Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.8% → 99.4%

Time: 1.1min

Alternatives: 25

Speedup: 5.1×

• 46.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 70.8% 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: 99.4% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (- (+ t_0 (* 2.0 x2)) x1))
        (t_2 (/ t_1 (- -1.0 (* x1 x1))))
        (t_3 (fma x1 (* x1 3.0) (* 2.0 x2)))
        (t_4 (/ (- t_3 x1) (fma x1 x1 1.0)))
        (t_5 (+ (* x1 x1) 1.0))
        (t_6 (/ t_1 t_5))
        (t_7 (/ (- x1 t_3) (fma x1 x1 1.0)))
        (t_8 (* 3.0 (* x1 x1))))
   (if (<=
        (+
         x1
         (+
          (+
           x1
           (+
            (+
             (*
              t_5
              (+
               (* (* (* x1 2.0) t_2) (+ 3.0 t_2))
               (* (* x1 x1) (- (* t_6 4.0) 6.0))))
             (* t_0 t_6))
            (* x1 (* x1 x1))))
          (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_5))))
        INFINITY)
     (+
      x1
      (fma
       3.0
       (/ (- t_8 (fma 2.0 x2 x1)) (fma x1 x1 1.0))
       (+
        x1
        (fma
         (fma x1 x1 1.0)
         (fma x1 (* x1 (fma t_4 4.0 -6.0)) (* (* x1 (* 2.0 t_7)) (- t_7 -3.0)))
         (fma t_8 t_4 (pow x1 3.0))))))
     (+ x1 (* 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)) - x1;
	double t_2 = t_1 / (-1.0 - (x1 * x1));
	double t_3 = fma(x1, (x1 * 3.0), (2.0 * x2));
	double t_4 = (t_3 - x1) / fma(x1, x1, 1.0);
	double t_5 = (x1 * x1) + 1.0;
	double t_6 = t_1 / t_5;
	double t_7 = (x1 - t_3) / fma(x1, x1, 1.0);
	double t_8 = 3.0 * (x1 * x1);
	double tmp;
	if ((x1 + ((x1 + (((t_5 * ((((x1 * 2.0) * t_2) * (3.0 + t_2)) + ((x1 * x1) * ((t_6 * 4.0) - 6.0)))) + (t_0 * t_6)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_5)))) <= ((double) INFINITY)) {
		tmp = x1 + fma(3.0, ((t_8 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), (x1 + fma(fma(x1, x1, 1.0), fma(x1, (x1 * fma(t_4, 4.0, -6.0)), ((x1 * (2.0 * t_7)) * (t_7 - -3.0))), fma(t_8, t_4, pow(x1, 3.0)))));
	} else {
		tmp = x1 + (6.0 * pow(x1, 4.0));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(t_0 + Float64(2.0 * x2)) - x1)
	t_2 = Float64(t_1 / Float64(-1.0 - Float64(x1 * x1)))
	t_3 = fma(x1, Float64(x1 * 3.0), Float64(2.0 * x2))
	t_4 = Float64(Float64(t_3 - x1) / fma(x1, x1, 1.0))
	t_5 = Float64(Float64(x1 * x1) + 1.0)
	t_6 = Float64(t_1 / t_5)
	t_7 = Float64(Float64(x1 - t_3) / fma(x1, x1, 1.0))
	t_8 = Float64(3.0 * Float64(x1 * x1))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_5 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(3.0 + t_2)) + Float64(Float64(x1 * x1) * Float64(Float64(t_6 * 4.0) - 6.0)))) + Float64(t_0 * t_6)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_5)))) <= Inf)
		tmp = Float64(x1 + fma(3.0, Float64(Float64(t_8 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), Float64(x1 + fma(fma(x1, x1, 1.0), fma(x1, Float64(x1 * fma(t_4, 4.0, -6.0)), Float64(Float64(x1 * Float64(2.0 * t_7)) * Float64(t_7 - -3.0))), fma(t_8, t_4, (x1 ^ 3.0))))));
	else
		tmp = Float64(x1 + 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[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision] + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$1 / t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x1 - t$95$3), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$5 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(3.0 + t$95$2), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$6 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$6), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(3.0 * N[(N[(t$95$8 - N[(2.0 * x2 + x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * x1 + 1.0), $MachinePrecision] * N[(x1 * N[(x1 * N[(t$95$4 * 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$8 * t$95$4 + N[Power[x1, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.3%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x1 + \mathsf{fma}\left(3, \frac{3 \cdot \left(x1 \cdot x1\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 + \mathsf{fma}\left(\mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, 4, -6\right), \left(x1 \cdot \left(2 \cdot \frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right) \cdot \left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} + -3\right)\right), \mathsf{fma}\left(3 \cdot \left(x1 \cdot x1\right), \frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, {x1}^{3}\right)\right)\right)} \]
   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 20.9%

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

   4. Taylor expanded in x1 around inf 98.8%

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

4. Final simplification 99.4%

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

Alternative 2: 99.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.3%

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

   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 20.9%

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

   4. Taylor expanded in x1 around inf 98.8%

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

4. Final simplification 99.2%

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

Alternative 3: 96.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 + 6 \cdot {x1}^{4}\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \left(t\_2 + 2 \cdot x2\right) - x1\\ t_4 := \frac{t\_3}{t\_0}\\ t_5 := \frac{t\_3}{-1 - x1 \cdot x1}\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -0.004:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t\_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_5\right) \cdot \left(3 + t\_5\right) + \left(x1 \cdot x1\right) \cdot \left(t\_4 \cdot 4 - 6\right)\right) + t\_2 \cdot t\_4\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 9\right)\\ \mathbf{elif}\;x1 \leq 2.85 \cdot 10^{+23}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (+ x1 (* 6.0 (pow x1 4.0))))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (- (+ t_2 (* 2.0 x2)) x1))
        (t_4 (/ t_3 t_0))
        (t_5 (/ t_3 (- -1.0 (* x1 x1)))))
   (if (<= x1 -5e+102)
     t_1
     (if (<= x1 -0.004)
       (+
        x1
        (+
         (+
          x1
          (+
           (+
            (*
             t_0
             (+
              (* (* (* x1 2.0) t_5) (+ 3.0 t_5))
              (* (* x1 x1) (- (* t_4 4.0) 6.0))))
            (* t_2 t_4))
           (* x1 (* x1 x1))))
         9.0))
       (if (<= x1 2.85e+23)
         (+
          x1
          (+
           (* x2 -6.0)
           (+
            (* x1 (- (* x1 9.0) 2.0))
            (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 6.0) 12.0)))))))
         t_1)))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 + (6.0 * pow(x1, 4.0));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = (t_2 + (2.0 * x2)) - x1;
	double t_4 = t_3 / t_0;
	double t_5 = t_3 / (-1.0 - (x1 * x1));
	double tmp;
	if (x1 <= -5e+102) {
		tmp = t_1;
	} else if (x1 <= -0.004) {
		tmp = x1 + ((x1 + (((t_0 * ((((x1 * 2.0) * t_5) * (3.0 + t_5)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + (t_2 * t_4)) + (x1 * (x1 * x1)))) + 9.0);
	} else if (x1 <= 2.85e+23) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 + (6.0d0 * (x1 ** 4.0d0))
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = (t_2 + (2.0d0 * x2)) - x1
    t_4 = t_3 / t_0
    t_5 = t_3 / ((-1.0d0) - (x1 * x1))
    if (x1 <= (-5d+102)) then
        tmp = t_1
    else if (x1 <= (-0.004d0)) then
        tmp = x1 + ((x1 + (((t_0 * ((((x1 * 2.0d0) * t_5) * (3.0d0 + t_5)) + ((x1 * x1) * ((t_4 * 4.0d0) - 6.0d0)))) + (t_2 * t_4)) + (x1 * (x1 * x1)))) + 9.0d0)
    else if (x1 <= 2.85d+23) then
        tmp = x1 + ((x2 * (-6.0d0)) + ((x1 * ((x1 * 9.0d0) - 2.0d0)) + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 6.0d0) - 12.0d0))))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 + (6.0 * Math.pow(x1, 4.0));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = (t_2 + (2.0 * x2)) - x1;
	double t_4 = t_3 / t_0;
	double t_5 = t_3 / (-1.0 - (x1 * x1));
	double tmp;
	if (x1 <= -5e+102) {
		tmp = t_1;
	} else if (x1 <= -0.004) {
		tmp = x1 + ((x1 + (((t_0 * ((((x1 * 2.0) * t_5) * (3.0 + t_5)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + (t_2 * t_4)) + (x1 * (x1 * x1)))) + 9.0);
	} else if (x1 <= 2.85e+23) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 + (6.0 * math.pow(x1, 4.0))
	t_2 = x1 * (x1 * 3.0)
	t_3 = (t_2 + (2.0 * x2)) - x1
	t_4 = t_3 / t_0
	t_5 = t_3 / (-1.0 - (x1 * x1))
	tmp = 0
	if x1 <= -5e+102:
		tmp = t_1
	elif x1 <= -0.004:
		tmp = x1 + ((x1 + (((t_0 * ((((x1 * 2.0) * t_5) * (3.0 + t_5)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + (t_2 * t_4)) + (x1 * (x1 * x1)))) + 9.0)
	elif x1 <= 2.85e+23:
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 + Float64(6.0 * (x1 ^ 4.0)))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(t_2 + Float64(2.0 * x2)) - x1)
	t_4 = Float64(t_3 / t_0)
	t_5 = Float64(t_3 / Float64(-1.0 - Float64(x1 * x1)))
	tmp = 0.0
	if (x1 <= -5e+102)
		tmp = t_1;
	elseif (x1 <= -0.004)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_0 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_5) * Float64(3.0 + t_5)) + Float64(Float64(x1 * x1) * Float64(Float64(t_4 * 4.0) - 6.0)))) + Float64(t_2 * t_4)) + Float64(x1 * Float64(x1 * x1)))) + 9.0));
	elseif (x1 <= 2.85e+23)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0)) + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 + (6.0 * (x1 ^ 4.0));
	t_2 = x1 * (x1 * 3.0);
	t_3 = (t_2 + (2.0 * x2)) - x1;
	t_4 = t_3 / t_0;
	t_5 = t_3 / (-1.0 - (x1 * x1));
	tmp = 0.0;
	if (x1 <= -5e+102)
		tmp = t_1;
	elseif (x1 <= -0.004)
		tmp = x1 + ((x1 + (((t_0 * ((((x1 * 2.0) * t_5) * (3.0 + t_5)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + (t_2 * t_4)) + (x1 * (x1 * x1)))) + 9.0);
	elseif (x1 <= 2.85e+23)
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 / t$95$0), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$3 / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5e+102], t$95$1, If[LessEqual[x1, -0.004], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$0 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$5), $MachinePrecision] * N[(3.0 + t$95$5), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$4 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.85e+23], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5e102 or 2.85e23 < x1

   1. Initial program 19.8%

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

   3. Taylor expanded in x1 around inf 34.8%

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

   4. Taylor expanded in x1 around inf 98.2%

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

   if -5e102 < x1 < -0.0040000000000000001

   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 95.8%

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

   if -0.0040000000000000001 < x1 < 2.85e23

   1. Initial program 98.5%

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

   3. Taylor expanded in x1 around 0 84.9%

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

   4. Taylor expanded in x1 around 0 84.7%

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

   5. Taylor expanded in x2 around 0 98.4%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 + 6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq -0.004:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 9\right)\\ \mathbf{elif}\;x1 \leq 2.85 \cdot 10^{+23}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + 6 \cdot {x1}^{4}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 - x1 \cdot x1\\ t_1 := x1 + 6 \cdot {x1}^{4}\\ t_2 := 3 + \frac{-1 - \frac{3 - 2 \cdot x2}{x1}}{x1}\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := \frac{\left(t\_3 + 2 \cdot x2\right) - x1}{t\_0}\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -0.86:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_4\right) + \left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(3 + t\_4\right)\right) \cdot t\_0 + t\_3 \cdot t\_2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.85 \cdot 10^{+23}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- -1.0 (* x1 x1)))
        (t_1 (+ x1 (* 6.0 (pow x1 4.0))))
        (t_2 (+ 3.0 (/ (- -1.0 (/ (- 3.0 (* 2.0 x2)) x1)) x1)))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (/ (- (+ t_3 (* 2.0 x2)) x1) t_0)))
   (if (<= x1 -5e+102)
     t_1
     (if (<= x1 -0.86)
       (+
        x1
        (+
         9.0
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (*
             (+
              (* (* x1 x1) (+ 6.0 (* 4.0 t_4)))
              (* (* (* x1 2.0) t_2) (+ 3.0 t_4)))
             t_0)
            (* t_3 t_2))))))
       (if (<= x1 2.85e+23)
         (+
          x1
          (+
           (* x2 -6.0)
           (+
            (* x1 (- (* x1 9.0) 2.0))
            (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 6.0) 12.0)))))))
         t_1)))))

C

double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = x1 + (6.0 * pow(x1, 4.0));
	double t_2 = 3.0 + ((-1.0 - ((3.0 - (2.0 * x2)) / x1)) / x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	double tmp;
	if (x1 <= -5e+102) {
		tmp = t_1;
	} else if (x1 <= -0.86) {
		tmp = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + (((((x1 * x1) * (6.0 + (4.0 * t_4))) + (((x1 * 2.0) * t_2) * (3.0 + t_4))) * t_0) + (t_3 * t_2)))));
	} else if (x1 <= 2.85e+23) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = (-1.0d0) - (x1 * x1)
    t_1 = x1 + (6.0d0 * (x1 ** 4.0d0))
    t_2 = 3.0d0 + (((-1.0d0) - ((3.0d0 - (2.0d0 * x2)) / x1)) / x1)
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = ((t_3 + (2.0d0 * x2)) - x1) / t_0
    if (x1 <= (-5d+102)) then
        tmp = t_1
    else if (x1 <= (-0.86d0)) then
        tmp = x1 + (9.0d0 + (x1 + ((x1 * (x1 * x1)) + (((((x1 * x1) * (6.0d0 + (4.0d0 * t_4))) + (((x1 * 2.0d0) * t_2) * (3.0d0 + t_4))) * t_0) + (t_3 * t_2)))))
    else if (x1 <= 2.85d+23) then
        tmp = x1 + ((x2 * (-6.0d0)) + ((x1 * ((x1 * 9.0d0) - 2.0d0)) + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 6.0d0) - 12.0d0))))))
    else
        tmp = 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 = x1 + (6.0 * Math.pow(x1, 4.0));
	double t_2 = 3.0 + ((-1.0 - ((3.0 - (2.0 * x2)) / x1)) / x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	double tmp;
	if (x1 <= -5e+102) {
		tmp = t_1;
	} else if (x1 <= -0.86) {
		tmp = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + (((((x1 * x1) * (6.0 + (4.0 * t_4))) + (((x1 * 2.0) * t_2) * (3.0 + t_4))) * t_0) + (t_3 * t_2)))));
	} else if (x1 <= 2.85e+23) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = -1.0 - (x1 * x1)
	t_1 = x1 + (6.0 * math.pow(x1, 4.0))
	t_2 = 3.0 + ((-1.0 - ((3.0 - (2.0 * x2)) / x1)) / x1)
	t_3 = x1 * (x1 * 3.0)
	t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0
	tmp = 0
	if x1 <= -5e+102:
		tmp = t_1
	elif x1 <= -0.86:
		tmp = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + (((((x1 * x1) * (6.0 + (4.0 * t_4))) + (((x1 * 2.0) * t_2) * (3.0 + t_4))) * t_0) + (t_3 * t_2)))))
	elif x1 <= 2.85e+23:
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(-1.0 - Float64(x1 * x1))
	t_1 = Float64(x1 + Float64(6.0 * (x1 ^ 4.0)))
	t_2 = Float64(3.0 + Float64(Float64(-1.0 - Float64(Float64(3.0 - Float64(2.0 * x2)) / x1)) / x1))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(Float64(Float64(t_3 + Float64(2.0 * x2)) - x1) / t_0)
	tmp = 0.0
	if (x1 <= -5e+102)
		tmp = t_1;
	elseif (x1 <= -0.86)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_4))) + Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(3.0 + t_4))) * t_0) + Float64(t_3 * t_2))))));
	elseif (x1 <= 2.85e+23)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0)) + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = -1.0 - (x1 * x1);
	t_1 = x1 + (6.0 * (x1 ^ 4.0));
	t_2 = 3.0 + ((-1.0 - ((3.0 - (2.0 * x2)) / x1)) / x1);
	t_3 = x1 * (x1 * 3.0);
	t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	tmp = 0.0;
	if (x1 <= -5e+102)
		tmp = t_1;
	elseif (x1 <= -0.86)
		tmp = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + (((((x1 * x1) * (6.0 + (4.0 * t_4))) + (((x1 * 2.0) * t_2) * (3.0 + t_4))) * t_0) + (t_3 * t_2)))));
	elseif (x1 <= 2.85e+23)
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	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[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 + N[(N[(-1.0 - N[(N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[LessEqual[x1, -5e+102], t$95$1, If[LessEqual[x1, -0.86], N[(x1 + N[(9.0 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(3.0 + t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision] + N[(t$95$3 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.85e+23], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5e102 or 2.85e23 < x1

   1. Initial program 19.8%

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

   3. Taylor expanded in x1 around inf 34.8%

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

   4. Taylor expanded in x1 around inf 98.2%

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

   if -5e102 < x1 < -0.859999999999999987

   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 93.4%

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

   4. Taylor expanded in x1 around inf 93.1%

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

   5. Taylor expanded in x1 around -inf 93.4%

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

   if -0.859999999999999987 < x1 < 2.85e23

   1. Initial program 98.5%

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

   3. Taylor expanded in x1 around 0 84.9%

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

   4. Taylor expanded in x1 around 0 84.7%

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

   5. Taylor expanded in x2 around 0 98.4%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 + 6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq -0.86:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) + \left(\left(x1 \cdot 2\right) \cdot \left(3 + \frac{-1 - \frac{3 - 2 \cdot x2}{x1}}{x1}\right)\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 + \frac{-1 - \frac{3 - 2 \cdot x2}{x1}}{x1}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.85 \cdot 10^{+23}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + 6 \cdot {x1}^{4}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + 6 \cdot {x1}^{4}\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := -1 - x1 \cdot x1\\ t_3 := \left(t\_1 + 2 \cdot x2\right) - x1\\ t_4 := \frac{t\_3}{x1 \cdot x1 + 1}\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -0.62:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_1 \cdot t\_4 + \left(\frac{x2 \cdot 4}{x1} \cdot \left(3 + \frac{t\_3}{t\_2}\right) - \left(x1 \cdot x1\right) \cdot \left(t\_4 \cdot 4 - 6\right)\right) \cdot t\_2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.85 \cdot 10^{+23}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* 6.0 (pow x1 4.0))))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (- -1.0 (* x1 x1)))
        (t_3 (- (+ t_1 (* 2.0 x2)) x1))
        (t_4 (/ t_3 (+ (* x1 x1) 1.0))))
   (if (<= x1 -5e+102)
     t_0
     (if (<= x1 -0.62)
       (+
        x1
        (+
         9.0
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* t_1 t_4)
            (*
             (-
              (* (/ (* x2 4.0) x1) (+ 3.0 (/ t_3 t_2)))
              (* (* x1 x1) (- (* t_4 4.0) 6.0)))
             t_2))))))
       (if (<= x1 2.85e+23)
         (+
          x1
          (+
           (* x2 -6.0)
           (+
            (* x1 (- (* x1 9.0) 2.0))
            (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 6.0) 12.0)))))))
         t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (6.0 * pow(x1, 4.0));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = -1.0 - (x1 * x1);
	double t_3 = (t_1 + (2.0 * x2)) - x1;
	double t_4 = t_3 / ((x1 * x1) + 1.0);
	double tmp;
	if (x1 <= -5e+102) {
		tmp = t_0;
	} else if (x1 <= -0.62) {
		tmp = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_4) + (((((x2 * 4.0) / x1) * (3.0 + (t_3 / t_2))) - ((x1 * x1) * ((t_4 * 4.0) - 6.0))) * t_2)))));
	} else if (x1 <= 2.85e+23) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = x1 + (6.0d0 * (x1 ** 4.0d0))
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (-1.0d0) - (x1 * x1)
    t_3 = (t_1 + (2.0d0 * x2)) - x1
    t_4 = t_3 / ((x1 * x1) + 1.0d0)
    if (x1 <= (-5d+102)) then
        tmp = t_0
    else if (x1 <= (-0.62d0)) then
        tmp = x1 + (9.0d0 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_4) + (((((x2 * 4.0d0) / x1) * (3.0d0 + (t_3 / t_2))) - ((x1 * x1) * ((t_4 * 4.0d0) - 6.0d0))) * t_2)))))
    else if (x1 <= 2.85d+23) then
        tmp = x1 + ((x2 * (-6.0d0)) + ((x1 * ((x1 * 9.0d0) - 2.0d0)) + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 6.0d0) - 12.0d0))))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (6.0 * Math.pow(x1, 4.0));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = -1.0 - (x1 * x1);
	double t_3 = (t_1 + (2.0 * x2)) - x1;
	double t_4 = t_3 / ((x1 * x1) + 1.0);
	double tmp;
	if (x1 <= -5e+102) {
		tmp = t_0;
	} else if (x1 <= -0.62) {
		tmp = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_4) + (((((x2 * 4.0) / x1) * (3.0 + (t_3 / t_2))) - ((x1 * x1) * ((t_4 * 4.0) - 6.0))) * t_2)))));
	} else if (x1 <= 2.85e+23) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (6.0 * math.pow(x1, 4.0))
	t_1 = x1 * (x1 * 3.0)
	t_2 = -1.0 - (x1 * x1)
	t_3 = (t_1 + (2.0 * x2)) - x1
	t_4 = t_3 / ((x1 * x1) + 1.0)
	tmp = 0
	if x1 <= -5e+102:
		tmp = t_0
	elif x1 <= -0.62:
		tmp = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_4) + (((((x2 * 4.0) / x1) * (3.0 + (t_3 / t_2))) - ((x1 * x1) * ((t_4 * 4.0) - 6.0))) * t_2)))))
	elif x1 <= 2.85e+23:
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(6.0 * (x1 ^ 4.0)))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(-1.0 - Float64(x1 * x1))
	t_3 = Float64(Float64(t_1 + Float64(2.0 * x2)) - x1)
	t_4 = Float64(t_3 / Float64(Float64(x1 * x1) + 1.0))
	tmp = 0.0
	if (x1 <= -5e+102)
		tmp = t_0;
	elseif (x1 <= -0.62)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * t_4) + Float64(Float64(Float64(Float64(Float64(x2 * 4.0) / x1) * Float64(3.0 + Float64(t_3 / t_2))) - Float64(Float64(x1 * x1) * Float64(Float64(t_4 * 4.0) - 6.0))) * t_2))))));
	elseif (x1 <= 2.85e+23)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0)) + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)))))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (6.0 * (x1 ^ 4.0));
	t_1 = x1 * (x1 * 3.0);
	t_2 = -1.0 - (x1 * x1);
	t_3 = (t_1 + (2.0 * x2)) - x1;
	t_4 = t_3 / ((x1 * x1) + 1.0);
	tmp = 0.0;
	if (x1 <= -5e+102)
		tmp = t_0;
	elseif (x1 <= -0.62)
		tmp = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_4) + (((((x2 * 4.0) / x1) * (3.0 + (t_3 / t_2))) - ((x1 * x1) * ((t_4 * 4.0) - 6.0))) * t_2)))));
	elseif (x1 <= 2.85e+23)
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5e+102], t$95$0, If[LessEqual[x1, -0.62], N[(x1 + N[(9.0 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * t$95$4), $MachinePrecision] + N[(N[(N[(N[(N[(x2 * 4.0), $MachinePrecision] / x1), $MachinePrecision] * N[(3.0 + N[(t$95$3 / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$4 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.85e+23], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5e102 or 2.85e23 < x1

   1. Initial program 19.8%

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

   3. Taylor expanded in x1 around inf 34.8%

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

   4. Taylor expanded in x1 around inf 98.2%

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

   if -5e102 < x1 < -0.619999999999999996

   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 93.4%

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

   4. Taylor expanded in x1 around inf 93.1%

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

   5. Taylor expanded in x2 around inf 92.7%

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

      1. associate-*r/ 92.7%

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

      2. *-commutative 92.7%

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

   7. Simplified 92.7%

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

   if -0.619999999999999996 < x1 < 2.85e23

   1. Initial program 98.5%

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

   3. Taylor expanded in x1 around 0 84.9%

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

   4. Taylor expanded in x1 around 0 84.7%

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

   5. Taylor expanded in x2 around 0 98.4%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 + 6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq -0.62:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(\frac{x2 \cdot 4}{x1} \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) - \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.85 \cdot 10^{+23}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + 6 \cdot {x1}^{4}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 - x1 \cdot x1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \left(t\_1 + 2 \cdot x2\right) - x1\\ t_3 := \frac{t\_2}{x1 \cdot x1 + 1}\\ t_4 := x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_1 \cdot t\_3 + \left(\frac{x2 \cdot 4}{x1} \cdot \left(3 + \frac{t\_2}{t\_0}\right) - \left(x1 \cdot x1\right) \cdot \left(t\_3 \cdot 4 - 6\right)\right) \cdot t\_0\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x2 \cdot -4 + x1 \cdot \left(2 - x1 \cdot \left(6 + \left(\left(\left(\left(2 \cdot x2 - 3\right) \cdot -2 - \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - x2 \cdot -4\right) - x1 \cdot -6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -0.6:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x1 \leq 102000000:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.5 \cdot 10^{+151}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- -1.0 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (- (+ t_1 (* 2.0 x2)) x1))
        (t_3 (/ t_2 (+ (* x1 x1) 1.0)))
        (t_4
         (+
          x1
          (+
           9.0
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* t_1 t_3)
              (*
               (-
                (* (/ (* x2 4.0) x1) (+ 3.0 (/ t_2 t_0)))
                (* (* x1 x1) (- (* t_3 4.0) 6.0)))
               t_0))))))))
   (if (<= x1 -5e+102)
     (+
      x1
      (+
       9.0
       (+
        x1
        (+
         (* x2 -4.0)
         (*
          x1
          (-
           2.0
           (*
            x1
            (+
             6.0
             (-
              (-
               (- (* (- (* 2.0 x2) 3.0) -2.0) (+ (* x2 6.0) (* x2 8.0)))
               (* x2 -4.0))
              (* x1 -6.0))))))))))
     (if (<= x1 -0.6)
       t_4
       (if (<= x1 102000000.0)
         (+
          x1
          (+
           (* x2 -6.0)
           (+
            (* x1 (- (* x1 9.0) 2.0))
            (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 6.0) 12.0)))))))
         (if (<= x1 8.5e+151)
           t_4
           (- x1 (* x2 (+ 6.0 (/ (* x1 (- 2.0 (* x1 9.0))) x2))))))))))

C

double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (t_1 + (2.0 * x2)) - x1;
	double t_3 = t_2 / ((x1 * x1) + 1.0);
	double t_4 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_3) + (((((x2 * 4.0) / x1) * (3.0 + (t_2 / t_0))) - ((x1 * x1) * ((t_3 * 4.0) - 6.0))) * t_0)))));
	double tmp;
	if (x1 <= -5e+102) {
		tmp = x1 + (9.0 + (x1 + ((x2 * -4.0) + (x1 * (2.0 - (x1 * (6.0 + ((((((2.0 * x2) - 3.0) * -2.0) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))))))));
	} else if (x1 <= -0.6) {
		tmp = t_4;
	} else if (x1 <= 102000000.0) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else if (x1 <= 8.5e+151) {
		tmp = t_4;
	} else {
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / 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 = (-1.0d0) - (x1 * x1)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (t_1 + (2.0d0 * x2)) - x1
    t_3 = t_2 / ((x1 * x1) + 1.0d0)
    t_4 = x1 + (9.0d0 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_3) + (((((x2 * 4.0d0) / x1) * (3.0d0 + (t_2 / t_0))) - ((x1 * x1) * ((t_3 * 4.0d0) - 6.0d0))) * t_0)))))
    if (x1 <= (-5d+102)) then
        tmp = x1 + (9.0d0 + (x1 + ((x2 * (-4.0d0)) + (x1 * (2.0d0 - (x1 * (6.0d0 + ((((((2.0d0 * x2) - 3.0d0) * (-2.0d0)) - ((x2 * 6.0d0) + (x2 * 8.0d0))) - (x2 * (-4.0d0))) - (x1 * (-6.0d0))))))))))
    else if (x1 <= (-0.6d0)) then
        tmp = t_4
    else if (x1 <= 102000000.0d0) then
        tmp = x1 + ((x2 * (-6.0d0)) + ((x1 * ((x1 * 9.0d0) - 2.0d0)) + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 6.0d0) - 12.0d0))))))
    else if (x1 <= 8.5d+151) then
        tmp = t_4
    else
        tmp = x1 - (x2 * (6.0d0 + ((x1 * (2.0d0 - (x1 * 9.0d0))) / x2)))
    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 * 3.0);
	double t_2 = (t_1 + (2.0 * x2)) - x1;
	double t_3 = t_2 / ((x1 * x1) + 1.0);
	double t_4 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_3) + (((((x2 * 4.0) / x1) * (3.0 + (t_2 / t_0))) - ((x1 * x1) * ((t_3 * 4.0) - 6.0))) * t_0)))));
	double tmp;
	if (x1 <= -5e+102) {
		tmp = x1 + (9.0 + (x1 + ((x2 * -4.0) + (x1 * (2.0 - (x1 * (6.0 + ((((((2.0 * x2) - 3.0) * -2.0) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))))))));
	} else if (x1 <= -0.6) {
		tmp = t_4;
	} else if (x1 <= 102000000.0) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else if (x1 <= 8.5e+151) {
		tmp = t_4;
	} else {
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = -1.0 - (x1 * x1)
	t_1 = x1 * (x1 * 3.0)
	t_2 = (t_1 + (2.0 * x2)) - x1
	t_3 = t_2 / ((x1 * x1) + 1.0)
	t_4 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_3) + (((((x2 * 4.0) / x1) * (3.0 + (t_2 / t_0))) - ((x1 * x1) * ((t_3 * 4.0) - 6.0))) * t_0)))))
	tmp = 0
	if x1 <= -5e+102:
		tmp = x1 + (9.0 + (x1 + ((x2 * -4.0) + (x1 * (2.0 - (x1 * (6.0 + ((((((2.0 * x2) - 3.0) * -2.0) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))))))))
	elif x1 <= -0.6:
		tmp = t_4
	elif x1 <= 102000000.0:
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))))
	elif x1 <= 8.5e+151:
		tmp = t_4
	else:
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(-1.0 - Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(t_1 + Float64(2.0 * x2)) - x1)
	t_3 = Float64(t_2 / Float64(Float64(x1 * x1) + 1.0))
	t_4 = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * t_3) + Float64(Float64(Float64(Float64(Float64(x2 * 4.0) / x1) * Float64(3.0 + Float64(t_2 / t_0))) - Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0))) * t_0))))))
	tmp = 0.0
	if (x1 <= -5e+102)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(Float64(x2 * -4.0) + Float64(x1 * Float64(2.0 - Float64(x1 * Float64(6.0 + Float64(Float64(Float64(Float64(Float64(Float64(2.0 * x2) - 3.0) * -2.0) - Float64(Float64(x2 * 6.0) + Float64(x2 * 8.0))) - Float64(x2 * -4.0)) - Float64(x1 * -6.0))))))))));
	elseif (x1 <= -0.6)
		tmp = t_4;
	elseif (x1 <= 102000000.0)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0)) + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)))))));
	elseif (x1 <= 8.5e+151)
		tmp = t_4;
	else
		tmp = Float64(x1 - Float64(x2 * Float64(6.0 + Float64(Float64(x1 * Float64(2.0 - Float64(x1 * 9.0))) / x2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = -1.0 - (x1 * x1);
	t_1 = x1 * (x1 * 3.0);
	t_2 = (t_1 + (2.0 * x2)) - x1;
	t_3 = t_2 / ((x1 * x1) + 1.0);
	t_4 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_3) + (((((x2 * 4.0) / x1) * (3.0 + (t_2 / t_0))) - ((x1 * x1) * ((t_3 * 4.0) - 6.0))) * t_0)))));
	tmp = 0.0;
	if (x1 <= -5e+102)
		tmp = x1 + (9.0 + (x1 + ((x2 * -4.0) + (x1 * (2.0 - (x1 * (6.0 + ((((((2.0 * x2) - 3.0) * -2.0) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))))))));
	elseif (x1 <= -0.6)
		tmp = t_4;
	elseif (x1 <= 102000000.0)
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	elseif (x1 <= 8.5e+151)
		tmp = t_4;
	else
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(9.0 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * t$95$3), $MachinePrecision] + N[(N[(N[(N[(N[(x2 * 4.0), $MachinePrecision] / x1), $MachinePrecision] * N[(3.0 + N[(t$95$2 / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5e+102], N[(x1 + N[(9.0 + N[(x1 + N[(N[(x2 * -4.0), $MachinePrecision] + N[(x1 * N[(2.0 - N[(x1 * N[(6.0 + N[(N[(N[(N[(N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision] * -2.0), $MachinePrecision] - N[(N[(x2 * 6.0), $MachinePrecision] + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision] - N[(x1 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -0.6], t$95$4, If[LessEqual[x1, 102000000.0], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 8.5e+151], t$95$4, N[(x1 - N[(x2 * N[(6.0 + N[(N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x2), $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 0.0%

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

   4. Taylor expanded in x1 around inf 0.0%

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

   5. Taylor expanded in x1 around 0 92.0%

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

   if -5e102 < x1 < -0.599999999999999978 or 1.02e8 < x1 < 8.50000000000000051e151

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around -inf 96.7%

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

   4. Taylor expanded in x1 around inf 96.6%

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

   5. Taylor expanded in x2 around inf 96.4%

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

      1. associate-*r/ 96.4%

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

      2. *-commutative 96.4%

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

   7. Simplified 96.4%

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

   if -0.599999999999999978 < x1 < 1.02e8

   1. Initial program 98.5%

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

   3. Taylor expanded in x1 around 0 85.4%

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

   4. Taylor expanded in x1 around 0 85.1%

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

   5. Taylor expanded in x2 around 0 99.1%

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

   if 8.50000000000000051e151 < x1

   1. Initial program 3.1%

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

   3. Taylor expanded in x1 around 0 0.1%

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

   4. Taylor expanded in x1 around 0 87.9%

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

   5. Taylor expanded in x2 around 0 97.3%

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

      1. *-commutative 97.3%

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

   7. Simplified 97.3%

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

   8. Taylor expanded in x2 around inf 100.0%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x2 \cdot -4 + x1 \cdot \left(2 - x1 \cdot \left(6 + \left(\left(\left(\left(2 \cdot x2 - 3\right) \cdot -2 - \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - x2 \cdot -4\right) - x1 \cdot -6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -0.6:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(\frac{x2 \cdot 4}{x1} \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) - \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 102000000:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.5 \cdot 10^{+151}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(\frac{x2 \cdot 4}{x1} \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) - \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 94.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 - x1 \cdot x1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \left(t\_1 + 2 \cdot x2\right) - x1\\ t_3 := \frac{t\_2}{x1 \cdot x1 + 1}\\ t_4 := x1 + \left(9 - \left(\left(\left(t\_1 \cdot \frac{t\_2}{t\_0} + \left(\left(x1 \cdot x1\right) \cdot \left(t\_3 \cdot 4 - 6\right) + \left(t\_3 - 3\right) \cdot \left(x1 \cdot 6\right)\right) \cdot t\_0\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x2 \cdot -4 + x1 \cdot \left(2 - x1 \cdot \left(6 + \left(\left(\left(\left(2 \cdot x2 - 3\right) \cdot -2 - \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - x2 \cdot -4\right) - x1 \cdot -6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2.4:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x1 \leq 2.85 \cdot 10^{+23}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.5 \cdot 10^{+151}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- -1.0 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (- (+ t_1 (* 2.0 x2)) x1))
        (t_3 (/ t_2 (+ (* x1 x1) 1.0)))
        (t_4
         (+
          x1
          (-
           9.0
           (-
            (-
             (+
              (* t_1 (/ t_2 t_0))
              (*
               (+ (* (* x1 x1) (- (* t_3 4.0) 6.0)) (* (- t_3 3.0) (* x1 6.0)))
               t_0))
             (* x1 (* x1 x1)))
            x1)))))
   (if (<= x1 -5e+102)
     (+
      x1
      (+
       9.0
       (+
        x1
        (+
         (* x2 -4.0)
         (*
          x1
          (-
           2.0
           (*
            x1
            (+
             6.0
             (-
              (-
               (- (* (- (* 2.0 x2) 3.0) -2.0) (+ (* x2 6.0) (* x2 8.0)))
               (* x2 -4.0))
              (* x1 -6.0))))))))))
     (if (<= x1 -2.4)
       t_4
       (if (<= x1 2.85e+23)
         (+
          x1
          (+
           (* x2 -6.0)
           (+
            (* x1 (- (* x1 9.0) 2.0))
            (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 6.0) 12.0)))))))
         (if (<= x1 8.5e+151)
           t_4
           (- x1 (* x2 (+ 6.0 (/ (* x1 (- 2.0 (* x1 9.0))) x2))))))))))

C

double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (t_1 + (2.0 * x2)) - x1;
	double t_3 = t_2 / ((x1 * x1) + 1.0);
	double t_4 = x1 + (9.0 - ((((t_1 * (t_2 / t_0)) + ((((x1 * x1) * ((t_3 * 4.0) - 6.0)) + ((t_3 - 3.0) * (x1 * 6.0))) * t_0)) - (x1 * (x1 * x1))) - x1));
	double tmp;
	if (x1 <= -5e+102) {
		tmp = x1 + (9.0 + (x1 + ((x2 * -4.0) + (x1 * (2.0 - (x1 * (6.0 + ((((((2.0 * x2) - 3.0) * -2.0) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))))))));
	} else if (x1 <= -2.4) {
		tmp = t_4;
	} else if (x1 <= 2.85e+23) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else if (x1 <= 8.5e+151) {
		tmp = t_4;
	} else {
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / 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 = (-1.0d0) - (x1 * x1)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (t_1 + (2.0d0 * x2)) - x1
    t_3 = t_2 / ((x1 * x1) + 1.0d0)
    t_4 = x1 + (9.0d0 - ((((t_1 * (t_2 / t_0)) + ((((x1 * x1) * ((t_3 * 4.0d0) - 6.0d0)) + ((t_3 - 3.0d0) * (x1 * 6.0d0))) * t_0)) - (x1 * (x1 * x1))) - x1))
    if (x1 <= (-5d+102)) then
        tmp = x1 + (9.0d0 + (x1 + ((x2 * (-4.0d0)) + (x1 * (2.0d0 - (x1 * (6.0d0 + ((((((2.0d0 * x2) - 3.0d0) * (-2.0d0)) - ((x2 * 6.0d0) + (x2 * 8.0d0))) - (x2 * (-4.0d0))) - (x1 * (-6.0d0))))))))))
    else if (x1 <= (-2.4d0)) then
        tmp = t_4
    else if (x1 <= 2.85d+23) then
        tmp = x1 + ((x2 * (-6.0d0)) + ((x1 * ((x1 * 9.0d0) - 2.0d0)) + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 6.0d0) - 12.0d0))))))
    else if (x1 <= 8.5d+151) then
        tmp = t_4
    else
        tmp = x1 - (x2 * (6.0d0 + ((x1 * (2.0d0 - (x1 * 9.0d0))) / x2)))
    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 * 3.0);
	double t_2 = (t_1 + (2.0 * x2)) - x1;
	double t_3 = t_2 / ((x1 * x1) + 1.0);
	double t_4 = x1 + (9.0 - ((((t_1 * (t_2 / t_0)) + ((((x1 * x1) * ((t_3 * 4.0) - 6.0)) + ((t_3 - 3.0) * (x1 * 6.0))) * t_0)) - (x1 * (x1 * x1))) - x1));
	double tmp;
	if (x1 <= -5e+102) {
		tmp = x1 + (9.0 + (x1 + ((x2 * -4.0) + (x1 * (2.0 - (x1 * (6.0 + ((((((2.0 * x2) - 3.0) * -2.0) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))))))));
	} else if (x1 <= -2.4) {
		tmp = t_4;
	} else if (x1 <= 2.85e+23) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else if (x1 <= 8.5e+151) {
		tmp = t_4;
	} else {
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = -1.0 - (x1 * x1)
	t_1 = x1 * (x1 * 3.0)
	t_2 = (t_1 + (2.0 * x2)) - x1
	t_3 = t_2 / ((x1 * x1) + 1.0)
	t_4 = x1 + (9.0 - ((((t_1 * (t_2 / t_0)) + ((((x1 * x1) * ((t_3 * 4.0) - 6.0)) + ((t_3 - 3.0) * (x1 * 6.0))) * t_0)) - (x1 * (x1 * x1))) - x1))
	tmp = 0
	if x1 <= -5e+102:
		tmp = x1 + (9.0 + (x1 + ((x2 * -4.0) + (x1 * (2.0 - (x1 * (6.0 + ((((((2.0 * x2) - 3.0) * -2.0) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))))))))
	elif x1 <= -2.4:
		tmp = t_4
	elif x1 <= 2.85e+23:
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))))
	elif x1 <= 8.5e+151:
		tmp = t_4
	else:
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(-1.0 - Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(t_1 + Float64(2.0 * x2)) - x1)
	t_3 = Float64(t_2 / Float64(Float64(x1 * x1) + 1.0))
	t_4 = Float64(x1 + Float64(9.0 - Float64(Float64(Float64(Float64(t_1 * Float64(t_2 / t_0)) + Float64(Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0)) + Float64(Float64(t_3 - 3.0) * Float64(x1 * 6.0))) * t_0)) - Float64(x1 * Float64(x1 * x1))) - x1)))
	tmp = 0.0
	if (x1 <= -5e+102)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(Float64(x2 * -4.0) + Float64(x1 * Float64(2.0 - Float64(x1 * Float64(6.0 + Float64(Float64(Float64(Float64(Float64(Float64(2.0 * x2) - 3.0) * -2.0) - Float64(Float64(x2 * 6.0) + Float64(x2 * 8.0))) - Float64(x2 * -4.0)) - Float64(x1 * -6.0))))))))));
	elseif (x1 <= -2.4)
		tmp = t_4;
	elseif (x1 <= 2.85e+23)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0)) + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)))))));
	elseif (x1 <= 8.5e+151)
		tmp = t_4;
	else
		tmp = Float64(x1 - Float64(x2 * Float64(6.0 + Float64(Float64(x1 * Float64(2.0 - Float64(x1 * 9.0))) / x2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = -1.0 - (x1 * x1);
	t_1 = x1 * (x1 * 3.0);
	t_2 = (t_1 + (2.0 * x2)) - x1;
	t_3 = t_2 / ((x1 * x1) + 1.0);
	t_4 = x1 + (9.0 - ((((t_1 * (t_2 / t_0)) + ((((x1 * x1) * ((t_3 * 4.0) - 6.0)) + ((t_3 - 3.0) * (x1 * 6.0))) * t_0)) - (x1 * (x1 * x1))) - x1));
	tmp = 0.0;
	if (x1 <= -5e+102)
		tmp = x1 + (9.0 + (x1 + ((x2 * -4.0) + (x1 * (2.0 - (x1 * (6.0 + ((((((2.0 * x2) - 3.0) * -2.0) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))))))));
	elseif (x1 <= -2.4)
		tmp = t_4;
	elseif (x1 <= 2.85e+23)
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	elseif (x1 <= 8.5e+151)
		tmp = t_4;
	else
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(9.0 - N[(N[(N[(N[(t$95$1 * N[(t$95$2 / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$3 - 3.0), $MachinePrecision] * N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5e+102], N[(x1 + N[(9.0 + N[(x1 + N[(N[(x2 * -4.0), $MachinePrecision] + N[(x1 * N[(2.0 - N[(x1 * N[(6.0 + N[(N[(N[(N[(N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision] * -2.0), $MachinePrecision] - N[(N[(x2 * 6.0), $MachinePrecision] + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision] - N[(x1 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.4], t$95$4, If[LessEqual[x1, 2.85e+23], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 8.5e+151], t$95$4, N[(x1 - N[(x2 * N[(6.0 + N[(N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x2), $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 0.0%

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

   4. Taylor expanded in x1 around inf 0.0%

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

   5. Taylor expanded in x1 around 0 92.0%

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

   if -5e102 < x1 < -2.39999999999999991 or 2.85e23 < x1 < 8.50000000000000051e151

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around -inf 96.6%

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

   4. Taylor expanded in x1 around inf 96.4%

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

   5. Taylor expanded in x1 around inf 82.7%

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

      1. *-commutative 82.7%

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

   7. Simplified 82.7%

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

   if -2.39999999999999991 < x1 < 2.85e23

   1. Initial program 98.5%

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

   3. Taylor expanded in x1 around 0 84.9%

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

   4. Taylor expanded in x1 around 0 84.7%

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

   5. Taylor expanded in x2 around 0 98.4%

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

   if 8.50000000000000051e151 < x1

   1. Initial program 3.1%

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

   3. Taylor expanded in x1 around 0 0.1%

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

   4. Taylor expanded in x1 around 0 87.9%

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

   5. Taylor expanded in x2 around 0 97.3%

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

      1. *-commutative 97.3%

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

   7. Simplified 97.3%

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

   8. Taylor expanded in x2 around inf 100.0%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x2 \cdot -4 + x1 \cdot \left(2 - x1 \cdot \left(6 + \left(\left(\left(\left(2 \cdot x2 - 3\right) \cdot -2 - \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - x2 \cdot -4\right) - x1 \cdot -6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2.4:\\ \;\;\;\;x1 + \left(9 - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(x1 \cdot 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 2.85 \cdot 10^{+23}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.5 \cdot 10^{+151}:\\ \;\;\;\;x1 + \left(9 - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(x1 \cdot 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 94.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 - x1 \cdot x1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \left(t\_1 + 2 \cdot x2\right) - x1\\ t_3 := \frac{t\_2}{x1 \cdot x1 + 1}\\ t_4 := \frac{t\_2}{t\_0}\\ t_5 := x1 \cdot \left(x1 \cdot x1\right)\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x2 \cdot -4 + x1 \cdot \left(2 - x1 \cdot \left(6 + \left(\left(\left(\left(2 \cdot x2 - 3\right) \cdot -2 - \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - x2 \cdot -4\right) - x1 \cdot -6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2.4:\\ \;\;\;\;x1 + \left(9 - \left(\left(\left(t\_1 \cdot t\_4 + \left(\left(x1 \cdot x1\right) \cdot \left(t\_3 \cdot 4 - 6\right) + \left(t\_3 - 3\right) \cdot \left(x1 \cdot 6\right)\right) \cdot t\_0\right) - t\_5\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 2.85 \cdot 10^{+23}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.5 \cdot 10^{+151}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(t\_5 + \left(t\_1 \cdot t\_3 + \left(\frac{-1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot t\_4\right) - \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(3 + \frac{-1 - \frac{3 - 2 \cdot x2}{x1}}{x1}\right) - 6\right)\right) \cdot t\_0\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- -1.0 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (- (+ t_1 (* 2.0 x2)) x1))
        (t_3 (/ t_2 (+ (* x1 x1) 1.0)))
        (t_4 (/ t_2 t_0))
        (t_5 (* x1 (* x1 x1))))
   (if (<= x1 -5e+102)
     (+
      x1
      (+
       9.0
       (+
        x1
        (+
         (* x2 -4.0)
         (*
          x1
          (-
           2.0
           (*
            x1
            (+
             6.0
             (-
              (-
               (- (* (- (* 2.0 x2) 3.0) -2.0) (+ (* x2 6.0) (* x2 8.0)))
               (* x2 -4.0))
              (* x1 -6.0))))))))))
     (if (<= x1 -2.4)
       (+
        x1
        (-
         9.0
         (-
          (-
           (+
            (* t_1 t_4)
            (*
             (+ (* (* x1 x1) (- (* t_3 4.0) 6.0)) (* (- t_3 3.0) (* x1 6.0)))
             t_0))
           t_5)
          x1)))
       (if (<= x1 2.85e+23)
         (+
          x1
          (+
           (* x2 -6.0)
           (+
            (* x1 (- (* x1 9.0) 2.0))
            (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 6.0) 12.0)))))))
         (if (<= x1 8.5e+151)
           (+
            x1
            (+
             9.0
             (+
              x1
              (+
               t_5
               (+
                (* t_1 t_3)
                (*
                 (-
                  (* (/ -1.0 x1) (* (* x1 2.0) t_4))
                  (*
                   (* x1 x1)
                   (-
                    (* 4.0 (+ 3.0 (/ (- -1.0 (/ (- 3.0 (* 2.0 x2)) x1)) x1)))
                    6.0)))
                 t_0))))))
           (- x1 (* x2 (+ 6.0 (/ (* x1 (- 2.0 (* x1 9.0))) x2))))))))))

C

double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (t_1 + (2.0 * x2)) - x1;
	double t_3 = t_2 / ((x1 * x1) + 1.0);
	double t_4 = t_2 / t_0;
	double t_5 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -5e+102) {
		tmp = x1 + (9.0 + (x1 + ((x2 * -4.0) + (x1 * (2.0 - (x1 * (6.0 + ((((((2.0 * x2) - 3.0) * -2.0) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))))))));
	} else if (x1 <= -2.4) {
		tmp = x1 + (9.0 - ((((t_1 * t_4) + ((((x1 * x1) * ((t_3 * 4.0) - 6.0)) + ((t_3 - 3.0) * (x1 * 6.0))) * t_0)) - t_5) - x1));
	} else if (x1 <= 2.85e+23) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else if (x1 <= 8.5e+151) {
		tmp = x1 + (9.0 + (x1 + (t_5 + ((t_1 * t_3) + ((((-1.0 / x1) * ((x1 * 2.0) * t_4)) - ((x1 * x1) * ((4.0 * (3.0 + ((-1.0 - ((3.0 - (2.0 * x2)) / x1)) / x1))) - 6.0))) * t_0)))));
	} else {
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / 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) :: t_5
    real(8) :: tmp
    t_0 = (-1.0d0) - (x1 * x1)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (t_1 + (2.0d0 * x2)) - x1
    t_3 = t_2 / ((x1 * x1) + 1.0d0)
    t_4 = t_2 / t_0
    t_5 = x1 * (x1 * x1)
    if (x1 <= (-5d+102)) then
        tmp = x1 + (9.0d0 + (x1 + ((x2 * (-4.0d0)) + (x1 * (2.0d0 - (x1 * (6.0d0 + ((((((2.0d0 * x2) - 3.0d0) * (-2.0d0)) - ((x2 * 6.0d0) + (x2 * 8.0d0))) - (x2 * (-4.0d0))) - (x1 * (-6.0d0))))))))))
    else if (x1 <= (-2.4d0)) then
        tmp = x1 + (9.0d0 - ((((t_1 * t_4) + ((((x1 * x1) * ((t_3 * 4.0d0) - 6.0d0)) + ((t_3 - 3.0d0) * (x1 * 6.0d0))) * t_0)) - t_5) - x1))
    else if (x1 <= 2.85d+23) then
        tmp = x1 + ((x2 * (-6.0d0)) + ((x1 * ((x1 * 9.0d0) - 2.0d0)) + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 6.0d0) - 12.0d0))))))
    else if (x1 <= 8.5d+151) then
        tmp = x1 + (9.0d0 + (x1 + (t_5 + ((t_1 * t_3) + (((((-1.0d0) / x1) * ((x1 * 2.0d0) * t_4)) - ((x1 * x1) * ((4.0d0 * (3.0d0 + (((-1.0d0) - ((3.0d0 - (2.0d0 * x2)) / x1)) / x1))) - 6.0d0))) * t_0)))))
    else
        tmp = x1 - (x2 * (6.0d0 + ((x1 * (2.0d0 - (x1 * 9.0d0))) / x2)))
    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 * 3.0);
	double t_2 = (t_1 + (2.0 * x2)) - x1;
	double t_3 = t_2 / ((x1 * x1) + 1.0);
	double t_4 = t_2 / t_0;
	double t_5 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -5e+102) {
		tmp = x1 + (9.0 + (x1 + ((x2 * -4.0) + (x1 * (2.0 - (x1 * (6.0 + ((((((2.0 * x2) - 3.0) * -2.0) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))))))));
	} else if (x1 <= -2.4) {
		tmp = x1 + (9.0 - ((((t_1 * t_4) + ((((x1 * x1) * ((t_3 * 4.0) - 6.0)) + ((t_3 - 3.0) * (x1 * 6.0))) * t_0)) - t_5) - x1));
	} else if (x1 <= 2.85e+23) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else if (x1 <= 8.5e+151) {
		tmp = x1 + (9.0 + (x1 + (t_5 + ((t_1 * t_3) + ((((-1.0 / x1) * ((x1 * 2.0) * t_4)) - ((x1 * x1) * ((4.0 * (3.0 + ((-1.0 - ((3.0 - (2.0 * x2)) / x1)) / x1))) - 6.0))) * t_0)))));
	} else {
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = -1.0 - (x1 * x1)
	t_1 = x1 * (x1 * 3.0)
	t_2 = (t_1 + (2.0 * x2)) - x1
	t_3 = t_2 / ((x1 * x1) + 1.0)
	t_4 = t_2 / t_0
	t_5 = x1 * (x1 * x1)
	tmp = 0
	if x1 <= -5e+102:
		tmp = x1 + (9.0 + (x1 + ((x2 * -4.0) + (x1 * (2.0 - (x1 * (6.0 + ((((((2.0 * x2) - 3.0) * -2.0) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))))))))
	elif x1 <= -2.4:
		tmp = x1 + (9.0 - ((((t_1 * t_4) + ((((x1 * x1) * ((t_3 * 4.0) - 6.0)) + ((t_3 - 3.0) * (x1 * 6.0))) * t_0)) - t_5) - x1))
	elif x1 <= 2.85e+23:
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))))
	elif x1 <= 8.5e+151:
		tmp = x1 + (9.0 + (x1 + (t_5 + ((t_1 * t_3) + ((((-1.0 / x1) * ((x1 * 2.0) * t_4)) - ((x1 * x1) * ((4.0 * (3.0 + ((-1.0 - ((3.0 - (2.0 * x2)) / x1)) / x1))) - 6.0))) * t_0)))))
	else:
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(-1.0 - Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(t_1 + Float64(2.0 * x2)) - x1)
	t_3 = Float64(t_2 / Float64(Float64(x1 * x1) + 1.0))
	t_4 = Float64(t_2 / t_0)
	t_5 = Float64(x1 * Float64(x1 * x1))
	tmp = 0.0
	if (x1 <= -5e+102)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(Float64(x2 * -4.0) + Float64(x1 * Float64(2.0 - Float64(x1 * Float64(6.0 + Float64(Float64(Float64(Float64(Float64(Float64(2.0 * x2) - 3.0) * -2.0) - Float64(Float64(x2 * 6.0) + Float64(x2 * 8.0))) - Float64(x2 * -4.0)) - Float64(x1 * -6.0))))))))));
	elseif (x1 <= -2.4)
		tmp = Float64(x1 + Float64(9.0 - Float64(Float64(Float64(Float64(t_1 * t_4) + Float64(Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0)) + Float64(Float64(t_3 - 3.0) * Float64(x1 * 6.0))) * t_0)) - t_5) - x1)));
	elseif (x1 <= 2.85e+23)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0)) + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)))))));
	elseif (x1 <= 8.5e+151)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_5 + Float64(Float64(t_1 * t_3) + Float64(Float64(Float64(Float64(-1.0 / x1) * Float64(Float64(x1 * 2.0) * t_4)) - Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(3.0 + Float64(Float64(-1.0 - Float64(Float64(3.0 - Float64(2.0 * x2)) / x1)) / x1))) - 6.0))) * t_0))))));
	else
		tmp = Float64(x1 - Float64(x2 * Float64(6.0 + Float64(Float64(x1 * Float64(2.0 - Float64(x1 * 9.0))) / x2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = -1.0 - (x1 * x1);
	t_1 = x1 * (x1 * 3.0);
	t_2 = (t_1 + (2.0 * x2)) - x1;
	t_3 = t_2 / ((x1 * x1) + 1.0);
	t_4 = t_2 / t_0;
	t_5 = x1 * (x1 * x1);
	tmp = 0.0;
	if (x1 <= -5e+102)
		tmp = x1 + (9.0 + (x1 + ((x2 * -4.0) + (x1 * (2.0 - (x1 * (6.0 + ((((((2.0 * x2) - 3.0) * -2.0) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))))))));
	elseif (x1 <= -2.4)
		tmp = x1 + (9.0 - ((((t_1 * t_4) + ((((x1 * x1) * ((t_3 * 4.0) - 6.0)) + ((t_3 - 3.0) * (x1 * 6.0))) * t_0)) - t_5) - x1));
	elseif (x1 <= 2.85e+23)
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	elseif (x1 <= 8.5e+151)
		tmp = x1 + (9.0 + (x1 + (t_5 + ((t_1 * t_3) + ((((-1.0 / x1) * ((x1 * 2.0) * t_4)) - ((x1 * x1) * ((4.0 * (3.0 + ((-1.0 - ((3.0 - (2.0 * x2)) / x1)) / x1))) - 6.0))) * t_0)))));
	else
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 / t$95$0), $MachinePrecision]}, Block[{t$95$5 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5e+102], N[(x1 + N[(9.0 + N[(x1 + N[(N[(x2 * -4.0), $MachinePrecision] + N[(x1 * N[(2.0 - N[(x1 * N[(6.0 + N[(N[(N[(N[(N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision] * -2.0), $MachinePrecision] - N[(N[(x2 * 6.0), $MachinePrecision] + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision] - N[(x1 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.4], N[(x1 + N[(9.0 - N[(N[(N[(N[(t$95$1 * t$95$4), $MachinePrecision] + N[(N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$3 - 3.0), $MachinePrecision] * N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision] - t$95$5), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.85e+23], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 8.5e+151], N[(x1 + N[(9.0 + N[(x1 + N[(t$95$5 + N[(N[(t$95$1 * t$95$3), $MachinePrecision] + N[(N[(N[(N[(-1.0 / x1), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * N[(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] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 - N[(x2 * N[(6.0 + N[(N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -5e102

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around inf 0.0%

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

   5. Taylor expanded in x1 around 0 92.0%

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

   if -5e102 < x1 < -2.39999999999999991

   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 93.4%

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

   4. Taylor expanded in x1 around inf 93.1%

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

   5. Taylor expanded in x1 around inf 75.5%

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

      1. *-commutative 75.5%

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

   7. Simplified 75.5%

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

   if -2.39999999999999991 < x1 < 2.85e23

   1. Initial program 98.5%

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

   3. Taylor expanded in x1 around 0 84.9%

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

   4. Taylor expanded in x1 around 0 84.7%

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

   5. Taylor expanded in x2 around 0 98.4%

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

   if 2.85e23 < x1 < 8.50000000000000051e151

   1. Initial program 99.8%

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

   3. Taylor expanded in x1 around inf 89.9%

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

   4. Taylor expanded in x1 around inf 89.9%

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

   5. Taylor expanded in x1 around -inf 90.0%

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

   if 8.50000000000000051e151 < x1

   1. Initial program 3.1%

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

   3. Taylor expanded in x1 around 0 0.1%

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

   4. Taylor expanded in x1 around 0 87.9%

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

   5. Taylor expanded in x2 around 0 97.3%

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

      1. *-commutative 97.3%

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

   7. Simplified 97.3%

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

   8. Taylor expanded in x2 around inf 100.0%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x2 \cdot -4 + x1 \cdot \left(2 - x1 \cdot \left(6 + \left(\left(\left(\left(2 \cdot x2 - 3\right) \cdot -2 - \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - x2 \cdot -4\right) - x1 \cdot -6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2.4:\\ \;\;\;\;x1 + \left(9 - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(x1 \cdot 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 2.85 \cdot 10^{+23}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.5 \cdot 10^{+151}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(\frac{-1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) - \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(3 + \frac{-1 - \frac{3 - 2 \cdot x2}{x1}}{x1}\right) - 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 94.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\\ t_2 := x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_0 \cdot t\_1 - \left(\left(x1 \cdot x1\right) \cdot \left(t\_1 \cdot 4 - 6\right) + -6\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x2 \cdot -4 + x1 \cdot \left(2 - x1 \cdot \left(6 + \left(\left(\left(\left(2 \cdot x2 - 3\right) \cdot -2 - \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - x2 \cdot -4\right) - x1 \cdot -6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2.4:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq 3.6 \cdot 10^{+23}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.5 \cdot 10^{+151}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (/ (- (+ t_0 (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
        (t_2
         (+
          x1
          (+
           9.0
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (-
              (* t_0 t_1)
              (*
               (+ (* (* x1 x1) (- (* t_1 4.0) 6.0)) -6.0)
               (- -1.0 (* x1 x1))))))))))
   (if (<= x1 -5e+102)
     (+
      x1
      (+
       9.0
       (+
        x1
        (+
         (* x2 -4.0)
         (*
          x1
          (-
           2.0
           (*
            x1
            (+
             6.0
             (-
              (-
               (- (* (- (* 2.0 x2) 3.0) -2.0) (+ (* x2 6.0) (* x2 8.0)))
               (* x2 -4.0))
              (* x1 -6.0))))))))))
     (if (<= x1 -2.4)
       t_2
       (if (<= x1 3.6e+23)
         (+
          x1
          (+
           (* x2 -6.0)
           (+
            (* x1 (- (* x1 9.0) 2.0))
            (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 6.0) 12.0)))))))
         (if (<= x1 8.5e+151)
           t_2
           (- x1 (* x2 (+ 6.0 (/ (* x1 (- 2.0 (* x1 9.0))) x2))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = ((t_0 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0);
	double t_2 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_1) - ((((x1 * x1) * ((t_1 * 4.0) - 6.0)) + -6.0) * (-1.0 - (x1 * x1)))))));
	double tmp;
	if (x1 <= -5e+102) {
		tmp = x1 + (9.0 + (x1 + ((x2 * -4.0) + (x1 * (2.0 - (x1 * (6.0 + ((((((2.0 * x2) - 3.0) * -2.0) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))))))));
	} else if (x1 <= -2.4) {
		tmp = t_2;
	} else if (x1 <= 3.6e+23) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else if (x1 <= 8.5e+151) {
		tmp = t_2;
	} else {
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / 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) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = ((t_0 + (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0)
    t_2 = x1 + (9.0d0 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_1) - ((((x1 * x1) * ((t_1 * 4.0d0) - 6.0d0)) + (-6.0d0)) * ((-1.0d0) - (x1 * x1)))))))
    if (x1 <= (-5d+102)) then
        tmp = x1 + (9.0d0 + (x1 + ((x2 * (-4.0d0)) + (x1 * (2.0d0 - (x1 * (6.0d0 + ((((((2.0d0 * x2) - 3.0d0) * (-2.0d0)) - ((x2 * 6.0d0) + (x2 * 8.0d0))) - (x2 * (-4.0d0))) - (x1 * (-6.0d0))))))))))
    else if (x1 <= (-2.4d0)) then
        tmp = t_2
    else if (x1 <= 3.6d+23) then
        tmp = x1 + ((x2 * (-6.0d0)) + ((x1 * ((x1 * 9.0d0) - 2.0d0)) + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 6.0d0) - 12.0d0))))))
    else if (x1 <= 8.5d+151) then
        tmp = t_2
    else
        tmp = x1 - (x2 * (6.0d0 + ((x1 * (2.0d0 - (x1 * 9.0d0))) / 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 = ((t_0 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0);
	double t_2 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_1) - ((((x1 * x1) * ((t_1 * 4.0) - 6.0)) + -6.0) * (-1.0 - (x1 * x1)))))));
	double tmp;
	if (x1 <= -5e+102) {
		tmp = x1 + (9.0 + (x1 + ((x2 * -4.0) + (x1 * (2.0 - (x1 * (6.0 + ((((((2.0 * x2) - 3.0) * -2.0) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))))))));
	} else if (x1 <= -2.4) {
		tmp = t_2;
	} else if (x1 <= 3.6e+23) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else if (x1 <= 8.5e+151) {
		tmp = t_2;
	} else {
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = ((t_0 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0)
	t_2 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_1) - ((((x1 * x1) * ((t_1 * 4.0) - 6.0)) + -6.0) * (-1.0 - (x1 * x1)))))))
	tmp = 0
	if x1 <= -5e+102:
		tmp = x1 + (9.0 + (x1 + ((x2 * -4.0) + (x1 * (2.0 - (x1 * (6.0 + ((((((2.0 * x2) - 3.0) * -2.0) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))))))))
	elif x1 <= -2.4:
		tmp = t_2
	elif x1 <= 3.6e+23:
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))))
	elif x1 <= 8.5e+151:
		tmp = t_2
	else:
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))
	t_2 = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * t_1) - Float64(Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_1 * 4.0) - 6.0)) + -6.0) * Float64(-1.0 - Float64(x1 * x1))))))))
	tmp = 0.0
	if (x1 <= -5e+102)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(Float64(x2 * -4.0) + Float64(x1 * Float64(2.0 - Float64(x1 * Float64(6.0 + Float64(Float64(Float64(Float64(Float64(Float64(2.0 * x2) - 3.0) * -2.0) - Float64(Float64(x2 * 6.0) + Float64(x2 * 8.0))) - Float64(x2 * -4.0)) - Float64(x1 * -6.0))))))))));
	elseif (x1 <= -2.4)
		tmp = t_2;
	elseif (x1 <= 3.6e+23)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0)) + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)))))));
	elseif (x1 <= 8.5e+151)
		tmp = t_2;
	else
		tmp = Float64(x1 - Float64(x2 * Float64(6.0 + Float64(Float64(x1 * Float64(2.0 - Float64(x1 * 9.0))) / x2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = ((t_0 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0);
	t_2 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_1) - ((((x1 * x1) * ((t_1 * 4.0) - 6.0)) + -6.0) * (-1.0 - (x1 * x1)))))));
	tmp = 0.0;
	if (x1 <= -5e+102)
		tmp = x1 + (9.0 + (x1 + ((x2 * -4.0) + (x1 * (2.0 - (x1 * (6.0 + ((((((2.0 * x2) - 3.0) * -2.0) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))))))));
	elseif (x1 <= -2.4)
		tmp = t_2;
	elseif (x1 <= 3.6e+23)
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	elseif (x1 <= 8.5e+151)
		tmp = t_2;
	else
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / 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[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(9.0 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * t$95$1), $MachinePrecision] - N[(N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$1 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + -6.0), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5e+102], N[(x1 + N[(9.0 + N[(x1 + N[(N[(x2 * -4.0), $MachinePrecision] + N[(x1 * N[(2.0 - N[(x1 * N[(6.0 + N[(N[(N[(N[(N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision] * -2.0), $MachinePrecision] - N[(N[(x2 * 6.0), $MachinePrecision] + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision] - N[(x1 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.4], t$95$2, If[LessEqual[x1, 3.6e+23], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 8.5e+151], t$95$2, N[(x1 - N[(x2 * N[(6.0 + N[(N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x2), $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 0.0%

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

   4. Taylor expanded in x1 around inf 0.0%

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

   5. Taylor expanded in x1 around 0 92.0%

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

   if -5e102 < x1 < -2.39999999999999991 or 3.5999999999999998e23 < x1 < 8.50000000000000051e151

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around inf 82.4%

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

   4. Taylor expanded in x1 around inf 82.4%

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

   5. Taylor expanded in x1 around inf 82.4%

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

   if -2.39999999999999991 < x1 < 3.5999999999999998e23

   1. Initial program 98.5%

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

   3. Taylor expanded in x1 around 0 84.9%

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

   4. Taylor expanded in x1 around 0 84.7%

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

   5. Taylor expanded in x2 around 0 98.4%

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

   if 8.50000000000000051e151 < x1

   1. Initial program 3.1%

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

   3. Taylor expanded in x1 around 0 0.1%

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

   4. Taylor expanded in x1 around 0 87.9%

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

   5. Taylor expanded in x2 around 0 97.3%

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

      1. *-commutative 97.3%

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

   7. Simplified 97.3%

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

   8. Taylor expanded in x2 around inf 100.0%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x2 \cdot -4 + x1 \cdot \left(2 - x1 \cdot \left(6 + \left(\left(\left(\left(2 \cdot x2 - 3\right) \cdot -2 - \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - x2 \cdot -4\right) - x1 \cdot -6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2.4:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + -6\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.6 \cdot 10^{+23}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.5 \cdot 10^{+151}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + -6\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 84.3% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -3 \cdot 10^{+46}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x2 \cdot -4 + x1 \cdot \left(2 - x1 \cdot \left(6 + \left(\left(\left(\left(2 \cdot x2 - 3\right) \cdot -2 - \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - x2 \cdot -4\right) - x1 \cdot -6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6.8 \cdot 10^{+90}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - x1 \cdot \left(x1 \cdot 3 - 3 \cdot \left(x2 \cdot -2 - 3\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -3e+46)
   (+
    x1
    (+
     9.0
     (+
      x1
      (+
       (* x2 -4.0)
       (*
        x1
        (-
         2.0
         (*
          x1
          (+
           6.0
           (-
            (-
             (- (* (- (* 2.0 x2) 3.0) -2.0) (+ (* x2 6.0) (* x2 8.0)))
             (* x2 -4.0))
            (* x1 -6.0))))))))))
   (if (<= x1 6.8e+90)
     (+
      x1
      (+
       (* x2 -6.0)
       (+
        (* x1 (- (* x1 9.0) 2.0))
        (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 6.0) 12.0)))))))
     (+
      x1
      (-
       (* x2 -6.0)
       (*
        x1
        (+
         2.0
         (-
          (* 4.0 (* x2 (- 3.0 (* 2.0 x2))))
          (* x1 (- (* x1 3.0) (* 3.0 (- (* x2 -2.0) 3.0))))))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3e+46) {
		tmp = x1 + (9.0 + (x1 + ((x2 * -4.0) + (x1 * (2.0 - (x1 * (6.0 + ((((((2.0 * x2) - 3.0) * -2.0) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))))))));
	} else if (x1 <= 6.8e+90) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * ((x1 * 3.0) - (3.0 * ((x2 * -2.0) - 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 <= (-3d+46)) then
        tmp = x1 + (9.0d0 + (x1 + ((x2 * (-4.0d0)) + (x1 * (2.0d0 - (x1 * (6.0d0 + ((((((2.0d0 * x2) - 3.0d0) * (-2.0d0)) - ((x2 * 6.0d0) + (x2 * 8.0d0))) - (x2 * (-4.0d0))) - (x1 * (-6.0d0))))))))))
    else if (x1 <= 6.8d+90) then
        tmp = x1 + ((x2 * (-6.0d0)) + ((x1 * ((x1 * 9.0d0) - 2.0d0)) + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 6.0d0) - 12.0d0))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))) - (x1 * ((x1 * 3.0d0) - (3.0d0 * ((x2 * (-2.0d0)) - 3.0d0))))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3e+46) {
		tmp = x1 + (9.0 + (x1 + ((x2 * -4.0) + (x1 * (2.0 - (x1 * (6.0 + ((((((2.0 * x2) - 3.0) * -2.0) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))))))));
	} else if (x1 <= 6.8e+90) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * ((x1 * 3.0) - (3.0 * ((x2 * -2.0) - 3.0))))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -3e+46:
		tmp = x1 + (9.0 + (x1 + ((x2 * -4.0) + (x1 * (2.0 - (x1 * (6.0 + ((((((2.0 * x2) - 3.0) * -2.0) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))))))))
	elif x1 <= 6.8e+90:
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * ((x1 * 3.0) - (3.0 * ((x2 * -2.0) - 3.0))))))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -3e+46)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(Float64(x2 * -4.0) + Float64(x1 * Float64(2.0 - Float64(x1 * Float64(6.0 + Float64(Float64(Float64(Float64(Float64(Float64(2.0 * x2) - 3.0) * -2.0) - Float64(Float64(x2 * 6.0) + Float64(x2 * 8.0))) - Float64(x2 * -4.0)) - Float64(x1 * -6.0))))))))));
	elseif (x1 <= 6.8e+90)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0)) + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))) - Float64(x1 * Float64(Float64(x1 * 3.0) - Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -3e+46)
		tmp = x1 + (9.0 + (x1 + ((x2 * -4.0) + (x1 * (2.0 - (x1 * (6.0 + ((((((2.0 * x2) - 3.0) * -2.0) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))))))));
	elseif (x1 <= 6.8e+90)
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * ((x1 * 3.0) - (3.0 * ((x2 * -2.0) - 3.0))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -3e+46], N[(x1 + N[(9.0 + N[(x1 + N[(N[(x2 * -4.0), $MachinePrecision] + N[(x1 * N[(2.0 - N[(x1 * N[(6.0 + N[(N[(N[(N[(N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision] * -2.0), $MachinePrecision] - N[(N[(x2 * 6.0), $MachinePrecision] + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision] - N[(x1 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6.8e+90], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] - N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.00000000000000023e46

   1. Initial program 13.7%

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

   3. Taylor expanded in x1 around inf 13.7%

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

   4. Taylor expanded in x1 around inf 13.7%

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

   5. Taylor expanded in x1 around 0 83.6%

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

   if -3.00000000000000023e46 < x1 < 6.80000000000000036e90

   1. Initial program 98.6%

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

   3. Taylor expanded in x1 around 0 78.6%

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

   4. Taylor expanded in x1 around 0 77.3%

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

   5. Taylor expanded in x2 around 0 90.9%

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

   if 6.80000000000000036e90 < x1

   1. Initial program 31.1%

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

   3. Taylor expanded in x1 around 0 12.2%

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

   4. Taylor expanded in x1 around 0 89.8%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3 \cdot 10^{+46}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x2 \cdot -4 + x1 \cdot \left(2 - x1 \cdot \left(6 + \left(\left(\left(\left(2 \cdot x2 - 3\right) \cdot -2 - \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - x2 \cdot -4\right) - x1 \cdot -6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6.8 \cdot 10^{+90}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - x1 \cdot \left(x1 \cdot 3 - 3 \cdot \left(x2 \cdot -2 - 3\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 78.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 - \left(x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{if}\;x1 \leq -9 \cdot 10^{+92}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \mathbf{elif}\;x1 \leq -1.15 \cdot 10^{-226}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 4.8 \cdot 10^{-266}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 1.2 \cdot 10^{+97}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 - 3 \cdot \left(x2 \cdot -2 - 3\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (-
          x1
          (- (* x1 (+ 2.0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))) (* x2 -6.0)))))
   (if (<= x1 -9e+92)
     (- x1 (* x2 (+ 6.0 (/ (* x1 (- 2.0 (* x1 9.0))) x2))))
     (if (<= x1 -1.15e-226)
       t_0
       (if (<= x1 4.8e-266)
         (- (* x2 -6.0) x1)
         (if (<= x1 1.2e+97)
           t_0
           (+
            x1
            (+
             (* x2 -6.0)
             (*
              x1
              (-
               (* x1 (- (* x1 3.0) (* 3.0 (- (* x2 -2.0) 3.0))))
               2.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 - ((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - (x2 * -6.0));
	double tmp;
	if (x1 <= -9e+92) {
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	} else if (x1 <= -1.15e-226) {
		tmp = t_0;
	} else if (x1 <= 4.8e-266) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 1.2e+97) {
		tmp = t_0;
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) - (3.0 * ((x2 * -2.0) - 3.0)))) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 - ((x1 * (2.0d0 + (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))))) - (x2 * (-6.0d0)))
    if (x1 <= (-9d+92)) then
        tmp = x1 - (x2 * (6.0d0 + ((x1 * (2.0d0 - (x1 * 9.0d0))) / x2)))
    else if (x1 <= (-1.15d-226)) then
        tmp = t_0
    else if (x1 <= 4.8d-266) then
        tmp = (x2 * (-6.0d0)) - x1
    else if (x1 <= 1.2d+97) then
        tmp = t_0
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * ((x1 * 3.0d0) - (3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)))) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 - ((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - (x2 * -6.0));
	double tmp;
	if (x1 <= -9e+92) {
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	} else if (x1 <= -1.15e-226) {
		tmp = t_0;
	} else if (x1 <= 4.8e-266) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 1.2e+97) {
		tmp = t_0;
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) - (3.0 * ((x2 * -2.0) - 3.0)))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 - ((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - (x2 * -6.0))
	tmp = 0
	if x1 <= -9e+92:
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)))
	elif x1 <= -1.15e-226:
		tmp = t_0
	elif x1 <= 4.8e-266:
		tmp = (x2 * -6.0) - x1
	elif x1 <= 1.2e+97:
		tmp = t_0
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) - (3.0 * ((x2 * -2.0) - 3.0)))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 - Float64(Float64(x1 * Float64(2.0 + Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))) - Float64(x2 * -6.0)))
	tmp = 0.0
	if (x1 <= -9e+92)
		tmp = Float64(x1 - Float64(x2 * Float64(6.0 + Float64(Float64(x1 * Float64(2.0 - Float64(x1 * 9.0))) / x2))));
	elseif (x1 <= -1.15e-226)
		tmp = t_0;
	elseif (x1 <= 4.8e-266)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	elseif (x1 <= 1.2e+97)
		tmp = t_0;
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x1 * 3.0) - Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)))) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 - ((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - (x2 * -6.0));
	tmp = 0.0;
	if (x1 <= -9e+92)
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	elseif (x1 <= -1.15e-226)
		tmp = t_0;
	elseif (x1 <= 4.8e-266)
		tmp = (x2 * -6.0) - x1;
	elseif (x1 <= 1.2e+97)
		tmp = t_0;
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) - (3.0 * ((x2 * -2.0) - 3.0)))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 - N[(N[(x1 * N[(2.0 + N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -9e+92], N[(x1 - N[(x2 * N[(6.0 + N[(N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.15e-226], t$95$0, If[LessEqual[x1, 4.8e-266], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 1.2e+97], t$95$0, N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] - N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -8.9999999999999998e92

   1. Initial program 2.0%

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

   3. Taylor expanded in x1 around 0 0.1%

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

   4. Taylor expanded in x1 around 0 46.9%

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

   5. Taylor expanded in x2 around 0 67.3%

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

      1. *-commutative 67.3%

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

   7. Simplified 67.3%

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

   8. Taylor expanded in x2 around inf 87.3%

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

   if -8.9999999999999998e92 < x1 < -1.15e-226 or 4.7999999999999999e-266 < x1 < 1.2e97

   1. Initial program 98.5%

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

   3. Taylor expanded in x1 around 0 74.8%

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

   4. Taylor expanded in x1 around 0 74.6%

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

   if -1.15e-226 < x1 < 4.7999999999999999e-266

   1. Initial program 99.6%

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

   3. Taylor expanded in x1 around 0 77.4%

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

   4. Taylor expanded in x1 around 0 77.5%

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

   5. Taylor expanded in x2 around 0 99.7%

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

      1. *-commutative 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in x1 around 0 99.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + -1 \cdot x1} \]
   9. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \color{blue}{x2 \cdot -6} + -1 \cdot x1 \]

      2. mul-1-neg 99.8%

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

      3. unsub-neg 99.8%

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

   10. Simplified 99.8%

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

   if 1.2e97 < x1

   1. Initial program 26.2%

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

   3. Taylor expanded in x1 around inf 26.2%

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

   4. Taylor expanded in x1 around 0 88.6%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9 \cdot 10^{+92}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \mathbf{elif}\;x1 \leq -1.15 \cdot 10^{-226}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 4.8 \cdot 10^{-266}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 1.2 \cdot 10^{+97}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 - 3 \cdot \left(x2 \cdot -2 - 3\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 83.3% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -5.2 \cdot 10^{+92}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \mathbf{elif}\;x1 \leq 9.2 \cdot 10^{+87}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - x1 \cdot \left(x1 \cdot 3 - 3 \cdot \left(x2 \cdot -2 - 3\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -5.2e+92)
   (- x1 (* x2 (+ 6.0 (/ (* x1 (- 2.0 (* x1 9.0))) x2))))
   (if (<= x1 9.2e+87)
     (+
      x1
      (+
       (* x2 -6.0)
       (+
        (* x1 (- (* x1 9.0) 2.0))
        (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 6.0) 12.0)))))))
     (+
      x1
      (-
       (* x2 -6.0)
       (*
        x1
        (+
         2.0
         (-
          (* 4.0 (* x2 (- 3.0 (* 2.0 x2))))
          (* x1 (- (* x1 3.0) (* 3.0 (- (* x2 -2.0) 3.0))))))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -5.2e+92) {
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	} else if (x1 <= 9.2e+87) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * ((x1 * 3.0) - (3.0 * ((x2 * -2.0) - 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 <= (-5.2d+92)) then
        tmp = x1 - (x2 * (6.0d0 + ((x1 * (2.0d0 - (x1 * 9.0d0))) / x2)))
    else if (x1 <= 9.2d+87) then
        tmp = x1 + ((x2 * (-6.0d0)) + ((x1 * ((x1 * 9.0d0) - 2.0d0)) + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 6.0d0) - 12.0d0))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))) - (x1 * ((x1 * 3.0d0) - (3.0d0 * ((x2 * (-2.0d0)) - 3.0d0))))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -5.2e+92) {
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	} else if (x1 <= 9.2e+87) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * ((x1 * 3.0) - (3.0 * ((x2 * -2.0) - 3.0))))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -5.2e+92:
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)))
	elif x1 <= 9.2e+87:
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * ((x1 * 3.0) - (3.0 * ((x2 * -2.0) - 3.0))))))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -5.2e+92)
		tmp = Float64(x1 - Float64(x2 * Float64(6.0 + Float64(Float64(x1 * Float64(2.0 - Float64(x1 * 9.0))) / x2))));
	elseif (x1 <= 9.2e+87)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0)) + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))) - Float64(x1 * Float64(Float64(x1 * 3.0) - Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -5.2e+92)
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	elseif (x1 <= 9.2e+87)
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * ((x1 * 3.0) - (3.0 * ((x2 * -2.0) - 3.0))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -5.2e+92], N[(x1 - N[(x2 * N[(6.0 + N[(N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 9.2e+87], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] - N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.1999999999999998e92

   1. Initial program 2.0%

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

   3. Taylor expanded in x1 around 0 0.1%

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

   4. Taylor expanded in x1 around 0 46.9%

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

   5. Taylor expanded in x2 around 0 67.3%

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

      1. *-commutative 67.3%

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

   7. Simplified 67.3%

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

   8. Taylor expanded in x2 around inf 87.3%

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

   if -5.1999999999999998e92 < x1 < 9.2000000000000007e87

   1. Initial program 98.6%

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

   3. Taylor expanded in x1 around 0 75.8%

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

   4. Taylor expanded in x1 around 0 74.7%

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

   5. Taylor expanded in x2 around 0 87.6%

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

   if 9.2000000000000007e87 < x1

   1. Initial program 31.1%

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

   3. Taylor expanded in x1 around 0 12.2%

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

   4. Taylor expanded in x1 around 0 89.8%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.2 \cdot 10^{+92}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \mathbf{elif}\;x1 \leq 9.2 \cdot 10^{+87}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - x1 \cdot \left(x1 \cdot 3 - 3 \cdot \left(x2 \cdot -2 - 3\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 77.8% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 - \left(x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ t_1 := x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \mathbf{if}\;x1 \leq -5.2 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{-226}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 1.25 \cdot 10^{-266}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 1.15 \cdot 10^{+98}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (-
          x1
          (- (* x1 (+ 2.0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))) (* x2 -6.0))))
        (t_1 (- x1 (* x2 (+ 6.0 (/ (* x1 (- 2.0 (* x1 9.0))) x2))))))
   (if (<= x1 -5.2e+92)
     t_1
     (if (<= x1 -5.6e-226)
       t_0
       (if (<= x1 1.25e-266)
         (- (* x2 -6.0) x1)
         (if (<= x1 1.15e+98) t_0 t_1))))))

C

double code(double x1, double x2) {
	double t_0 = x1 - ((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - (x2 * -6.0));
	double t_1 = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	double tmp;
	if (x1 <= -5.2e+92) {
		tmp = t_1;
	} else if (x1 <= -5.6e-226) {
		tmp = t_0;
	} else if (x1 <= 1.25e-266) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 1.15e+98) {
		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 - ((x1 * (2.0d0 + (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))))) - (x2 * (-6.0d0)))
    t_1 = x1 - (x2 * (6.0d0 + ((x1 * (2.0d0 - (x1 * 9.0d0))) / x2)))
    if (x1 <= (-5.2d+92)) then
        tmp = t_1
    else if (x1 <= (-5.6d-226)) then
        tmp = t_0
    else if (x1 <= 1.25d-266) then
        tmp = (x2 * (-6.0d0)) - x1
    else if (x1 <= 1.15d+98) 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 - ((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - (x2 * -6.0));
	double t_1 = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	double tmp;
	if (x1 <= -5.2e+92) {
		tmp = t_1;
	} else if (x1 <= -5.6e-226) {
		tmp = t_0;
	} else if (x1 <= 1.25e-266) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 1.15e+98) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 - ((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - (x2 * -6.0))
	t_1 = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)))
	tmp = 0
	if x1 <= -5.2e+92:
		tmp = t_1
	elif x1 <= -5.6e-226:
		tmp = t_0
	elif x1 <= 1.25e-266:
		tmp = (x2 * -6.0) - x1
	elif x1 <= 1.15e+98:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 - Float64(Float64(x1 * Float64(2.0 + Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))) - Float64(x2 * -6.0)))
	t_1 = Float64(x1 - Float64(x2 * Float64(6.0 + Float64(Float64(x1 * Float64(2.0 - Float64(x1 * 9.0))) / x2))))
	tmp = 0.0
	if (x1 <= -5.2e+92)
		tmp = t_1;
	elseif (x1 <= -5.6e-226)
		tmp = t_0;
	elseif (x1 <= 1.25e-266)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	elseif (x1 <= 1.15e+98)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 - ((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - (x2 * -6.0));
	t_1 = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	tmp = 0.0;
	if (x1 <= -5.2e+92)
		tmp = t_1;
	elseif (x1 <= -5.6e-226)
		tmp = t_0;
	elseif (x1 <= 1.25e-266)
		tmp = (x2 * -6.0) - x1;
	elseif (x1 <= 1.15e+98)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 - N[(N[(x1 * N[(2.0 + N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 - N[(x2 * N[(6.0 + N[(N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.2e+92], t$95$1, If[LessEqual[x1, -5.6e-226], t$95$0, If[LessEqual[x1, 1.25e-266], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 1.15e+98], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.1999999999999998e92 or 1.15000000000000007e98 < x1

   1. Initial program 12.0%

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

   3. Taylor expanded in x1 around 0 3.7%

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

   4. Taylor expanded in x1 around 0 60.2%

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

   5. Taylor expanded in x2 around 0 71.8%

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

      1. *-commutative 71.8%

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

   7. Simplified 71.8%

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

   8. Taylor expanded in x2 around inf 86.9%

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

   if -5.1999999999999998e92 < x1 < -5.60000000000000016e-226 or 1.24999999999999998e-266 < x1 < 1.15000000000000007e98

   1. Initial program 98.5%

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

   3. Taylor expanded in x1 around 0 74.9%

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

   4. Taylor expanded in x1 around 0 74.8%

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

   if -5.60000000000000016e-226 < x1 < 1.24999999999999998e-266

   1. Initial program 99.6%

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

   3. Taylor expanded in x1 around 0 77.4%

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

   4. Taylor expanded in x1 around 0 77.5%

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

   5. Taylor expanded in x2 around 0 99.7%

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

      1. *-commutative 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in x1 around 0 99.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + -1 \cdot x1} \]
   9. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \color{blue}{x2 \cdot -6} + -1 \cdot x1 \]

      2. mul-1-neg 99.8%

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

      3. unsub-neg 99.8%

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

   10. Simplified 99.8%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.2 \cdot 10^{+92}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{-226}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 1.25 \cdot 10^{-266}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 1.15 \cdot 10^{+98}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 83.2% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -5.2 \cdot 10^{+92}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \mathbf{elif}\;x1 \leq 2.25 \cdot 10^{+97}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 - 3 \cdot \left(x2 \cdot -2 - 3\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -5.2e+92)
   (- x1 (* x2 (+ 6.0 (/ (* x1 (- 2.0 (* x1 9.0))) x2))))
   (if (<= x1 2.25e+97)
     (+
      x1
      (+
       (* x2 -6.0)
       (+
        (* x1 (- (* x1 9.0) 2.0))
        (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 6.0) 12.0)))))))
     (+
      x1
      (+
       (* x2 -6.0)
       (* x1 (- (* x1 (- (* x1 3.0) (* 3.0 (- (* x2 -2.0) 3.0)))) 2.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -5.2e+92) {
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	} else if (x1 <= 2.25e+97) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) - (3.0 * ((x2 * -2.0) - 3.0)))) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-5.2d+92)) then
        tmp = x1 - (x2 * (6.0d0 + ((x1 * (2.0d0 - (x1 * 9.0d0))) / x2)))
    else if (x1 <= 2.25d+97) then
        tmp = x1 + ((x2 * (-6.0d0)) + ((x1 * ((x1 * 9.0d0) - 2.0d0)) + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 6.0d0) - 12.0d0))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * ((x1 * 3.0d0) - (3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)))) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -5.2e+92) {
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	} else if (x1 <= 2.25e+97) {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) - (3.0 * ((x2 * -2.0) - 3.0)))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -5.2e+92:
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)))
	elif x1 <= 2.25e+97:
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) - (3.0 * ((x2 * -2.0) - 3.0)))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -5.2e+92)
		tmp = Float64(x1 - Float64(x2 * Float64(6.0 + Float64(Float64(x1 * Float64(2.0 - Float64(x1 * 9.0))) / x2))));
	elseif (x1 <= 2.25e+97)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0)) + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x1 * 3.0) - Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)))) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -5.2e+92)
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	elseif (x1 <= 2.25e+97)
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) - (3.0 * ((x2 * -2.0) - 3.0)))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -5.2e+92], N[(x1 - N[(x2 * N[(6.0 + N[(N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.25e+97], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] - N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.1999999999999998e92

   1. Initial program 2.0%

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

   3. Taylor expanded in x1 around 0 0.1%

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

   4. Taylor expanded in x1 around 0 46.9%

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

   5. Taylor expanded in x2 around 0 67.3%

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

      1. *-commutative 67.3%

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

   7. Simplified 67.3%

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

   8. Taylor expanded in x2 around inf 87.3%

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

   if -5.1999999999999998e92 < x1 < 2.24999999999999988e97

   1. Initial program 98.6%

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

   3. Taylor expanded in x1 around 0 75.1%

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

   4. Taylor expanded in x1 around 0 74.0%

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

   5. Taylor expanded in x2 around 0 86.7%

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

   if 2.24999999999999988e97 < x1

   1. Initial program 26.2%

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

   3. Taylor expanded in x1 around inf 26.2%

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

   4. Taylor expanded in x1 around 0 88.6%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.2 \cdot 10^{+92}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \mathbf{elif}\;x1 \leq 2.25 \cdot 10^{+97}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 - 3 \cdot \left(x2 \cdot -2 - 3\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 73.2% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -1.8 \cdot 10^{+263}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x2 \leq 5 \cdot 10^{-79}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 3 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right)\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 -1.8e+263)
   (+ x1 (* x1 (- 1.0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))))
   (if (<= x2 5e-79)
     (- x1 (* x2 (+ 6.0 (/ (* x1 (- 2.0 (* x1 9.0))) x2))))
     (+
      x1
      (+
       (* x2 -6.0)
       (*
        x1
        (-
         (-
          (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))
          (* 3.0 (* x1 (- (* x2 -2.0) 3.0))))
         2.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= -1.8e+263) {
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	} else if (x2 <= 5e-79) {
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) - (3.0 * (x1 * ((x2 * -2.0) - 3.0)))) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x2 <= (-1.8d+263)) then
        tmp = x1 + (x1 * (1.0d0 - (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2))))))
    else if (x2 <= 5d-79) then
        tmp = x1 - (x2 * (6.0d0 + ((x1 * (2.0d0 - (x1 * 9.0d0))) / x2)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - (3.0d0 * (x1 * ((x2 * (-2.0d0)) - 3.0d0)))) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x2 <= -1.8e+263) {
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	} else if (x2 <= 5e-79) {
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) - (3.0 * (x1 * ((x2 * -2.0) - 3.0)))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= -1.8e+263:
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))))
	elif x2 <= 5e-79:
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) - (3.0 * (x1 * ((x2 * -2.0) - 3.0)))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= -1.8e+263)
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 - Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))));
	elseif (x2 <= 5e-79)
		tmp = Float64(x1 - Float64(x2 * Float64(6.0 + Float64(Float64(x1 * Float64(2.0 - Float64(x1 * 9.0))) / x2))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - Float64(3.0 * Float64(x1 * Float64(Float64(x2 * -2.0) - 3.0)))) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= -1.8e+263)
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	elseif (x2 <= 5e-79)
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) - (3.0 * (x1 * ((x2 * -2.0) - 3.0)))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, -1.8e+263], N[(x1 + N[(x1 * N[(1.0 - N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x2, 5e-79], N[(x1 - N[(x2 * N[(6.0 + N[(N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * N[(x1 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -1.79999999999999989e263

   1. Initial program 75.0%

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

   3. Taylor expanded in x1 around 0 87.5%

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

   4. Taylor expanded in x1 around inf 100.0%

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

   if -1.79999999999999989e263 < x2 < 4.99999999999999999e-79

   1. Initial program 62.4%

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

   3. Taylor expanded in x1 around 0 47.0%

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

   4. Taylor expanded in x1 around 0 68.2%

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

   5. Taylor expanded in x2 around 0 72.6%

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

      1. *-commutative 72.6%

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

   7. Simplified 72.6%

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

   8. Taylor expanded in x2 around inf 81.6%

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

   if 4.99999999999999999e-79 < x2

   1. Initial program 76.9%

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

   3. Taylor expanded in x1 around 0 50.9%

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

   4. Taylor expanded in x1 around 0 70.4%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.8 \cdot 10^{+263}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x2 \leq 5 \cdot 10^{-79}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 3 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right)\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 72.1% accurate, 5.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -1.8 \cdot 10^{+263} \lor \neg \left(x2 \leq 3.85 \cdot 10^{+214}\right):\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -1.8e+263) (not (<= x2 3.85e+214)))
   (+ x1 (* x1 (- 1.0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))))
   (- x1 (* x2 (+ 6.0 (/ (* x1 (- 2.0 (* x1 9.0))) x2))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.8e+263) || !(x2 <= 3.85e+214)) {
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	} else {
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-1.8d+263)) .or. (.not. (x2 <= 3.85d+214))) then
        tmp = x1 + (x1 * (1.0d0 - (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2))))))
    else
        tmp = x1 - (x2 * (6.0d0 + ((x1 * (2.0d0 - (x1 * 9.0d0))) / x2)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.8e+263) || !(x2 <= 3.85e+214)) {
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	} else {
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -1.8e+263) or not (x2 <= 3.85e+214):
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))))
	else:
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -1.8e+263) || !(x2 <= 3.85e+214))
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 - Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))));
	else
		tmp = Float64(x1 - Float64(x2 * Float64(6.0 + Float64(Float64(x1 * Float64(2.0 - Float64(x1 * 9.0))) / x2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -1.8e+263) || ~((x2 <= 3.85e+214)))
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	else
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -1.8e+263], N[Not[LessEqual[x2, 3.85e+214]], $MachinePrecision]], N[(x1 + N[(x1 * N[(1.0 - N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 - N[(x2 * N[(6.0 + N[(N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -1.79999999999999989e263 or 3.8500000000000001e214 < x2

   1. Initial program 82.1%

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

   3. Taylor expanded in x1 around 0 65.9%

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

   4. Taylor expanded in x1 around inf 73.0%

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

   if -1.79999999999999989e263 < x2 < 3.8500000000000001e214

   1. Initial program 65.7%

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

   3. Taylor expanded in x1 around 0 47.5%

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

   4. Taylor expanded in x1 around 0 70.0%

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

   5. Taylor expanded in x2 around 0 72.1%

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

      1. *-commutative 72.1%

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

   7. Simplified 72.1%

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

   8. Taylor expanded in x2 around inf 78.6%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.8 \cdot 10^{+263} \lor \neg \left(x2 \leq 3.85 \cdot 10^{+214}\right):\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 67.9% accurate, 5.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -1.8 \cdot 10^{+263} \lor \neg \left(x2 \leq 7.2 \cdot 10^{+214}\right):\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -1.8e+263) (not (<= x2 7.2e+214)))
   (+ x1 (* x1 (- 1.0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))))
   (+ (* x2 -6.0) (* x1 (+ (* x1 9.0) -1.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.8e+263) || !(x2 <= 7.2e+214)) {
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-1.8d+263)) .or. (.not. (x2 <= 7.2d+214))) then
        tmp = x1 + (x1 * (1.0d0 - (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2))))))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.8e+263) || !(x2 <= 7.2e+214)) {
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -1.8e+263) or not (x2 <= 7.2e+214):
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))))
	else:
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -1.8e+263) || !(x2 <= 7.2e+214))
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 - Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -1.8e+263) || ~((x2 <= 7.2e+214)))
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	else
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -1.8e+263], N[Not[LessEqual[x2, 7.2e+214]], $MachinePrecision]], N[(x1 + N[(x1 * N[(1.0 - N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -1.79999999999999989e263 or 7.2000000000000002e214 < x2

   1. Initial program 82.1%

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

   3. Taylor expanded in x1 around 0 65.9%

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

   4. Taylor expanded in x1 around inf 73.0%

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

   if -1.79999999999999989e263 < x2 < 7.2000000000000002e214

   1. Initial program 65.7%

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

   3. Taylor expanded in x1 around 0 47.5%

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

   4. Taylor expanded in x1 around 0 70.0%

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

   5. Taylor expanded in x2 around 0 72.1%

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

      1. *-commutative 72.1%

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

   7. Simplified 72.1%

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

   8. Taylor expanded in x1 around 0 72.2%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.8 \cdot 10^{+263} \lor \neg \left(x2 \leq 7.2 \cdot 10^{+214}\right):\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 62.8% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -4.6 \cdot 10^{-46} \lor \neg \left(x1 \leq 102000000\right):\\ \;\;\;\;x1 - x1 \cdot \left(2 - x1 \cdot 9\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -4.6e-46) (not (<= x1 102000000.0)))
   (- x1 (* x1 (- 2.0 (* x1 9.0))))
   (- (* x2 -6.0) x1)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -4.6e-46) || !(x1 <= 102000000.0)) {
		tmp = x1 - (x1 * (2.0 - (x1 * 9.0)));
	} else {
		tmp = (x2 * -6.0) - x1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-4.6d-46)) .or. (.not. (x1 <= 102000000.0d0))) then
        tmp = x1 - (x1 * (2.0d0 - (x1 * 9.0d0)))
    else
        tmp = (x2 * (-6.0d0)) - x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -4.6e-46) || !(x1 <= 102000000.0)) {
		tmp = x1 - (x1 * (2.0 - (x1 * 9.0)));
	} else {
		tmp = (x2 * -6.0) - x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -4.6e-46) or not (x1 <= 102000000.0):
		tmp = x1 - (x1 * (2.0 - (x1 * 9.0)))
	else:
		tmp = (x2 * -6.0) - x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -4.6e-46) || !(x1 <= 102000000.0))
		tmp = Float64(x1 - Float64(x1 * Float64(2.0 - Float64(x1 * 9.0))));
	else
		tmp = Float64(Float64(x2 * -6.0) - x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -4.6e-46) || ~((x1 <= 102000000.0)))
		tmp = x1 - (x1 * (2.0 - (x1 * 9.0)));
	else
		tmp = (x2 * -6.0) - x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -4.6e-46], N[Not[LessEqual[x1, 102000000.0]], $MachinePrecision]], N[(x1 - N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -4.5999999999999998e-46 or 1.02e8 < x1

   1. Initial program 37.5%

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

   3. Taylor expanded in x1 around 0 15.6%

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

   4. Taylor expanded in x1 around 0 54.5%

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

   5. Taylor expanded in x2 around 0 55.8%

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

      1. *-commutative 55.8%

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

   7. Simplified 55.8%

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

   8. Taylor expanded in x2 around 0 55.9%

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

   if -4.5999999999999998e-46 < x1 < 1.02e8

   1. Initial program 98.5%

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

   3. Taylor expanded in x1 around 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 84.2%

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

   5. Taylor expanded in x2 around 0 77.6%

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

      1. *-commutative 77.6%

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

   7. Simplified 77.6%

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

   8. Taylor expanded in x1 around 0 77.5%

      \[\leadsto \color{blue}{-6 \cdot x2 + -1 \cdot x1} \]
   9. Step-by-step derivation

      1. *-commutative 77.5%

         \[\leadsto \color{blue}{x2 \cdot -6} + -1 \cdot x1 \]

      2. mul-1-neg 77.5%

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

      3. unsub-neg 77.5%

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

   10. Simplified 77.5%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.6 \cdot 10^{-46} \lor \neg \left(x1 \leq 102000000\right):\\ \;\;\;\;x1 - x1 \cdot \left(2 - x1 \cdot 9\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 44.7% accurate, 10.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq 1.15 \cdot 10^{-12}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 10\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 1.15e-12) (- (* x2 -6.0) x1) (* x2 (- (/ x1 x2) 10.0))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= 1.15e-12) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = x2 * ((x1 / x2) - 10.0);
	}
	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-12) then
        tmp = (x2 * (-6.0d0)) - x1
    else
        tmp = x2 * ((x1 / x2) - 10.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= 1.15e-12) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = x2 * ((x1 / x2) - 10.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= 1.15e-12:
		tmp = (x2 * -6.0) - x1
	else:
		tmp = x2 * ((x1 / x2) - 10.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= 1.15e-12)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	else
		tmp = Float64(x2 * Float64(Float64(x1 / x2) - 10.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= 1.15e-12)
		tmp = (x2 * -6.0) - x1;
	else
		tmp = x2 * ((x1 / x2) - 10.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, 1.15e-12], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], N[(x2 * N[(N[(x1 / x2), $MachinePrecision] - 10.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < 1.14999999999999995e-12

   1. Initial program 74.2%

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

   3. Taylor expanded in x1 around 0 58.0%

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

   4. Taylor expanded in x1 around 0 70.1%

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

   5. Taylor expanded in x2 around 0 69.1%

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

      1. *-commutative 69.1%

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

   7. Simplified 69.1%

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

   8. Taylor expanded in x1 around 0 52.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + -1 \cdot x1} \]
   9. Step-by-step derivation

      1. *-commutative 52.8%

         \[\leadsto \color{blue}{x2 \cdot -6} + -1 \cdot x1 \]

      2. mul-1-neg 52.8%

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

      3. unsub-neg 52.8%

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

   10. Simplified 52.8%

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

   if 1.14999999999999995e-12 < x1

   1. Initial program 44.7%

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

   3. Taylor expanded in x1 around inf 35.0%

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

   4. Taylor expanded in x1 around 0 7.3%

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

      1. distribute-rgt-out 7.3%

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

      2. metadata-eval 7.3%

         \[\leadsto x1 + x2 \cdot \color{blue}{-10} \]

   6. Simplified 7.3%

      \[\leadsto x1 + \color{blue}{x2 \cdot -10} \]

   7. Taylor expanded in x2 around inf 34.7%

      \[\leadsto \color{blue}{x2 \cdot \left(\frac{x1}{x2} - 10\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 63.4% accurate, 11.5× speedup

Math

\[\begin{array}{l} \\ x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right) \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (+ (* x2 -6.0) (* x1 (+ (* x1 9.0) -1.0))))

C

double code(double x1, double x2) {
	return (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = (x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) + (-1.0d0)))
end function

Java

public static double code(double x1, double x2) {
	return (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
}

Python

def code(x1, x2):
	return (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0))

Julia

function code(x1, x2)
	return Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0)))
end

MATLAB

function tmp = code(x1, x2)
	tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
end

Wolfram

code[x1_, x2_] := N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 67.5%

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

3. Taylor expanded in x1 around 0 49.5%

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

4. Taylor expanded in x1 around 0 69.1%

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

5. Taylor expanded in x2 around 0 66.5%

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

   1. *-commutative 66.5%

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

7. Simplified 66.5%

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

8. Taylor expanded in x1 around 0 66.5%

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

9. Final simplification 66.5%

   \[\leadsto x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right) \]
10. Add Preprocessing

Alternative 21: 38.7% accurate, 25.4× speedup

Math

\[\begin{array}{l} \\ x2 \cdot -6 - x1 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 67.5%

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

3. Taylor expanded in x1 around 0 49.5%

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

4. Taylor expanded in x1 around 0 69.1%

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

5. Taylor expanded in x2 around 0 66.5%

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

   1. *-commutative 66.5%

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

7. Simplified 66.5%

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

8. Taylor expanded in x1 around 0 41.5%

   \[\leadsto \color{blue}{-6 \cdot x2 + -1 \cdot x1} \]
9. Step-by-step derivation

   1. *-commutative 41.5%

      \[\leadsto \color{blue}{x2 \cdot -6} + -1 \cdot x1 \]

   2. mul-1-neg 41.5%

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

   3. unsub-neg 41.5%

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

10. Simplified 41.5%

    \[\leadsto \color{blue}{x2 \cdot -6 - x1} \]
11. Add Preprocessing

Alternative 22: 25.9% accurate, 25.4× speedup

Math

\[\begin{array}{l} \\ x1 + x2 \cdot -6 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 67.5%

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

3. Taylor expanded in x1 around 0 49.5%

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

4. Taylor expanded in x1 around 0 26.2%

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

   1. *-commutative 26.2%

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

6. Simplified 26.2%

   \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
7. Add Preprocessing

Alternative 23: 7.2% accurate, 25.4× speedup

Math

\[\begin{array}{l} \\ x1 + x2 \cdot -10 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (+ x1 (* x2 -10.0)))

C

double code(double x1, double x2) {
	return x1 + (x2 * -10.0);
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x1 + (x2 * (-10.0d0))
end function

Java

public static double code(double x1, double x2) {
	return x1 + (x2 * -10.0);
}

Python

def code(x1, x2):
	return x1 + (x2 * -10.0)

Julia

function code(x1, x2)
	return Float64(x1 + Float64(x2 * -10.0))
end

MATLAB

function tmp = code(x1, x2)
	tmp = x1 + (x2 * -10.0);
end

Wolfram

code[x1_, x2_] := N[(x1 + N[(x2 * -10.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 67.5%

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

3. Taylor expanded in x1 around inf 25.7%

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

4. Taylor expanded in x1 around 0 7.5%

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

   1. distribute-rgt-out 7.5%

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

   2. metadata-eval 7.5%

      \[\leadsto x1 + x2 \cdot \color{blue}{-10} \]

6. Simplified 7.5%

   \[\leadsto x1 + \color{blue}{x2 \cdot -10} \]
7. Add Preprocessing

Alternative 24: 7.1% accurate, 42.3× speedup

Math

\[\begin{array}{l} \\ x2 \cdot -10 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (* x2 -10.0))

C

double code(double x1, double x2) {
	return x2 * -10.0;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x2 * (-10.0d0)
end function

Java

public static double code(double x1, double x2) {
	return x2 * -10.0;
}

Python

def code(x1, x2):
	return x2 * -10.0

Julia

function code(x1, x2)
	return Float64(x2 * -10.0)
end

MATLAB

function tmp = code(x1, x2)
	tmp = x2 * -10.0;
end

Wolfram

code[x1_, x2_] := N[(x2 * -10.0), $MachinePrecision]

Derivation

1. Initial program 67.5%

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

3. Taylor expanded in x1 around inf 25.7%

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

4. Taylor expanded in x1 around 0 7.5%

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

   1. distribute-rgt-out 7.5%

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

   2. metadata-eval 7.5%

      \[\leadsto x1 + x2 \cdot \color{blue}{-10} \]

6. Simplified 7.5%

   \[\leadsto x1 + \color{blue}{x2 \cdot -10} \]

7. Taylor expanded in x1 around 0 7.3%

   \[\leadsto \color{blue}{-10 \cdot x2} \]
8. Step-by-step derivation

   1. *-commutative 7.3%

      \[\leadsto \color{blue}{x2 \cdot -10} \]

9. Simplified 7.3%

   \[\leadsto \color{blue}{x2 \cdot -10} \]
10. Add Preprocessing

Alternative 25: 3.2% accurate, 127.0× speedup

Math

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

FPCore

(FPCore (x1 x2) :precision binary64 x1)

C

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

Fortran

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

Java

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

Python

def code(x1, x2):
	return x1

Julia

function code(x1, x2)
	return x1
end

MATLAB

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

Wolfram

code[x1_, x2_] := x1

Derivation

1. Initial program 67.5%

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

3. Taylor expanded in x1 around inf 25.7%

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

4. Taylor expanded in x1 around 0 7.5%

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

   1. distribute-rgt-out 7.5%

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

   2. metadata-eval 7.5%

      \[\leadsto x1 + x2 \cdot \color{blue}{-10} \]

6. Simplified 7.5%

   \[\leadsto x1 + \color{blue}{x2 \cdot -10} \]

7. Taylor expanded in x1 around inf 3.2%

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

Reproduce

herbie shell --seed 2024108 
(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))))))