * t_0
    t_4 = (((2.0d0 * x2) + t_1) - x1) / t_2
    if (x1 <= (-4.5d+153)) then
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    else if (x1 <= (-1.02d+98)) then
        tmp = x1 + ((3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_2)) + (x1 + (x1 * (t_3 + (x1 * (((x2 * 6.0d0) + ((x2 * 8.0d0) + (x1 * ((t_3 + (6.0d0 * (3.0d0 + (x2 * (-2.0d0))))) - 6.0d0)))) - 12.0d0))))))
    else if (x1 <= 4d+102) then
        tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_2 * ((((x1 * 2.0d0) * t_4) * (t_4 - 3.0d0)) + ((x1 * x1) * 6.0d0))) + (t_1 * ((2.0d0 * x2) - x1))))) + (3.0d0 * ((x2 * (-2.0d0)) - x1)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((4.0d0 * (x2 * t_0)) + (x1 * ((x1 * 3.0d0) + (3.0d0 * (3.0d0 - (x2 * (-2.0d0))))))) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = 1.0 + (x1 * x1);
	double t_3 = 6.0 * t_0;
	double t_4 = (((2.0 * x2) + t_1) - x1) / t_2;
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -1.02e+98) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + (x1 * (t_3 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_3 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))));
	} else if (x1 <= 4e+102) {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_2 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * 6.0))) + (t_1 * ((2.0 * x2) - x1))))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_0)) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (2.0 * x2) - 3.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = 1.0 + (x1 * x1)
	t_3 = 6.0 * t_0
	t_4 = (((2.0 * x2) + t_1) - x1) / t_2
	tmp = 0
	if x1 <= -4.5e+153:
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	elif x1 <= -1.02e+98:
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + (x1 * (t_3 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_3 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))))
	elif x1 <= 4e+102:
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_2 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * 6.0))) + (t_1 * ((2.0 * x2) - x1))))) + (3.0 * ((x2 * -2.0) - x1)))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_0)) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(2.0 * x2) - 3.0)
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(1.0 + Float64(x1 * x1))
	t_3 = Float64(6.0 * t_0)
	t_4 = Float64(Float64(Float64(Float64(2.0 * x2) + t_1) - x1) / t_2)
	tmp = 0.0
	if (x1 <= -4.5e+153)
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))));
	elseif (x1 <= -1.02e+98)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2)) + Float64(x1 + Float64(x1 * Float64(t_3 + Float64(x1 * Float64(Float64(Float64(x2 * 6.0) + Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_3 + Float64(6.0 * Float64(3.0 + Float64(x2 * -2.0)))) - 6.0)))) - 12.0)))))));
	elseif (x1 <= 4e+102)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_2 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(t_4 - 3.0)) + Float64(Float64(x1 * x1) * 6.0))) + Float64(t_1 * Float64(Float64(2.0 * x2) - x1))))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(4.0 * Float64(x2 * t_0)) + Float64(x1 * Float64(Float64(x1 * 3.0) + Float64(3.0 * Float64(3.0 - Float64(x2 * -2.0)))))) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (2.0 * x2) - 3.0;
	t_1 = x1 * (x1 * 3.0);
	t_2 = 1.0 + (x1 * x1);
	t_3 = 6.0 * t_0;
	t_4 = (((2.0 * x2) + t_1) - x1) / t_2;
	tmp = 0.0;
	if (x1 <= -4.5e+153)
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	elseif (x1 <= -1.02e+98)
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + (x1 * (t_3 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_3 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))));
	elseif (x1 <= 4e+102)
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_2 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * 6.0))) + (t_1 * ((2.0 * x2) - x1))))) + (3.0 * ((x2 * -2.0) - x1)));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_0)) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(6.0 * t$95$0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(N[(2.0 * x2), $MachinePrecision] + t$95$1), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[x1, -4.5e+153], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.02e+98], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x1 * N[(t$95$3 + N[(x1 * N[(N[(N[(x2 * 6.0), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$3 + N[(6.0 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4e+102], N[(x1 + N[(N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(4.0 * N[(x2 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + N[(3.0 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.5000000000000001e153

   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 60.0%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -4.5000000000000001e153 < x1 < -1.02000000000000007e98

   1. Initial program 7.7%

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

   3. Taylor expanded in x1 around inf 7.7%

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

   4. Taylor expanded in x1 around 0 92.3%

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

   if -1.02000000000000007e98 < x1 < 3.99999999999999991e102

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around inf 96.8%

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

   4. Taylor expanded in x1 around 0 95.0%

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

      1. +-commutative 95.0%

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

      2. mul-1-neg 95.0%

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

      3. sub-neg 95.0%

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

   6. Simplified 95.0%

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

   7. Taylor expanded in x1 around 0 95.0%

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

      1. mul-1-neg 95.0%

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

      2. unsub-neg 95.0%

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

      3. *-commutative 95.0%

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

   9. Simplified 95.0%

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

   if 3.99999999999999991e102 < x1

   1. Initial program 26.0%

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

   3. Taylor expanded in x1 around 0 12.7%

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

   4. Taylor expanded in x1 around 0 96.0%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.02 \cdot 10^{+98}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + x1 \cdot \left(6 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(\left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(6 \cdot \left(2 \cdot x2 - 3\right) + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 6\right)\right)\right) - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(1 + x1 \cdot x1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(\frac{\left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2 - x1\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(x1 \cdot 3 + 3 \cdot \left(3 - x2 \cdot -2\right)\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 84.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot x2 - 3\\ t_1 := 6 \cdot t\_0\\ \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{+77}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + x1 \cdot \left(t\_1 + x1 \cdot \left(\left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(t\_1 + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 6\right)\right)\right) - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{-16}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot t\_0\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 + x1 \cdot \left(\left(x1 + 3\right) - x2 \cdot -2\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* 2.0 x2) 3.0)) (t_1 (* 6.0 t_0)))
   (if (<= x1 -4.5e+153)
     (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))
     (if (<= x1 -9.5e+77)
       (+
        x1
        (+
         (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) (+ 1.0 (* x1 x1))))
         (+
          x1
          (*
           x1
           (+
            t_1
            (*
             x1
             (-
              (+
               (* x2 6.0)
               (+
                (* x2 8.0)
                (* x1 (- (+ t_1 (* 6.0 (+ 3.0 (* x2 -2.0)))) 6.0))))
              12.0)))))))
       (if (<= x1 1e-16)
         (+
          x1
          (+
           (* x2 -6.0)
           (+
            (* x1 (- (* x1 9.0) 2.0))
            (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 6.0) 12.0)))))))
         (+
          x1
          (+
           (+ x1 (* 4.0 (* x1 (* x2 t_0))))
           (*
            3.0
            (+
             (* x2 -2.0)
             (* x1 (+ -1.0 (* x1 (- (+ x1 3.0) (* x2 -2.0))))))))))))))

C

double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = 6.0 * t_0;
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -9.5e+77) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / (1.0 + (x1 * x1)))) + (x1 + (x1 * (t_1 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_1 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))));
	} else if (x1 <= 1e-16) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else {
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * t_0)))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * ((x1 + 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) :: tmp
    t_0 = (2.0d0 * x2) - 3.0d0
    t_1 = 6.0d0 * t_0
    if (x1 <= (-4.5d+153)) then
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    else if (x1 <= (-9.5d+77)) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / (1.0d0 + (x1 * x1)))) + (x1 + (x1 * (t_1 + (x1 * (((x2 * 6.0d0) + ((x2 * 8.0d0) + (x1 * ((t_1 + (6.0d0 * (3.0d0 + (x2 * (-2.0d0))))) - 6.0d0)))) - 12.0d0))))))
    else if (x1 <= 1d-16) then
        tmp = x1 + ((x2 * (-6.0d0)) + ((x1 * ((x1 * 9.0d0) - 2.0d0)) + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 6.0d0) - 12.0d0))))))
    else
        tmp = x1 + ((x1 + (4.0d0 * (x1 * (x2 * t_0)))) + (3.0d0 * ((x2 * (-2.0d0)) + (x1 * ((-1.0d0) + (x1 * ((x1 + 3.0d0) - (x2 * (-2.0d0)))))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = 6.0 * t_0;
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -9.5e+77) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / (1.0 + (x1 * x1)))) + (x1 + (x1 * (t_1 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_1 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))));
	} else if (x1 <= 1e-16) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else {
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * t_0)))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * ((x1 + 3.0) - (x2 * -2.0))))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (2.0 * x2) - 3.0
	t_1 = 6.0 * t_0
	tmp = 0
	if x1 <= -4.5e+153:
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	elif x1 <= -9.5e+77:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / (1.0 + (x1 * x1)))) + (x1 + (x1 * (t_1 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_1 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))))
	elif x1 <= 1e-16:
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))))
	else:
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * t_0)))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * ((x1 + 3.0) - (x2 * -2.0))))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(2.0 * x2) - 3.0)
	t_1 = Float64(6.0 * t_0)
	tmp = 0.0
	if (x1 <= -4.5e+153)
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))));
	elseif (x1 <= -9.5e+77)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / Float64(1.0 + Float64(x1 * x1)))) + Float64(x1 + Float64(x1 * Float64(t_1 + Float64(x1 * Float64(Float64(Float64(x2 * 6.0) + Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_1 + Float64(6.0 * Float64(3.0 + Float64(x2 * -2.0)))) - 6.0)))) - 12.0)))))));
	elseif (x1 <= 1e-16)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0)) + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x1 * Float64(x2 * t_0)))) + Float64(3.0 * Float64(Float64(x2 * -2.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(Float64(x1 + 3.0) - Float64(x2 * -2.0)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (2.0 * x2) - 3.0;
	t_1 = 6.0 * t_0;
	tmp = 0.0;
	if (x1 <= -4.5e+153)
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	elseif (x1 <= -9.5e+77)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / (1.0 + (x1 * x1)))) + (x1 + (x1 * (t_1 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_1 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))));
	elseif (x1 <= 1e-16)
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	else
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * t_0)))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * ((x1 + 3.0) - (x2 * -2.0))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * t$95$0), $MachinePrecision]}, If[LessEqual[x1, -4.5e+153], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -9.5e+77], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x1 * N[(t$95$1 + N[(x1 * N[(N[(N[(x2 * 6.0), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$1 + N[(6.0 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1e-16], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(4.0 * N[(x1 * N[(x2 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(N[(x1 + 3.0), $MachinePrecision] - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.5000000000000001e153

   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 60.0%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -4.5000000000000001e153 < x1 < -9.4999999999999998e77

   1. Initial program 25.0%

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

   3. Taylor expanded in x1 around inf 25.0%

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

   4. Taylor expanded in x1 around 0 82.4%

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

   if -9.4999999999999998e77 < x1 < 9.9999999999999998e-17

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around 0 82.9%

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

   4. Taylor expanded in x1 around 0 82.0%

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

   5. Taylor expanded in x2 around 0 94.9%

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

   if 9.9999999999999998e-17 < x1

   1. Initial program 52.3%

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

   3. Taylor expanded in x1 around 0 20.7%

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

   4. Taylor expanded in x1 around 0 74.7%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{+77}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + x1 \cdot \left(6 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(\left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(6 \cdot \left(2 \cdot x2 - 3\right) + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 6\right)\right)\right) - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{-16}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 + x1 \cdot \left(\left(x1 + 3\right) - x2 \cdot -2\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 81.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(3 \cdot \left(x2 \cdot \left(x1 \cdot 2 + 3 \cdot \frac{x1}{x2}\right)\right) + 4 \cdot \left(x2 \cdot -3\right)\right) - 2\right)\right)\\ \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+157}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -8.5 \cdot 10^{+76}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 850000000:\\ \;\;\;\;x1 + \left(x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot -12\right) - 6\right) + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 1.85 \cdot 10^{+152}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (+
          x1
          (+
           (* x2 -6.0)
           (*
            x1
            (-
             (+
              (* 3.0 (* x2 (+ (* x1 2.0) (* 3.0 (/ x1 x2)))))
              (* 4.0 (* x2 -3.0)))
             2.0))))))
   (if (<= x1 -5.5e+157)
     (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))
     (if (<= x1 -8.5e+76)
       t_0
       (if (<= x1 850000000.0)
         (+
          x1
          (+ (* x2 (- (+ (* 8.0 (* x1 x2)) (* x1 -12.0)) 6.0)) (* x1 -2.0)))
         (if (<= x1 1.85e+152)
           t_0
           (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 9.0) 2.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * (((3.0 * (x2 * ((x1 * 2.0) + (3.0 * (x1 / x2))))) + (4.0 * (x2 * -3.0))) - 2.0)));
	double tmp;
	if (x1 <= -5.5e+157) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -8.5e+76) {
		tmp = t_0;
	} else if (x1 <= 850000000.0) {
		tmp = x1 + ((x2 * (((8.0 * (x1 * x2)) + (x1 * -12.0)) - 6.0)) + (x1 * -2.0));
	} else if (x1 <= 1.85e+152) {
		tmp = t_0;
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + ((x2 * (-6.0d0)) + (x1 * (((3.0d0 * (x2 * ((x1 * 2.0d0) + (3.0d0 * (x1 / x2))))) + (4.0d0 * (x2 * (-3.0d0)))) - 2.0d0)))
    if (x1 <= (-5.5d+157)) then
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    else if (x1 <= (-8.5d+76)) then
        tmp = t_0
    else if (x1 <= 850000000.0d0) then
        tmp = x1 + ((x2 * (((8.0d0 * (x1 * x2)) + (x1 * (-12.0d0))) - 6.0d0)) + (x1 * (-2.0d0)))
    else if (x1 <= 1.85d+152) then
        tmp = t_0
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * (((3.0 * (x2 * ((x1 * 2.0) + (3.0 * (x1 / x2))))) + (4.0 * (x2 * -3.0))) - 2.0)));
	double tmp;
	if (x1 <= -5.5e+157) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -8.5e+76) {
		tmp = t_0;
	} else if (x1 <= 850000000.0) {
		tmp = x1 + ((x2 * (((8.0 * (x1 * x2)) + (x1 * -12.0)) - 6.0)) + (x1 * -2.0));
	} else if (x1 <= 1.85e+152) {
		tmp = t_0;
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x2 * -6.0) + (x1 * (((3.0 * (x2 * ((x1 * 2.0) + (3.0 * (x1 / x2))))) + (4.0 * (x2 * -3.0))) - 2.0)))
	tmp = 0
	if x1 <= -5.5e+157:
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	elif x1 <= -8.5e+76:
		tmp = t_0
	elif x1 <= 850000000.0:
		tmp = x1 + ((x2 * (((8.0 * (x1 * x2)) + (x1 * -12.0)) - 6.0)) + (x1 * -2.0))
	elif x1 <= 1.85e+152:
		tmp = t_0
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(3.0 * Float64(x2 * Float64(Float64(x1 * 2.0) + Float64(3.0 * Float64(x1 / x2))))) + Float64(4.0 * Float64(x2 * -3.0))) - 2.0))))
	tmp = 0.0
	if (x1 <= -5.5e+157)
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))));
	elseif (x1 <= -8.5e+76)
		tmp = t_0;
	elseif (x1 <= 850000000.0)
		tmp = Float64(x1 + Float64(Float64(x2 * Float64(Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * -12.0)) - 6.0)) + Float64(x1 * -2.0)));
	elseif (x1 <= 1.85e+152)
		tmp = t_0;
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x2 * -6.0) + (x1 * (((3.0 * (x2 * ((x1 * 2.0) + (3.0 * (x1 / x2))))) + (4.0 * (x2 * -3.0))) - 2.0)));
	tmp = 0.0;
	if (x1 <= -5.5e+157)
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	elseif (x1 <= -8.5e+76)
		tmp = t_0;
	elseif (x1 <= 850000000.0)
		tmp = x1 + ((x2 * (((8.0 * (x1 * x2)) + (x1 * -12.0)) - 6.0)) + (x1 * -2.0));
	elseif (x1 <= 1.85e+152)
		tmp = t_0;
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(3.0 * N[(x2 * N[(N[(x1 * 2.0), $MachinePrecision] + N[(3.0 * N[(x1 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x2 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.5e+157], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -8.5e+76], t$95$0, If[LessEqual[x1, 850000000.0], N[(x1 + N[(N[(x2 * N[(N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * -12.0), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.85e+152], t$95$0, N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.5000000000000003e157

   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 60.7%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -5.5000000000000003e157 < x1 < -8.49999999999999992e76 or 8.5e8 < x1 < 1.84999999999999998e152

   1. Initial program 71.7%

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

   3. Taylor expanded in x1 around 0 20.5%

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

   4. Taylor expanded in x1 around 0 27.6%

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

   5. Taylor expanded in x2 around inf 40.6%

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

   6. Taylor expanded in x2 around 0 46.6%

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

      1. *-commutative 46.6%

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

   8. Simplified 46.6%

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

   if -8.49999999999999992e76 < x1 < 8.5e8

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 82.4%

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

   4. Taylor expanded in x1 around 0 82.1%

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

   5. Taylor expanded in x2 around 0 92.9%

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

   if 1.84999999999999998e152 < x1

   1. Initial program 2.6%

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

   3. Taylor expanded in x1 around 0 2.6%

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

   4. Taylor expanded in x1 around 0 81.6%

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

   5. Taylor expanded in x2 around 0 97.7%

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

      1. *-commutative 97.7%

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

   7. Simplified 97.7%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+157}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -8.5 \cdot 10^{+76}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(3 \cdot \left(x2 \cdot \left(x1 \cdot 2 + 3 \cdot \frac{x1}{x2}\right)\right) + 4 \cdot \left(x2 \cdot -3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 850000000:\\ \;\;\;\;x1 + \left(x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot -12\right) - 6\right) + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 1.85 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(3 \cdot \left(x2 \cdot \left(x1 \cdot 2 + 3 \cdot \frac{x1}{x2}\right)\right) + 4 \cdot \left(x2 \cdot -3\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 80.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+157}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{-16}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 + x1 \cdot \left(\left(x1 + 3\right) - x2 \cdot -2\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -5.5e+157)
   (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))
   (if (<= x1 1e-16)
     (+
      x1
      (+
       (* x2 -6.0)
       (+
        (* x1 (- (* x1 9.0) 2.0))
        (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 6.0) 12.0)))))))
     (+
      x1
      (+
       (+ x1 (* 4.0 (* x1 (* x2 (- (* 2.0 x2) 3.0)))))
       (*
        3.0
        (+ (* x2 -2.0) (* x1 (+ -1.0 (* x1 (- (+ x1 3.0) (* x2 -2.0))))))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -5.5e+157) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= 1e-16) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else {
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * ((x1 + 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 <= (-5.5d+157)) then
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    else if (x1 <= 1d-16) then
        tmp = x1 + ((x2 * (-6.0d0)) + ((x1 * ((x1 * 9.0d0) - 2.0d0)) + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 6.0d0) - 12.0d0))))))
    else
        tmp = x1 + ((x1 + (4.0d0 * (x1 * (x2 * ((2.0d0 * x2) - 3.0d0))))) + (3.0d0 * ((x2 * (-2.0d0)) + (x1 * ((-1.0d0) + (x1 * ((x1 + 3.0d0) - (x2 * (-2.0d0)))))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -5.5e+157) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= 1e-16) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else {
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * ((x1 + 3.0) - (x2 * -2.0))))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -5.5e+157:
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	elif x1 <= 1e-16:
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))))
	else:
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * ((x1 + 3.0) - (x2 * -2.0))))))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -5.5e+157)
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))));
	elseif (x1 <= 1e-16)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0)) + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x1 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))) + Float64(3.0 * Float64(Float64(x2 * -2.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(Float64(x1 + 3.0) - Float64(x2 * -2.0)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -5.5e+157)
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	elseif (x1 <= 1e-16)
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	else
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * ((x1 + 3.0) - (x2 * -2.0))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -5.5e+157], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1e-16], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(4.0 * N[(x1 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(N[(x1 + 3.0), $MachinePrecision] - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.5000000000000003e157

   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 60.7%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -5.5000000000000003e157 < x1 < 9.9999999999999998e-17

   1. Initial program 90.2%

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

   3. Taylor expanded in x1 around 0 73.7%

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

   4. Taylor expanded in x1 around 0 76.4%

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

   5. Taylor expanded in x2 around 0 87.8%

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

   if 9.9999999999999998e-17 < x1

   1. Initial program 52.3%

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

   3. Taylor expanded in x1 around 0 20.7%

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

   4. Taylor expanded in x1 around 0 74.7%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+157}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{-16}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 + x1 \cdot \left(\left(x1 + 3\right) - x2 \cdot -2\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 80.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 9 - 2\right)\\ \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+157}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+70}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(t\_0 + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.85 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(3 \cdot \left(x2 \cdot \left(x1 \cdot 2 + 3 \cdot \frac{x1}{x2}\right)\right) + 4 \cdot \left(x2 \cdot -3\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (- (* x1 9.0) 2.0))))
   (if (<= x1 -5.5e+157)
     (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))
     (if (<= x1 1.35e+70)
       (+
        x1
        (+
         (* x2 -6.0)
         (+ t_0 (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 6.0) 12.0)))))))
       (if (<= x1 1.85e+152)
         (+
          x1
          (+
           (* x2 -6.0)
           (*
            x1
            (-
             (+
              (* 3.0 (* x2 (+ (* x1 2.0) (* 3.0 (/ x1 x2)))))
              (* 4.0 (* x2 -3.0)))
             2.0))))
         (+ x1 (+ (* x2 -6.0) t_0)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 9.0) - 2.0);
	double tmp;
	if (x1 <= -5.5e+157) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= 1.35e+70) {
		tmp = x1 + ((x2 * -6.0) + (t_0 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else if (x1 <= 1.85e+152) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((3.0 * (x2 * ((x1 * 2.0) + (3.0 * (x1 / x2))))) + (4.0 * (x2 * -3.0))) - 2.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) + t_0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 * ((x1 * 9.0d0) - 2.0d0)
    if (x1 <= (-5.5d+157)) then
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    else if (x1 <= 1.35d+70) then
        tmp = x1 + ((x2 * (-6.0d0)) + (t_0 + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 6.0d0) - 12.0d0))))))
    else if (x1 <= 1.85d+152) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((3.0d0 * (x2 * ((x1 * 2.0d0) + (3.0d0 * (x1 / x2))))) + (4.0d0 * (x2 * (-3.0d0)))) - 2.0d0)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + t_0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 9.0) - 2.0);
	double tmp;
	if (x1 <= -5.5e+157) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= 1.35e+70) {
		tmp = x1 + ((x2 * -6.0) + (t_0 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else if (x1 <= 1.85e+152) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((3.0 * (x2 * ((x1 * 2.0) + (3.0 * (x1 / x2))))) + (4.0 * (x2 * -3.0))) - 2.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) + t_0);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((x1 * 9.0) - 2.0)
	tmp = 0
	if x1 <= -5.5e+157:
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	elif x1 <= 1.35e+70:
		tmp = x1 + ((x2 * -6.0) + (t_0 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))))
	elif x1 <= 1.85e+152:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((3.0 * (x2 * ((x1 * 2.0) + (3.0 * (x1 / x2))))) + (4.0 * (x2 * -3.0))) - 2.0)))
	else:
		tmp = x1 + ((x2 * -6.0) + t_0)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))
	tmp = 0.0
	if (x1 <= -5.5e+157)
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))));
	elseif (x1 <= 1.35e+70)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(t_0 + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)))))));
	elseif (x1 <= 1.85e+152)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(3.0 * Float64(x2 * Float64(Float64(x1 * 2.0) + Float64(3.0 * Float64(x1 / x2))))) + Float64(4.0 * Float64(x2 * -3.0))) - 2.0))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + t_0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((x1 * 9.0) - 2.0);
	tmp = 0.0;
	if (x1 <= -5.5e+157)
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	elseif (x1 <= 1.35e+70)
		tmp = x1 + ((x2 * -6.0) + (t_0 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	elseif (x1 <= 1.85e+152)
		tmp = x1 + ((x2 * -6.0) + (x1 * (((3.0 * (x2 * ((x1 * 2.0) + (3.0 * (x1 / x2))))) + (4.0 * (x2 * -3.0))) - 2.0)));
	else
		tmp = x1 + ((x2 * -6.0) + t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.5e+157], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+70], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(t$95$0 + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.85e+152], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(3.0 * N[(x2 * N[(N[(x1 * 2.0), $MachinePrecision] + N[(3.0 * N[(x1 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x2 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.5000000000000003e157

   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 60.7%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -5.5000000000000003e157 < x1 < 1.35e70

   1. Initial program 91.2%

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

   3. Taylor expanded in x1 around 0 70.0%

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

   4. Taylor expanded in x1 around 0 72.5%

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

   5. Taylor expanded in x2 around 0 82.5%

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

   if 1.35e70 < x1 < 1.84999999999999998e152

   1. Initial program 99.9%

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

   3. Taylor expanded in x1 around 0 32.8%

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

   4. Taylor expanded in x1 around 0 23.3%

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

   5. Taylor expanded in x2 around inf 51.4%

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

   6. Taylor expanded in x2 around 0 56.4%

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

      1. *-commutative 56.4%

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

   8. Simplified 56.4%

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

   if 1.84999999999999998e152 < x1

   1. Initial program 2.6%

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

   3. Taylor expanded in x1 around 0 2.6%

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

   4. Taylor expanded in x1 around 0 81.6%

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

   5. Taylor expanded in x2 around 0 97.7%

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

      1. *-commutative 97.7%

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

   7. Simplified 97.7%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+157}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+70}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.85 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(3 \cdot \left(x2 \cdot \left(x1 \cdot 2 + 3 \cdot \frac{x1}{x2}\right)\right) + 4 \cdot \left(x2 \cdot -3\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 68.3% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ t_1 := x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{if}\;x1 \leq -3 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -1.1 \cdot 10^{-131}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 1.02 \cdot 10^{-175}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 6.8 \cdot 10^{+72}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 1.4 \cdot 10^{+112}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) -1.0)))
        (t_1 (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))))
   (if (<= x1 -3e+95)
     t_1
     (if (<= x1 -1.1e-131)
       t_0
       (if (<= x1 1.02e-175)
         (+ x1 (+ (* x2 -6.0) (* x1 -2.0)))
         (if (<= x1 6.8e+72)
           t_0
           (if (<= x1 1.4e+112)
             (* x2 (- (/ x1 x2) 6.0))
             (if (<= x1 4.5e+153) t_0 t_1))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0);
	double t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double tmp;
	if (x1 <= -3e+95) {
		tmp = t_1;
	} else if (x1 <= -1.1e-131) {
		tmp = t_0;
	} else if (x1 <= 1.02e-175) {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	} else if (x1 <= 6.8e+72) {
		tmp = t_0;
	} else if (x1 <= 1.4e+112) {
		tmp = x2 * ((x1 / x2) - 6.0);
	} else if (x1 <= 4.5e+153) {
		tmp = t_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) :: tmp
    t_0 = x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + (-1.0d0))
    t_1 = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    if (x1 <= (-3d+95)) then
        tmp = t_1
    else if (x1 <= (-1.1d-131)) then
        tmp = t_0
    else if (x1 <= 1.02d-175) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (-2.0d0)))
    else if (x1 <= 6.8d+72) then
        tmp = t_0
    else if (x1 <= 1.4d+112) then
        tmp = x2 * ((x1 / x2) - 6.0d0)
    else if (x1 <= 4.5d+153) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0);
	double t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double tmp;
	if (x1 <= -3e+95) {
		tmp = t_1;
	} else if (x1 <= -1.1e-131) {
		tmp = t_0;
	} else if (x1 <= 1.02e-175) {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	} else if (x1 <= 6.8e+72) {
		tmp = t_0;
	} else if (x1 <= 1.4e+112) {
		tmp = x2 * ((x1 / x2) - 6.0);
	} else if (x1 <= 4.5e+153) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0)
	t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	tmp = 0
	if x1 <= -3e+95:
		tmp = t_1
	elif x1 <= -1.1e-131:
		tmp = t_0
	elif x1 <= 1.02e-175:
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0))
	elif x1 <= 6.8e+72:
		tmp = t_0
	elif x1 <= 1.4e+112:
		tmp = x2 * ((x1 / x2) - 6.0)
	elif x1 <= 4.5e+153:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) + -1.0))
	t_1 = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))))
	tmp = 0.0
	if (x1 <= -3e+95)
		tmp = t_1;
	elseif (x1 <= -1.1e-131)
		tmp = t_0;
	elseif (x1 <= 1.02e-175)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * -2.0)));
	elseif (x1 <= 6.8e+72)
		tmp = t_0;
	elseif (x1 <= 1.4e+112)
		tmp = Float64(x2 * Float64(Float64(x1 / x2) - 6.0));
	elseif (x1 <= 4.5e+153)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0);
	t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	tmp = 0.0;
	if (x1 <= -3e+95)
		tmp = t_1;
	elseif (x1 <= -1.1e-131)
		tmp = t_0;
	elseif (x1 <= 1.02e-175)
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	elseif (x1 <= 6.8e+72)
		tmp = t_0;
	elseif (x1 <= 1.4e+112)
		tmp = x2 * ((x1 / x2) - 6.0);
	elseif (x1 <= 4.5e+153)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3e+95], t$95$1, If[LessEqual[x1, -1.1e-131], t$95$0, If[LessEqual[x1, 1.02e-175], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6.8e+72], t$95$0, If[LessEqual[x1, 1.4e+112], N[(x2 * N[(N[(x1 / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.5e+153], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.99999999999999991e95 or 4.5000000000000001e153 < x1

   1. Initial program 2.5%

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

   3. Taylor expanded in x1 around 0 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 64.7%

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

   5. Taylor expanded in x2 around 0 84.1%

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

   if -2.99999999999999991e95 < x1 < -1.1e-131 or 1.0200000000000001e-175 < x1 < 6.7999999999999997e72 or 1.4000000000000001e112 < x1 < 4.5000000000000001e153

   1. Initial program 99.2%

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

   3. Taylor expanded in x1 around 0 74.6%

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

   4. Taylor expanded in x1 around 0 73.6%

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

   5. Taylor expanded in x1 around inf 65.6%

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

   if -1.1e-131 < x1 < 1.0200000000000001e-175

   1. Initial program 99.8%

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

   3. Taylor expanded in x1 around 0 77.7%

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

   4. Taylor expanded in x1 around 0 77.8%

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

   5. Taylor expanded in x2 around 0 77.4%

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

      1. *-commutative 77.4%

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

   7. Simplified 77.4%

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

   if 6.7999999999999997e72 < x1 < 1.4000000000000001e112

   1. Initial program 100.0%

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

   3. Taylor expanded in x1 around 0 3.5%

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

   4. Taylor expanded in x1 around 0 3.5%

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

      1. *-commutative 3.5%

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

   6. Simplified 3.5%

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

   7. Taylor expanded in x2 around inf 52.3%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3 \cdot 10^{+95}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.1 \cdot 10^{-131}:\\ \;\;\;\;x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{elif}\;x1 \leq 1.02 \cdot 10^{-175}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 6.8 \cdot 10^{+72}:\\ \;\;\;\;x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{elif}\;x1 \leq 1.4 \cdot 10^{+112}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 80.5% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+157}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{-16}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(x1 \cdot 3 + 3 \cdot \left(3 - x2 \cdot -2\right)\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -5.5e+157)
   (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))
   (if (<= x1 1e-16)
     (+
      x1
      (+
       (* x2 -6.0)
       (+
        (* x1 (- (* x1 9.0) 2.0))
        (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 6.0) 12.0)))))))
     (+
      x1
      (+
       (* x2 -6.0)
       (*
        x1
        (-
         (+
          (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))
          (* x1 (+ (* x1 3.0) (* 3.0 (- 3.0 (* x2 -2.0))))))
         2.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -5.5e+157) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= 1e-16) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-5.5d+157)) then
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    else if (x1 <= 1d-16) then
        tmp = x1 + ((x2 * (-6.0d0)) + ((x1 * ((x1 * 9.0d0) - 2.0d0)) + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 6.0d0) - 12.0d0))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + (x1 * ((x1 * 3.0d0) + (3.0d0 * (3.0d0 - (x2 * (-2.0d0))))))) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -5.5e+157) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= 1e-16) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -5.5e+157:
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	elif x1 <= 1e-16:
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -5.5e+157)
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))));
	elseif (x1 <= 1e-16)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0)) + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) + Float64(x1 * Float64(Float64(x1 * 3.0) + Float64(3.0 * Float64(3.0 - Float64(x2 * -2.0)))))) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -5.5e+157)
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	elseif (x1 <= 1e-16)
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -5.5e+157], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1e-16], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + N[(3.0 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.5000000000000003e157

   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 60.7%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -5.5000000000000003e157 < x1 < 9.9999999999999998e-17

   1. Initial program 90.2%

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

   3. Taylor expanded in x1 around 0 73.7%

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

   4. Taylor expanded in x1 around 0 76.4%

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

   5. Taylor expanded in x2 around 0 87.8%

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

   if 9.9999999999999998e-17 < x1

   1. Initial program 52.3%

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

   3. Taylor expanded in x1 around 0 20.7%

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

   4. Taylor expanded in x1 around 0 74.7%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+157}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{-16}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(x1 \cdot 3 + 3 \cdot \left(3 - x2 \cdot -2\right)\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 75.1% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ t_1 := x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+157}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -1.15 \cdot 10^{+78}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x2 \cdot 6 + 9\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -1.2 \cdot 10^{-256}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 2.5 \cdot 10^{-265}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x2 -6.0) (* x1 (+ (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) -1.0))))
        (t_1 (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))))
   (if (<= x1 -5.5e+157)
     t_1
     (if (<= x1 -1.15e+78)
       (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 (+ (* x2 6.0) 9.0)) 2.0))))
       (if (<= x1 -1.2e-256)
         t_0
         (if (<= x1 2.5e-265)
           (+ x1 (+ (* x2 -6.0) (* x1 -2.0)))
           (if (<= x1 4.5e+153) t_0 t_1)))))))

C

double code(double x1, double x2) {
	double t_0 = (x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0));
	double t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double tmp;
	if (x1 <= -5.5e+157) {
		tmp = t_1;
	} else if (x1 <= -1.15e+78) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x2 * 6.0) + 9.0)) - 2.0)));
	} else if (x1 <= -1.2e-256) {
		tmp = t_0;
	} else if (x1 <= 2.5e-265) {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	} else if (x1 <= 4.5e+153) {
		tmp = t_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) :: tmp
    t_0 = (x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + (-1.0d0)))
    t_1 = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    if (x1 <= (-5.5d+157)) then
        tmp = t_1
    else if (x1 <= (-1.15d+78)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * ((x2 * 6.0d0) + 9.0d0)) - 2.0d0)))
    else if (x1 <= (-1.2d-256)) then
        tmp = t_0
    else if (x1 <= 2.5d-265) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (-2.0d0)))
    else if (x1 <= 4.5d+153) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0));
	double t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double tmp;
	if (x1 <= -5.5e+157) {
		tmp = t_1;
	} else if (x1 <= -1.15e+78) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x2 * 6.0) + 9.0)) - 2.0)));
	} else if (x1 <= -1.2e-256) {
		tmp = t_0;
	} else if (x1 <= 2.5e-265) {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	} else if (x1 <= 4.5e+153) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0))
	t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	tmp = 0
	if x1 <= -5.5e+157:
		tmp = t_1
	elif x1 <= -1.15e+78:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x2 * 6.0) + 9.0)) - 2.0)))
	elif x1 <= -1.2e-256:
		tmp = t_0
	elif x1 <= 2.5e-265:
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0))
	elif x1 <= 4.5e+153:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) + -1.0)))
	t_1 = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))))
	tmp = 0.0
	if (x1 <= -5.5e+157)
		tmp = t_1;
	elseif (x1 <= -1.15e+78)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x2 * 6.0) + 9.0)) - 2.0))));
	elseif (x1 <= -1.2e-256)
		tmp = t_0;
	elseif (x1 <= 2.5e-265)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * -2.0)));
	elseif (x1 <= 4.5e+153)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0));
	t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	tmp = 0.0;
	if (x1 <= -5.5e+157)
		tmp = t_1;
	elseif (x1 <= -1.15e+78)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x2 * 6.0) + 9.0)) - 2.0)));
	elseif (x1 <= -1.2e-256)
		tmp = t_0;
	elseif (x1 <= 2.5e-265)
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	elseif (x1 <= 4.5e+153)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.5e+157], t$95$1, If[LessEqual[x1, -1.15e+78], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(N[(x2 * 6.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.2e-256], t$95$0, If[LessEqual[x1, 2.5e-265], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.5e+153], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.5000000000000003e157 or 4.5000000000000001e153 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 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 73.8%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -5.5000000000000003e157 < x1 < -1.1500000000000001e78

   1. Initial program 22.2%

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

   3. Taylor expanded in x1 around 0 5.7%

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

   4. Taylor expanded in x1 around 0 35.5%

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

   5. Taylor expanded in x1 around inf 47.1%

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

      1. associate-*r* 47.1%

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

      2. *-commutative 47.1%

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

      3. associate-*r* 47.1%

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

      4. cancel-sign-sub-inv 47.1%

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

      5. metadata-eval 47.1%

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

      6. distribute-lft-in 47.1%

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

      7. metadata-eval 47.1%

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

      8. metadata-eval 47.1%

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

      9. distribute-lft-neg-in 47.1%

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

      10. distribute-rgt-neg-in 47.1%

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

      11. associate-*r* 47.1%

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

      12. metadata-eval 47.1%

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

      13. *-commutative 47.1%

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

      14. distribute-rgt-neg-in 47.1%

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

      15. metadata-eval 47.1%

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

   7. Simplified 47.1%

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

   if -1.1500000000000001e78 < x1 < -1.2e-256 or 2.5e-265 < x1 < 4.5000000000000001e153

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 72.8%

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

   4. Taylor expanded in x1 around 0 72.0%

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

   5. Taylor expanded in x1 around 0 72.0%

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

   if -1.2e-256 < x1 < 2.5e-265

   1. Initial program 99.9%

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

   3. Taylor expanded in x1 around 0 70.9%

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

   4. Taylor expanded in x1 around 0 71.1%

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

   5. Taylor expanded in x2 around 0 98.8%

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

      1. *-commutative 98.8%

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

   7. Simplified 98.8%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+157}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.15 \cdot 10^{+78}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x2 \cdot 6 + 9\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -1.2 \cdot 10^{-256}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{elif}\;x1 \leq 2.5 \cdot 10^{-265}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 79.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+157}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -1 \cdot 10^{+78}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x2 \cdot 6 + 9\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+73}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot -12\right) - 6\right) + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{+111}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))))
   (if (<= x1 -5.5e+157)
     t_0
     (if (<= x1 -1e+78)
       (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 (+ (* x2 6.0) 9.0)) 2.0))))
       (if (<= x1 1.8e+73)
         (+
          x1
          (+ (* x2 (- (+ (* 8.0 (* x1 x2)) (* x1 -12.0)) 6.0)) (* x1 -2.0)))
         (if (<= x1 6e+111)
           (* x2 (- (/ x1 x2) 6.0))
           (if (<= x1 4.5e+153)
             (+ x1 (* x1 (+ 1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))))
             t_0)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double tmp;
	if (x1 <= -5.5e+157) {
		tmp = t_0;
	} else if (x1 <= -1e+78) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x2 * 6.0) + 9.0)) - 2.0)));
	} else if (x1 <= 1.8e+73) {
		tmp = x1 + ((x2 * (((8.0 * (x1 * x2)) + (x1 * -12.0)) - 6.0)) + (x1 * -2.0));
	} else if (x1 <= 6e+111) {
		tmp = x2 * ((x1 / x2) - 6.0);
	} else if (x1 <= 4.5e+153) {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    if (x1 <= (-5.5d+157)) then
        tmp = t_0
    else if (x1 <= (-1d+78)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * ((x2 * 6.0d0) + 9.0d0)) - 2.0d0)))
    else if (x1 <= 1.8d+73) then
        tmp = x1 + ((x2 * (((8.0d0 * (x1 * x2)) + (x1 * (-12.0d0))) - 6.0d0)) + (x1 * (-2.0d0)))
    else if (x1 <= 6d+111) then
        tmp = x2 * ((x1 / x2) - 6.0d0)
    else if (x1 <= 4.5d+153) then
        tmp = x1 + (x1 * (1.0d0 + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0)))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double tmp;
	if (x1 <= -5.5e+157) {
		tmp = t_0;
	} else if (x1 <= -1e+78) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x2 * 6.0) + 9.0)) - 2.0)));
	} else if (x1 <= 1.8e+73) {
		tmp = x1 + ((x2 * (((8.0 * (x1 * x2)) + (x1 * -12.0)) - 6.0)) + (x1 * -2.0));
	} else if (x1 <= 6e+111) {
		tmp = x2 * ((x1 / x2) - 6.0);
	} else if (x1 <= 4.5e+153) {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	tmp = 0
	if x1 <= -5.5e+157:
		tmp = t_0
	elif x1 <= -1e+78:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x2 * 6.0) + 9.0)) - 2.0)))
	elif x1 <= 1.8e+73:
		tmp = x1 + ((x2 * (((8.0 * (x1 * x2)) + (x1 * -12.0)) - 6.0)) + (x1 * -2.0))
	elif x1 <= 6e+111:
		tmp = x2 * ((x1 / x2) - 6.0)
	elif x1 <= 4.5e+153:
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))))
	tmp = 0.0
	if (x1 <= -5.5e+157)
		tmp = t_0;
	elseif (x1 <= -1e+78)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x2 * 6.0) + 9.0)) - 2.0))));
	elseif (x1 <= 1.8e+73)
		tmp = Float64(x1 + Float64(Float64(x2 * Float64(Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * -12.0)) - 6.0)) + Float64(x1 * -2.0)));
	elseif (x1 <= 6e+111)
		tmp = Float64(x2 * Float64(Float64(x1 / x2) - 6.0));
	elseif (x1 <= 4.5e+153)
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	tmp = 0.0;
	if (x1 <= -5.5e+157)
		tmp = t_0;
	elseif (x1 <= -1e+78)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x2 * 6.0) + 9.0)) - 2.0)));
	elseif (x1 <= 1.8e+73)
		tmp = x1 + ((x2 * (((8.0 * (x1 * x2)) + (x1 * -12.0)) - 6.0)) + (x1 * -2.0));
	elseif (x1 <= 6e+111)
		tmp = x2 * ((x1 / x2) - 6.0);
	elseif (x1 <= 4.5e+153)
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.5e+157], t$95$0, If[LessEqual[x1, -1e+78], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(N[(x2 * 6.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.8e+73], N[(x1 + N[(N[(x2 * N[(N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * -12.0), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6e+111], N[(x2 * N[(N[(x1 / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.5e+153], N[(x1 + N[(x1 * N[(1.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -5.5000000000000003e157 or 4.5000000000000001e153 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 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 73.8%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -5.5000000000000003e157 < x1 < -1.00000000000000001e78

   1. Initial program 22.2%

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

   3. Taylor expanded in x1 around 0 5.7%

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

   4. Taylor expanded in x1 around 0 35.5%

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

   5. Taylor expanded in x1 around inf 47.1%

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

      1. associate-*r* 47.1%

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

      2. *-commutative 47.1%

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

      3. associate-*r* 47.1%

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

      4. cancel-sign-sub-inv 47.1%

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

      5. metadata-eval 47.1%

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

      6. distribute-lft-in 47.1%

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

      7. metadata-eval 47.1%

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

      8. metadata-eval 47.1%

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

      9. distribute-lft-neg-in 47.1%

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

      10. distribute-rgt-neg-in 47.1%

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

      11. associate-*r* 47.1%

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

      12. metadata-eval 47.1%

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

      13. *-commutative 47.1%

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

      14. distribute-rgt-neg-in 47.1%

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

      15. metadata-eval 47.1%

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

   7. Simplified 47.1%

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

   if -1.00000000000000001e78 < x1 < 1.7999999999999999e73

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 77.3%

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

   4. Taylor expanded in x1 around 0 76.8%

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

   5. Taylor expanded in x2 around 0 86.6%

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

   if 1.7999999999999999e73 < x1 < 6e111

   1. Initial program 100.0%

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

   3. Taylor expanded in x1 around 0 3.5%

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

   4. Taylor expanded in x1 around 0 3.5%

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

      1. *-commutative 3.5%

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

   6. Simplified 3.5%

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

   7. Taylor expanded in x2 around inf 52.3%

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

   if 6e111 < x1 < 4.5000000000000001e153

   1. Initial program 100.0%

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

   3. Taylor expanded in x1 around 0 56.8%

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

   4. Taylor expanded in x1 around inf 56.8%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+157}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1 \cdot 10^{+78}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x2 \cdot 6 + 9\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+73}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot -12\right) - 6\right) + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{+111}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 66.6% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{if}\;x2 \leq -2 \cdot 10^{+65}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x2 \leq 4 \cdot 10^{-147}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x2 \leq 2.35 \cdot 10^{+188}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x2 \cdot 6 + 9\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) -1.0))))
   (if (<= x2 -2e+65)
     t_0
     (if (<= x2 4e-147)
       (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 9.0) 2.0))))
       (if (<= x2 2.35e+188)
         (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 (+ (* x2 6.0) 9.0)) 2.0))))
         t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0);
	double tmp;
	if (x2 <= -2e+65) {
		tmp = t_0;
	} else if (x2 <= 4e-147) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	} else if (x2 <= 2.35e+188) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x2 * 6.0) + 9.0)) - 2.0)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + (-1.0d0))
    if (x2 <= (-2d+65)) then
        tmp = t_0
    else if (x2 <= 4d-147) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) - 2.0d0)))
    else if (x2 <= 2.35d+188) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * ((x2 * 6.0d0) + 9.0d0)) - 2.0d0)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0);
	double tmp;
	if (x2 <= -2e+65) {
		tmp = t_0;
	} else if (x2 <= 4e-147) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	} else if (x2 <= 2.35e+188) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x2 * 6.0) + 9.0)) - 2.0)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0)
	tmp = 0
	if x2 <= -2e+65:
		tmp = t_0
	elif x2 <= 4e-147:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)))
	elif x2 <= 2.35e+188:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x2 * 6.0) + 9.0)) - 2.0)))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) + -1.0))
	tmp = 0.0
	if (x2 <= -2e+65)
		tmp = t_0;
	elseif (x2 <= 4e-147)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))));
	elseif (x2 <= 2.35e+188)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x2 * 6.0) + 9.0)) - 2.0))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0);
	tmp = 0.0;
	if (x2 <= -2e+65)
		tmp = t_0;
	elseif (x2 <= 4e-147)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	elseif (x2 <= 2.35e+188)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x2 * 6.0) + 9.0)) - 2.0)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x2, -2e+65], t$95$0, If[LessEqual[x2, 4e-147], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x2, 2.35e+188], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(N[(x2 * 6.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -2e65 or 2.3499999999999999e188 < x2

   1. Initial program 78.1%

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

   3. Taylor expanded in x1 around 0 56.3%

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

   4. Taylor expanded in x1 around 0 67.9%

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

   5. Taylor expanded in x1 around inf 65.9%

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

   if -2e65 < x2 < 3.9999999999999999e-147

   1. Initial program 66.4%

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

   3. Taylor expanded in x1 around 0 45.4%

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

   4. Taylor expanded in x1 around 0 69.3%

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

   5. Taylor expanded in x2 around 0 72.9%

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

      1. *-commutative 72.9%

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

   7. Simplified 72.9%

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

   if 3.9999999999999999e-147 < x2 < 2.3499999999999999e188

   1. Initial program 62.5%

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

   3. Taylor expanded in x1 around 0 47.8%

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

   4. Taylor expanded in x1 around 0 81.6%

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

   5. Taylor expanded in x1 around inf 78.6%

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

      1. associate-*r* 78.6%

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

      2. *-commutative 78.6%

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

      3. associate-*r* 78.6%

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

      4. cancel-sign-sub-inv 78.6%

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

      5. metadata-eval 78.6%

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

      6. distribute-lft-in 78.6%

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

      7. metadata-eval 78.6%

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

      8. metadata-eval 78.6%

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

      9. distribute-lft-neg-in 78.6%

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

      10. distribute-rgt-neg-in 78.6%

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

      11. associate-*r* 78.6%

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

      12. metadata-eval 78.6%

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

      13. *-commutative 78.6%

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

      14. distribute-rgt-neg-in 78.6%

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

      15. metadata-eval 78.6%

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

   7. Simplified 78.6%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -2 \cdot 10^{+65}:\\ \;\;\;\;x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{elif}\;x2 \leq 4 \cdot 10^{-147}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x2 \leq 2.35 \cdot 10^{+188}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x2 \cdot 6 + 9\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 47.2% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -4 \cdot 10^{+56} \lor \neg \left(x2 \leq 5.4 \cdot 10^{+41}\right):\\ \;\;\;\;x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -4e+56) (not (<= x2 5.4e+41)))
   (* x1 (+ (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) -1.0))
   (+ x1 (+ (* x2 -6.0) (* x1 -2.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -4e+56) || !(x2 <= 5.4e+41)) {
		tmp = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0);
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-4d+56)) .or. (.not. (x2 <= 5.4d+41))) then
        tmp = x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + (-1.0d0))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -4e+56) || !(x2 <= 5.4e+41)) {
		tmp = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0);
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -4e+56) or not (x2 <= 5.4e+41):
		tmp = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0)
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -4e+56) || !(x2 <= 5.4e+41))
		tmp = Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) + -1.0));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -4e+56) || ~((x2 <= 5.4e+41)))
		tmp = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0);
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -4e+56], N[Not[LessEqual[x2, 5.4e+41]], $MachinePrecision]], N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -4.00000000000000037e56 or 5.39999999999999999e41 < x2

   1. Initial program 73.1%

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

   3. Taylor expanded in x1 around 0 53.7%

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

   4. Taylor expanded in x1 around 0 67.1%

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

   5. Taylor expanded in x1 around inf 60.4%

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

   if -4.00000000000000037e56 < x2 < 5.39999999999999999e41

   1. Initial program 65.4%

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

   3. Taylor expanded in x1 around 0 46.2%

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

   4. Taylor expanded in x1 around 0 47.1%

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

   5. Taylor expanded in x2 around 0 46.0%

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

      1. *-commutative 46.0%

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

   7. Simplified 46.0%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -4 \cdot 10^{+56} \lor \neg \left(x2 \leq 5.4 \cdot 10^{+41}\right):\\ \;\;\;\;x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 64.9% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -3.1 \cdot 10^{+65} \lor \neg \left(x2 \leq 10^{+121}\right):\\ \;\;\;\;x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -3.1e+65) (not (<= x2 1e+121)))
   (* x1 (+ (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) -1.0))
   (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 9.0) 2.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -3.1e+65) || !(x2 <= 1e+121)) {
		tmp = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0);
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-3.1d+65)) .or. (.not. (x2 <= 1d+121))) then
        tmp = x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + (-1.0d0))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -3.1e+65) || !(x2 <= 1e+121)) {
		tmp = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0);
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -3.1e+65) or not (x2 <= 1e+121):
		tmp = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0)
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -3.1e+65) || !(x2 <= 1e+121))
		tmp = Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) + -1.0));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -3.1e+65) || ~((x2 <= 1e+121)))
		tmp = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0);
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -3.1e+65], N[Not[LessEqual[x2, 1e+121]], $MachinePrecision]], N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -3.09999999999999991e65 or 1.00000000000000004e121 < x2

   1. Initial program 77.3%

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

   3. Taylor expanded in x1 around 0 54.9%

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

   4. Taylor expanded in x1 around 0 66.7%

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

   5. Taylor expanded in x1 around inf 64.1%

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

   if -3.09999999999999991e65 < x2 < 1.00000000000000004e121

   1. Initial program 63.9%

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

   3. Taylor expanded in x1 around 0 46.4%

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

   4. Taylor expanded in x1 around 0 76.0%

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

   5. Taylor expanded in x2 around 0 73.8%

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

      1. *-commutative 73.8%

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

   7. Simplified 73.8%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -3.1 \cdot 10^{+65} \lor \neg \left(x2 \leq 10^{+121}\right):\\ \;\;\;\;x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 31.9% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -3.15 \cdot 10^{-133}:\\ \;\;\;\;-x1\\ \mathbf{elif}\;x1 \leq 1.4 \cdot 10^{-152}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{-46}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -3.15e-133)
   (- x1)
   (if (<= x1 1.4e-152)
     (* x2 -6.0)
     (if (<= x1 4.5e-46) (- x1) (* x2 (- (/ x1 x2) 6.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3.15e-133) {
		tmp = -x1;
	} else if (x1 <= 1.4e-152) {
		tmp = x2 * -6.0;
	} else if (x1 <= 4.5e-46) {
		tmp = -x1;
	} else {
		tmp = x2 * ((x1 / x2) - 6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-3.15d-133)) then
        tmp = -x1
    else if (x1 <= 1.4d-152) then
        tmp = x2 * (-6.0d0)
    else if (x1 <= 4.5d-46) then
        tmp = -x1
    else
        tmp = x2 * ((x1 / x2) - 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3.15e-133) {
		tmp = -x1;
	} else if (x1 <= 1.4e-152) {
		tmp = x2 * -6.0;
	} else if (x1 <= 4.5e-46) {
		tmp = -x1;
	} else {
		tmp = x2 * ((x1 / x2) - 6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -3.15e-133:
		tmp = -x1
	elif x1 <= 1.4e-152:
		tmp = x2 * -6.0
	elif x1 <= 4.5e-46:
		tmp = -x1
	else:
		tmp = x2 * ((x1 / x2) - 6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -3.15e-133)
		tmp = Float64(-x1);
	elseif (x1 <= 1.4e-152)
		tmp = Float64(x2 * -6.0);
	elseif (x1 <= 4.5e-46)
		tmp = Float64(-x1);
	else
		tmp = Float64(x2 * Float64(Float64(x1 / x2) - 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -3.15e-133)
		tmp = -x1;
	elseif (x1 <= 1.4e-152)
		tmp = x2 * -6.0;
	elseif (x1 <= 4.5e-46)
		tmp = -x1;
	else
		tmp = x2 * ((x1 / x2) - 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -3.15e-133], (-x1), If[LessEqual[x1, 1.4e-152], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x1, 4.5e-46], (-x1), N[(x2 * N[(N[(x1 / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.1500000000000001e-133 or 1.39999999999999992e-152 < x1 < 4.50000000000000001e-46

   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 52.9%

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

   4. Taylor expanded in x1 around 0 54.2%

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

   5. Taylor expanded in x2 around 0 26.1%

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

      1. distribute-rgt1-in 26.1%

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

      2. metadata-eval 26.1%

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

      3. neg-mul-1 26.1%

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

   7. Simplified 26.1%

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

   if -3.1500000000000001e-133 < x1 < 1.39999999999999992e-152

   1. Initial program 99.8%

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

   3. Taylor expanded in x1 around 0 77.2%

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

   4. Taylor expanded in x1 around 0 63.1%

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

      1. *-commutative 63.1%

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

   6. Simplified 63.1%

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

   7. Taylor expanded in x1 around 0 63.5%

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

      1. *-commutative 63.5%

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

   9. Simplified 63.5%

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

   if 4.50000000000000001e-46 < x1

   1. Initial program 55.7%

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

   3. Taylor expanded in x1 around 0 25.3%

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

   4. Taylor expanded in x1 around 0 5.9%

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

      1. *-commutative 5.9%

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

   6. Simplified 5.9%

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

   7. Taylor expanded in x2 around inf 29.3%

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

4. Final simplification 35.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.15 \cdot 10^{-133}:\\ \;\;\;\;-x1\\ \mathbf{elif}\;x1 \leq 1.4 \cdot 10^{-152}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{-46}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 27.8% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -2.35 \cdot 10^{-129} \lor \neg \left(x2 \leq 4.7 \cdot 10^{-142}\right):\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -2.35e-129) (not (<= x2 4.7e-142))) (+ x1 (* x2 -6.0)) (- x1)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -2.35e-129) || !(x2 <= 4.7e-142)) {
		tmp = x1 + (x2 * -6.0);
	} else {
		tmp = -x1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-2.35d-129)) .or. (.not. (x2 <= 4.7d-142))) then
        tmp = x1 + (x2 * (-6.0d0))
    else
        tmp = -x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -2.35e-129) || !(x2 <= 4.7e-142)) {
		tmp = x1 + (x2 * -6.0);
	} else {
		tmp = -x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -2.35e-129) or not (x2 <= 4.7e-142):
		tmp = x1 + (x2 * -6.0)
	else:
		tmp = -x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -2.35e-129) || !(x2 <= 4.7e-142))
		tmp = Float64(x1 + Float64(x2 * -6.0));
	else
		tmp = Float64(-x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -2.35e-129) || ~((x2 <= 4.7e-142)))
		tmp = x1 + (x2 * -6.0);
	else
		tmp = -x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -2.35e-129], N[Not[LessEqual[x2, 4.7e-142]], $MachinePrecision]], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision], (-x1)]

Derivation

1. Split input into 2 regimes

2. if x2 < -2.3500000000000001e-129 or 4.6999999999999999e-142 < x2

   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 50.7%

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

   4. Taylor expanded in x1 around 0 24.0%

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

      1. *-commutative 24.0%

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

   6. Simplified 24.0%

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

   if -2.3500000000000001e-129 < x2 < 4.6999999999999999e-142

   1. Initial program 66.8%

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

   3. Taylor expanded in x1 around 0 46.1%

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

   4. Taylor expanded in x1 around 0 46.5%

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

   5. Taylor expanded in x2 around 0 40.2%

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

      1. distribute-rgt1-in 40.2%

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

      2. metadata-eval 40.2%

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

      3. neg-mul-1 40.2%

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

   7. Simplified 40.2%

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

4. Final simplification 28.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -2.35 \cdot 10^{-129} \lor \neg \left(x2 \leq 4.7 \cdot 10^{-142}\right):\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 41.2% accurate, 9.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq 1.35:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 1.35) (+ x1 (+ (* x2 -6.0) (* x1 -2.0))) (* x2 (- (/ x1 x2) 6.0))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= 1.35) {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	} else {
		tmp = x2 * ((x1 / x2) - 6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= 1.35d0) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (-2.0d0)))
    else
        tmp = x2 * ((x1 / x2) - 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= 1.35) {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	} else {
		tmp = x2 * ((x1 / x2) - 6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= 1.35:
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0))
	else:
		tmp = x2 * ((x1 / x2) - 6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= 1.35)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * -2.0)));
	else
		tmp = Float64(x2 * Float64(Float64(x1 / x2) - 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= 1.35)
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	else
		tmp = x2 * ((x1 / x2) - 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, 1.35], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * N[(N[(x1 / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < 1.3500000000000001

   1. Initial program 76.6%

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

   3. Taylor expanded in x1 around 0 62.9%

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

   4. Taylor expanded in x1 around 0 63.5%

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

   5. Taylor expanded in x2 around 0 44.7%

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

      1. *-commutative 44.7%

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

   7. Simplified 44.7%

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

   if 1.3500000000000001 < x1

   1. Initial program 49.1%

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

   3. Taylor expanded in x1 around 0 15.7%

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

   4. Taylor expanded in x1 around 0 5.5%

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

      1. *-commutative 5.5%

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

   6. Simplified 5.5%

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

   7. Taylor expanded in x2 around inf 32.4%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq 1.35:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 27.6% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -5.2 \cdot 10^{-128} \lor \neg \left(x2 \leq 5 \cdot 10^{-142}\right):\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -5.2e-128) (not (<= x2 5e-142))) (* x2 -6.0) (- x1)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -5.2e-128) || !(x2 <= 5e-142)) {
		tmp = x2 * -6.0;
	} else {
		tmp = -x1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-5.2d-128)) .or. (.not. (x2 <= 5d-142))) then
        tmp = x2 * (-6.0d0)
    else
        tmp = -x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -5.2e-128) || !(x2 <= 5e-142)) {
		tmp = x2 * -6.0;
	} else {
		tmp = -x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -5.2e-128) or not (x2 <= 5e-142):
		tmp = x2 * -6.0
	else:
		tmp = -x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -5.2e-128) || !(x2 <= 5e-142))
		tmp = Float64(x2 * -6.0);
	else
		tmp = Float64(-x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -5.2e-128) || ~((x2 <= 5e-142)))
		tmp = x2 * -6.0;
	else
		tmp = -x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -5.2e-128], N[Not[LessEqual[x2, 5e-142]], $MachinePrecision]], N[(x2 * -6.0), $MachinePrecision], (-x1)]

Derivation

1. Split input into 2 regimes

2. if x2 < -5.19999999999999961e-128 or 5.0000000000000002e-142 < x2

   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 50.7%

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

   4. Taylor expanded in x1 around 0 24.0%

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

      1. *-commutative 24.0%

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

   6. Simplified 24.0%

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

   7. Taylor expanded in x1 around 0 23.5%

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

      1. *-commutative 23.5%

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

   9. Simplified 23.5%

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

   if -5.19999999999999961e-128 < x2 < 5.0000000000000002e-142

   1. Initial program 66.8%

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

   3. Taylor expanded in x1 around 0 46.1%

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

   4. Taylor expanded in x1 around 0 46.5%

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

   5. Taylor expanded in x2 around 0 40.2%

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

      1. distribute-rgt1-in 40.2%

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

      2. metadata-eval 40.2%

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

      3. neg-mul-1 40.2%

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

   7. Simplified 40.2%

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

4. Final simplification 27.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -5.2 \cdot 10^{-128} \lor \neg \left(x2 \leq 5 \cdot 10^{-142}\right):\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 16.2% accurate, 18.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq 2.8 \cdot 10^{-7}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (if (<= x1 2.8e-7) (- x1) x1))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= 2.8e-7) {
		tmp = -x1;
	} 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 (x1 <= 2.8d-7) then
        tmp = -x1
    else
        tmp = x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= 2.8e-7) {
		tmp = -x1;
	} else {
		tmp = x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= 2.8e-7:
		tmp = -x1
	else:
		tmp = x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= 2.8e-7)
		tmp = Float64(-x1);
	else
		tmp = x1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= 2.8e-7)
		tmp = -x1;
	else
		tmp = x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, 2.8e-7], (-x1), x1]

Derivation

1. Split input into 2 regimes

2. if x1 < 2.80000000000000019e-7

   1. Initial program 76.5%

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

   3. Taylor expanded in x1 around 0 62.8%

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

   4. Taylor expanded in x1 around 0 63.4%

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

   5. Taylor expanded in x2 around 0 20.1%

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

      1. distribute-rgt1-in 20.1%

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

      2. metadata-eval 20.1%

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

      3. neg-mul-1 20.1%

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

   7. Simplified 20.1%

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

   if 2.80000000000000019e-7 < x1

   1. Initial program 49.8%

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

   3. Taylor expanded in x1 around 0 16.6%

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

   4. Taylor expanded in x1 around 0 5.6%

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

      1. *-commutative 5.6%

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

   6. Simplified 5.6%

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

   7. Taylor expanded in x1 around inf 6.1%

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

4. Final simplification 16.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq 2.8 \cdot 10^{-7}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x1\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 3.2% accurate, 127.0× speedup

Math

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

FPCore

(FPCore (x1 x2) :precision binary64 x1)

C

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

Fortran

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

Java

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

Python

def code(x1, x2):
	return x1

Julia

function code(x1, x2)
	return x1
end

MATLAB

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

Wolfram

code[x1_, x2_] := x1

Derivation

1. Initial program 68.8%

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

3. Taylor expanded in x1 around 0 49.5%

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

4. Taylor expanded in x1 around 0 19.7%

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

   1. *-commutative 19.7%

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

6. Simplified 19.7%

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

7. Taylor expanded in x1 around inf 3.5%

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

8. Final simplification 3.5%

   \[\leadsto x1 \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024075 
(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))))))