Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 69.9% → 99.5%

Time: 1.4min

Alternatives: 25

Speedup: 4.4×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 69.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

   3. Simplified 99.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around -inf 13.4%

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

   4. Taylor expanded in x1 around inf 100.0%

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

   5. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.7%

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

Alternative 2: 99.3% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

   3. Taylor expanded in x2 around inf 99.5%

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

      1. +-commutative 99.5%

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

      2. associate--r+ 99.5%

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

      3. associate-*r/ 99.5%

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

      4. div-sub 99.5%

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

      5. +-commutative 99.5%

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

      6. unpow2 99.5%

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

      7. fma-undefine 99.5%

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

      8. associate-*r/ 99.5%

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

      9. metadata-eval 99.5%

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

      10. +-commutative 99.5%

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

      11. unpow2 99.5%

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

      12. fma-undefine 99.5%

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

   5. Simplified 99.5%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around -inf 13.4%

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

   4. Taylor expanded in x1 around inf 100.0%

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

   5. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.6%

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

Alternative 3: 99.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around -inf 13.4%

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

   4. Taylor expanded in x1 around inf 100.0%

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

   5. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.6%

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

Alternative 4: 97.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 - x1 \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := 6 \cdot {x1}^{4}\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := t\_3 + 2 \cdot x2\\ t_5 := \frac{t\_4 - x1}{t\_0}\\ t_6 := \frac{x1 - t\_4}{t\_0}\\ t_7 := \left(x1 \cdot x1\right) \cdot \left(6 - t\_6 \cdot 4\right)\\ t_8 := x1 \cdot \left(x1 \cdot x1\right)\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq -0.155:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(t\_7 + \left(\left(x1 \cdot 2\right) \cdot t\_6\right) \cdot \left(3 + t\_5\right)\right) \cdot t\_0 + t\_3 \cdot t\_6\right) + t\_8\right)\right) + 9\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+74}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_3 - 2 \cdot x2\right) - x1}{t\_1} + \left(x1 + \left(t\_8 - \left(t\_3 \cdot t\_5 + t\_1 \cdot \left(t\_7 + \left(t\_6 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x1 - 2 \cdot x2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- -1.0 (* x1 x1)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* 6.0 (pow x1 4.0)))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (+ t_3 (* 2.0 x2)))
        (t_5 (/ (- t_4 x1) t_0))
        (t_6 (/ (- x1 t_4) t_0))
        (t_7 (* (* x1 x1) (- 6.0 (* t_6 4.0))))
        (t_8 (* x1 (* x1 x1))))
   (if (<= x1 -5e+102)
     t_2
     (if (<= x1 -0.155)
       (+
        x1
        (+
         (+
          x1
          (+
           (+ (* (+ t_7 (* (* (* x1 2.0) t_6) (+ 3.0 t_5))) t_0) (* t_3 t_6))
           t_8))
         9.0))
       (if (<= x1 4e+74)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_3 (* 2.0 x2)) x1) t_1))
           (+
            x1
            (-
             t_8
             (+
              (* t_3 t_5)
              (*
               t_1
               (+ t_7 (* (- t_6 3.0) (* (* x1 2.0) (- x1 (* 2.0 x2)))))))))))
         t_2)))))

C

double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = 6.0 * pow(x1, 4.0);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = t_3 + (2.0 * x2);
	double t_5 = (t_4 - x1) / t_0;
	double t_6 = (x1 - t_4) / t_0;
	double t_7 = (x1 * x1) * (6.0 - (t_6 * 4.0));
	double t_8 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -5e+102) {
		tmp = t_2;
	} else if (x1 <= -0.155) {
		tmp = x1 + ((x1 + ((((t_7 + (((x1 * 2.0) * t_6) * (3.0 + t_5))) * t_0) + (t_3 * t_6)) + t_8)) + 9.0);
	} else if (x1 <= 4e+74) {
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_1)) + (x1 + (t_8 - ((t_3 * t_5) + (t_1 * (t_7 + ((t_6 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: tmp
    t_0 = (-1.0d0) - (x1 * x1)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = 6.0d0 * (x1 ** 4.0d0)
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = t_3 + (2.0d0 * x2)
    t_5 = (t_4 - x1) / t_0
    t_6 = (x1 - t_4) / t_0
    t_7 = (x1 * x1) * (6.0d0 - (t_6 * 4.0d0))
    t_8 = x1 * (x1 * x1)
    if (x1 <= (-5d+102)) then
        tmp = t_2
    else if (x1 <= (-0.155d0)) then
        tmp = x1 + ((x1 + ((((t_7 + (((x1 * 2.0d0) * t_6) * (3.0d0 + t_5))) * t_0) + (t_3 * t_6)) + t_8)) + 9.0d0)
    else if (x1 <= 4d+74) then
        tmp = x1 + ((3.0d0 * (((t_3 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + (t_8 - ((t_3 * t_5) + (t_1 * (t_7 + ((t_6 - 3.0d0) * ((x1 * 2.0d0) * (x1 - (2.0d0 * x2))))))))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = 6.0 * Math.pow(x1, 4.0);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = t_3 + (2.0 * x2);
	double t_5 = (t_4 - x1) / t_0;
	double t_6 = (x1 - t_4) / t_0;
	double t_7 = (x1 * x1) * (6.0 - (t_6 * 4.0));
	double t_8 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -5e+102) {
		tmp = t_2;
	} else if (x1 <= -0.155) {
		tmp = x1 + ((x1 + ((((t_7 + (((x1 * 2.0) * t_6) * (3.0 + t_5))) * t_0) + (t_3 * t_6)) + t_8)) + 9.0);
	} else if (x1 <= 4e+74) {
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_1)) + (x1 + (t_8 - ((t_3 * t_5) + (t_1 * (t_7 + ((t_6 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = -1.0 - (x1 * x1)
	t_1 = (x1 * x1) + 1.0
	t_2 = 6.0 * math.pow(x1, 4.0)
	t_3 = x1 * (x1 * 3.0)
	t_4 = t_3 + (2.0 * x2)
	t_5 = (t_4 - x1) / t_0
	t_6 = (x1 - t_4) / t_0
	t_7 = (x1 * x1) * (6.0 - (t_6 * 4.0))
	t_8 = x1 * (x1 * x1)
	tmp = 0
	if x1 <= -5e+102:
		tmp = t_2
	elif x1 <= -0.155:
		tmp = x1 + ((x1 + ((((t_7 + (((x1 * 2.0) * t_6) * (3.0 + t_5))) * t_0) + (t_3 * t_6)) + t_8)) + 9.0)
	elif x1 <= 4e+74:
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_1)) + (x1 + (t_8 - ((t_3 * t_5) + (t_1 * (t_7 + ((t_6 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(-1.0 - Float64(x1 * x1))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(6.0 * (x1 ^ 4.0))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(t_3 + Float64(2.0 * x2))
	t_5 = Float64(Float64(t_4 - x1) / t_0)
	t_6 = Float64(Float64(x1 - t_4) / t_0)
	t_7 = Float64(Float64(x1 * x1) * Float64(6.0 - Float64(t_6 * 4.0)))
	t_8 = Float64(x1 * Float64(x1 * x1))
	tmp = 0.0
	if (x1 <= -5e+102)
		tmp = t_2;
	elseif (x1 <= -0.155)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(Float64(t_7 + Float64(Float64(Float64(x1 * 2.0) * t_6) * Float64(3.0 + t_5))) * t_0) + Float64(t_3 * t_6)) + t_8)) + 9.0));
	elseif (x1 <= 4e+74)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_3 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(t_8 - Float64(Float64(t_3 * t_5) + Float64(t_1 * Float64(t_7 + Float64(Float64(t_6 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(x1 - Float64(2.0 * x2)))))))))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = -1.0 - (x1 * x1);
	t_1 = (x1 * x1) + 1.0;
	t_2 = 6.0 * (x1 ^ 4.0);
	t_3 = x1 * (x1 * 3.0);
	t_4 = t_3 + (2.0 * x2);
	t_5 = (t_4 - x1) / t_0;
	t_6 = (x1 - t_4) / t_0;
	t_7 = (x1 * x1) * (6.0 - (t_6 * 4.0));
	t_8 = x1 * (x1 * x1);
	tmp = 0.0;
	if (x1 <= -5e+102)
		tmp = t_2;
	elseif (x1 <= -0.155)
		tmp = x1 + ((x1 + ((((t_7 + (((x1 * 2.0) * t_6) * (3.0 + t_5))) * t_0) + (t_3 * t_6)) + t_8)) + 9.0);
	elseif (x1 <= 4e+74)
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_1)) + (x1 + (t_8 - ((t_3 * t_5) + (t_1 * (t_7 + ((t_6 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$4 - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 - t$95$4), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(t$95$6 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5e+102], t$95$2, If[LessEqual[x1, -0.155], N[(x1 + N[(N[(x1 + N[(N[(N[(N[(t$95$7 + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$6), $MachinePrecision] * N[(3.0 + t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision] + N[(t$95$3 * t$95$6), $MachinePrecision]), $MachinePrecision] + t$95$8), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4e+74], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$3 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$8 - N[(N[(t$95$3 * t$95$5), $MachinePrecision] + N[(t$95$1 * N[(t$95$7 + N[(N[(t$95$6 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(x1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5e102 or 3.99999999999999981e74 < x1

   1. Initial program 20.2%

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

   3. Taylor expanded in x1 around -inf 31.0%

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

   4. Taylor expanded in x1 around inf 100.0%

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

   5. Taylor expanded in x1 around inf 97.6%

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

   if -5e102 < x1 < -0.154999999999999999

   1. Initial program 99.1%

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

   3. Taylor expanded in x1 around inf 99.1%

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

   if -0.154999999999999999 < x1 < 3.99999999999999981e74

   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 97.7%

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

      1. +-commutative 97.7%

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

      2. mul-1-neg 97.7%

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

      3. sub-neg 97.7%

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

   5. Simplified 97.7%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq -0.155:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1} \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 9\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+74}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1} \cdot 4\right) + \left(\frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x1 - 2 \cdot x2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := t\_0 + 2 \cdot x2\\ t_2 := 6 \cdot {x1}^{4}\\ t_3 := x1 \cdot x1 + 1\\ t_4 := -1 - x1 \cdot x1\\ t_5 := \frac{x1 - t\_1}{t\_4}\\ t_6 := t\_5 - 3\\ t_7 := x1 \cdot \left(x1 \cdot x1\right)\\ t_8 := 3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_3}\\ t_9 := t\_0 \cdot \frac{t\_1 - x1}{t\_4}\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq -0.39:\\ \;\;\;\;x1 + \left(t\_8 - \left(\left(\left(t\_9 - t\_3 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_5\right) \cdot t\_6 + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(x1 \cdot 6 - 4\right)\right)\right)\right) - t\_7\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 7.6 \cdot 10^{+73}:\\ \;\;\;\;x1 + \left(t\_8 + \left(x1 + \left(t\_7 - \left(t\_9 + t\_3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - t\_5 \cdot 4\right) + t\_6 \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x1 - 2 \cdot x2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ t_0 (* 2.0 x2)))
        (t_2 (* 6.0 (pow x1 4.0)))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (- -1.0 (* x1 x1)))
        (t_5 (/ (- x1 t_1) t_4))
        (t_6 (- t_5 3.0))
        (t_7 (* x1 (* x1 x1)))
        (t_8 (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_3)))
        (t_9 (* t_0 (/ (- t_1 x1) t_4))))
   (if (<= x1 -5.6e+102)
     t_2
     (if (<= x1 -0.39)
       (+
        x1
        (-
         t_8
         (-
          (-
           (-
            t_9
            (*
             t_3
             (+
              (* (* (* x1 2.0) t_5) t_6)
              (+ (* 4.0 (- (* 2.0 x2) 3.0)) (* x1 (- (* x1 6.0) 4.0))))))
           t_7)
          x1)))
       (if (<= x1 7.6e+73)
         (+
          x1
          (+
           t_8
           (+
            x1
            (-
             t_7
             (+
              t_9
              (*
               t_3
               (+
                (* (* x1 x1) (- 6.0 (* t_5 4.0)))
                (* t_6 (* (* x1 2.0) (- x1 (* 2.0 x2)))))))))))
         t_2)))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = t_0 + (2.0 * x2);
	double t_2 = 6.0 * pow(x1, 4.0);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = -1.0 - (x1 * x1);
	double t_5 = (x1 - t_1) / t_4;
	double t_6 = t_5 - 3.0;
	double t_7 = x1 * (x1 * x1);
	double t_8 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3);
	double t_9 = t_0 * ((t_1 - x1) / t_4);
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_2;
	} else if (x1 <= -0.39) {
		tmp = x1 + (t_8 - (((t_9 - (t_3 * ((((x1 * 2.0) * t_5) * t_6) + ((4.0 * ((2.0 * x2) - 3.0)) + (x1 * ((x1 * 6.0) - 4.0)))))) - t_7) - x1));
	} else if (x1 <= 7.6e+73) {
		tmp = x1 + (t_8 + (x1 + (t_7 - (t_9 + (t_3 * (((x1 * x1) * (6.0 - (t_5 * 4.0))) + (t_6 * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = t_0 + (2.0d0 * x2)
    t_2 = 6.0d0 * (x1 ** 4.0d0)
    t_3 = (x1 * x1) + 1.0d0
    t_4 = (-1.0d0) - (x1 * x1)
    t_5 = (x1 - t_1) / t_4
    t_6 = t_5 - 3.0d0
    t_7 = x1 * (x1 * x1)
    t_8 = 3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_3)
    t_9 = t_0 * ((t_1 - x1) / t_4)
    if (x1 <= (-5.6d+102)) then
        tmp = t_2
    else if (x1 <= (-0.39d0)) then
        tmp = x1 + (t_8 - (((t_9 - (t_3 * ((((x1 * 2.0d0) * t_5) * t_6) + ((4.0d0 * ((2.0d0 * x2) - 3.0d0)) + (x1 * ((x1 * 6.0d0) - 4.0d0)))))) - t_7) - x1))
    else if (x1 <= 7.6d+73) then
        tmp = x1 + (t_8 + (x1 + (t_7 - (t_9 + (t_3 * (((x1 * x1) * (6.0d0 - (t_5 * 4.0d0))) + (t_6 * ((x1 * 2.0d0) * (x1 - (2.0d0 * x2))))))))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = t_0 + (2.0 * x2);
	double t_2 = 6.0 * Math.pow(x1, 4.0);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = -1.0 - (x1 * x1);
	double t_5 = (x1 - t_1) / t_4;
	double t_6 = t_5 - 3.0;
	double t_7 = x1 * (x1 * x1);
	double t_8 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3);
	double t_9 = t_0 * ((t_1 - x1) / t_4);
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_2;
	} else if (x1 <= -0.39) {
		tmp = x1 + (t_8 - (((t_9 - (t_3 * ((((x1 * 2.0) * t_5) * t_6) + ((4.0 * ((2.0 * x2) - 3.0)) + (x1 * ((x1 * 6.0) - 4.0)))))) - t_7) - x1));
	} else if (x1 <= 7.6e+73) {
		tmp = x1 + (t_8 + (x1 + (t_7 - (t_9 + (t_3 * (((x1 * x1) * (6.0 - (t_5 * 4.0))) + (t_6 * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = t_0 + (2.0 * x2)
	t_2 = 6.0 * math.pow(x1, 4.0)
	t_3 = (x1 * x1) + 1.0
	t_4 = -1.0 - (x1 * x1)
	t_5 = (x1 - t_1) / t_4
	t_6 = t_5 - 3.0
	t_7 = x1 * (x1 * x1)
	t_8 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3)
	t_9 = t_0 * ((t_1 - x1) / t_4)
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = t_2
	elif x1 <= -0.39:
		tmp = x1 + (t_8 - (((t_9 - (t_3 * ((((x1 * 2.0) * t_5) * t_6) + ((4.0 * ((2.0 * x2) - 3.0)) + (x1 * ((x1 * 6.0) - 4.0)))))) - t_7) - x1))
	elif x1 <= 7.6e+73:
		tmp = x1 + (t_8 + (x1 + (t_7 - (t_9 + (t_3 * (((x1 * x1) * (6.0 - (t_5 * 4.0))) + (t_6 * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(t_0 + Float64(2.0 * x2))
	t_2 = Float64(6.0 * (x1 ^ 4.0))
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(-1.0 - Float64(x1 * x1))
	t_5 = Float64(Float64(x1 - t_1) / t_4)
	t_6 = Float64(t_5 - 3.0)
	t_7 = Float64(x1 * Float64(x1 * x1))
	t_8 = Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_3))
	t_9 = Float64(t_0 * Float64(Float64(t_1 - x1) / t_4))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = t_2;
	elseif (x1 <= -0.39)
		tmp = Float64(x1 + Float64(t_8 - Float64(Float64(Float64(t_9 - Float64(t_3 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_5) * t_6) + Float64(Float64(4.0 * Float64(Float64(2.0 * x2) - 3.0)) + Float64(x1 * Float64(Float64(x1 * 6.0) - 4.0)))))) - t_7) - x1)));
	elseif (x1 <= 7.6e+73)
		tmp = Float64(x1 + Float64(t_8 + Float64(x1 + Float64(t_7 - Float64(t_9 + Float64(t_3 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(t_5 * 4.0))) + Float64(t_6 * Float64(Float64(x1 * 2.0) * Float64(x1 - Float64(2.0 * x2)))))))))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = t_0 + (2.0 * x2);
	t_2 = 6.0 * (x1 ^ 4.0);
	t_3 = (x1 * x1) + 1.0;
	t_4 = -1.0 - (x1 * x1);
	t_5 = (x1 - t_1) / t_4;
	t_6 = t_5 - 3.0;
	t_7 = x1 * (x1 * x1);
	t_8 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3);
	t_9 = t_0 * ((t_1 - x1) / t_4);
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = t_2;
	elseif (x1 <= -0.39)
		tmp = x1 + (t_8 - (((t_9 - (t_3 * ((((x1 * 2.0) * t_5) * t_6) + ((4.0 * ((2.0 * x2) - 3.0)) + (x1 * ((x1 * 6.0) - 4.0)))))) - t_7) - x1));
	elseif (x1 <= 7.6e+73)
		tmp = x1 + (t_8 + (x1 + (t_7 - (t_9 + (t_3 * (((x1 * x1) * (6.0 - (t_5 * 4.0))) + (t_6 * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 - t$95$1), $MachinePrecision] / t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$5 - 3.0), $MachinePrecision]}, Block[{t$95$7 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(t$95$0 * N[(N[(t$95$1 - x1), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], t$95$2, If[LessEqual[x1, -0.39], N[(x1 + N[(t$95$8 - N[(N[(N[(t$95$9 - N[(t$95$3 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$5), $MachinePrecision] * t$95$6), $MachinePrecision] + N[(N[(4.0 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$7), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7.6e+73], N[(x1 + N[(t$95$8 + N[(x1 + N[(t$95$7 - N[(t$95$9 + N[(t$95$3 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(t$95$5 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$6 * N[(N[(x1 * 2.0), $MachinePrecision] * N[(x1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.60000000000000037e102 or 7.60000000000000044e73 < x1

   1. Initial program 20.2%

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

   3. Taylor expanded in x1 around -inf 31.0%

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

   4. Taylor expanded in x1 around inf 100.0%

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

   5. Taylor expanded in x1 around inf 97.6%

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

   if -5.60000000000000037e102 < x1 < -0.39000000000000001

   1. Initial program 99.1%

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

   3. Taylor expanded in x1 around -inf 98.9%

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

   4. Taylor expanded in x1 around 0 99.1%

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

   if -0.39000000000000001 < x1 < 7.60000000000000044e73

   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 97.7%

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

      1. +-commutative 97.7%

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

      2. mul-1-neg 97.7%

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

      3. sub-neg 97.7%

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

   5. Simplified 97.7%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq -0.39:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1}\right) \cdot \left(\frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1} - 3\right) + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(x1 \cdot 6 - 4\right)\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 7.6 \cdot 10^{+73}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1} \cdot 4\right) + \left(\frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x1 - 2 \cdot x2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := t\_0 + 2 \cdot x2\\ t_3 := -1 - x1 \cdot x1\\ t_4 := \frac{x1 - t\_2}{t\_3}\\ \mathbf{if}\;x1 \leq -2.5 \cdot 10^{+23} \lor \neg \left(x1 \leq 1.85 \cdot 10^{+29}\right):\\ \;\;\;\;{x1}^{4} \cdot \left(6 - \frac{3 - \frac{9 - 4 \cdot \left(3 - 2 \cdot x2\right)}{x1}}{x1}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(t\_0 \cdot \frac{t\_2 - x1}{t\_3} + t\_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - t\_4 \cdot 4\right) + \left(t\_4 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x1 - 2 \cdot x2\right)\right)\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (+ t_0 (* 2.0 x2)))
        (t_3 (- -1.0 (* x1 x1)))
        (t_4 (/ (- x1 t_2) t_3)))
   (if (or (<= x1 -2.5e+23) (not (<= x1 1.85e+29)))
     (*
      (pow x1 4.0)
      (- 6.0 (/ (- 3.0 (/ (- 9.0 (* 4.0 (- 3.0 (* 2.0 x2)))) x1)) x1)))
     (+
      x1
      (+
       (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))
       (+
        x1
        (-
         (* x1 (* x1 x1))
         (+
          (* t_0 (/ (- t_2 x1) t_3))
          (*
           t_1
           (+
            (* (* x1 x1) (- 6.0 (* t_4 4.0)))
            (* (- t_4 3.0) (* (* x1 2.0) (- x1 (* 2.0 x2))))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = t_0 + (2.0 * x2);
	double t_3 = -1.0 - (x1 * x1);
	double t_4 = (x1 - t_2) / t_3;
	double tmp;
	if ((x1 <= -2.5e+23) || !(x1 <= 1.85e+29)) {
		tmp = pow(x1, 4.0) * (6.0 - ((3.0 - ((9.0 - (4.0 * (3.0 - (2.0 * x2)))) / x1)) / x1));
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) - ((t_0 * ((t_2 - x1) / t_3)) + (t_1 * (((x1 * x1) * (6.0 - (t_4 * 4.0))) + ((t_4 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = t_0 + (2.0d0 * x2)
    t_3 = (-1.0d0) - (x1 * x1)
    t_4 = (x1 - t_2) / t_3
    if ((x1 <= (-2.5d+23)) .or. (.not. (x1 <= 1.85d+29))) then
        tmp = (x1 ** 4.0d0) * (6.0d0 - ((3.0d0 - ((9.0d0 - (4.0d0 * (3.0d0 - (2.0d0 * x2)))) / x1)) / x1))
    else
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) - ((t_0 * ((t_2 - x1) / t_3)) + (t_1 * (((x1 * x1) * (6.0d0 - (t_4 * 4.0d0))) + ((t_4 - 3.0d0) * ((x1 * 2.0d0) * (x1 - (2.0d0 * x2))))))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = t_0 + (2.0 * x2);
	double t_3 = -1.0 - (x1 * x1);
	double t_4 = (x1 - t_2) / t_3;
	double tmp;
	if ((x1 <= -2.5e+23) || !(x1 <= 1.85e+29)) {
		tmp = Math.pow(x1, 4.0) * (6.0 - ((3.0 - ((9.0 - (4.0 * (3.0 - (2.0 * x2)))) / x1)) / x1));
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) - ((t_0 * ((t_2 - x1) / t_3)) + (t_1 * (((x1 * x1) * (6.0 - (t_4 * 4.0))) + ((t_4 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = t_0 + (2.0 * x2)
	t_3 = -1.0 - (x1 * x1)
	t_4 = (x1 - t_2) / t_3
	tmp = 0
	if (x1 <= -2.5e+23) or not (x1 <= 1.85e+29):
		tmp = math.pow(x1, 4.0) * (6.0 - ((3.0 - ((9.0 - (4.0 * (3.0 - (2.0 * x2)))) / x1)) / x1))
	else:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) - ((t_0 * ((t_2 - x1) / t_3)) + (t_1 * (((x1 * x1) * (6.0 - (t_4 * 4.0))) + ((t_4 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(t_0 + Float64(2.0 * x2))
	t_3 = Float64(-1.0 - Float64(x1 * x1))
	t_4 = Float64(Float64(x1 - t_2) / t_3)
	tmp = 0.0
	if ((x1 <= -2.5e+23) || !(x1 <= 1.85e+29))
		tmp = Float64((x1 ^ 4.0) * Float64(6.0 - Float64(Float64(3.0 - Float64(Float64(9.0 - Float64(4.0 * Float64(3.0 - Float64(2.0 * x2)))) / x1)) / x1)));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) - Float64(Float64(t_0 * Float64(Float64(t_2 - x1) / t_3)) + Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(t_4 * 4.0))) + Float64(Float64(t_4 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(x1 - Float64(2.0 * x2)))))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = t_0 + (2.0 * x2);
	t_3 = -1.0 - (x1 * x1);
	t_4 = (x1 - t_2) / t_3;
	tmp = 0.0;
	if ((x1 <= -2.5e+23) || ~((x1 <= 1.85e+29)))
		tmp = (x1 ^ 4.0) * (6.0 - ((3.0 - ((9.0 - (4.0 * (3.0 - (2.0 * x2)))) / x1)) / x1));
	else
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) - ((t_0 * ((t_2 - x1) / t_3)) + (t_1 * (((x1 * x1) * (6.0 - (t_4 * 4.0))) + ((t_4 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 - t$95$2), $MachinePrecision] / t$95$3), $MachinePrecision]}, If[Or[LessEqual[x1, -2.5e+23], N[Not[LessEqual[x1, 1.85e+29]], $MachinePrecision]], N[(N[Power[x1, 4.0], $MachinePrecision] * N[(6.0 - N[(N[(3.0 - N[(N[(9.0 - N[(4.0 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$0 * N[(N[(t$95$2 - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(t$95$4 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$4 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(x1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -2.5e23 or 1.84999999999999987e29 < x1

   1. Initial program 37.2%

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

   3. Taylor expanded in x1 around -inf 44.1%

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

   4. Taylor expanded in x1 around inf 98.3%

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

   5. Taylor expanded in x1 around -inf 98.3%

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

   if -2.5e23 < x1 < 1.84999999999999987e29

   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 97.7%

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

      1. +-commutative 97.7%

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

      2. mul-1-neg 97.7%

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

      3. sub-neg 97.7%

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

   5. Simplified 97.7%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.5 \cdot 10^{+23} \lor \neg \left(x1 \leq 1.85 \cdot 10^{+29}\right):\\ \;\;\;\;{x1}^{4} \cdot \left(6 - \frac{3 - \frac{9 - 4 \cdot \left(3 - 2 \cdot x2\right)}{x1}}{x1}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1} \cdot 4\right) + \left(\frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x1 - 2 \cdot x2\right)\right)\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 - x1 \cdot x1\\ t_1 := 6 \cdot {x1}^{4}\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := 3 - 2 \cdot x2\\ t_4 := t\_2 + 2 \cdot x2\\ t_5 := \frac{t\_4 - x1}{t\_0}\\ t_6 := \frac{x1 - t\_4}{t\_0}\\ t_7 := \left(x1 \cdot 2\right) \cdot t\_6\\ t_8 := t\_7 \cdot \left(3 + t\_5\right)\\ t_9 := t\_6 \cdot 4\\ t_10 := t\_2 \cdot t\_5\\ t_11 := x1 \cdot \left(x1 \cdot x1\right)\\ \mathbf{if}\;x1 \leq -2 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -0.185:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(\left(x1 \cdot x1\right) \cdot \left(6 - t\_9\right) + t\_8\right) \cdot t\_0 + t\_2 \cdot t\_6\right) + t\_11\right)\right) + 9\right)\\ \mathbf{elif}\;x1 \leq 0.0085:\\ \;\;\;\;x1 - \left(3 \cdot \frac{\left(t\_2 - 2 \cdot x2\right) - x1}{t\_0} + \left(\left(\left(t\_10 + \left(\left(x1 \cdot x1\right) \cdot \left(t\_9 - 6\right) - t\_7 \cdot t\_3\right) \cdot t\_0\right) - t\_11\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 5.5 \cdot 10^{+90}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(t\_11 - \left(t\_10 + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - 4 \cdot \left(3 + \frac{-1 - \frac{t\_3}{x1}}{x1}\right)\right) + t\_8\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- -1.0 (* x1 x1)))
        (t_1 (* 6.0 (pow x1 4.0)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (- 3.0 (* 2.0 x2)))
        (t_4 (+ t_2 (* 2.0 x2)))
        (t_5 (/ (- t_4 x1) t_0))
        (t_6 (/ (- x1 t_4) t_0))
        (t_7 (* (* x1 2.0) t_6))
        (t_8 (* t_7 (+ 3.0 t_5)))
        (t_9 (* t_6 4.0))
        (t_10 (* t_2 t_5))
        (t_11 (* x1 (* x1 x1))))
   (if (<= x1 -2e+105)
     t_1
     (if (<= x1 -0.185)
       (+
        x1
        (+
         (+
          x1
          (+ (+ (* (+ (* (* x1 x1) (- 6.0 t_9)) t_8) t_0) (* t_2 t_6)) t_11))
         9.0))
       (if (<= x1 0.0085)
         (-
          x1
          (+
           (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_0))
           (-
            (- (+ t_10 (* (- (* (* x1 x1) (- t_9 6.0)) (* t_7 t_3)) t_0)) t_11)
            x1)))
         (if (<= x1 5.5e+90)
           (+
            x1
            (+
             9.0
             (+
              x1
              (-
               t_11
               (+
                t_10
                (*
                 (+ (* x1 x1) 1.0)
                 (+
                  (*
                   (* x1 x1)
                   (- 6.0 (* 4.0 (+ 3.0 (/ (- -1.0 (/ t_3 x1)) x1)))))
                  t_8)))))))
           t_1))))))

C

double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = 6.0 * pow(x1, 4.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 3.0 - (2.0 * x2);
	double t_4 = t_2 + (2.0 * x2);
	double t_5 = (t_4 - x1) / t_0;
	double t_6 = (x1 - t_4) / t_0;
	double t_7 = (x1 * 2.0) * t_6;
	double t_8 = t_7 * (3.0 + t_5);
	double t_9 = t_6 * 4.0;
	double t_10 = t_2 * t_5;
	double t_11 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -2e+105) {
		tmp = t_1;
	} else if (x1 <= -0.185) {
		tmp = x1 + ((x1 + ((((((x1 * x1) * (6.0 - t_9)) + t_8) * t_0) + (t_2 * t_6)) + t_11)) + 9.0);
	} else if (x1 <= 0.0085) {
		tmp = x1 - ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (((t_10 + ((((x1 * x1) * (t_9 - 6.0)) - (t_7 * t_3)) * t_0)) - t_11) - x1));
	} else if (x1 <= 5.5e+90) {
		tmp = x1 + (9.0 + (x1 + (t_11 - (t_10 + (((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 - (t_3 / x1)) / x1))))) + t_8))))));
	} 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_10
    real(8) :: t_11
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_0 = (-1.0d0) - (x1 * x1)
    t_1 = 6.0d0 * (x1 ** 4.0d0)
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = 3.0d0 - (2.0d0 * x2)
    t_4 = t_2 + (2.0d0 * x2)
    t_5 = (t_4 - x1) / t_0
    t_6 = (x1 - t_4) / t_0
    t_7 = (x1 * 2.0d0) * t_6
    t_8 = t_7 * (3.0d0 + t_5)
    t_9 = t_6 * 4.0d0
    t_10 = t_2 * t_5
    t_11 = x1 * (x1 * x1)
    if (x1 <= (-2d+105)) then
        tmp = t_1
    else if (x1 <= (-0.185d0)) then
        tmp = x1 + ((x1 + ((((((x1 * x1) * (6.0d0 - t_9)) + t_8) * t_0) + (t_2 * t_6)) + t_11)) + 9.0d0)
    else if (x1 <= 0.0085d0) then
        tmp = x1 - ((3.0d0 * (((t_2 - (2.0d0 * x2)) - x1) / t_0)) + (((t_10 + ((((x1 * x1) * (t_9 - 6.0d0)) - (t_7 * t_3)) * t_0)) - t_11) - x1))
    else if (x1 <= 5.5d+90) then
        tmp = x1 + (9.0d0 + (x1 + (t_11 - (t_10 + (((x1 * x1) + 1.0d0) * (((x1 * x1) * (6.0d0 - (4.0d0 * (3.0d0 + (((-1.0d0) - (t_3 / x1)) / x1))))) + t_8))))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = 6.0 * Math.pow(x1, 4.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 3.0 - (2.0 * x2);
	double t_4 = t_2 + (2.0 * x2);
	double t_5 = (t_4 - x1) / t_0;
	double t_6 = (x1 - t_4) / t_0;
	double t_7 = (x1 * 2.0) * t_6;
	double t_8 = t_7 * (3.0 + t_5);
	double t_9 = t_6 * 4.0;
	double t_10 = t_2 * t_5;
	double t_11 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -2e+105) {
		tmp = t_1;
	} else if (x1 <= -0.185) {
		tmp = x1 + ((x1 + ((((((x1 * x1) * (6.0 - t_9)) + t_8) * t_0) + (t_2 * t_6)) + t_11)) + 9.0);
	} else if (x1 <= 0.0085) {
		tmp = x1 - ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (((t_10 + ((((x1 * x1) * (t_9 - 6.0)) - (t_7 * t_3)) * t_0)) - t_11) - x1));
	} else if (x1 <= 5.5e+90) {
		tmp = x1 + (9.0 + (x1 + (t_11 - (t_10 + (((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 - (t_3 / x1)) / x1))))) + t_8))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = -1.0 - (x1 * x1)
	t_1 = 6.0 * math.pow(x1, 4.0)
	t_2 = x1 * (x1 * 3.0)
	t_3 = 3.0 - (2.0 * x2)
	t_4 = t_2 + (2.0 * x2)
	t_5 = (t_4 - x1) / t_0
	t_6 = (x1 - t_4) / t_0
	t_7 = (x1 * 2.0) * t_6
	t_8 = t_7 * (3.0 + t_5)
	t_9 = t_6 * 4.0
	t_10 = t_2 * t_5
	t_11 = x1 * (x1 * x1)
	tmp = 0
	if x1 <= -2e+105:
		tmp = t_1
	elif x1 <= -0.185:
		tmp = x1 + ((x1 + ((((((x1 * x1) * (6.0 - t_9)) + t_8) * t_0) + (t_2 * t_6)) + t_11)) + 9.0)
	elif x1 <= 0.0085:
		tmp = x1 - ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (((t_10 + ((((x1 * x1) * (t_9 - 6.0)) - (t_7 * t_3)) * t_0)) - t_11) - x1))
	elif x1 <= 5.5e+90:
		tmp = x1 + (9.0 + (x1 + (t_11 - (t_10 + (((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 - (t_3 / x1)) / x1))))) + t_8))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(-1.0 - Float64(x1 * x1))
	t_1 = Float64(6.0 * (x1 ^ 4.0))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(3.0 - Float64(2.0 * x2))
	t_4 = Float64(t_2 + Float64(2.0 * x2))
	t_5 = Float64(Float64(t_4 - x1) / t_0)
	t_6 = Float64(Float64(x1 - t_4) / t_0)
	t_7 = Float64(Float64(x1 * 2.0) * t_6)
	t_8 = Float64(t_7 * Float64(3.0 + t_5))
	t_9 = Float64(t_6 * 4.0)
	t_10 = Float64(t_2 * t_5)
	t_11 = Float64(x1 * Float64(x1 * x1))
	tmp = 0.0
	if (x1 <= -2e+105)
		tmp = t_1;
	elseif (x1 <= -0.185)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(x1 * x1) * Float64(6.0 - t_9)) + t_8) * t_0) + Float64(t_2 * t_6)) + t_11)) + 9.0));
	elseif (x1 <= 0.0085)
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(Float64(Float64(t_10 + Float64(Float64(Float64(Float64(x1 * x1) * Float64(t_9 - 6.0)) - Float64(t_7 * t_3)) * t_0)) - t_11) - x1)));
	elseif (x1 <= 5.5e+90)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_11 - Float64(t_10 + Float64(Float64(Float64(x1 * x1) + 1.0) * Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(4.0 * Float64(3.0 + Float64(Float64(-1.0 - Float64(t_3 / x1)) / x1))))) + t_8)))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = -1.0 - (x1 * x1);
	t_1 = 6.0 * (x1 ^ 4.0);
	t_2 = x1 * (x1 * 3.0);
	t_3 = 3.0 - (2.0 * x2);
	t_4 = t_2 + (2.0 * x2);
	t_5 = (t_4 - x1) / t_0;
	t_6 = (x1 - t_4) / t_0;
	t_7 = (x1 * 2.0) * t_6;
	t_8 = t_7 * (3.0 + t_5);
	t_9 = t_6 * 4.0;
	t_10 = t_2 * t_5;
	t_11 = x1 * (x1 * x1);
	tmp = 0.0;
	if (x1 <= -2e+105)
		tmp = t_1;
	elseif (x1 <= -0.185)
		tmp = x1 + ((x1 + ((((((x1 * x1) * (6.0 - t_9)) + t_8) * t_0) + (t_2 * t_6)) + t_11)) + 9.0);
	elseif (x1 <= 0.0085)
		tmp = x1 - ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (((t_10 + ((((x1 * x1) * (t_9 - 6.0)) - (t_7 * t_3)) * t_0)) - t_11) - x1));
	elseif (x1 <= 5.5e+90)
		tmp = x1 + (9.0 + (x1 + (t_11 - (t_10 + (((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 - (t_3 / x1)) / x1))))) + t_8))))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$4 - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 - t$95$4), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x1 * 2.0), $MachinePrecision] * t$95$6), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$7 * N[(3.0 + t$95$5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(t$95$6 * 4.0), $MachinePrecision]}, Block[{t$95$10 = N[(t$95$2 * t$95$5), $MachinePrecision]}, Block[{t$95$11 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2e+105], t$95$1, If[LessEqual[x1, -0.185], N[(x1 + N[(N[(x1 + N[(N[(N[(N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - t$95$9), $MachinePrecision]), $MachinePrecision] + t$95$8), $MachinePrecision] * t$95$0), $MachinePrecision] + N[(t$95$2 * t$95$6), $MachinePrecision]), $MachinePrecision] + t$95$11), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.0085], N[(x1 - N[(N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t$95$10 + N[(N[(N[(N[(x1 * x1), $MachinePrecision] * N[(t$95$9 - 6.0), $MachinePrecision]), $MachinePrecision] - N[(t$95$7 * t$95$3), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision] - t$95$11), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.5e+90], N[(x1 + N[(9.0 + N[(x1 + N[(t$95$11 - N[(t$95$10 + N[(N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision] * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(4.0 * N[(3.0 + N[(N[(-1.0 - N[(t$95$3 / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.9999999999999999e105 or 5.49999999999999999e90 < x1

   1. Initial program 14.1%

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

   3. Taylor expanded in x1 around -inf 25.6%

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

   4. Taylor expanded in x1 around inf 100.0%

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

   5. Taylor expanded in x1 around inf 100.0%

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

   if -1.9999999999999999e105 < x1 < -0.185

   1. Initial program 99.1%

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

   3. Taylor expanded in x1 around inf 99.1%

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

   if -0.185 < x1 < 0.0085000000000000006

   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 98.9%

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

   if 0.0085000000000000006 < x1 < 5.49999999999999999e90

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around -inf 99.6%

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

   4. Taylor expanded in x1 around inf 99.6%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(3 + -1 \cdot \frac{1 + -1 \cdot \frac{2 \cdot x2 - 3}{x1}}{x1}\right) - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + \color{blue}{9}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2 \cdot 10^{+105}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq -0.185:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1} \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 9\right)\\ \mathbf{elif}\;x1 \leq 0.0085:\\ \;\;\;\;x1 - \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(\left(x1 \cdot x1\right) \cdot \left(\frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1} \cdot 4 - 6\right) - \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1}\right) \cdot \left(3 - 2 \cdot x2\right)\right) \cdot \left(-1 - x1 \cdot x1\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 5.5 \cdot 10^{+90}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - 4 \cdot \left(3 + \frac{-1 - \frac{3 - 2 \cdot x2}{x1}}{x1}\right)\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 - x1 \cdot x1\\ t_1 := 6 \cdot {x1}^{4}\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := t\_2 + 2 \cdot x2\\ t_4 := \frac{t\_3 - x1}{t\_0}\\ t_5 := x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(t\_2 \cdot t\_4 + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - 4 \cdot \left(3 + \frac{-1 - \frac{3 - 2 \cdot x2}{x1}}{x1}\right)\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - t\_3}{t\_0}\right) \cdot \left(3 + t\_4\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -2 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -0.165:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x1 \leq 0.0012:\\ \;\;\;\;x1 + \left(\left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right) - \left(x1 \cdot \left(3 - x2 \cdot \left(x1 \cdot 6 + 9 \cdot \frac{x1}{x2}\right)\right) - x2 \cdot -6\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+89}:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- -1.0 (* x1 x1)))
        (t_1 (* 6.0 (pow x1 4.0)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (+ t_2 (* 2.0 x2)))
        (t_4 (/ (- t_3 x1) t_0))
        (t_5
         (+
          x1
          (+
           9.0
           (+
            x1
            (-
             (* x1 (* x1 x1))
             (+
              (* t_2 t_4)
              (*
               (+ (* x1 x1) 1.0)
               (+
                (*
                 (* x1 x1)
                 (-
                  6.0
                  (* 4.0 (+ 3.0 (/ (- -1.0 (/ (- 3.0 (* 2.0 x2)) x1)) x1)))))
                (* (* (* x1 2.0) (/ (- x1 t_3) t_0)) (+ 3.0 t_4)))))))))))
   (if (<= x1 -2e+105)
     t_1
     (if (<= x1 -0.165)
       t_5
       (if (<= x1 0.0012)
         (+
          x1
          (-
           (+ x1 (* x2 (+ (* x1 -12.0) (* 8.0 (* x1 x2)))))
           (-
            (* x1 (- 3.0 (* x2 (+ (* x1 6.0) (* 9.0 (/ x1 x2))))))
            (* x2 -6.0))))
         (if (<= x1 2e+89) t_5 t_1))))))

C

double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = 6.0 * pow(x1, 4.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = t_2 + (2.0 * x2);
	double t_4 = (t_3 - x1) / t_0;
	double t_5 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) - ((t_2 * t_4) + (((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 - ((3.0 - (2.0 * x2)) / x1)) / x1))))) + (((x1 * 2.0) * ((x1 - t_3) / t_0)) * (3.0 + t_4))))))));
	double tmp;
	if (x1 <= -2e+105) {
		tmp = t_1;
	} else if (x1 <= -0.165) {
		tmp = t_5;
	} else if (x1 <= 0.0012) {
		tmp = x1 + ((x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))) - ((x1 * (3.0 - (x2 * ((x1 * 6.0) + (9.0 * (x1 / x2)))))) - (x2 * -6.0)));
	} else if (x1 <= 2e+89) {
		tmp = 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 = (-1.0d0) - (x1 * x1)
    t_1 = 6.0d0 * (x1 ** 4.0d0)
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = t_2 + (2.0d0 * x2)
    t_4 = (t_3 - x1) / t_0
    t_5 = x1 + (9.0d0 + (x1 + ((x1 * (x1 * x1)) - ((t_2 * t_4) + (((x1 * x1) + 1.0d0) * (((x1 * x1) * (6.0d0 - (4.0d0 * (3.0d0 + (((-1.0d0) - ((3.0d0 - (2.0d0 * x2)) / x1)) / x1))))) + (((x1 * 2.0d0) * ((x1 - t_3) / t_0)) * (3.0d0 + t_4))))))))
    if (x1 <= (-2d+105)) then
        tmp = t_1
    else if (x1 <= (-0.165d0)) then
        tmp = t_5
    else if (x1 <= 0.0012d0) then
        tmp = x1 + ((x1 + (x2 * ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))))) - ((x1 * (3.0d0 - (x2 * ((x1 * 6.0d0) + (9.0d0 * (x1 / x2)))))) - (x2 * (-6.0d0))))
    else if (x1 <= 2d+89) then
        tmp = t_5
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = 6.0 * Math.pow(x1, 4.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = t_2 + (2.0 * x2);
	double t_4 = (t_3 - x1) / t_0;
	double t_5 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) - ((t_2 * t_4) + (((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 - ((3.0 - (2.0 * x2)) / x1)) / x1))))) + (((x1 * 2.0) * ((x1 - t_3) / t_0)) * (3.0 + t_4))))))));
	double tmp;
	if (x1 <= -2e+105) {
		tmp = t_1;
	} else if (x1 <= -0.165) {
		tmp = t_5;
	} else if (x1 <= 0.0012) {
		tmp = x1 + ((x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))) - ((x1 * (3.0 - (x2 * ((x1 * 6.0) + (9.0 * (x1 / x2)))))) - (x2 * -6.0)));
	} else if (x1 <= 2e+89) {
		tmp = t_5;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = -1.0 - (x1 * x1)
	t_1 = 6.0 * math.pow(x1, 4.0)
	t_2 = x1 * (x1 * 3.0)
	t_3 = t_2 + (2.0 * x2)
	t_4 = (t_3 - x1) / t_0
	t_5 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) - ((t_2 * t_4) + (((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 - ((3.0 - (2.0 * x2)) / x1)) / x1))))) + (((x1 * 2.0) * ((x1 - t_3) / t_0)) * (3.0 + t_4))))))))
	tmp = 0
	if x1 <= -2e+105:
		tmp = t_1
	elif x1 <= -0.165:
		tmp = t_5
	elif x1 <= 0.0012:
		tmp = x1 + ((x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))) - ((x1 * (3.0 - (x2 * ((x1 * 6.0) + (9.0 * (x1 / x2)))))) - (x2 * -6.0)))
	elif x1 <= 2e+89:
		tmp = t_5
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(-1.0 - Float64(x1 * x1))
	t_1 = Float64(6.0 * (x1 ^ 4.0))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(t_2 + Float64(2.0 * x2))
	t_4 = Float64(Float64(t_3 - x1) / t_0)
	t_5 = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) - Float64(Float64(t_2 * t_4) + Float64(Float64(Float64(x1 * x1) + 1.0) * Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(4.0 * Float64(3.0 + Float64(Float64(-1.0 - Float64(Float64(3.0 - Float64(2.0 * x2)) / x1)) / x1))))) + Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(x1 - t_3) / t_0)) * Float64(3.0 + t_4)))))))))
	tmp = 0.0
	if (x1 <= -2e+105)
		tmp = t_1;
	elseif (x1 <= -0.165)
		tmp = t_5;
	elseif (x1 <= 0.0012)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))))) - Float64(Float64(x1 * Float64(3.0 - Float64(x2 * Float64(Float64(x1 * 6.0) + Float64(9.0 * Float64(x1 / x2)))))) - Float64(x2 * -6.0))));
	elseif (x1 <= 2e+89)
		tmp = t_5;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = -1.0 - (x1 * x1);
	t_1 = 6.0 * (x1 ^ 4.0);
	t_2 = x1 * (x1 * 3.0);
	t_3 = t_2 + (2.0 * x2);
	t_4 = (t_3 - x1) / t_0;
	t_5 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) - ((t_2 * t_4) + (((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 - ((3.0 - (2.0 * x2)) / x1)) / x1))))) + (((x1 * 2.0) * ((x1 - t_3) / t_0)) * (3.0 + t_4))))))));
	tmp = 0.0;
	if (x1 <= -2e+105)
		tmp = t_1;
	elseif (x1 <= -0.165)
		tmp = t_5;
	elseif (x1 <= 0.0012)
		tmp = x1 + ((x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))) - ((x1 * (3.0 - (x2 * ((x1 * 6.0) + (9.0 * (x1 / x2)))))) - (x2 * -6.0)));
	elseif (x1 <= 2e+89)
		tmp = t_5;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(9.0 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$2 * t$95$4), $MachinePrecision] + N[(N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision] * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(4.0 * N[(3.0 + N[(N[(-1.0 - N[(N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(x1 - t$95$3), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] * N[(3.0 + t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2e+105], t$95$1, If[LessEqual[x1, -0.165], t$95$5, If[LessEqual[x1, 0.0012], N[(x1 + N[(N[(x1 + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * N[(3.0 - N[(x2 * N[(N[(x1 * 6.0), $MachinePrecision] + N[(9.0 * N[(x1 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+89], t$95$5, t$95$1]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.9999999999999999e105 or 1.99999999999999999e89 < x1

   1. Initial program 14.1%

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

   3. Taylor expanded in x1 around -inf 25.6%

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

   4. Taylor expanded in x1 around inf 100.0%

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

   5. Taylor expanded in x1 around inf 100.0%

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

   if -1.9999999999999999e105 < x1 < -0.165000000000000008 or 0.00119999999999999989 < x1 < 1.99999999999999999e89

   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 -inf 99.2%

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

   4. Taylor expanded in x1 around inf 99.2%

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

   if -0.165000000000000008 < x1 < 0.00119999999999999989

   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 85.2%

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

   4. Taylor expanded in x1 around 0 85.2%

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

   5. Taylor expanded in x2 around 0 98.9%

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

   6. Taylor expanded in x2 around inf 98.9%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2 \cdot 10^{+105}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq -0.165:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - 4 \cdot \left(3 + \frac{-1 - \frac{3 - 2 \cdot x2}{x1}}{x1}\right)\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.0012:\\ \;\;\;\;x1 + \left(\left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right) - \left(x1 \cdot \left(3 - x2 \cdot \left(x1 \cdot 6 + 9 \cdot \frac{x1}{x2}\right)\right) - x2 \cdot -6\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+89}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - 4 \cdot \left(3 + \frac{-1 - \frac{3 - 2 \cdot x2}{x1}}{x1}\right)\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 - x1 \cdot x1\\ t_1 := 6 \cdot {x1}^{4}\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := t\_2 + 2 \cdot x2\\ t_4 := \frac{t\_3 - x1}{t\_0}\\ t_5 := \frac{x1 - t\_3}{t\_0}\\ t_6 := \left(\left(x1 \cdot 2\right) \cdot t\_5\right) \cdot \left(3 + t\_4\right)\\ t_7 := x1 \cdot \left(x1 \cdot x1\right)\\ \mathbf{if}\;x1 \leq -2 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -0.15:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(\left(x1 \cdot x1\right) \cdot \left(6 - t\_5 \cdot 4\right) + t\_6\right) \cdot t\_0 + t\_2 \cdot t\_5\right) + t\_7\right)\right) + 9\right)\\ \mathbf{elif}\;x1 \leq 0.0006:\\ \;\;\;\;x1 + \left(\left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right) - \left(x1 \cdot \left(3 - x2 \cdot \left(x1 \cdot 6 + 9 \cdot \frac{x1}{x2}\right)\right) - x2 \cdot -6\right)\right)\\ \mathbf{elif}\;x1 \leq 5.8 \cdot 10^{+90}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(t\_7 - \left(t\_2 \cdot t\_4 + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - 4 \cdot \left(3 + \frac{-1 - \frac{3 - 2 \cdot x2}{x1}}{x1}\right)\right) + t\_6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- -1.0 (* x1 x1)))
        (t_1 (* 6.0 (pow x1 4.0)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (+ t_2 (* 2.0 x2)))
        (t_4 (/ (- t_3 x1) t_0))
        (t_5 (/ (- x1 t_3) t_0))
        (t_6 (* (* (* x1 2.0) t_5) (+ 3.0 t_4)))
        (t_7 (* x1 (* x1 x1))))
   (if (<= x1 -2e+105)
     t_1
     (if (<= x1 -0.15)
       (+
        x1
        (+
         (+
          x1
          (+
           (+ (* (+ (* (* x1 x1) (- 6.0 (* t_5 4.0))) t_6) t_0) (* t_2 t_5))
           t_7))
         9.0))
       (if (<= x1 0.0006)
         (+
          x1
          (-
           (+ x1 (* x2 (+ (* x1 -12.0) (* 8.0 (* x1 x2)))))
           (-
            (* x1 (- 3.0 (* x2 (+ (* x1 6.0) (* 9.0 (/ x1 x2))))))
            (* x2 -6.0))))
         (if (<= x1 5.8e+90)
           (+
            x1
            (+
             9.0
             (+
              x1
              (-
               t_7
               (+
                (* t_2 t_4)
                (*
                 (+ (* x1 x1) 1.0)
                 (+
                  (*
                   (* x1 x1)
                   (-
                    6.0
                    (* 4.0 (+ 3.0 (/ (- -1.0 (/ (- 3.0 (* 2.0 x2)) x1)) x1)))))
                  t_6)))))))
           t_1))))))

C

double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = 6.0 * pow(x1, 4.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = t_2 + (2.0 * x2);
	double t_4 = (t_3 - x1) / t_0;
	double t_5 = (x1 - t_3) / t_0;
	double t_6 = ((x1 * 2.0) * t_5) * (3.0 + t_4);
	double t_7 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -2e+105) {
		tmp = t_1;
	} else if (x1 <= -0.15) {
		tmp = x1 + ((x1 + ((((((x1 * x1) * (6.0 - (t_5 * 4.0))) + t_6) * t_0) + (t_2 * t_5)) + t_7)) + 9.0);
	} else if (x1 <= 0.0006) {
		tmp = x1 + ((x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))) - ((x1 * (3.0 - (x2 * ((x1 * 6.0) + (9.0 * (x1 / x2)))))) - (x2 * -6.0)));
	} else if (x1 <= 5.8e+90) {
		tmp = x1 + (9.0 + (x1 + (t_7 - ((t_2 * t_4) + (((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 - ((3.0 - (2.0 * x2)) / x1)) / x1))))) + t_6))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = (-1.0d0) - (x1 * x1)
    t_1 = 6.0d0 * (x1 ** 4.0d0)
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = t_2 + (2.0d0 * x2)
    t_4 = (t_3 - x1) / t_0
    t_5 = (x1 - t_3) / t_0
    t_6 = ((x1 * 2.0d0) * t_5) * (3.0d0 + t_4)
    t_7 = x1 * (x1 * x1)
    if (x1 <= (-2d+105)) then
        tmp = t_1
    else if (x1 <= (-0.15d0)) then
        tmp = x1 + ((x1 + ((((((x1 * x1) * (6.0d0 - (t_5 * 4.0d0))) + t_6) * t_0) + (t_2 * t_5)) + t_7)) + 9.0d0)
    else if (x1 <= 0.0006d0) then
        tmp = x1 + ((x1 + (x2 * ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))))) - ((x1 * (3.0d0 - (x2 * ((x1 * 6.0d0) + (9.0d0 * (x1 / x2)))))) - (x2 * (-6.0d0))))
    else if (x1 <= 5.8d+90) then
        tmp = x1 + (9.0d0 + (x1 + (t_7 - ((t_2 * t_4) + (((x1 * x1) + 1.0d0) * (((x1 * x1) * (6.0d0 - (4.0d0 * (3.0d0 + (((-1.0d0) - ((3.0d0 - (2.0d0 * x2)) / x1)) / x1))))) + t_6))))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = 6.0 * Math.pow(x1, 4.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = t_2 + (2.0 * x2);
	double t_4 = (t_3 - x1) / t_0;
	double t_5 = (x1 - t_3) / t_0;
	double t_6 = ((x1 * 2.0) * t_5) * (3.0 + t_4);
	double t_7 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -2e+105) {
		tmp = t_1;
	} else if (x1 <= -0.15) {
		tmp = x1 + ((x1 + ((((((x1 * x1) * (6.0 - (t_5 * 4.0))) + t_6) * t_0) + (t_2 * t_5)) + t_7)) + 9.0);
	} else if (x1 <= 0.0006) {
		tmp = x1 + ((x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))) - ((x1 * (3.0 - (x2 * ((x1 * 6.0) + (9.0 * (x1 / x2)))))) - (x2 * -6.0)));
	} else if (x1 <= 5.8e+90) {
		tmp = x1 + (9.0 + (x1 + (t_7 - ((t_2 * t_4) + (((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 - ((3.0 - (2.0 * x2)) / x1)) / x1))))) + t_6))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = -1.0 - (x1 * x1)
	t_1 = 6.0 * math.pow(x1, 4.0)
	t_2 = x1 * (x1 * 3.0)
	t_3 = t_2 + (2.0 * x2)
	t_4 = (t_3 - x1) / t_0
	t_5 = (x1 - t_3) / t_0
	t_6 = ((x1 * 2.0) * t_5) * (3.0 + t_4)
	t_7 = x1 * (x1 * x1)
	tmp = 0
	if x1 <= -2e+105:
		tmp = t_1
	elif x1 <= -0.15:
		tmp = x1 + ((x1 + ((((((x1 * x1) * (6.0 - (t_5 * 4.0))) + t_6) * t_0) + (t_2 * t_5)) + t_7)) + 9.0)
	elif x1 <= 0.0006:
		tmp = x1 + ((x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))) - ((x1 * (3.0 - (x2 * ((x1 * 6.0) + (9.0 * (x1 / x2)))))) - (x2 * -6.0)))
	elif x1 <= 5.8e+90:
		tmp = x1 + (9.0 + (x1 + (t_7 - ((t_2 * t_4) + (((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 - ((3.0 - (2.0 * x2)) / x1)) / x1))))) + t_6))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(-1.0 - Float64(x1 * x1))
	t_1 = Float64(6.0 * (x1 ^ 4.0))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(t_2 + Float64(2.0 * x2))
	t_4 = Float64(Float64(t_3 - x1) / t_0)
	t_5 = Float64(Float64(x1 - t_3) / t_0)
	t_6 = Float64(Float64(Float64(x1 * 2.0) * t_5) * Float64(3.0 + t_4))
	t_7 = Float64(x1 * Float64(x1 * x1))
	tmp = 0.0
	if (x1 <= -2e+105)
		tmp = t_1;
	elseif (x1 <= -0.15)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(t_5 * 4.0))) + t_6) * t_0) + Float64(t_2 * t_5)) + t_7)) + 9.0));
	elseif (x1 <= 0.0006)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))))) - Float64(Float64(x1 * Float64(3.0 - Float64(x2 * Float64(Float64(x1 * 6.0) + Float64(9.0 * Float64(x1 / x2)))))) - Float64(x2 * -6.0))));
	elseif (x1 <= 5.8e+90)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_7 - Float64(Float64(t_2 * t_4) + Float64(Float64(Float64(x1 * x1) + 1.0) * Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(4.0 * Float64(3.0 + Float64(Float64(-1.0 - Float64(Float64(3.0 - Float64(2.0 * x2)) / x1)) / x1))))) + t_6)))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = -1.0 - (x1 * x1);
	t_1 = 6.0 * (x1 ^ 4.0);
	t_2 = x1 * (x1 * 3.0);
	t_3 = t_2 + (2.0 * x2);
	t_4 = (t_3 - x1) / t_0;
	t_5 = (x1 - t_3) / t_0;
	t_6 = ((x1 * 2.0) * t_5) * (3.0 + t_4);
	t_7 = x1 * (x1 * x1);
	tmp = 0.0;
	if (x1 <= -2e+105)
		tmp = t_1;
	elseif (x1 <= -0.15)
		tmp = x1 + ((x1 + ((((((x1 * x1) * (6.0 - (t_5 * 4.0))) + t_6) * t_0) + (t_2 * t_5)) + t_7)) + 9.0);
	elseif (x1 <= 0.0006)
		tmp = x1 + ((x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))) - ((x1 * (3.0 - (x2 * ((x1 * 6.0) + (9.0 * (x1 / x2)))))) - (x2 * -6.0)));
	elseif (x1 <= 5.8e+90)
		tmp = x1 + (9.0 + (x1 + (t_7 - ((t_2 * t_4) + (((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 - ((3.0 - (2.0 * x2)) / x1)) / x1))))) + t_6))))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 - t$95$3), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$5), $MachinePrecision] * N[(3.0 + t$95$4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2e+105], t$95$1, If[LessEqual[x1, -0.15], N[(x1 + N[(N[(x1 + N[(N[(N[(N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(t$95$5 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision] * t$95$0), $MachinePrecision] + N[(t$95$2 * t$95$5), $MachinePrecision]), $MachinePrecision] + t$95$7), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.0006], N[(x1 + N[(N[(x1 + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * N[(3.0 - N[(x2 * N[(N[(x1 * 6.0), $MachinePrecision] + N[(9.0 * N[(x1 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.8e+90], N[(x1 + N[(9.0 + N[(x1 + N[(t$95$7 - N[(N[(t$95$2 * t$95$4), $MachinePrecision] + N[(N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision] * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(4.0 * N[(3.0 + N[(N[(-1.0 - N[(N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.9999999999999999e105 or 5.8000000000000003e90 < x1

   1. Initial program 14.1%

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

   3. Taylor expanded in x1 around -inf 25.6%

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

   4. Taylor expanded in x1 around inf 100.0%

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

   5. Taylor expanded in x1 around inf 100.0%

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

   if -1.9999999999999999e105 < x1 < -0.149999999999999994

   1. Initial program 99.1%

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

   3. Taylor expanded in x1 around inf 99.1%

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

   if -0.149999999999999994 < x1 < 5.99999999999999947e-4

   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 85.2%

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

   4. Taylor expanded in x1 around 0 85.2%

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

   5. Taylor expanded in x2 around 0 98.9%

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

   6. Taylor expanded in x2 around inf 98.9%

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

   if 5.99999999999999947e-4 < x1 < 5.8000000000000003e90

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around -inf 99.6%

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

   4. Taylor expanded in x1 around inf 99.6%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(3 + -1 \cdot \frac{1 + -1 \cdot \frac{2 \cdot x2 - 3}{x1}}{x1}\right) - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + \color{blue}{9}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2 \cdot 10^{+105}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq -0.15:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1} \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 9\right)\\ \mathbf{elif}\;x1 \leq 0.0006:\\ \;\;\;\;x1 + \left(\left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right) - \left(x1 \cdot \left(3 - x2 \cdot \left(x1 \cdot 6 + 9 \cdot \frac{x1}{x2}\right)\right) - x2 \cdot -6\right)\right)\\ \mathbf{elif}\;x1 \leq 5.8 \cdot 10^{+90}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - 4 \cdot \left(3 + \frac{-1 - \frac{3 - 2 \cdot x2}{x1}}{x1}\right)\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 92.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -12000000000 \lor \neg \left(x1 \leq 1.25 \cdot 10^{+24}\right):\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -12000000000.0) (not (<= x1 1.25e+24)))
   (* 6.0 (pow x1 4.0))
   (+ x1 (- (* x1 -2.0) (* x2 (- 6.0 (+ (* x1 -12.0) (* 8.0 (* x1 x2)))))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -12000000000.0) || !(x1 <= 1.25e+24)) {
		tmp = 6.0 * pow(x1, 4.0);
	} else {
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-12000000000.0d0)) .or. (.not. (x1 <= 1.25d+24))) then
        tmp = 6.0d0 * (x1 ** 4.0d0)
    else
        tmp = x1 + ((x1 * (-2.0d0)) - (x2 * (6.0d0 - ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -12000000000.0) || !(x1 <= 1.25e+24)) {
		tmp = 6.0 * Math.pow(x1, 4.0);
	} else {
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -12000000000.0) or not (x1 <= 1.25e+24):
		tmp = 6.0 * math.pow(x1, 4.0)
	else:
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2))))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -12000000000.0) || !(x1 <= 1.25e+24))
		tmp = Float64(6.0 * (x1 ^ 4.0));
	else
		tmp = Float64(x1 + Float64(Float64(x1 * -2.0) - Float64(x2 * Float64(6.0 - Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -12000000000.0) || ~((x1 <= 1.25e+24)))
		tmp = 6.0 * (x1 ^ 4.0);
	else
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -12000000000.0], N[Not[LessEqual[x1, 1.25e+24]], $MachinePrecision]], N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] - N[(x2 * N[(6.0 - N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.2e10 or 1.25000000000000011e24 < x1

   1. Initial program 41.0%

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

   3. Taylor expanded in x1 around -inf 45.8%

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

   4. Taylor expanded in x1 around inf 96.7%

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

   5. Taylor expanded in x1 around inf 90.1%

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

   if -1.2e10 < x1 < 1.25000000000000011e24

   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 84.5%

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

   4. Taylor expanded in x1 around 0 83.9%

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

   5. Taylor expanded in x1 around 0 84.6%

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

   6. Taylor expanded in x2 around 0 97.6%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -12000000000 \lor \neg \left(x1 \leq 1.25 \cdot 10^{+24}\right):\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 92.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -210000000:\\ \;\;\;\;{x1}^{4} \cdot \left(6 - \frac{3}{x1}\right)\\ \mathbf{elif}\;x1 \leq 2.9 \cdot 10^{+25}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -210000000.0)
   (* (pow x1 4.0) (- 6.0 (/ 3.0 x1)))
   (if (<= x1 2.9e+25)
     (+ x1 (- (* x1 -2.0) (* x2 (- 6.0 (+ (* x1 -12.0) (* 8.0 (* x1 x2)))))))
     (* 6.0 (pow x1 4.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -210000000.0) {
		tmp = pow(x1, 4.0) * (6.0 - (3.0 / x1));
	} else if (x1 <= 2.9e+25) {
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else {
		tmp = 6.0 * pow(x1, 4.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-210000000.0d0)) then
        tmp = (x1 ** 4.0d0) * (6.0d0 - (3.0d0 / x1))
    else if (x1 <= 2.9d+25) then
        tmp = x1 + ((x1 * (-2.0d0)) - (x2 * (6.0d0 - ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))))))
    else
        tmp = 6.0d0 * (x1 ** 4.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -210000000.0) {
		tmp = Math.pow(x1, 4.0) * (6.0 - (3.0 / x1));
	} else if (x1 <= 2.9e+25) {
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else {
		tmp = 6.0 * Math.pow(x1, 4.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -210000000.0:
		tmp = math.pow(x1, 4.0) * (6.0 - (3.0 / x1))
	elif x1 <= 2.9e+25:
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2))))))
	else:
		tmp = 6.0 * math.pow(x1, 4.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -210000000.0)
		tmp = Float64((x1 ^ 4.0) * Float64(6.0 - Float64(3.0 / x1)));
	elseif (x1 <= 2.9e+25)
		tmp = Float64(x1 + Float64(Float64(x1 * -2.0) - Float64(x2 * Float64(6.0 - Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2)))))));
	else
		tmp = Float64(6.0 * (x1 ^ 4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -210000000.0)
		tmp = (x1 ^ 4.0) * (6.0 - (3.0 / x1));
	elseif (x1 <= 2.9e+25)
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	else
		tmp = 6.0 * (x1 ^ 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -210000000.0], N[(N[Power[x1, 4.0], $MachinePrecision] * N[(6.0 - N[(3.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.9e+25], N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] - N[(x2 * N[(6.0 - N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.1e8

   1. Initial program 37.2%

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

   3. Taylor expanded in x1 around -inf 46.9%

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

   4. Taylor expanded in x1 around inf 93.3%

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

   5. Taylor expanded in x1 around inf 87.3%

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

      1. associate-*r/ 87.3%

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

      2. metadata-eval 87.3%

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

   7. Simplified 87.3%

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

   if -2.1e8 < x1 < 2.8999999999999999e25

   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 84.5%

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

   4. Taylor expanded in x1 around 0 83.9%

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

   5. Taylor expanded in x1 around 0 84.6%

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

   6. Taylor expanded in x2 around 0 97.6%

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

   if 2.8999999999999999e25 < x1

   1. Initial program 44.6%

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

   3. Taylor expanded in x1 around -inf 44.8%

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

   4. Taylor expanded in x1 around inf 100.0%

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

   5. Taylor expanded in x1 around inf 93.4%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -210000000:\\ \;\;\;\;{x1}^{4} \cdot \left(6 - \frac{3}{x1}\right)\\ \mathbf{elif}\;x1 \leq 2.9 \cdot 10^{+25}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 92.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := -1 - x1 \cdot x1\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := t\_2 + 2 \cdot x2\\ t_4 := x1 + \left(3 \cdot \frac{\left(t\_2 - 2 \cdot x2\right) - x1}{t\_0} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(t\_2 \cdot \frac{t\_3 - x1}{t\_1} + t\_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{x1 - t\_3}{t\_1} \cdot 4\right) - -6\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;9 + x1 \cdot \left(2 + x1 \cdot \left(9 - \left(4 \cdot \left(3 - 2 \cdot x2\right) - x1 \cdot -3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -62000000:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x1 \leq 1.25 \cdot 10^{+24}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (- -1.0 (* x1 x1)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (+ t_2 (* 2.0 x2)))
        (t_4
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_0))
           (+
            x1
            (-
             (* x1 (* x1 x1))
             (+
              (* t_2 (/ (- t_3 x1) t_1))
              (*
               t_0
               (-
                (* (* x1 x1) (- 6.0 (* (/ (- x1 t_3) t_1) 4.0)))
                -6.0)))))))))
   (if (<= x1 -5e+102)
     (+
      9.0
      (* x1 (+ 2.0 (* x1 (- 9.0 (- (* 4.0 (- 3.0 (* 2.0 x2))) (* x1 -3.0)))))))
     (if (<= x1 -62000000.0)
       t_4
       (if (<= x1 1.25e+24)
         (+
          x1
          (- (* x1 -2.0) (* x2 (- 6.0 (+ (* x1 -12.0) (* 8.0 (* x1 x2)))))))
         (if (<= x1 5e+153) t_4 (+ x1 (+ x1 (* x1 (- (* x1 9.0) 3.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = -1.0 - (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = t_2 + (2.0 * x2);
	double t_4 = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) - ((t_2 * ((t_3 - x1) / t_1)) + (t_0 * (((x1 * x1) * (6.0 - (((x1 - t_3) / t_1) * 4.0))) - -6.0))))));
	double tmp;
	if (x1 <= -5e+102) {
		tmp = 9.0 + (x1 * (2.0 + (x1 * (9.0 - ((4.0 * (3.0 - (2.0 * x2))) - (x1 * -3.0))))));
	} else if (x1 <= -62000000.0) {
		tmp = t_4;
	} else if (x1 <= 1.25e+24) {
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else if (x1 <= 5e+153) {
		tmp = t_4;
	} else {
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = (-1.0d0) - (x1 * x1)
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = t_2 + (2.0d0 * x2)
    t_4 = x1 + ((3.0d0 * (((t_2 - (2.0d0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) - ((t_2 * ((t_3 - x1) / t_1)) + (t_0 * (((x1 * x1) * (6.0d0 - (((x1 - t_3) / t_1) * 4.0d0))) - (-6.0d0)))))))
    if (x1 <= (-5d+102)) then
        tmp = 9.0d0 + (x1 * (2.0d0 + (x1 * (9.0d0 - ((4.0d0 * (3.0d0 - (2.0d0 * x2))) - (x1 * (-3.0d0)))))))
    else if (x1 <= (-62000000.0d0)) then
        tmp = t_4
    else if (x1 <= 1.25d+24) then
        tmp = x1 + ((x1 * (-2.0d0)) - (x2 * (6.0d0 - ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))))))
    else if (x1 <= 5d+153) then
        tmp = t_4
    else
        tmp = x1 + (x1 + (x1 * ((x1 * 9.0d0) - 3.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = -1.0 - (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = t_2 + (2.0 * x2);
	double t_4 = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) - ((t_2 * ((t_3 - x1) / t_1)) + (t_0 * (((x1 * x1) * (6.0 - (((x1 - t_3) / t_1) * 4.0))) - -6.0))))));
	double tmp;
	if (x1 <= -5e+102) {
		tmp = 9.0 + (x1 * (2.0 + (x1 * (9.0 - ((4.0 * (3.0 - (2.0 * x2))) - (x1 * -3.0))))));
	} else if (x1 <= -62000000.0) {
		tmp = t_4;
	} else if (x1 <= 1.25e+24) {
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else if (x1 <= 5e+153) {
		tmp = t_4;
	} else {
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = -1.0 - (x1 * x1)
	t_2 = x1 * (x1 * 3.0)
	t_3 = t_2 + (2.0 * x2)
	t_4 = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) - ((t_2 * ((t_3 - x1) / t_1)) + (t_0 * (((x1 * x1) * (6.0 - (((x1 - t_3) / t_1) * 4.0))) - -6.0))))))
	tmp = 0
	if x1 <= -5e+102:
		tmp = 9.0 + (x1 * (2.0 + (x1 * (9.0 - ((4.0 * (3.0 - (2.0 * x2))) - (x1 * -3.0))))))
	elif x1 <= -62000000.0:
		tmp = t_4
	elif x1 <= 1.25e+24:
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2))))))
	elif x1 <= 5e+153:
		tmp = t_4
	else:
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(-1.0 - Float64(x1 * x1))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(t_2 + Float64(2.0 * x2))
	t_4 = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) - Float64(Float64(t_2 * Float64(Float64(t_3 - x1) / t_1)) + Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(Float64(Float64(x1 - t_3) / t_1) * 4.0))) - -6.0)))))))
	tmp = 0.0
	if (x1 <= -5e+102)
		tmp = Float64(9.0 + Float64(x1 * Float64(2.0 + Float64(x1 * Float64(9.0 - Float64(Float64(4.0 * Float64(3.0 - Float64(2.0 * x2))) - Float64(x1 * -3.0)))))));
	elseif (x1 <= -62000000.0)
		tmp = t_4;
	elseif (x1 <= 1.25e+24)
		tmp = Float64(x1 + Float64(Float64(x1 * -2.0) - Float64(x2 * Float64(6.0 - Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2)))))));
	elseif (x1 <= 5e+153)
		tmp = t_4;
	else
		tmp = Float64(x1 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * 9.0) - 3.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = -1.0 - (x1 * x1);
	t_2 = x1 * (x1 * 3.0);
	t_3 = t_2 + (2.0 * x2);
	t_4 = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) - ((t_2 * ((t_3 - x1) / t_1)) + (t_0 * (((x1 * x1) * (6.0 - (((x1 - t_3) / t_1) * 4.0))) - -6.0))))));
	tmp = 0.0;
	if (x1 <= -5e+102)
		tmp = 9.0 + (x1 * (2.0 + (x1 * (9.0 - ((4.0 * (3.0 - (2.0 * x2))) - (x1 * -3.0))))));
	elseif (x1 <= -62000000.0)
		tmp = t_4;
	elseif (x1 <= 1.25e+24)
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	elseif (x1 <= 5e+153)
		tmp = t_4;
	else
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$2 * N[(N[(t$95$3 - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(N[(N[(x1 - t$95$3), $MachinePrecision] / t$95$1), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5e+102], N[(9.0 + N[(x1 * N[(2.0 + N[(x1 * N[(9.0 - N[(N[(4.0 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -62000000.0], t$95$4, If[LessEqual[x1, 1.25e+24], N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] - N[(x2 * N[(6.0 - N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], t$95$4, N[(x1 + N[(x1 + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5e102

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around -inf 25.7%

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

   4. Taylor expanded in x1 around inf 100.0%

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

   5. Taylor expanded in x1 around 0 97.1%

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

   if -5e102 < x1 < -6.2e7 or 1.25000000000000011e24 < x1 < 5.00000000000000018e153

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around inf 91.5%

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

   4. Taylor expanded in x1 around inf 91.5%

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

   if -6.2e7 < x1 < 1.25000000000000011e24

   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 84.5%

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

   4. Taylor expanded in x1 around 0 83.9%

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

   5. Taylor expanded in x1 around 0 84.6%

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

   6. Taylor expanded in x2 around 0 97.6%

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

   if 5.00000000000000018e153 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around 0 75.0%

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

   5. Taylor expanded in x2 around 0 100.0%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;9 + x1 \cdot \left(2 + x1 \cdot \left(9 - \left(4 \cdot \left(3 - 2 \cdot x2\right) - x1 \cdot -3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -62000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1} \cdot 4\right) - -6\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.25 \cdot 10^{+24}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1} \cdot 4\right) - -6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 84.8% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.5 \cdot 10^{+23}:\\ \;\;\;\;9 + x1 \cdot \left(2 + x1 \cdot \left(9 - \left(4 \cdot \left(3 - 2 \cdot x2\right) - x1 \cdot -3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.65 \cdot 10^{+91}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + x2 \cdot 8\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -2.5e+23)
   (+
    9.0
    (* x1 (+ 2.0 (* x1 (- 9.0 (- (* 4.0 (- 3.0 (* 2.0 x2))) (* x1 -3.0)))))))
   (if (<= x1 2.65e+91)
     (+ x1 (- (* x1 -2.0) (* x2 (- 6.0 (+ (* x1 -12.0) (* 8.0 (* x1 x2)))))))
     (if (<= x1 5e+153)
       (+
        x1
        (+
         (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
         (+ x1 (+ (* x1 (* x1 x1)) (* x2 8.0)))))
       (+ x1 (+ x1 (* x1 (- (* x1 9.0) 3.0))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.5e+23) {
		tmp = 9.0 + (x1 * (2.0 + (x1 * (9.0 - ((4.0 * (3.0 - (2.0 * x2))) - (x1 * -3.0))))));
	} else if (x1 <= 2.65e+91) {
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + ((x1 * (x1 * x1)) + (x2 * 8.0))));
	} else {
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-2.5d+23)) then
        tmp = 9.0d0 + (x1 * (2.0d0 + (x1 * (9.0d0 - ((4.0d0 * (3.0d0 - (2.0d0 * x2))) - (x1 * (-3.0d0)))))))
    else if (x1 <= 2.65d+91) then
        tmp = x1 + ((x1 * (-2.0d0)) - (x2 * (6.0d0 - ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))))))
    else if (x1 <= 5d+153) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0))) + (x1 + ((x1 * (x1 * x1)) + (x2 * 8.0d0))))
    else
        tmp = x1 + (x1 + (x1 * ((x1 * 9.0d0) - 3.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.5e+23) {
		tmp = 9.0 + (x1 * (2.0 + (x1 * (9.0 - ((4.0 * (3.0 - (2.0 * x2))) - (x1 * -3.0))))));
	} else if (x1 <= 2.65e+91) {
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + ((x1 * (x1 * x1)) + (x2 * 8.0))));
	} else {
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -2.5e+23:
		tmp = 9.0 + (x1 * (2.0 + (x1 * (9.0 - ((4.0 * (3.0 - (2.0 * x2))) - (x1 * -3.0))))))
	elif x1 <= 2.65e+91:
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2))))))
	elif x1 <= 5e+153:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + ((x1 * (x1 * x1)) + (x2 * 8.0))))
	else:
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -2.5e+23)
		tmp = Float64(9.0 + Float64(x1 * Float64(2.0 + Float64(x1 * Float64(9.0 - Float64(Float64(4.0 * Float64(3.0 - Float64(2.0 * x2))) - Float64(x1 * -3.0)))))));
	elseif (x1 <= 2.65e+91)
		tmp = Float64(x1 + Float64(Float64(x1 * -2.0) - Float64(x2 * Float64(6.0 - Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2)))))));
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(x2 * 8.0)))));
	else
		tmp = Float64(x1 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * 9.0) - 3.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -2.5e+23)
		tmp = 9.0 + (x1 * (2.0 + (x1 * (9.0 - ((4.0 * (3.0 - (2.0 * x2))) - (x1 * -3.0))))));
	elseif (x1 <= 2.65e+91)
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	elseif (x1 <= 5e+153)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + ((x1 * (x1 * x1)) + (x2 * 8.0))));
	else
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -2.5e+23], N[(9.0 + N[(x1 * N[(2.0 + N[(x1 * N[(9.0 - N[(N[(4.0 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.65e+91], N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] - N[(x2 * N[(6.0 - N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.5e23

   1. Initial program 28.4%

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

   3. Taylor expanded in x1 around -inf 43.2%

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

   4. Taylor expanded in x1 around inf 96.3%

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

   5. Taylor expanded in x1 around 0 77.2%

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

   if -2.5e23 < x1 < 2.64999999999999998e91

   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 76.1%

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

   4. Taylor expanded in x1 around 0 75.9%

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

   5. Taylor expanded in x1 around 0 76.1%

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

   6. Taylor expanded in x2 around 0 87.4%

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

   if 2.64999999999999998e91 < x1 < 5.00000000000000018e153

   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 -inf 100.0%

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

   4. Taylor expanded in x2 around inf 51.9%

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

      1. *-commutative 51.9%

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

   6. Simplified 51.9%

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

   7. Taylor expanded in x1 around 0 81.9%

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

      1. *-commutative 81.9%

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

   9. Simplified 81.9%

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

   if 5.00000000000000018e153 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around 0 75.0%

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

   5. Taylor expanded in x2 around 0 100.0%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.5 \cdot 10^{+23}:\\ \;\;\;\;9 + x1 \cdot \left(2 + x1 \cdot \left(9 - \left(4 \cdot \left(3 - 2 \cdot x2\right) - x1 \cdot -3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.65 \cdot 10^{+91}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + x2 \cdot 8\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 83.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.5 \cdot 10^{+23}:\\ \;\;\;\;9 + x1 \cdot \left(2 + x1 \cdot \left(9 - \left(4 \cdot \left(3 - 2 \cdot x2\right) - x1 \cdot -3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.3 \cdot 10^{+24}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 - x1 \cdot \left(x2 \cdot -2 - \left(x1 + 3\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -2.5e+23)
   (+
    9.0
    (* x1 (+ 2.0 (* x1 (- 9.0 (- (* 4.0 (- 3.0 (* 2.0 x2))) (* x1 -3.0)))))))
   (if (<= x1 3.3e+24)
     (+ x1 (- (* x1 -2.0) (* x2 (- 6.0 (+ (* x1 -12.0) (* 8.0 (* x1 x2)))))))
     (+
      x1
      (+
       (+ x1 (* 4.0 (* x1 (* x2 (- (* 2.0 x2) 3.0)))))
       (*
        3.0
        (+ (* x2 -2.0) (* x1 (- -1.0 (* x1 (- (* x2 -2.0) (+ x1 3.0))))))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.5e+23) {
		tmp = 9.0 + (x1 * (2.0 + (x1 * (9.0 - ((4.0 * (3.0 - (2.0 * x2))) - (x1 * -3.0))))));
	} else if (x1 <= 3.3e+24) {
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else {
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 - (x1 * ((x2 * -2.0) - (x1 + 3.0))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-2.5d+23)) then
        tmp = 9.0d0 + (x1 * (2.0d0 + (x1 * (9.0d0 - ((4.0d0 * (3.0d0 - (2.0d0 * x2))) - (x1 * (-3.0d0)))))))
    else if (x1 <= 3.3d+24) then
        tmp = x1 + ((x1 * (-2.0d0)) - (x2 * (6.0d0 - ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))))))
    else
        tmp = x1 + ((x1 + (4.0d0 * (x1 * (x2 * ((2.0d0 * x2) - 3.0d0))))) + (3.0d0 * ((x2 * (-2.0d0)) + (x1 * ((-1.0d0) - (x1 * ((x2 * (-2.0d0)) - (x1 + 3.0d0))))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.5e+23) {
		tmp = 9.0 + (x1 * (2.0 + (x1 * (9.0 - ((4.0 * (3.0 - (2.0 * x2))) - (x1 * -3.0))))));
	} else if (x1 <= 3.3e+24) {
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else {
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 - (x1 * ((x2 * -2.0) - (x1 + 3.0))))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -2.5e+23:
		tmp = 9.0 + (x1 * (2.0 + (x1 * (9.0 - ((4.0 * (3.0 - (2.0 * x2))) - (x1 * -3.0))))))
	elif x1 <= 3.3e+24:
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2))))))
	else:
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 - (x1 * ((x2 * -2.0) - (x1 + 3.0))))))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -2.5e+23)
		tmp = Float64(9.0 + Float64(x1 * Float64(2.0 + Float64(x1 * Float64(9.0 - Float64(Float64(4.0 * Float64(3.0 - Float64(2.0 * x2))) - Float64(x1 * -3.0)))))));
	elseif (x1 <= 3.3e+24)
		tmp = Float64(x1 + Float64(Float64(x1 * -2.0) - Float64(x2 * Float64(6.0 - Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2)))))));
	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(x2 * -2.0) - Float64(x1 + 3.0)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -2.5e+23)
		tmp = 9.0 + (x1 * (2.0 + (x1 * (9.0 - ((4.0 * (3.0 - (2.0 * x2))) - (x1 * -3.0))))));
	elseif (x1 <= 3.3e+24)
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	else
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 - (x1 * ((x2 * -2.0) - (x1 + 3.0))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -2.5e+23], N[(9.0 + N[(x1 * N[(2.0 + N[(x1 * N[(9.0 - N[(N[(4.0 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.3e+24], N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] - N[(x2 * N[(6.0 - N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $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[(x2 * -2.0), $MachinePrecision] - N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.5e23

   1. Initial program 28.4%

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

   3. Taylor expanded in x1 around -inf 43.2%

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

   4. Taylor expanded in x1 around inf 96.3%

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

   5. Taylor expanded in x1 around 0 77.2%

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

   if -2.5e23 < x1 < 3.2999999999999999e24

   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 81.9%

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

   4. Taylor expanded in x1 around 0 81.6%

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

   5. Taylor expanded in x1 around 0 82.2%

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

   6. Taylor expanded in x2 around 0 94.6%

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

   if 3.2999999999999999e24 < x1

   1. Initial program 44.6%

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

   3. Taylor expanded in x1 around 0 11.9%

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

   4. Taylor expanded in x1 around 0 70.7%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.5 \cdot 10^{+23}:\\ \;\;\;\;9 + x1 \cdot \left(2 + x1 \cdot \left(9 - \left(4 \cdot \left(3 - 2 \cdot x2\right) - x1 \cdot -3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.3 \cdot 10^{+24}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 - x1 \cdot \left(x2 \cdot -2 - \left(x1 + 3\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 71.4% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ t_1 := x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{if}\;x1 \leq -8.6 \cdot 10^{+142}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -1.18 \cdot 10^{+39}:\\ \;\;\;\;9 + x1 \cdot \left(2 + x1 \cdot \left(9 - 4 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq 7.5 \cdot 10^{-105}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (+ x1 (* x1 (- (* x1 9.0) 3.0)))))
        (t_1 (* x1 (+ -1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))))))
   (if (<= x1 -8.6e+142)
     t_0
     (if (<= x1 -1.18e+39)
       (+ 9.0 (* x1 (+ 2.0 (* x1 (- 9.0 (* 4.0 (- 3.0 (* 2.0 x2))))))))
       (if (<= x1 -3e-43)
         t_1
         (if (<= x1 7.5e-105)
           (+ x1 (+ (* x2 -6.0) (* x1 -2.0)))
           (if (<= x1 4.5e+153) t_1 t_0)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	double t_1 = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	double tmp;
	if (x1 <= -8.6e+142) {
		tmp = t_0;
	} else if (x1 <= -1.18e+39) {
		tmp = 9.0 + (x1 * (2.0 + (x1 * (9.0 - (4.0 * (3.0 - (2.0 * x2)))))));
	} else if (x1 <= -3e-43) {
		tmp = t_1;
	} else if (x1 <= 7.5e-105) {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	} else if (x1 <= 4.5e+153) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x1 + (x1 + (x1 * ((x1 * 9.0d0) - 3.0d0)))
    t_1 = x1 * ((-1.0d0) + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))))
    if (x1 <= (-8.6d+142)) then
        tmp = t_0
    else if (x1 <= (-1.18d+39)) then
        tmp = 9.0d0 + (x1 * (2.0d0 + (x1 * (9.0d0 - (4.0d0 * (3.0d0 - (2.0d0 * x2)))))))
    else if (x1 <= (-3d-43)) then
        tmp = t_1
    else if (x1 <= 7.5d-105) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (-2.0d0)))
    else if (x1 <= 4.5d+153) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	double t_1 = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	double tmp;
	if (x1 <= -8.6e+142) {
		tmp = t_0;
	} else if (x1 <= -1.18e+39) {
		tmp = 9.0 + (x1 * (2.0 + (x1 * (9.0 - (4.0 * (3.0 - (2.0 * x2)))))));
	} else if (x1 <= -3e-43) {
		tmp = t_1;
	} else if (x1 <= 7.5e-105) {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	} else if (x1 <= 4.5e+153) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)))
	t_1 = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))))
	tmp = 0
	if x1 <= -8.6e+142:
		tmp = t_0
	elif x1 <= -1.18e+39:
		tmp = 9.0 + (x1 * (2.0 + (x1 * (9.0 - (4.0 * (3.0 - (2.0 * x2)))))))
	elif x1 <= -3e-43:
		tmp = t_1
	elif x1 <= 7.5e-105:
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0))
	elif x1 <= 4.5e+153:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * 9.0) - 3.0))))
	t_1 = Float64(x1 * Float64(-1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))))
	tmp = 0.0
	if (x1 <= -8.6e+142)
		tmp = t_0;
	elseif (x1 <= -1.18e+39)
		tmp = Float64(9.0 + Float64(x1 * Float64(2.0 + Float64(x1 * Float64(9.0 - Float64(4.0 * Float64(3.0 - Float64(2.0 * x2))))))));
	elseif (x1 <= -3e-43)
		tmp = t_1;
	elseif (x1 <= 7.5e-105)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * -2.0)));
	elseif (x1 <= 4.5e+153)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	t_1 = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	tmp = 0.0;
	if (x1 <= -8.6e+142)
		tmp = t_0;
	elseif (x1 <= -1.18e+39)
		tmp = 9.0 + (x1 * (2.0 + (x1 * (9.0 - (4.0 * (3.0 - (2.0 * x2)))))));
	elseif (x1 <= -3e-43)
		tmp = t_1;
	elseif (x1 <= 7.5e-105)
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	elseif (x1 <= 4.5e+153)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(-1.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -8.6e+142], t$95$0, If[LessEqual[x1, -1.18e+39], N[(9.0 + N[(x1 * N[(2.0 + N[(x1 * N[(9.0 - N[(4.0 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -3e-43], t$95$1, If[LessEqual[x1, 7.5e-105], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.5e+153], t$95$1, t$95$0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -8.60000000000000025e142 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 69.6%

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

   5. Taylor expanded in x2 around 0 98.5%

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

   if -8.60000000000000025e142 < x1 < -1.17999999999999996e39

   1. Initial program 57.6%

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

   3. Taylor expanded in x1 around -inf 95.2%

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

   4. Taylor expanded in x1 around inf 95.2%

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

   5. Taylor expanded in x1 around 0 37.6%

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

   if -1.17999999999999996e39 < x1 < -3.00000000000000003e-43 or 7.5000000000000006e-105 < x1 < 4.5000000000000001e153

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 56.0%

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

   4. Taylor expanded in x1 around 0 55.7%

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

   5. Taylor expanded in x1 around 0 55.4%

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

   6. Taylor expanded in x1 around inf 49.5%

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

   if -3.00000000000000003e-43 < x1 < 7.5000000000000006e-105

   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 82.7%

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

   4. Taylor expanded in x1 around 0 82.7%

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

   5. Taylor expanded in x1 around 0 82.9%

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

   6. Taylor expanded in x2 around 0 80.9%

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

      1. *-commutative 80.9%

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

   8. Simplified 80.9%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -8.6 \cdot 10^{+142}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{elif}\;x1 \leq -1.18 \cdot 10^{+39}:\\ \;\;\;\;9 + x1 \cdot \left(2 + x1 \cdot \left(9 - 4 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3 \cdot 10^{-43}:\\ \;\;\;\;x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7.5 \cdot 10^{-105}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 80.7% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{if}\;x1 \leq -9 \cdot 10^{+142}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -4.6 \cdot 10^{+38}:\\ \;\;\;\;9 + x1 \cdot \left(2 + x1 \cdot \left(9 - 4 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (+ x1 (* x1 (- (* x1 9.0) 3.0))))))
   (if (<= x1 -9e+142)
     t_0
     (if (<= x1 -4.6e+38)
       (+ 9.0 (* x1 (+ 2.0 (* x1 (- 9.0 (* 4.0 (- 3.0 (* 2.0 x2))))))))
       (if (<= x1 4.5e+153)
         (+
          x1
          (- (* x1 -2.0) (* x2 (- 6.0 (+ (* x1 -12.0) (* 8.0 (* x1 x2)))))))
         t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	double tmp;
	if (x1 <= -9e+142) {
		tmp = t_0;
	} else if (x1 <= -4.6e+38) {
		tmp = 9.0 + (x1 * (2.0 + (x1 * (9.0 - (4.0 * (3.0 - (2.0 * x2)))))));
	} else if (x1 <= 4.5e+153) {
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} 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 + (x1 * ((x1 * 9.0d0) - 3.0d0)))
    if (x1 <= (-9d+142)) then
        tmp = t_0
    else if (x1 <= (-4.6d+38)) then
        tmp = 9.0d0 + (x1 * (2.0d0 + (x1 * (9.0d0 - (4.0d0 * (3.0d0 - (2.0d0 * x2)))))))
    else if (x1 <= 4.5d+153) then
        tmp = x1 + ((x1 * (-2.0d0)) - (x2 * (6.0d0 - ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	double tmp;
	if (x1 <= -9e+142) {
		tmp = t_0;
	} else if (x1 <= -4.6e+38) {
		tmp = 9.0 + (x1 * (2.0 + (x1 * (9.0 - (4.0 * (3.0 - (2.0 * x2)))))));
	} else if (x1 <= 4.5e+153) {
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)))
	tmp = 0
	if x1 <= -9e+142:
		tmp = t_0
	elif x1 <= -4.6e+38:
		tmp = 9.0 + (x1 * (2.0 + (x1 * (9.0 - (4.0 * (3.0 - (2.0 * x2)))))))
	elif x1 <= 4.5e+153:
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2))))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * 9.0) - 3.0))))
	tmp = 0.0
	if (x1 <= -9e+142)
		tmp = t_0;
	elseif (x1 <= -4.6e+38)
		tmp = Float64(9.0 + Float64(x1 * Float64(2.0 + Float64(x1 * Float64(9.0 - Float64(4.0 * Float64(3.0 - Float64(2.0 * x2))))))));
	elseif (x1 <= 4.5e+153)
		tmp = Float64(x1 + Float64(Float64(x1 * -2.0) - Float64(x2 * Float64(6.0 - Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2)))))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	tmp = 0.0;
	if (x1 <= -9e+142)
		tmp = t_0;
	elseif (x1 <= -4.6e+38)
		tmp = 9.0 + (x1 * (2.0 + (x1 * (9.0 - (4.0 * (3.0 - (2.0 * x2)))))));
	elseif (x1 <= 4.5e+153)
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -9e+142], t$95$0, If[LessEqual[x1, -4.6e+38], N[(9.0 + N[(x1 * N[(2.0 + N[(x1 * N[(9.0 - N[(4.0 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.5e+153], N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] - N[(x2 * N[(6.0 - N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -8.9999999999999998e142 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 69.6%

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

   5. Taylor expanded in x2 around 0 98.5%

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

   if -8.9999999999999998e142 < x1 < -4.6000000000000002e38

   1. Initial program 57.6%

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

   3. Taylor expanded in x1 around -inf 95.2%

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

   4. Taylor expanded in x1 around inf 95.2%

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

   5. Taylor expanded in x1 around 0 37.6%

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

   if -4.6000000000000002e38 < 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 72.5%

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

   4. Taylor expanded in x1 around 0 72.4%

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

   5. Taylor expanded in x1 around 0 72.4%

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

   6. Taylor expanded in x2 around 0 82.8%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9 \cdot 10^{+142}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{elif}\;x1 \leq -4.6 \cdot 10^{+38}:\\ \;\;\;\;9 + x1 \cdot \left(2 + x1 \cdot \left(9 - 4 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 68.2% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ t_1 := x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{if}\;x1 \leq -5.8 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -1.9 \cdot 10^{-29}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{-44}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ 2.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))))
        (t_1 (+ x1 (+ x1 (* x1 (- (* x1 9.0) 3.0))))))
   (if (<= x1 -5.8e+98)
     t_1
     (if (<= x1 -1.9e-29)
       t_0
       (if (<= x1 2.1e-44)
         (+ 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 = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	double t_1 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	double tmp;
	if (x1 <= -5.8e+98) {
		tmp = t_1;
	} else if (x1 <= -1.9e-29) {
		tmp = t_0;
	} else if (x1 <= 2.1e-44) {
		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 = x1 * (2.0d0 + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))))
    t_1 = x1 + (x1 + (x1 * ((x1 * 9.0d0) - 3.0d0)))
    if (x1 <= (-5.8d+98)) then
        tmp = t_1
    else if (x1 <= (-1.9d-29)) then
        tmp = t_0
    else if (x1 <= 2.1d-44) 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 = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	double t_1 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	double tmp;
	if (x1 <= -5.8e+98) {
		tmp = t_1;
	} else if (x1 <= -1.9e-29) {
		tmp = t_0;
	} else if (x1 <= 2.1e-44) {
		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 = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))))
	t_1 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)))
	tmp = 0
	if x1 <= -5.8e+98:
		tmp = t_1
	elif x1 <= -1.9e-29:
		tmp = t_0
	elif x1 <= 2.1e-44:
		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(x1 * Float64(2.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))))
	t_1 = Float64(x1 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * 9.0) - 3.0))))
	tmp = 0.0
	if (x1 <= -5.8e+98)
		tmp = t_1;
	elseif (x1 <= -1.9e-29)
		tmp = t_0;
	elseif (x1 <= 2.1e-44)
		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 = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	t_1 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	tmp = 0.0;
	if (x1 <= -5.8e+98)
		tmp = t_1;
	elseif (x1 <= -1.9e-29)
		tmp = t_0;
	elseif (x1 <= 2.1e-44)
		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[(x1 * N[(2.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x1 + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.8e+98], t$95$1, If[LessEqual[x1, -1.9e-29], t$95$0, If[LessEqual[x1, 2.1e-44], 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 3 regimes

2. if x1 < -5.8000000000000002e98 or 4.5000000000000001e153 < x1

   1. Initial program 1.5%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   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 62.3%

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

   5. Taylor expanded in x2 around 0 86.3%

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

   if -5.8000000000000002e98 < x1 < -1.89999999999999988e-29 or 2.10000000000000001e-44 < 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 43.8%

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

   4. Taylor expanded in x1 around inf 36.6%

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

   5. Taylor expanded in x1 around inf 36.4%

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

   if -1.89999999999999988e-29 < x1 < 2.10000000000000001e-44

   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 84.2%

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

   4. Taylor expanded in x1 around 0 84.2%

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

   5. Taylor expanded in x1 around 0 84.5%

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

   6. Taylor expanded in x2 around 0 78.8%

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

      1. *-commutative 78.8%

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

   8. Simplified 78.8%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.8 \cdot 10^{+98}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{elif}\;x1 \leq -1.9 \cdot 10^{-29}:\\ \;\;\;\;x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{-44}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 70.7% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ t_1 := x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{if}\;x1 \leq -5.8 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -3 \cdot 10^{-43}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 3.1 \cdot 10^{-102}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ -1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))))
        (t_1 (+ x1 (+ x1 (* x1 (- (* x1 9.0) 3.0))))))
   (if (<= x1 -5.8e+98)
     t_1
     (if (<= x1 -3e-43)
       t_0
       (if (<= x1 3.1e-102)
         (+ 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 = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	double t_1 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	double tmp;
	if (x1 <= -5.8e+98) {
		tmp = t_1;
	} else if (x1 <= -3e-43) {
		tmp = t_0;
	} else if (x1 <= 3.1e-102) {
		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 = x1 * ((-1.0d0) + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))))
    t_1 = x1 + (x1 + (x1 * ((x1 * 9.0d0) - 3.0d0)))
    if (x1 <= (-5.8d+98)) then
        tmp = t_1
    else if (x1 <= (-3d-43)) then
        tmp = t_0
    else if (x1 <= 3.1d-102) 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 = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	double t_1 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	double tmp;
	if (x1 <= -5.8e+98) {
		tmp = t_1;
	} else if (x1 <= -3e-43) {
		tmp = t_0;
	} else if (x1 <= 3.1e-102) {
		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 = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))))
	t_1 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)))
	tmp = 0
	if x1 <= -5.8e+98:
		tmp = t_1
	elif x1 <= -3e-43:
		tmp = t_0
	elif x1 <= 3.1e-102:
		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(x1 * Float64(-1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))))
	t_1 = Float64(x1 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * 9.0) - 3.0))))
	tmp = 0.0
	if (x1 <= -5.8e+98)
		tmp = t_1;
	elseif (x1 <= -3e-43)
		tmp = t_0;
	elseif (x1 <= 3.1e-102)
		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 = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	t_1 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	tmp = 0.0;
	if (x1 <= -5.8e+98)
		tmp = t_1;
	elseif (x1 <= -3e-43)
		tmp = t_0;
	elseif (x1 <= 3.1e-102)
		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[(x1 * N[(-1.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x1 + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.8e+98], t$95$1, If[LessEqual[x1, -3e-43], t$95$0, If[LessEqual[x1, 3.1e-102], 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 3 regimes

2. if x1 < -5.8000000000000002e98 or 4.5000000000000001e153 < x1

   1. Initial program 1.5%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   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 62.3%

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

   5. Taylor expanded in x2 around 0 86.3%

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

   if -5.8000000000000002e98 < x1 < -3.00000000000000003e-43 or 3.10000000000000013e-102 < x1 < 4.5000000000000001e153

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 51.5%

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

   4. Taylor expanded in x1 around 0 51.4%

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

   5. Taylor expanded in x1 around 0 51.2%

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

   6. Taylor expanded in x1 around inf 46.0%

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

   if -3.00000000000000003e-43 < x1 < 3.10000000000000013e-102

   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 82.7%

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

   4. Taylor expanded in x1 around 0 82.7%

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

   5. Taylor expanded in x1 around 0 82.9%

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

   6. Taylor expanded in x2 around 0 80.9%

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

      1. *-commutative 80.9%

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

   8. Simplified 80.9%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.8 \cdot 10^{+98}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{elif}\;x1 \leq -3 \cdot 10^{-43}:\\ \;\;\;\;x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.1 \cdot 10^{-102}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 74.5% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{if}\;x1 \leq -9 \cdot 10^{+142}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -4.6 \cdot 10^{+38}:\\ \;\;\;\;9 + x1 \cdot \left(2 + x1 \cdot \left(9 - 4 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (+ x1 (* x1 (- (* x1 9.0) 3.0))))))
   (if (<= x1 -9e+142)
     t_0
     (if (<= x1 -4.6e+38)
       (+ 9.0 (* x1 (+ 2.0 (* x1 (- 9.0 (* 4.0 (- 3.0 (* 2.0 x2))))))))
       (if (<= x1 4.5e+153)
         (+ (* x2 -6.0) (* 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 + (x1 * ((x1 * 9.0) - 3.0)));
	double tmp;
	if (x1 <= -9e+142) {
		tmp = t_0;
	} else if (x1 <= -4.6e+38) {
		tmp = 9.0 + (x1 * (2.0 + (x1 * (9.0 - (4.0 * (3.0 - (2.0 * x2)))))));
	} else if (x1 <= 4.5e+153) {
		tmp = (x2 * -6.0) + (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 + (x1 * ((x1 * 9.0d0) - 3.0d0)))
    if (x1 <= (-9d+142)) then
        tmp = t_0
    else if (x1 <= (-4.6d+38)) then
        tmp = 9.0d0 + (x1 * (2.0d0 + (x1 * (9.0d0 - (4.0d0 * (3.0d0 - (2.0d0 * x2)))))))
    else if (x1 <= 4.5d+153) then
        tmp = (x2 * (-6.0d0)) + (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 + (x1 * ((x1 * 9.0) - 3.0)));
	double tmp;
	if (x1 <= -9e+142) {
		tmp = t_0;
	} else if (x1 <= -4.6e+38) {
		tmp = 9.0 + (x1 * (2.0 + (x1 * (9.0 - (4.0 * (3.0 - (2.0 * x2)))))));
	} else if (x1 <= 4.5e+153) {
		tmp = (x2 * -6.0) + (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 + (x1 * ((x1 * 9.0) - 3.0)))
	tmp = 0
	if x1 <= -9e+142:
		tmp = t_0
	elif x1 <= -4.6e+38:
		tmp = 9.0 + (x1 * (2.0 + (x1 * (9.0 - (4.0 * (3.0 - (2.0 * x2)))))))
	elif x1 <= 4.5e+153:
		tmp = (x2 * -6.0) + (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(x1 * Float64(Float64(x1 * 9.0) - 3.0))))
	tmp = 0.0
	if (x1 <= -9e+142)
		tmp = t_0;
	elseif (x1 <= -4.6e+38)
		tmp = Float64(9.0 + Float64(x1 * Float64(2.0 + Float64(x1 * Float64(9.0 - Float64(4.0 * Float64(3.0 - Float64(2.0 * x2))))))));
	elseif (x1 <= 4.5e+153)
		tmp = Float64(Float64(x2 * -6.0) + 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 + (x1 * ((x1 * 9.0) - 3.0)));
	tmp = 0.0;
	if (x1 <= -9e+142)
		tmp = t_0;
	elseif (x1 <= -4.6e+38)
		tmp = 9.0 + (x1 * (2.0 + (x1 * (9.0 - (4.0 * (3.0 - (2.0 * x2)))))));
	elseif (x1 <= 4.5e+153)
		tmp = (x2 * -6.0) + (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[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -9e+142], t$95$0, If[LessEqual[x1, -4.6e+38], N[(9.0 + N[(x1 * N[(2.0 + N[(x1 * N[(9.0 - N[(4.0 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.5e+153], N[(N[(x2 * -6.0), $MachinePrecision] + 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 3 regimes

2. if x1 < -8.9999999999999998e142 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 69.6%

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

   5. Taylor expanded in x2 around 0 98.5%

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

   if -8.9999999999999998e142 < x1 < -4.6000000000000002e38

   1. Initial program 57.6%

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

   3. Taylor expanded in x1 around -inf 95.2%

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

   4. Taylor expanded in x1 around inf 95.2%

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

   5. Taylor expanded in x1 around 0 37.6%

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

   if -4.6000000000000002e38 < 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 72.5%

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

   4. Taylor expanded in x1 around 0 72.4%

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

   5. Taylor expanded in x1 around 0 72.4%

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

   6. Taylor expanded in x1 around 0 72.5%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9 \cdot 10^{+142}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{elif}\;x1 \leq -4.6 \cdot 10^{+38}:\\ \;\;\;\;9 + x1 \cdot \left(2 + x1 \cdot \left(9 - 4 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 82.5% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.5 \cdot 10^{+23}:\\ \;\;\;\;9 + x1 \cdot \left(2 + x1 \cdot \left(9 - \left(4 \cdot \left(3 - 2 \cdot x2\right) - x1 \cdot -3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -2.5e+23)
   (+
    9.0
    (* x1 (+ 2.0 (* x1 (- 9.0 (- (* 4.0 (- 3.0 (* 2.0 x2))) (* x1 -3.0)))))))
   (if (<= x1 4.5e+153)
     (+ x1 (- (* x1 -2.0) (* x2 (- 6.0 (+ (* x1 -12.0) (* 8.0 (* x1 x2)))))))
     (+ x1 (+ x1 (* x1 (- (* x1 9.0) 3.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.5e+23) {
		tmp = 9.0 + (x1 * (2.0 + (x1 * (9.0 - ((4.0 * (3.0 - (2.0 * x2))) - (x1 * -3.0))))));
	} else if (x1 <= 4.5e+153) {
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else {
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-2.5d+23)) then
        tmp = 9.0d0 + (x1 * (2.0d0 + (x1 * (9.0d0 - ((4.0d0 * (3.0d0 - (2.0d0 * x2))) - (x1 * (-3.0d0)))))))
    else if (x1 <= 4.5d+153) then
        tmp = x1 + ((x1 * (-2.0d0)) - (x2 * (6.0d0 - ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))))))
    else
        tmp = x1 + (x1 + (x1 * ((x1 * 9.0d0) - 3.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.5e+23) {
		tmp = 9.0 + (x1 * (2.0 + (x1 * (9.0 - ((4.0 * (3.0 - (2.0 * x2))) - (x1 * -3.0))))));
	} else if (x1 <= 4.5e+153) {
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else {
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -2.5e+23:
		tmp = 9.0 + (x1 * (2.0 + (x1 * (9.0 - ((4.0 * (3.0 - (2.0 * x2))) - (x1 * -3.0))))))
	elif x1 <= 4.5e+153:
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2))))))
	else:
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -2.5e+23)
		tmp = Float64(9.0 + Float64(x1 * Float64(2.0 + Float64(x1 * Float64(9.0 - Float64(Float64(4.0 * Float64(3.0 - Float64(2.0 * x2))) - Float64(x1 * -3.0)))))));
	elseif (x1 <= 4.5e+153)
		tmp = Float64(x1 + Float64(Float64(x1 * -2.0) - Float64(x2 * Float64(6.0 - Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2)))))));
	else
		tmp = Float64(x1 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * 9.0) - 3.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -2.5e+23)
		tmp = 9.0 + (x1 * (2.0 + (x1 * (9.0 - ((4.0 * (3.0 - (2.0 * x2))) - (x1 * -3.0))))));
	elseif (x1 <= 4.5e+153)
		tmp = x1 + ((x1 * -2.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	else
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -2.5e+23], N[(9.0 + N[(x1 * N[(2.0 + N[(x1 * N[(9.0 - N[(N[(4.0 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.5e+153], N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] - N[(x2 * N[(6.0 - N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.5e23

   1. Initial program 28.4%

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

   3. Taylor expanded in x1 around -inf 43.2%

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

   4. Taylor expanded in x1 around inf 96.3%

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

   5. Taylor expanded in x1 around 0 77.2%

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

   if -2.5e23 < x1 < 4.5000000000000001e153

   1. Initial program 99.5%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. 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 73.5%

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

   5. Taylor expanded in x1 around 0 73.6%

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

   6. Taylor expanded in x2 around 0 84.2%

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

   if 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 75.0%

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

   5. Taylor expanded in x2 around 0 100.0%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.5 \cdot 10^{+23}:\\ \;\;\;\;9 + x1 \cdot \left(2 + x1 \cdot \left(9 - \left(4 \cdot \left(3 - 2 \cdot x2\right) - x1 \cdot -3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 - x2 \cdot \left(6 - \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 63.6% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.15 \cdot 10^{-10} \lor \neg \left(x1 \leq 1.95 \cdot 10^{-16}\right):\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -1.15e-10) (not (<= x1 1.95e-16)))
   (+ x1 (+ x1 (* x1 (- (* x1 9.0) 3.0))))
   (+ x1 (+ (* x2 -6.0) (* x1 -2.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -1.15e-10) || !(x1 <= 1.95e-16)) {
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	} 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 ((x1 <= (-1.15d-10)) .or. (.not. (x1 <= 1.95d-16))) then
        tmp = x1 + (x1 + (x1 * ((x1 * 9.0d0) - 3.0d0)))
    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 ((x1 <= -1.15e-10) || !(x1 <= 1.95e-16)) {
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -1.15e-10) or not (x1 <= 1.95e-16):
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -1.15e-10) || !(x1 <= 1.95e-16))
		tmp = Float64(x1 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * 9.0) - 3.0))));
	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 ((x1 <= -1.15e-10) || ~((x1 <= 1.95e-16)))
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -1.15e-10], N[Not[LessEqual[x1, 1.95e-16]], $MachinePrecision]], N[(x1 + N[(x1 + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $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 x1 < -1.15000000000000004e-10 or 1.94999999999999989e-16 < x1

   1. Initial program 45.2%

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

   3. Taylor expanded in x1 around 0 14.1%

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

   4. Taylor expanded in x1 around 0 48.4%

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

   5. Taylor expanded in x2 around 0 51.1%

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

   if -1.15000000000000004e-10 < x1 < 1.94999999999999989e-16

   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 85.6%

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

   4. Taylor expanded in x1 around 0 85.6%

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

   5. Taylor expanded in x1 around 0 85.6%

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

   6. Taylor expanded in x2 around 0 74.7%

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

      1. *-commutative 74.7%

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

   8. Simplified 74.7%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.15 \cdot 10^{-10} \lor \neg \left(x1 \leq 1.95 \cdot 10^{-16}\right):\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 31.3% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -2.5 \cdot 10^{-215} \lor \neg \left(x2 \leq 5.2 \cdot 10^{-177}\right):\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -2.5e-215) (not (<= x2 5.2e-177))) (+ x1 (* x2 -6.0)) (- x1)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -2.5e-215) || !(x2 <= 5.2e-177)) {
		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 <= (-2.5d-215)) .or. (.not. (x2 <= 5.2d-177))) 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 <= -2.5e-215) || !(x2 <= 5.2e-177)) {
		tmp = x1 + (x2 * -6.0);
	} else {
		tmp = -x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -2.5e-215) or not (x2 <= 5.2e-177):
		tmp = x1 + (x2 * -6.0)
	else:
		tmp = -x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -2.5e-215) || !(x2 <= 5.2e-177))
		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 <= -2.5e-215) || ~((x2 <= 5.2e-177)))
		tmp = x1 + (x2 * -6.0);
	else
		tmp = -x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -2.5e-215], N[Not[LessEqual[x2, 5.2e-177]], $MachinePrecision]], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision], (-x1)]

Derivation

1. Split input into 2 regimes

2. if x2 < -2.49999999999999978e-215 or 5.2000000000000002e-177 < x2

   1. Initial program 72.6%

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

   3. Taylor expanded in x1 around 0 49.2%

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

   4. Taylor expanded in x1 around 0 65.7%

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

   5. Taylor expanded in x1 around 0 33.1%

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

      1. *-commutative 33.1%

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

   7. Simplified 33.1%

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

   if -2.49999999999999978e-215 < x2 < 5.2000000000000002e-177

   1. Initial program 77.9%

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

   3. Taylor expanded in x1 around 0 62.6%

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

   4. Taylor expanded in x1 around 0 79.4%

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

   5. Taylor expanded in x1 around 0 64.2%

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

   6. Taylor expanded in x2 around 0 51.4%

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

      1. distribute-rgt1-in 51.4%

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

      2. metadata-eval 51.4%

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

      3. neg-mul-1 51.4%

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

   8. Simplified 51.4%

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

4. Final simplification 35.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -2.5 \cdot 10^{-215} \lor \neg \left(x2 \leq 5.2 \cdot 10^{-177}\right):\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 38.3% accurate, 14.1× speedup

Math

\[\begin{array}{l} \\ x1 + \left(x2 \cdot -6 + x1 \cdot -2\right) \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (+ x1 (+ (* x2 -6.0) (* x1 -2.0))))

C

double code(double x1, double x2) {
	return x1 + ((x2 * -6.0) + (x1 * -2.0));
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x1 + ((x2 * (-6.0d0)) + (x1 * (-2.0d0)))
end function

Java

public static double code(double x1, double x2) {
	return x1 + ((x2 * -6.0) + (x1 * -2.0));
}

Python

def code(x1, x2):
	return x1 + ((x2 * -6.0) + (x1 * -2.0))

Julia

function code(x1, x2)
	return Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * -2.0)))
end

MATLAB

function tmp = code(x1, x2)
	tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
end

Wolfram

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

Derivation

1. Initial program 73.4%

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

3. Taylor expanded in x1 around 0 51.2%

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

4. Taylor expanded in x1 around 0 67.7%

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

5. Taylor expanded in x1 around 0 58.0%

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

6. Taylor expanded in x2 around 0 40.6%

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

   1. *-commutative 40.6%

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

8. Simplified 40.6%

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

9. Final simplification 40.6%

   \[\leadsto x1 + \left(x2 \cdot -6 + x1 \cdot -2\right) \]
10. Add Preprocessing

Alternative 24: 14.4% accurate, 63.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x1, x2):
	return -x1

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.4%

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

3. Taylor expanded in x1 around 0 51.2%

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

4. Taylor expanded in x1 around 0 67.7%

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

5. Taylor expanded in x1 around 0 58.0%

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

6. Taylor expanded in x2 around 0 11.8%

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

   1. distribute-rgt1-in 11.8%

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

   2. metadata-eval 11.8%

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

   3. neg-mul-1 11.8%

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

8. Simplified 11.8%

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

9. Final simplification 11.8%

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

Alternative 25: 3.5% accurate, 127.0× speedup

Math

\[\begin{array}{l} \\ 9 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 9.0)

C

double code(double x1, double x2) {
	return 9.0;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = 9.0d0
end function

Java

public static double code(double x1, double x2) {
	return 9.0;
}

Python

def code(x1, x2):
	return 9.0

Julia

function code(x1, x2)
	return 9.0
end

MATLAB

function tmp = code(x1, x2)
	tmp = 9.0;
end

Wolfram

code[x1_, x2_] := 9.0

Derivation

1. Initial program 73.4%

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

3. Taylor expanded in x1 around 0 51.2%

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

4. Taylor expanded in x1 around inf 22.8%

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

5. Taylor expanded in x1 around 0 3.3%

   \[\leadsto \color{blue}{9} \]

6. Final simplification 3.3%

   \[\leadsto 9 \]
7. 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))))))