Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.8% → 99.5%

Time: 1.5min

Alternatives: 24

Speedup: 4.4×

• 46.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 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: 99.5% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision] + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$2 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(3.0 * N[(N[(t$95$4 - N[(2.0 * x2 + x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * x1 + 1.0), $MachinePrecision] * N[(x1 * N[(x1 * N[(t$95$0 * 4.0 + -6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(2.0 * t$95$0), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 + -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$4 * t$95$0 + N[Power[x1, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Power[x1, 4.0], $MachinePrecision] * N[(6.0 + N[(-3.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $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 99.5%

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

   3. Simplified 99.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x1 around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x2 around 0 100.0%

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

      1. associate-+r+ 100.0%

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

      2. distribute-rgt-out 100.0%

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

      3. metadata-eval 100.0%

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

      4. *-commutative 100.0%

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

      5. mul-1-neg 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-*r/ 100.0%

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

      8. metadata-eval 100.0%

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

      9. distribute-neg-frac 100.0%

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

      10. metadata-eval 100.0%

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

   10. Simplified 100.0%

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

4. Final simplification 99.7%

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

Alternative 2: 99.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(N[(x1 * 3.0), $MachinePrecision] * x1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$2 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * t$95$3), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(N[(t$95$0 + N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(-3.0 + t$95$4), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(4.0 * t$95$4 + -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x1 * x1 + 1.0), $MachinePrecision] + N[(t$95$1 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(3.0 * N[(N[(t$95$1 - N[(x1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Power[x1, 4.0], $MachinePrecision] * N[(6.0 + N[(-3.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $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 99.5%

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

   3. Simplified 99.5%

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

   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 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x1 around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x2 around 0 100.0%

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

      1. associate-+r+ 100.0%

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

      2. distribute-rgt-out 100.0%

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

      3. metadata-eval 100.0%

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

      4. *-commutative 100.0%

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

      5. mul-1-neg 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-*r/ 100.0%

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

      8. metadata-eval 100.0%

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

      9. distribute-neg-frac 100.0%

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

      10. metadata-eval 100.0%

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

   10. Simplified 100.0%

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

4. Final simplification 99.6%

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

Alternative 3: 99.3% accurate, 0.5× speedup

Math

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

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_1))
        (t_3
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               t_1
               (+
                (* (* (* x1 2.0) t_2) (- t_2 3.0))
                (* (* x1 x1) (- (* t_2 4.0) 6.0))))
              (* t_0 t_2))
             (* x1 (* x1 x1))))
           (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))))))
   (if (<= t_3 INFINITY) t_3 (- (* (pow x1 4.0) (+ 6.0 (/ -3.0 x1))) x1))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double t_3 = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)));
	double tmp;
	if (t_3 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = (pow(x1, 4.0) * (6.0 + (-3.0 / x1))) - x1;
	}
	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) / t_1;
	double t_3 = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)));
	double tmp;
	if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = (Math.pow(x1, 4.0) * (6.0 + (-3.0 / x1))) - x1;
	}
	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_1
	t_3 = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)))
	tmp = 0
	if t_3 <= math.inf:
		tmp = t_3
	else:
		tmp = (math.pow(x1, 4.0) * (6.0 + (-3.0 / x1))) - x1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	t_3 = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)))) + Float64(t_0 * t_2)) + 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_3 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(Float64((x1 ^ 4.0) * Float64(6.0 + Float64(-3.0 / x1))) - x1);
	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_1;
	t_3 = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)));
	tmp = 0.0;
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = ((x1 ^ 4.0) * (6.0 + (-3.0 / x1))) - x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$2), $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$3, Infinity], t$95$3, N[(N[(N[Power[x1, 4.0], $MachinePrecision] * N[(6.0 + N[(-3.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $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 99.5%

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

   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 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x1 around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x2 around 0 100.0%

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

      1. associate-+r+ 100.0%

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

      2. distribute-rgt-out 100.0%

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

      3. metadata-eval 100.0%

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

      4. *-commutative 100.0%

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

      5. mul-1-neg 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-*r/ 100.0%

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

      8. metadata-eval 100.0%

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

      9. distribute-neg-frac 100.0%

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

      10. metadata-eval 100.0%

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

   10. Simplified 100.0%

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

4. Final simplification 99.6%

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

Alternative 4: 98.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102} \lor \neg \left(x1 \leq 2 \cdot 10^{+77}\right):\\ \;\;\;\;{x1}^{4} \cdot \left(6 + \frac{-3}{x1}\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t\_2 \cdot 4 - 6\right)\right) + 3 \cdot t\_0\right)\right)\right) + \left(x2 \cdot -6 + x1 \cdot -3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (if (or (<= x1 -5.6e+102) (not (<= x1 2e+77)))
     (- (* (pow x1 4.0) (+ 6.0 (/ -3.0 x1))) x1)
     (+
      x1
      (+
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (*
           t_1
           (+
            (* (* (* x1 2.0) t_2) (- t_2 3.0))
            (* (* x1 x1) (- (* t_2 4.0) 6.0))))
          (* 3.0 t_0))))
       (+ (* x2 -6.0) (* x1 -3.0)))))))

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) / t_1;
	double tmp;
	if ((x1 <= -5.6e+102) || !(x1 <= 2e+77)) {
		tmp = (pow(x1, 4.0) * (6.0 + (-3.0 / x1))) - x1;
	} else {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (3.0 * t_0)))) + ((x2 * -6.0) + (x1 * -3.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    if ((x1 <= (-5.6d+102)) .or. (.not. (x1 <= 2d+77))) then
        tmp = ((x1 ** 4.0d0) * (6.0d0 + ((-3.0d0) / x1))) - x1
    else
        tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * ((t_2 * 4.0d0) - 6.0d0)))) + (3.0d0 * t_0)))) + ((x2 * (-6.0d0)) + (x1 * (-3.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -5.6e+102) || !(x1 <= 2e+77)) {
		tmp = (Math.pow(x1, 4.0) * (6.0 + (-3.0 / x1))) - x1;
	} else {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (3.0 * t_0)))) + ((x2 * -6.0) + (x1 * -3.0)));
	}
	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_1
	tmp = 0
	if (x1 <= -5.6e+102) or not (x1 <= 2e+77):
		tmp = (math.pow(x1, 4.0) * (6.0 + (-3.0 / x1))) - x1
	else:
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (3.0 * t_0)))) + ((x2 * -6.0) + (x1 * -3.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if ((x1 <= -5.6e+102) || !(x1 <= 2e+77))
		tmp = Float64(Float64((x1 ^ 4.0) * Float64(6.0 + Float64(-3.0 / x1))) - x1);
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)))) + Float64(3.0 * t_0)))) + Float64(Float64(x2 * -6.0) + Float64(x1 * -3.0))));
	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_1;
	tmp = 0.0;
	if ((x1 <= -5.6e+102) || ~((x1 <= 2e+77)))
		tmp = ((x1 ^ 4.0) * (6.0 + (-3.0 / x1))) - x1;
	else
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (3.0 * t_0)))) + ((x2 * -6.0) + (x1 * -3.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[x1, -5.6e+102], N[Not[LessEqual[x1, 2e+77]], $MachinePrecision]], N[(N[(N[Power[x1, 4.0], $MachinePrecision] * N[(6.0 + N[(-3.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -5.60000000000000037e102 or 1.99999999999999997e77 < x1

   1. Initial program 22.3%

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

   3. Taylor expanded in x1 around inf 22.3%

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

   4. Taylor expanded in x1 around 0 22.3%

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

   5. Taylor expanded in x1 around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x2 around 0 100.0%

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

      1. associate-+r+ 100.0%

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

      2. distribute-rgt-out 100.0%

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

      3. metadata-eval 100.0%

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

      4. *-commutative 100.0%

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

      5. mul-1-neg 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-*r/ 100.0%

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

      8. metadata-eval 100.0%

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

      9. distribute-neg-frac 100.0%

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

      10. metadata-eval 100.0%

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

   10. Simplified 100.0%

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

   if -5.60000000000000037e102 < x1 < 1.99999999999999997e77

   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 98.6%

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

   4. Taylor expanded in x1 around 0 99.4%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102} \lor \neg \left(x1 \leq 2 \cdot 10^{+77}\right):\\ \;\;\;\;{x1}^{4} \cdot \left(6 + \frac{-3}{x1}\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right) + \left(x2 \cdot -6 + x1 \cdot -3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\\ t_2 := x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ t_3 := x1 \cdot x1 + 1\\ t_4 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_3}\\ \mathbf{if}\;x1 \leq -8.5 \cdot 10^{+150}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + x1 \cdot \left(t\_1 + x1 \cdot \left(\left(x2 \cdot -4 + \left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(t\_1 + 4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right) - 6\right)\right)\right)\right) - 6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_3 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_4\right) \cdot \left(t\_4 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t\_4 \cdot 4 - 6\right)\right) + 3 \cdot t\_0\right)\right)\right) + \left(x2 \cdot -6 + x1 \cdot -3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))
        (t_2 (+ x1 (+ x1 (* x1 (- (* x1 9.0) 3.0)))))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (/ (- (+ t_0 (* 2.0 x2)) x1) t_3)))
   (if (<= x1 -8.5e+150)
     t_2
     (if (<= x1 -5.6e+102)
       (+
        x1
        (+
         9.0
         (+
          x1
          (*
           x1
           (+
            t_1
            (*
             x1
             (-
              (+
               (* x2 -4.0)
               (+
                (* x2 6.0)
                (+
                 (* x2 8.0)
                 (* x1 (- (+ t_1 (* 4.0 (* x2 (+ 3.0 (* x2 -2.0))))) 6.0)))))
              6.0)))))))
       (if (<= x1 5e+153)
         (+
          x1
          (+
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (*
               t_3
               (+
                (* (* (* x1 2.0) t_4) (- t_4 3.0))
                (* (* x1 x1) (- (* t_4 4.0) 6.0))))
              (* 3.0 t_0))))
           (+ (* x2 -6.0) (* x1 -3.0))))
         t_2)))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 4.0 * (x2 * ((2.0 * x2) - 3.0));
	double t_2 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = ((t_0 + (2.0 * x2)) - x1) / t_3;
	double tmp;
	if (x1 <= -8.5e+150) {
		tmp = t_2;
	} else if (x1 <= -5.6e+102) {
		tmp = x1 + (9.0 + (x1 + (x1 * (t_1 + (x1 * (((x2 * -4.0) + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_1 + (4.0 * (x2 * (3.0 + (x2 * -2.0))))) - 6.0))))) - 6.0))))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_3 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + (3.0 * t_0)))) + ((x2 * -6.0) + (x1 * -3.0)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = 4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))
    t_2 = x1 + (x1 + (x1 * ((x1 * 9.0d0) - 3.0d0)))
    t_3 = (x1 * x1) + 1.0d0
    t_4 = ((t_0 + (2.0d0 * x2)) - x1) / t_3
    if (x1 <= (-8.5d+150)) then
        tmp = t_2
    else if (x1 <= (-5.6d+102)) then
        tmp = x1 + (9.0d0 + (x1 + (x1 * (t_1 + (x1 * (((x2 * (-4.0d0)) + ((x2 * 6.0d0) + ((x2 * 8.0d0) + (x1 * ((t_1 + (4.0d0 * (x2 * (3.0d0 + (x2 * (-2.0d0)))))) - 6.0d0))))) - 6.0d0))))))
    else if (x1 <= 5d+153) then
        tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_3 * ((((x1 * 2.0d0) * t_4) * (t_4 - 3.0d0)) + ((x1 * x1) * ((t_4 * 4.0d0) - 6.0d0)))) + (3.0d0 * t_0)))) + ((x2 * (-6.0d0)) + (x1 * (-3.0d0))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 4.0 * (x2 * ((2.0 * x2) - 3.0));
	double t_2 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = ((t_0 + (2.0 * x2)) - x1) / t_3;
	double tmp;
	if (x1 <= -8.5e+150) {
		tmp = t_2;
	} else if (x1 <= -5.6e+102) {
		tmp = x1 + (9.0 + (x1 + (x1 * (t_1 + (x1 * (((x2 * -4.0) + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_1 + (4.0 * (x2 * (3.0 + (x2 * -2.0))))) - 6.0))))) - 6.0))))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_3 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + (3.0 * t_0)))) + ((x2 * -6.0) + (x1 * -3.0)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = 4.0 * (x2 * ((2.0 * x2) - 3.0))
	t_2 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)))
	t_3 = (x1 * x1) + 1.0
	t_4 = ((t_0 + (2.0 * x2)) - x1) / t_3
	tmp = 0
	if x1 <= -8.5e+150:
		tmp = t_2
	elif x1 <= -5.6e+102:
		tmp = x1 + (9.0 + (x1 + (x1 * (t_1 + (x1 * (((x2 * -4.0) + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_1 + (4.0 * (x2 * (3.0 + (x2 * -2.0))))) - 6.0))))) - 6.0))))))
	elif x1 <= 5e+153:
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_3 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + (3.0 * t_0)))) + ((x2 * -6.0) + (x1 * -3.0)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))
	t_2 = Float64(x1 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * 9.0) - 3.0))))
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_3)
	tmp = 0.0
	if (x1 <= -8.5e+150)
		tmp = t_2;
	elseif (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(x1 * Float64(t_1 + Float64(x1 * Float64(Float64(Float64(x2 * -4.0) + Float64(Float64(x2 * 6.0) + Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_1 + Float64(4.0 * Float64(x2 * Float64(3.0 + Float64(x2 * -2.0))))) - 6.0))))) - 6.0)))))));
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_3 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(t_4 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_4 * 4.0) - 6.0)))) + Float64(3.0 * t_0)))) + Float64(Float64(x2 * -6.0) + Float64(x1 * -3.0))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = 4.0 * (x2 * ((2.0 * x2) - 3.0));
	t_2 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	t_3 = (x1 * x1) + 1.0;
	t_4 = ((t_0 + (2.0 * x2)) - x1) / t_3;
	tmp = 0.0;
	if (x1 <= -8.5e+150)
		tmp = t_2;
	elseif (x1 <= -5.6e+102)
		tmp = x1 + (9.0 + (x1 + (x1 * (t_1 + (x1 * (((x2 * -4.0) + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_1 + (4.0 * (x2 * (3.0 + (x2 * -2.0))))) - 6.0))))) - 6.0))))));
	elseif (x1 <= 5e+153)
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_3 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + (3.0 * t_0)))) + ((x2 * -6.0) + (x1 * -3.0)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(x1 + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, If[LessEqual[x1, -8.5e+150], t$95$2, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(9.0 + N[(x1 + N[(x1 * N[(t$95$1 + N[(x1 * N[(N[(N[(x2 * -4.0), $MachinePrecision] + N[(N[(x2 * 6.0), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$1 + N[(4.0 * N[(x2 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], N[(x1 + N[(N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$3 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$4 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -8.4999999999999999e150 or 5.00000000000000018e153 < x1

   1. Initial program 1.5%

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

   3. Taylor expanded in x1 around 0 0.1%

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

   4. Taylor expanded in x1 around 0 59.7%

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

   5. Taylor expanded in x2 around 0 98.7%

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

   if -8.4999999999999999e150 < x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around inf 0.0%

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

   5. Taylor expanded in x1 around 0 85.7%

      \[\leadsto x1 + \left(\left(\color{blue}{x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(-4 \cdot x2 + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 6\right)\right)\right)\right) - 6\right)\right)} + x1\right) + 9\right) \]

   if -5.60000000000000037e102 < x1 < 5.00000000000000018e153

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around inf 98.8%

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

   4. Taylor expanded in x1 around 0 99.5%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -8.5 \cdot 10^{+150}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(x2 \cdot -4 + \left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + 4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right) - 6\right)\right)\right)\right) - 6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right) + \left(x2 \cdot -6 + x1 \cdot -3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot x2 - 3\\ t_1 := 4 \cdot \left(x2 \cdot t\_0\right)\\ t_2 := 3 - 2 \cdot x2\\ t_3 := x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ t_4 := x1 \cdot \left(x1 \cdot 3\right)\\ t_5 := x1 \cdot x1 + 1\\ t_6 := \frac{\left(t\_4 + 2 \cdot x2\right) - x1}{t\_5}\\ \mathbf{if}\;x1 \leq -8.5 \cdot 10^{+150}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_4 - 2 \cdot x2\right) - x1}{t\_5} + \left(x1 + x1 \cdot \left(t\_1 + x1 \cdot \left(3 + \left(2 \cdot \left(x2 \cdot -2 + t\_2\right) + \left(x2 \cdot 8 + x1 \cdot \left(\left(t\_1 + 2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + 3 \cdot t\_0\right)\right) + 2 \cdot \left(x2 \cdot t\_2\right)\right)\right) - 3\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_5 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_6\right) \cdot \left(t\_6 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t\_6 \cdot 4 - 6\right)\right) + 3 \cdot t\_4\right)\right)\right) + \left(x2 \cdot -6 + x1 \cdot -3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* 2.0 x2) 3.0))
        (t_1 (* 4.0 (* x2 t_0)))
        (t_2 (- 3.0 (* 2.0 x2)))
        (t_3 (+ x1 (+ x1 (* x1 (- (* x1 9.0) 3.0)))))
        (t_4 (* x1 (* x1 3.0)))
        (t_5 (+ (* x1 x1) 1.0))
        (t_6 (/ (- (+ t_4 (* 2.0 x2)) x1) t_5)))
   (if (<= x1 -8.5e+150)
     t_3
     (if (<= x1 -5.6e+102)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_4 (* 2.0 x2)) x1) t_5))
         (+
          x1
          (*
           x1
           (+
            t_1
            (*
             x1
             (+
              3.0
              (+
               (* 2.0 (+ (* x2 -2.0) t_2))
               (+
                (* x2 8.0)
                (*
                 x1
                 (-
                  (+
                   t_1
                   (*
                    2.0
                    (+
                     (+ 1.0 (+ (* 2.0 (* x2 (+ 3.0 (* x2 -2.0)))) (* 3.0 t_0)))
                     (* 2.0 (* x2 t_2)))))
                  3.0)))))))))))
       (if (<= x1 5e+153)
         (+
          x1
          (+
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (*
               t_5
               (+
                (* (* (* x1 2.0) t_6) (- t_6 3.0))
                (* (* x1 x1) (- (* t_6 4.0) 6.0))))
              (* 3.0 t_4))))
           (+ (* x2 -6.0) (* x1 -3.0))))
         t_3)))))

C

double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = 4.0 * (x2 * t_0);
	double t_2 = 3.0 - (2.0 * x2);
	double t_3 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	double t_4 = x1 * (x1 * 3.0);
	double t_5 = (x1 * x1) + 1.0;
	double t_6 = ((t_4 + (2.0 * x2)) - x1) / t_5;
	double tmp;
	if (x1 <= -8.5e+150) {
		tmp = t_3;
	} else if (x1 <= -5.6e+102) {
		tmp = x1 + ((3.0 * (((t_4 - (2.0 * x2)) - x1) / t_5)) + (x1 + (x1 * (t_1 + (x1 * (3.0 + ((2.0 * ((x2 * -2.0) + t_2)) + ((x2 * 8.0) + (x1 * ((t_1 + (2.0 * ((1.0 + ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_0))) + (2.0 * (x2 * t_2))))) - 3.0))))))))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_5 * ((((x1 * 2.0) * t_6) * (t_6 - 3.0)) + ((x1 * x1) * ((t_6 * 4.0) - 6.0)))) + (3.0 * t_4)))) + ((x2 * -6.0) + (x1 * -3.0)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = (2.0d0 * x2) - 3.0d0
    t_1 = 4.0d0 * (x2 * t_0)
    t_2 = 3.0d0 - (2.0d0 * x2)
    t_3 = x1 + (x1 + (x1 * ((x1 * 9.0d0) - 3.0d0)))
    t_4 = x1 * (x1 * 3.0d0)
    t_5 = (x1 * x1) + 1.0d0
    t_6 = ((t_4 + (2.0d0 * x2)) - x1) / t_5
    if (x1 <= (-8.5d+150)) then
        tmp = t_3
    else if (x1 <= (-5.6d+102)) then
        tmp = x1 + ((3.0d0 * (((t_4 - (2.0d0 * x2)) - x1) / t_5)) + (x1 + (x1 * (t_1 + (x1 * (3.0d0 + ((2.0d0 * ((x2 * (-2.0d0)) + t_2)) + ((x2 * 8.0d0) + (x1 * ((t_1 + (2.0d0 * ((1.0d0 + ((2.0d0 * (x2 * (3.0d0 + (x2 * (-2.0d0))))) + (3.0d0 * t_0))) + (2.0d0 * (x2 * t_2))))) - 3.0d0))))))))))
    else if (x1 <= 5d+153) then
        tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_5 * ((((x1 * 2.0d0) * t_6) * (t_6 - 3.0d0)) + ((x1 * x1) * ((t_6 * 4.0d0) - 6.0d0)))) + (3.0d0 * t_4)))) + ((x2 * (-6.0d0)) + (x1 * (-3.0d0))))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = 4.0 * (x2 * t_0);
	double t_2 = 3.0 - (2.0 * x2);
	double t_3 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	double t_4 = x1 * (x1 * 3.0);
	double t_5 = (x1 * x1) + 1.0;
	double t_6 = ((t_4 + (2.0 * x2)) - x1) / t_5;
	double tmp;
	if (x1 <= -8.5e+150) {
		tmp = t_3;
	} else if (x1 <= -5.6e+102) {
		tmp = x1 + ((3.0 * (((t_4 - (2.0 * x2)) - x1) / t_5)) + (x1 + (x1 * (t_1 + (x1 * (3.0 + ((2.0 * ((x2 * -2.0) + t_2)) + ((x2 * 8.0) + (x1 * ((t_1 + (2.0 * ((1.0 + ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_0))) + (2.0 * (x2 * t_2))))) - 3.0))))))))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_5 * ((((x1 * 2.0) * t_6) * (t_6 - 3.0)) + ((x1 * x1) * ((t_6 * 4.0) - 6.0)))) + (3.0 * t_4)))) + ((x2 * -6.0) + (x1 * -3.0)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (2.0 * x2) - 3.0
	t_1 = 4.0 * (x2 * t_0)
	t_2 = 3.0 - (2.0 * x2)
	t_3 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)))
	t_4 = x1 * (x1 * 3.0)
	t_5 = (x1 * x1) + 1.0
	t_6 = ((t_4 + (2.0 * x2)) - x1) / t_5
	tmp = 0
	if x1 <= -8.5e+150:
		tmp = t_3
	elif x1 <= -5.6e+102:
		tmp = x1 + ((3.0 * (((t_4 - (2.0 * x2)) - x1) / t_5)) + (x1 + (x1 * (t_1 + (x1 * (3.0 + ((2.0 * ((x2 * -2.0) + t_2)) + ((x2 * 8.0) + (x1 * ((t_1 + (2.0 * ((1.0 + ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_0))) + (2.0 * (x2 * t_2))))) - 3.0))))))))))
	elif x1 <= 5e+153:
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_5 * ((((x1 * 2.0) * t_6) * (t_6 - 3.0)) + ((x1 * x1) * ((t_6 * 4.0) - 6.0)))) + (3.0 * t_4)))) + ((x2 * -6.0) + (x1 * -3.0)))
	else:
		tmp = t_3
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(2.0 * x2) - 3.0)
	t_1 = Float64(4.0 * Float64(x2 * t_0))
	t_2 = Float64(3.0 - Float64(2.0 * x2))
	t_3 = Float64(x1 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * 9.0) - 3.0))))
	t_4 = Float64(x1 * Float64(x1 * 3.0))
	t_5 = Float64(Float64(x1 * x1) + 1.0)
	t_6 = Float64(Float64(Float64(t_4 + Float64(2.0 * x2)) - x1) / t_5)
	tmp = 0.0
	if (x1 <= -8.5e+150)
		tmp = t_3;
	elseif (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_4 - Float64(2.0 * x2)) - x1) / t_5)) + Float64(x1 + Float64(x1 * Float64(t_1 + Float64(x1 * Float64(3.0 + Float64(Float64(2.0 * Float64(Float64(x2 * -2.0) + t_2)) + Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_1 + Float64(2.0 * Float64(Float64(1.0 + Float64(Float64(2.0 * Float64(x2 * Float64(3.0 + Float64(x2 * -2.0)))) + Float64(3.0 * t_0))) + Float64(2.0 * Float64(x2 * t_2))))) - 3.0)))))))))));
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_5 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_6) * Float64(t_6 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_6 * 4.0) - 6.0)))) + Float64(3.0 * t_4)))) + Float64(Float64(x2 * -6.0) + Float64(x1 * -3.0))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (2.0 * x2) - 3.0;
	t_1 = 4.0 * (x2 * t_0);
	t_2 = 3.0 - (2.0 * x2);
	t_3 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	t_4 = x1 * (x1 * 3.0);
	t_5 = (x1 * x1) + 1.0;
	t_6 = ((t_4 + (2.0 * x2)) - x1) / t_5;
	tmp = 0.0;
	if (x1 <= -8.5e+150)
		tmp = t_3;
	elseif (x1 <= -5.6e+102)
		tmp = x1 + ((3.0 * (((t_4 - (2.0 * x2)) - x1) / t_5)) + (x1 + (x1 * (t_1 + (x1 * (3.0 + ((2.0 * ((x2 * -2.0) + t_2)) + ((x2 * 8.0) + (x1 * ((t_1 + (2.0 * ((1.0 + ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_0))) + (2.0 * (x2 * t_2))))) - 3.0))))))))));
	elseif (x1 <= 5e+153)
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_5 * ((((x1 * 2.0) * t_6) * (t_6 - 3.0)) + ((x1 * x1) * ((t_6 * 4.0) - 6.0)))) + (3.0 * t_4)))) + ((x2 * -6.0) + (x1 * -3.0)));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$1 = N[(4.0 * N[(x2 * t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(x1 + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$4 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$5), $MachinePrecision]}, If[LessEqual[x1, -8.5e+150], t$95$3, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$4 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$5), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x1 * N[(t$95$1 + N[(x1 * N[(3.0 + N[(N[(2.0 * N[(N[(x2 * -2.0), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$1 + N[(2.0 * N[(N[(1.0 + N[(N[(2.0 * N[(x2 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(x2 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], N[(x1 + N[(N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$5 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$6), $MachinePrecision] * N[(t$95$6 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$6 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -8.4999999999999999e150 or 5.00000000000000018e153 < x1

   1. Initial program 1.5%

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

   3. Taylor expanded in x1 around 0 0.1%

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

   4. Taylor expanded in x1 around 0 59.7%

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

   5. Taylor expanded in x2 around 0 98.7%

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

   if -8.4999999999999999e150 < x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around 0 100.0%

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

   if -5.60000000000000037e102 < x1 < 5.00000000000000018e153

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around inf 98.8%

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

   4. Taylor expanded in x1 around 0 99.5%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -8.5 \cdot 10^{+150}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(3 + \left(2 \cdot \left(x2 \cdot -2 + \left(3 - 2 \cdot x2\right)\right) + \left(x2 \cdot 8 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + 2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 2 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) - 3\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right) + \left(x2 \cdot -6 + x1 \cdot -3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\\ t_2 := x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := \frac{\left(t\_3 + 2 \cdot x2\right) - x1}{t\_0}\\ \mathbf{if}\;x1 \leq -8.5 \cdot 10^{+150}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + x1 \cdot \left(t\_1 + x1 \cdot \left(\left(x2 \cdot -4 + \left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(t\_1 + 4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right) - 6\right)\right)\right)\right) - 6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x2 \cdot -6 + x1 \cdot -3\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_3 + t\_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_4\right) \cdot \left(t\_4 - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))
        (t_2 (+ x1 (+ x1 (* x1 (- (* x1 9.0) 3.0)))))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (/ (- (+ t_3 (* 2.0 x2)) x1) t_0)))
   (if (<= x1 -8.5e+150)
     t_2
     (if (<= x1 -5.6e+102)
       (+
        x1
        (+
         9.0
         (+
          x1
          (*
           x1
           (+
            t_1
            (*
             x1
             (-
              (+
               (* x2 -4.0)
               (+
                (* x2 6.0)
                (+
                 (* x2 8.0)
                 (* x1 (- (+ t_1 (* 4.0 (* x2 (+ 3.0 (* x2 -2.0))))) 6.0)))))
              6.0)))))))
       (if (<= x1 5e+153)
         (+
          x1
          (+
           (+ (* x2 -6.0) (* x1 -3.0))
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* 3.0 t_3)
              (*
               t_0
               (+ (* (* (* x1 2.0) t_4) (- t_4 3.0)) (* (* x1 x1) 6.0))))))))
         t_2)))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 4.0 * (x2 * ((2.0 * x2) - 3.0));
	double t_2 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	double tmp;
	if (x1 <= -8.5e+150) {
		tmp = t_2;
	} else if (x1 <= -5.6e+102) {
		tmp = x1 + (9.0 + (x1 + (x1 * (t_1 + (x1 * (((x2 * -4.0) + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_1 + (4.0 * (x2 * (3.0 + (x2 * -2.0))))) - 6.0))))) - 6.0))))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_3) + (t_0 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * 6.0)))))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = 4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))
    t_2 = x1 + (x1 + (x1 * ((x1 * 9.0d0) - 3.0d0)))
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = ((t_3 + (2.0d0 * x2)) - x1) / t_0
    if (x1 <= (-8.5d+150)) then
        tmp = t_2
    else if (x1 <= (-5.6d+102)) then
        tmp = x1 + (9.0d0 + (x1 + (x1 * (t_1 + (x1 * (((x2 * (-4.0d0)) + ((x2 * 6.0d0) + ((x2 * 8.0d0) + (x1 * ((t_1 + (4.0d0 * (x2 * (3.0d0 + (x2 * (-2.0d0)))))) - 6.0d0))))) - 6.0d0))))))
    else if (x1 <= 5d+153) then
        tmp = x1 + (((x2 * (-6.0d0)) + (x1 * (-3.0d0))) + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_3) + (t_0 * ((((x1 * 2.0d0) * t_4) * (t_4 - 3.0d0)) + ((x1 * x1) * 6.0d0)))))))
    else
        tmp = t_2
    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 = 4.0 * (x2 * ((2.0 * x2) - 3.0));
	double t_2 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	double tmp;
	if (x1 <= -8.5e+150) {
		tmp = t_2;
	} else if (x1 <= -5.6e+102) {
		tmp = x1 + (9.0 + (x1 + (x1 * (t_1 + (x1 * (((x2 * -4.0) + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_1 + (4.0 * (x2 * (3.0 + (x2 * -2.0))))) - 6.0))))) - 6.0))))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_3) + (t_0 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * 6.0)))))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = 4.0 * (x2 * ((2.0 * x2) - 3.0))
	t_2 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)))
	t_3 = x1 * (x1 * 3.0)
	t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0
	tmp = 0
	if x1 <= -8.5e+150:
		tmp = t_2
	elif x1 <= -5.6e+102:
		tmp = x1 + (9.0 + (x1 + (x1 * (t_1 + (x1 * (((x2 * -4.0) + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_1 + (4.0 * (x2 * (3.0 + (x2 * -2.0))))) - 6.0))))) - 6.0))))))
	elif x1 <= 5e+153:
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_3) + (t_0 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * 6.0)))))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))
	t_2 = Float64(x1 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * 9.0) - 3.0))))
	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 <= -8.5e+150)
		tmp = t_2;
	elseif (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(x1 * Float64(t_1 + Float64(x1 * Float64(Float64(Float64(x2 * -4.0) + Float64(Float64(x2 * 6.0) + Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_1 + Float64(4.0 * Float64(x2 * Float64(3.0 + Float64(x2 * -2.0))))) - 6.0))))) - 6.0)))))));
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + Float64(Float64(Float64(x2 * -6.0) + Float64(x1 * -3.0)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_3) + Float64(t_0 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(t_4 - 3.0)) + Float64(Float64(x1 * x1) * 6.0))))))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = 4.0 * (x2 * ((2.0 * x2) - 3.0));
	t_2 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	t_3 = x1 * (x1 * 3.0);
	t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	tmp = 0.0;
	if (x1 <= -8.5e+150)
		tmp = t_2;
	elseif (x1 <= -5.6e+102)
		tmp = x1 + (9.0 + (x1 + (x1 * (t_1 + (x1 * (((x2 * -4.0) + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_1 + (4.0 * (x2 * (3.0 + (x2 * -2.0))))) - 6.0))))) - 6.0))))));
	elseif (x1 <= 5e+153)
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_3) + (t_0 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * 6.0)))))));
	else
		tmp = t_2;
	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[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(x1 + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $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, -8.5e+150], t$95$2, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(9.0 + N[(x1 + N[(x1 * N[(t$95$1 + N[(x1 * N[(N[(N[(x2 * -4.0), $MachinePrecision] + N[(N[(x2 * 6.0), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$1 + N[(4.0 * N[(x2 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], N[(x1 + N[(N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$3), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -8.4999999999999999e150 or 5.00000000000000018e153 < x1

   1. Initial program 1.5%

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

   3. Taylor expanded in x1 around 0 0.1%

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

   4. Taylor expanded in x1 around 0 59.7%

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

   5. Taylor expanded in x2 around 0 98.7%

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

   if -8.4999999999999999e150 < x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around inf 0.0%

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

   5. Taylor expanded in x1 around 0 85.7%

      \[\leadsto x1 + \left(\left(\color{blue}{x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(-4 \cdot x2 + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 6\right)\right)\right)\right) - 6\right)\right)} + x1\right) + 9\right) \]

   if -5.60000000000000037e102 < x1 < 5.00000000000000018e153

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around inf 98.8%

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

   4. Taylor expanded in x1 around 0 99.5%

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

   5. Taylor expanded in x1 around inf 97.4%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -8.5 \cdot 10^{+150}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(x2 \cdot -4 + \left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + 4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right) - 6\right)\right)\right)\right) - 6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x2 \cdot -6 + x1 \cdot -3\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 92.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{\left(t\_1 + 2 \cdot x2\right) - x1}{t\_2}\\ t_4 := x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ t_5 := x1 \cdot \left(x1 \cdot x1\right)\\ t_6 := \left(x1 \cdot 2\right) \cdot \left(2 \cdot x2\right)\\ \mathbf{if}\;x1 \leq -8.5 \cdot 10^{+150}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + x1 \cdot \left(t\_0 + x1 \cdot \left(\left(x2 \cdot -4 + \left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(t\_0 + 4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right) - 6\right)\right)\right)\right) - 6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.9 \cdot 10^{+14}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(t\_5 + \left(t\_1 \cdot t\_3 + t\_2 \cdot \left(\left(x1 \cdot x1\right) \cdot 6 + \left(t\_3 - 3\right) \cdot t\_6\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x2 \cdot -6 + x1 \cdot -3\right) + \left(x1 + \left(t\_5 + \left(3 \cdot t\_1 + t\_2 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t\_3 \cdot 4 - 6\right) + t\_6 \cdot \left(\left(2 \cdot x2 - x1\right) - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (/ (- (+ t_1 (* 2.0 x2)) x1) t_2))
        (t_4 (+ x1 (+ x1 (* x1 (- (* x1 9.0) 3.0)))))
        (t_5 (* x1 (* x1 x1)))
        (t_6 (* (* x1 2.0) (* 2.0 x2))))
   (if (<= x1 -8.5e+150)
     t_4
     (if (<= x1 -5.6e+102)
       (+
        x1
        (+
         9.0
         (+
          x1
          (*
           x1
           (+
            t_0
            (*
             x1
             (-
              (+
               (* x2 -4.0)
               (+
                (* x2 6.0)
                (+
                 (* x2 8.0)
                 (* x1 (- (+ t_0 (* 4.0 (* x2 (+ 3.0 (* x2 -2.0))))) 6.0)))))
              6.0)))))))
       (if (<= x1 -1.9e+14)
         (+
          x1
          (+
           9.0
           (+
            x1
            (+
             t_5
             (+
              (* t_1 t_3)
              (* t_2 (+ (* (* x1 x1) 6.0) (* (- t_3 3.0) t_6))))))))
         (if (<= x1 4.5e+153)
           (+
            x1
            (+
             (+ (* x2 -6.0) (* x1 -3.0))
             (+
              x1
              (+
               t_5
               (+
                (* 3.0 t_1)
                (*
                 t_2
                 (+
                  (* (* x1 x1) (- (* t_3 4.0) 6.0))
                  (* t_6 (- (- (* 2.0 x2) x1) 3.0)))))))))
           t_4))))))

C

double code(double x1, double x2) {
	double t_0 = 4.0 * (x2 * ((2.0 * x2) - 3.0));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	double t_4 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	double t_5 = x1 * (x1 * x1);
	double t_6 = (x1 * 2.0) * (2.0 * x2);
	double tmp;
	if (x1 <= -8.5e+150) {
		tmp = t_4;
	} else if (x1 <= -5.6e+102) {
		tmp = x1 + (9.0 + (x1 + (x1 * (t_0 + (x1 * (((x2 * -4.0) + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_0 + (4.0 * (x2 * (3.0 + (x2 * -2.0))))) - 6.0))))) - 6.0))))));
	} else if (x1 <= -1.9e+14) {
		tmp = x1 + (9.0 + (x1 + (t_5 + ((t_1 * t_3) + (t_2 * (((x1 * x1) * 6.0) + ((t_3 - 3.0) * t_6)))))));
	} else if (x1 <= 4.5e+153) {
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + (t_5 + ((3.0 * t_1) + (t_2 * (((x1 * x1) * ((t_3 * 4.0) - 6.0)) + (t_6 * (((2.0 * x2) - x1) - 3.0))))))));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = 4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = ((t_1 + (2.0d0 * x2)) - x1) / t_2
    t_4 = x1 + (x1 + (x1 * ((x1 * 9.0d0) - 3.0d0)))
    t_5 = x1 * (x1 * x1)
    t_6 = (x1 * 2.0d0) * (2.0d0 * x2)
    if (x1 <= (-8.5d+150)) then
        tmp = t_4
    else if (x1 <= (-5.6d+102)) then
        tmp = x1 + (9.0d0 + (x1 + (x1 * (t_0 + (x1 * (((x2 * (-4.0d0)) + ((x2 * 6.0d0) + ((x2 * 8.0d0) + (x1 * ((t_0 + (4.0d0 * (x2 * (3.0d0 + (x2 * (-2.0d0)))))) - 6.0d0))))) - 6.0d0))))))
    else if (x1 <= (-1.9d+14)) then
        tmp = x1 + (9.0d0 + (x1 + (t_5 + ((t_1 * t_3) + (t_2 * (((x1 * x1) * 6.0d0) + ((t_3 - 3.0d0) * t_6)))))))
    else if (x1 <= 4.5d+153) then
        tmp = x1 + (((x2 * (-6.0d0)) + (x1 * (-3.0d0))) + (x1 + (t_5 + ((3.0d0 * t_1) + (t_2 * (((x1 * x1) * ((t_3 * 4.0d0) - 6.0d0)) + (t_6 * (((2.0d0 * x2) - x1) - 3.0d0))))))))
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 4.0 * (x2 * ((2.0 * x2) - 3.0));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	double t_4 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	double t_5 = x1 * (x1 * x1);
	double t_6 = (x1 * 2.0) * (2.0 * x2);
	double tmp;
	if (x1 <= -8.5e+150) {
		tmp = t_4;
	} else if (x1 <= -5.6e+102) {
		tmp = x1 + (9.0 + (x1 + (x1 * (t_0 + (x1 * (((x2 * -4.0) + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_0 + (4.0 * (x2 * (3.0 + (x2 * -2.0))))) - 6.0))))) - 6.0))))));
	} else if (x1 <= -1.9e+14) {
		tmp = x1 + (9.0 + (x1 + (t_5 + ((t_1 * t_3) + (t_2 * (((x1 * x1) * 6.0) + ((t_3 - 3.0) * t_6)))))));
	} else if (x1 <= 4.5e+153) {
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + (t_5 + ((3.0 * t_1) + (t_2 * (((x1 * x1) * ((t_3 * 4.0) - 6.0)) + (t_6 * (((2.0 * x2) - x1) - 3.0))))))));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 4.0 * (x2 * ((2.0 * x2) - 3.0))
	t_1 = x1 * (x1 * 3.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2
	t_4 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)))
	t_5 = x1 * (x1 * x1)
	t_6 = (x1 * 2.0) * (2.0 * x2)
	tmp = 0
	if x1 <= -8.5e+150:
		tmp = t_4
	elif x1 <= -5.6e+102:
		tmp = x1 + (9.0 + (x1 + (x1 * (t_0 + (x1 * (((x2 * -4.0) + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_0 + (4.0 * (x2 * (3.0 + (x2 * -2.0))))) - 6.0))))) - 6.0))))))
	elif x1 <= -1.9e+14:
		tmp = x1 + (9.0 + (x1 + (t_5 + ((t_1 * t_3) + (t_2 * (((x1 * x1) * 6.0) + ((t_3 - 3.0) * t_6)))))))
	elif x1 <= 4.5e+153:
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + (t_5 + ((3.0 * t_1) + (t_2 * (((x1 * x1) * ((t_3 * 4.0) - 6.0)) + (t_6 * (((2.0 * x2) - x1) - 3.0))))))))
	else:
		tmp = t_4
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_2)
	t_4 = Float64(x1 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * 9.0) - 3.0))))
	t_5 = Float64(x1 * Float64(x1 * x1))
	t_6 = Float64(Float64(x1 * 2.0) * Float64(2.0 * x2))
	tmp = 0.0
	if (x1 <= -8.5e+150)
		tmp = t_4;
	elseif (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(x1 * Float64(t_0 + Float64(x1 * Float64(Float64(Float64(x2 * -4.0) + Float64(Float64(x2 * 6.0) + Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_0 + Float64(4.0 * Float64(x2 * Float64(3.0 + Float64(x2 * -2.0))))) - 6.0))))) - 6.0)))))));
	elseif (x1 <= -1.9e+14)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_5 + Float64(Float64(t_1 * t_3) + Float64(t_2 * Float64(Float64(Float64(x1 * x1) * 6.0) + Float64(Float64(t_3 - 3.0) * t_6))))))));
	elseif (x1 <= 4.5e+153)
		tmp = Float64(x1 + Float64(Float64(Float64(x2 * -6.0) + Float64(x1 * -3.0)) + Float64(x1 + Float64(t_5 + Float64(Float64(3.0 * t_1) + Float64(t_2 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0)) + Float64(t_6 * Float64(Float64(Float64(2.0 * x2) - x1) - 3.0)))))))));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 4.0 * (x2 * ((2.0 * x2) - 3.0));
	t_1 = x1 * (x1 * 3.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	t_4 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	t_5 = x1 * (x1 * x1);
	t_6 = (x1 * 2.0) * (2.0 * x2);
	tmp = 0.0;
	if (x1 <= -8.5e+150)
		tmp = t_4;
	elseif (x1 <= -5.6e+102)
		tmp = x1 + (9.0 + (x1 + (x1 * (t_0 + (x1 * (((x2 * -4.0) + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_0 + (4.0 * (x2 * (3.0 + (x2 * -2.0))))) - 6.0))))) - 6.0))))));
	elseif (x1 <= -1.9e+14)
		tmp = x1 + (9.0 + (x1 + (t_5 + ((t_1 * t_3) + (t_2 * (((x1 * x1) * 6.0) + ((t_3 - 3.0) * t_6)))))));
	elseif (x1 <= 4.5e+153)
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + (t_5 + ((3.0 * t_1) + (t_2 * (((x1 * x1) * ((t_3 * 4.0) - 6.0)) + (t_6 * (((2.0 * x2) - x1) - 3.0))))))));
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(x1 + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 * 2.0), $MachinePrecision] * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -8.5e+150], t$95$4, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(9.0 + N[(x1 + N[(x1 * N[(t$95$0 + N[(x1 * N[(N[(N[(x2 * -4.0), $MachinePrecision] + N[(N[(x2 * 6.0), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$0 + N[(4.0 * N[(x2 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.9e+14], N[(x1 + N[(9.0 + N[(x1 + N[(t$95$5 + N[(N[(t$95$1 * t$95$3), $MachinePrecision] + N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision] + N[(N[(t$95$3 - 3.0), $MachinePrecision] * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.5e+153], N[(x1 + N[(N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$5 + N[(N[(3.0 * t$95$1), $MachinePrecision] + N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$6 * N[(N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -8.4999999999999999e150 or 4.5000000000000001e153 < x1

   1. Initial program 1.5%

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

   3. Taylor expanded in x1 around 0 0.1%

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

   4. Taylor expanded in x1 around 0 59.7%

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

   5. Taylor expanded in x2 around 0 98.7%

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

   if -8.4999999999999999e150 < x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around inf 0.0%

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

   5. Taylor expanded in x1 around 0 85.7%

      \[\leadsto x1 + \left(\left(\color{blue}{x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(-4 \cdot x2 + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 6\right)\right)\right)\right) - 6\right)\right)} + x1\right) + 9\right) \]

   if -5.60000000000000037e102 < x1 < -1.9e14

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 91.3%

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

   4. Taylor expanded in x1 around inf 91.3%

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

   5. Taylor expanded in x1 around inf 91.4%

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

   if -1.9e14 < x1 < 4.5000000000000001e153

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around inf 98.7%

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

   4. Taylor expanded in x1 around 0 99.5%

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

   5. Taylor expanded in x1 around 0 89.8%

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

      1. +-commutative 89.8%

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

      2. mul-1-neg 89.8%

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

      3. sub-neg 89.8%

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

   7. Simplified 89.8%

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

   8. Taylor expanded in x1 around 0 95.4%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -8.5 \cdot 10^{+150}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(x2 \cdot -4 + \left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + 4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right) - 6\right)\right)\right)\right) - 6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.9 \cdot 10^{+14}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6 + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x2 \cdot -6 + x1 \cdot -3\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2\right)\right) \cdot \left(\left(2 \cdot x2 - x1\right) - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 91.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\\ t_2 := x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ \mathbf{if}\;x1 \leq -8.5 \cdot 10^{+150}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq -4.8 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + x1 \cdot \left(t\_1 + x1 \cdot \left(\left(x2 \cdot -4 + \left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(t\_1 + 4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right) - 6\right)\right)\right)\right) - 6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x2 \cdot -6 + x1 \cdot -3\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_3 + t\_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(t\_3 + 2 \cdot x2\right) - x1}{t\_0} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2\right)\right) \cdot \left(\left(2 \cdot x2 - x1\right) - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))
        (t_2 (+ x1 (+ x1 (* x1 (- (* x1 9.0) 3.0)))))
        (t_3 (* x1 (* x1 3.0))))
   (if (<= x1 -8.5e+150)
     t_2
     (if (<= x1 -4.8e+102)
       (+
        x1
        (+
         9.0
         (+
          x1
          (*
           x1
           (+
            t_1
            (*
             x1
             (-
              (+
               (* x2 -4.0)
               (+
                (* x2 6.0)
                (+
                 (* x2 8.0)
                 (* x1 (- (+ t_1 (* 4.0 (* x2 (+ 3.0 (* x2 -2.0))))) 6.0)))))
              6.0)))))))
       (if (<= x1 4.5e+153)
         (+
          x1
          (+
           (+ (* x2 -6.0) (* x1 -3.0))
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* 3.0 t_3)
              (*
               t_0
               (+
                (* (* x1 x1) (- (* (/ (- (+ t_3 (* 2.0 x2)) x1) t_0) 4.0) 6.0))
                (* (* (* x1 2.0) (* 2.0 x2)) (- (- (* 2.0 x2) x1) 3.0)))))))))
         t_2)))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 4.0 * (x2 * ((2.0 * x2) - 3.0));
	double t_2 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	double t_3 = x1 * (x1 * 3.0);
	double tmp;
	if (x1 <= -8.5e+150) {
		tmp = t_2;
	} else if (x1 <= -4.8e+102) {
		tmp = x1 + (9.0 + (x1 + (x1 * (t_1 + (x1 * (((x2 * -4.0) + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_1 + (4.0 * (x2 * (3.0 + (x2 * -2.0))))) - 6.0))))) - 6.0))))));
	} else if (x1 <= 4.5e+153) {
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_3) + (t_0 * (((x1 * x1) * (((((t_3 + (2.0 * x2)) - x1) / t_0) * 4.0) - 6.0)) + (((x1 * 2.0) * (2.0 * x2)) * (((2.0 * x2) - x1) - 3.0))))))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = 4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))
    t_2 = x1 + (x1 + (x1 * ((x1 * 9.0d0) - 3.0d0)))
    t_3 = x1 * (x1 * 3.0d0)
    if (x1 <= (-8.5d+150)) then
        tmp = t_2
    else if (x1 <= (-4.8d+102)) then
        tmp = x1 + (9.0d0 + (x1 + (x1 * (t_1 + (x1 * (((x2 * (-4.0d0)) + ((x2 * 6.0d0) + ((x2 * 8.0d0) + (x1 * ((t_1 + (4.0d0 * (x2 * (3.0d0 + (x2 * (-2.0d0)))))) - 6.0d0))))) - 6.0d0))))))
    else if (x1 <= 4.5d+153) then
        tmp = x1 + (((x2 * (-6.0d0)) + (x1 * (-3.0d0))) + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_3) + (t_0 * (((x1 * x1) * (((((t_3 + (2.0d0 * x2)) - x1) / t_0) * 4.0d0) - 6.0d0)) + (((x1 * 2.0d0) * (2.0d0 * x2)) * (((2.0d0 * x2) - x1) - 3.0d0))))))))
    else
        tmp = t_2
    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 = 4.0 * (x2 * ((2.0 * x2) - 3.0));
	double t_2 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	double t_3 = x1 * (x1 * 3.0);
	double tmp;
	if (x1 <= -8.5e+150) {
		tmp = t_2;
	} else if (x1 <= -4.8e+102) {
		tmp = x1 + (9.0 + (x1 + (x1 * (t_1 + (x1 * (((x2 * -4.0) + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_1 + (4.0 * (x2 * (3.0 + (x2 * -2.0))))) - 6.0))))) - 6.0))))));
	} else if (x1 <= 4.5e+153) {
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_3) + (t_0 * (((x1 * x1) * (((((t_3 + (2.0 * x2)) - x1) / t_0) * 4.0) - 6.0)) + (((x1 * 2.0) * (2.0 * x2)) * (((2.0 * x2) - x1) - 3.0))))))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = 4.0 * (x2 * ((2.0 * x2) - 3.0))
	t_2 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)))
	t_3 = x1 * (x1 * 3.0)
	tmp = 0
	if x1 <= -8.5e+150:
		tmp = t_2
	elif x1 <= -4.8e+102:
		tmp = x1 + (9.0 + (x1 + (x1 * (t_1 + (x1 * (((x2 * -4.0) + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_1 + (4.0 * (x2 * (3.0 + (x2 * -2.0))))) - 6.0))))) - 6.0))))))
	elif x1 <= 4.5e+153:
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_3) + (t_0 * (((x1 * x1) * (((((t_3 + (2.0 * x2)) - x1) / t_0) * 4.0) - 6.0)) + (((x1 * 2.0) * (2.0 * x2)) * (((2.0 * x2) - x1) - 3.0))))))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))
	t_2 = Float64(x1 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * 9.0) - 3.0))))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	tmp = 0.0
	if (x1 <= -8.5e+150)
		tmp = t_2;
	elseif (x1 <= -4.8e+102)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(x1 * Float64(t_1 + Float64(x1 * Float64(Float64(Float64(x2 * -4.0) + Float64(Float64(x2 * 6.0) + Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_1 + Float64(4.0 * Float64(x2 * Float64(3.0 + Float64(x2 * -2.0))))) - 6.0))))) - 6.0)))))));
	elseif (x1 <= 4.5e+153)
		tmp = Float64(x1 + Float64(Float64(Float64(x2 * -6.0) + Float64(x1 * -3.0)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_3) + Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(Float64(Float64(Float64(t_3 + Float64(2.0 * x2)) - x1) / t_0) * 4.0) - 6.0)) + Float64(Float64(Float64(x1 * 2.0) * Float64(2.0 * x2)) * Float64(Float64(Float64(2.0 * x2) - x1) - 3.0)))))))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = 4.0 * (x2 * ((2.0 * x2) - 3.0));
	t_2 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	t_3 = x1 * (x1 * 3.0);
	tmp = 0.0;
	if (x1 <= -8.5e+150)
		tmp = t_2;
	elseif (x1 <= -4.8e+102)
		tmp = x1 + (9.0 + (x1 + (x1 * (t_1 + (x1 * (((x2 * -4.0) + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_1 + (4.0 * (x2 * (3.0 + (x2 * -2.0))))) - 6.0))))) - 6.0))))));
	elseif (x1 <= 4.5e+153)
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_3) + (t_0 * (((x1 * x1) * (((((t_3 + (2.0 * x2)) - x1) / t_0) * 4.0) - 6.0)) + (((x1 * 2.0) * (2.0 * x2)) * (((2.0 * x2) - x1) - 3.0))))))));
	else
		tmp = t_2;
	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[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(x1 + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -8.5e+150], t$95$2, If[LessEqual[x1, -4.8e+102], N[(x1 + N[(9.0 + N[(x1 + N[(x1 * N[(t$95$1 + N[(x1 * N[(N[(N[(x2 * -4.0), $MachinePrecision] + N[(N[(x2 * 6.0), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$1 + N[(4.0 * N[(x2 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.5e+153], N[(x1 + N[(N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$3), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(N[(N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision] * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -8.4999999999999999e150 or 4.5000000000000001e153 < x1

   1. Initial program 1.5%

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

   3. Taylor expanded in x1 around 0 0.1%

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

   4. Taylor expanded in x1 around 0 59.7%

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

   5. Taylor expanded in x2 around 0 98.7%

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

   if -8.4999999999999999e150 < x1 < -4.79999999999999989e102

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around inf 0.0%

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

   5. Taylor expanded in x1 around 0 85.7%

      \[\leadsto x1 + \left(\left(\color{blue}{x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(-4 \cdot x2 + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 6\right)\right)\right)\right) - 6\right)\right)} + x1\right) + 9\right) \]

   if -4.79999999999999989e102 < x1 < 4.5000000000000001e153

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around inf 98.8%

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

   4. Taylor expanded in x1 around 0 99.5%

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

   5. Taylor expanded in x1 around 0 81.4%

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

      1. +-commutative 81.4%

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

      2. mul-1-neg 81.4%

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

      3. sub-neg 81.4%

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

   7. Simplified 81.4%

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

   8. Taylor expanded in x1 around 0 92.2%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -8.5 \cdot 10^{+150}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{elif}\;x1 \leq -4.8 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(x2 \cdot -4 + \left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + 4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right) - 6\right)\right)\right)\right) - 6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x2 \cdot -6 + x1 \cdot -3\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2\right)\right) \cdot \left(\left(2 \cdot x2 - x1\right) - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 83.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\\ t_2 := x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ \mathbf{if}\;x1 \leq -8.5 \cdot 10^{+150}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq -2.6 \cdot 10^{+98}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + x1 \cdot \left(t\_1 + x1 \cdot \left(\left(x2 \cdot -4 + \left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(t\_1 + 4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right) - 6\right)\right)\right)\right) - 6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5.6 \cdot 10^{+151}:\\ \;\;\;\;x1 + \left(\left(x2 \cdot -6 + x1 \cdot -3\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_3 + t\_0 \cdot \left(\left(x1 \cdot x1\right) \cdot 6 + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(t\_3 + 2 \cdot x2\right) - x1}{t\_0}\right) \cdot \left(\left(2 \cdot x2 - x1\right) - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))
        (t_2 (+ x1 (+ x1 (* x1 (- (* x1 9.0) 3.0)))))
        (t_3 (* x1 (* x1 3.0))))
   (if (<= x1 -8.5e+150)
     t_2
     (if (<= x1 -2.6e+98)
       (+
        x1
        (+
         9.0
         (+
          x1
          (*
           x1
           (+
            t_1
            (*
             x1
             (-
              (+
               (* x2 -4.0)
               (+
                (* x2 6.0)
                (+
                 (* x2 8.0)
                 (* x1 (- (+ t_1 (* 4.0 (* x2 (+ 3.0 (* x2 -2.0))))) 6.0)))))
              6.0)))))))
       (if (<= x1 5.6e+151)
         (+
          x1
          (+
           (+ (* x2 -6.0) (* x1 -3.0))
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* 3.0 t_3)
              (*
               t_0
               (+
                (* (* x1 x1) 6.0)
                (*
                 (* (* x1 2.0) (/ (- (+ t_3 (* 2.0 x2)) x1) t_0))
                 (- (- (* 2.0 x2) x1) 3.0)))))))))
         t_2)))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 4.0 * (x2 * ((2.0 * x2) - 3.0));
	double t_2 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	double t_3 = x1 * (x1 * 3.0);
	double tmp;
	if (x1 <= -8.5e+150) {
		tmp = t_2;
	} else if (x1 <= -2.6e+98) {
		tmp = x1 + (9.0 + (x1 + (x1 * (t_1 + (x1 * (((x2 * -4.0) + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_1 + (4.0 * (x2 * (3.0 + (x2 * -2.0))))) - 6.0))))) - 6.0))))));
	} else if (x1 <= 5.6e+151) {
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_3) + (t_0 * (((x1 * x1) * 6.0) + (((x1 * 2.0) * (((t_3 + (2.0 * x2)) - x1) / t_0)) * (((2.0 * x2) - x1) - 3.0))))))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = 4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))
    t_2 = x1 + (x1 + (x1 * ((x1 * 9.0d0) - 3.0d0)))
    t_3 = x1 * (x1 * 3.0d0)
    if (x1 <= (-8.5d+150)) then
        tmp = t_2
    else if (x1 <= (-2.6d+98)) then
        tmp = x1 + (9.0d0 + (x1 + (x1 * (t_1 + (x1 * (((x2 * (-4.0d0)) + ((x2 * 6.0d0) + ((x2 * 8.0d0) + (x1 * ((t_1 + (4.0d0 * (x2 * (3.0d0 + (x2 * (-2.0d0)))))) - 6.0d0))))) - 6.0d0))))))
    else if (x1 <= 5.6d+151) then
        tmp = x1 + (((x2 * (-6.0d0)) + (x1 * (-3.0d0))) + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_3) + (t_0 * (((x1 * x1) * 6.0d0) + (((x1 * 2.0d0) * (((t_3 + (2.0d0 * x2)) - x1) / t_0)) * (((2.0d0 * x2) - x1) - 3.0d0))))))))
    else
        tmp = t_2
    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 = 4.0 * (x2 * ((2.0 * x2) - 3.0));
	double t_2 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	double t_3 = x1 * (x1 * 3.0);
	double tmp;
	if (x1 <= -8.5e+150) {
		tmp = t_2;
	} else if (x1 <= -2.6e+98) {
		tmp = x1 + (9.0 + (x1 + (x1 * (t_1 + (x1 * (((x2 * -4.0) + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_1 + (4.0 * (x2 * (3.0 + (x2 * -2.0))))) - 6.0))))) - 6.0))))));
	} else if (x1 <= 5.6e+151) {
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_3) + (t_0 * (((x1 * x1) * 6.0) + (((x1 * 2.0) * (((t_3 + (2.0 * x2)) - x1) / t_0)) * (((2.0 * x2) - x1) - 3.0))))))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = 4.0 * (x2 * ((2.0 * x2) - 3.0))
	t_2 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)))
	t_3 = x1 * (x1 * 3.0)
	tmp = 0
	if x1 <= -8.5e+150:
		tmp = t_2
	elif x1 <= -2.6e+98:
		tmp = x1 + (9.0 + (x1 + (x1 * (t_1 + (x1 * (((x2 * -4.0) + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_1 + (4.0 * (x2 * (3.0 + (x2 * -2.0))))) - 6.0))))) - 6.0))))))
	elif x1 <= 5.6e+151:
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_3) + (t_0 * (((x1 * x1) * 6.0) + (((x1 * 2.0) * (((t_3 + (2.0 * x2)) - x1) / t_0)) * (((2.0 * x2) - x1) - 3.0))))))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))
	t_2 = Float64(x1 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * 9.0) - 3.0))))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	tmp = 0.0
	if (x1 <= -8.5e+150)
		tmp = t_2;
	elseif (x1 <= -2.6e+98)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(x1 * Float64(t_1 + Float64(x1 * Float64(Float64(Float64(x2 * -4.0) + Float64(Float64(x2 * 6.0) + Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_1 + Float64(4.0 * Float64(x2 * Float64(3.0 + Float64(x2 * -2.0))))) - 6.0))))) - 6.0)))))));
	elseif (x1 <= 5.6e+151)
		tmp = Float64(x1 + Float64(Float64(Float64(x2 * -6.0) + Float64(x1 * -3.0)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_3) + Float64(t_0 * Float64(Float64(Float64(x1 * x1) * 6.0) + Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(Float64(t_3 + Float64(2.0 * x2)) - x1) / t_0)) * Float64(Float64(Float64(2.0 * x2) - x1) - 3.0)))))))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = 4.0 * (x2 * ((2.0 * x2) - 3.0));
	t_2 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	t_3 = x1 * (x1 * 3.0);
	tmp = 0.0;
	if (x1 <= -8.5e+150)
		tmp = t_2;
	elseif (x1 <= -2.6e+98)
		tmp = x1 + (9.0 + (x1 + (x1 * (t_1 + (x1 * (((x2 * -4.0) + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_1 + (4.0 * (x2 * (3.0 + (x2 * -2.0))))) - 6.0))))) - 6.0))))));
	elseif (x1 <= 5.6e+151)
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_3) + (t_0 * (((x1 * x1) * 6.0) + (((x1 * 2.0) * (((t_3 + (2.0 * x2)) - x1) / t_0)) * (((2.0 * x2) - x1) - 3.0))))))));
	else
		tmp = t_2;
	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[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(x1 + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -8.5e+150], t$95$2, If[LessEqual[x1, -2.6e+98], N[(x1 + N[(9.0 + N[(x1 + N[(x1 * N[(t$95$1 + N[(x1 * N[(N[(N[(x2 * -4.0), $MachinePrecision] + N[(N[(x2 * 6.0), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$1 + N[(4.0 * N[(x2 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.6e+151], N[(x1 + N[(N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$3), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -8.4999999999999999e150 or 5.59999999999999975e151 < x1

   1. Initial program 1.5%

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

   3. Taylor expanded in x1 around 0 0.1%

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

   4. Taylor expanded in x1 around 0 59.7%

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

   5. Taylor expanded in x2 around 0 98.7%

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

   if -8.4999999999999999e150 < x1 < -2.6e98

   1. Initial program 22.2%

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

   3. Taylor expanded in x1 around 0 22.2%

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

   4. Taylor expanded in x1 around inf 22.2%

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

   5. Taylor expanded in x1 around 0 79.0%

      \[\leadsto x1 + \left(\left(\color{blue}{x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(-4 \cdot x2 + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 6\right)\right)\right)\right) - 6\right)\right)} + x1\right) + 9\right) \]

   if -2.6e98 < x1 < 5.59999999999999975e151

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around inf 98.8%

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

   4. Taylor expanded in x1 around 0 99.4%

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

   5. Taylor expanded in x1 around 0 82.4%

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

      1. +-commutative 82.4%

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

      2. mul-1-neg 82.4%

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

      3. sub-neg 82.4%

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

   7. Simplified 82.4%

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

   8. Taylor expanded in x1 around inf 83.7%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -8.5 \cdot 10^{+150}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{elif}\;x1 \leq -2.6 \cdot 10^{+98}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(x2 \cdot -4 + \left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + 4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right) - 6\right)\right)\right)\right) - 6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5.6 \cdot 10^{+151}:\\ \;\;\;\;x1 + \left(\left(x2 \cdot -6 + x1 \cdot -3\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6 + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\left(2 \cdot x2 - x1\right) - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 83.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x2 \cdot \left(2 \cdot x2 - 3\right)\\ t_1 := 4 \cdot t\_0\\ \mathbf{if}\;x1 \leq -8.5 \cdot 10^{+150}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{elif}\;x1 \leq -5 \cdot 10^{+89}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + x1 \cdot \left(t\_1 + x1 \cdot \left(\left(x2 \cdot -4 + \left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(t\_1 + 4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right) - 6\right)\right)\right)\right) - 6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.9 \cdot 10^{+73}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot t\_0\right)\right) + 3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 + x1 \cdot \left(\left(x1 + 3\right) - x2 \cdot -2\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x2 (- (* 2.0 x2) 3.0))) (t_1 (* 4.0 t_0)))
   (if (<= x1 -8.5e+150)
     (+ x1 (+ x1 (* x1 (- (* x1 9.0) 3.0))))
     (if (<= x1 -5e+89)
       (+
        x1
        (+
         9.0
         (+
          x1
          (*
           x1
           (+
            t_1
            (*
             x1
             (-
              (+
               (* x2 -4.0)
               (+
                (* x2 6.0)
                (+
                 (* x2 8.0)
                 (* x1 (- (+ t_1 (* 4.0 (* x2 (+ 3.0 (* x2 -2.0))))) 6.0)))))
              6.0)))))))
       (if (<= x1 1.9e+73)
         (+
          x1
          (+
           (*
            3.0
            (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
           (+ x1 (* 4.0 (* x2 (+ (* x1 -3.0) (* 2.0 (* x1 x2))))))))
         (+
          x1
          (+
           (+ x1 (* 4.0 (* x1 t_0)))
           (*
            3.0
            (+
             (* x2 -2.0)
             (* x1 (+ -1.0 (* x1 (- (+ x1 3.0) (* x2 -2.0))))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x2 * ((2.0 * x2) - 3.0);
	double t_1 = 4.0 * t_0;
	double tmp;
	if (x1 <= -8.5e+150) {
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	} else if (x1 <= -5e+89) {
		tmp = x1 + (9.0 + (x1 + (x1 * (t_1 + (x1 * (((x2 * -4.0) + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_1 + (4.0 * (x2 * (3.0 + (x2 * -2.0))))) - 6.0))))) - 6.0))))));
	} else if (x1 <= 1.9e+73) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else {
		tmp = x1 + ((x1 + (4.0 * (x1 * t_0))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * ((x1 + 3.0) - (x2 * -2.0))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x2 * ((2.0d0 * x2) - 3.0d0)
    t_1 = 4.0d0 * t_0
    if (x1 <= (-8.5d+150)) then
        tmp = x1 + (x1 + (x1 * ((x1 * 9.0d0) - 3.0d0)))
    else if (x1 <= (-5d+89)) then
        tmp = x1 + (9.0d0 + (x1 + (x1 * (t_1 + (x1 * (((x2 * (-4.0d0)) + ((x2 * 6.0d0) + ((x2 * 8.0d0) + (x1 * ((t_1 + (4.0d0 * (x2 * (3.0d0 + (x2 * (-2.0d0)))))) - 6.0d0))))) - 6.0d0))))))
    else if (x1 <= 1.9d+73) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0))) + (x1 + (4.0d0 * (x2 * ((x1 * (-3.0d0)) + (2.0d0 * (x1 * x2)))))))
    else
        tmp = x1 + ((x1 + (4.0d0 * (x1 * t_0))) + (3.0d0 * ((x2 * (-2.0d0)) + (x1 * ((-1.0d0) + (x1 * ((x1 + 3.0d0) - (x2 * (-2.0d0)))))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x2 * ((2.0 * x2) - 3.0);
	double t_1 = 4.0 * t_0;
	double tmp;
	if (x1 <= -8.5e+150) {
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	} else if (x1 <= -5e+89) {
		tmp = x1 + (9.0 + (x1 + (x1 * (t_1 + (x1 * (((x2 * -4.0) + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_1 + (4.0 * (x2 * (3.0 + (x2 * -2.0))))) - 6.0))))) - 6.0))))));
	} else if (x1 <= 1.9e+73) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else {
		tmp = x1 + ((x1 + (4.0 * (x1 * t_0))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * ((x1 + 3.0) - (x2 * -2.0))))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x2 * ((2.0 * x2) - 3.0)
	t_1 = 4.0 * t_0
	tmp = 0
	if x1 <= -8.5e+150:
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)))
	elif x1 <= -5e+89:
		tmp = x1 + (9.0 + (x1 + (x1 * (t_1 + (x1 * (((x2 * -4.0) + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_1 + (4.0 * (x2 * (3.0 + (x2 * -2.0))))) - 6.0))))) - 6.0))))))
	elif x1 <= 1.9e+73:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))))
	else:
		tmp = x1 + ((x1 + (4.0 * (x1 * t_0))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * ((x1 + 3.0) - (x2 * -2.0))))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))
	t_1 = Float64(4.0 * t_0)
	tmp = 0.0
	if (x1 <= -8.5e+150)
		tmp = Float64(x1 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * 9.0) - 3.0))));
	elseif (x1 <= -5e+89)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(x1 * Float64(t_1 + Float64(x1 * Float64(Float64(Float64(x2 * -4.0) + Float64(Float64(x2 * 6.0) + Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_1 + Float64(4.0 * Float64(x2 * Float64(3.0 + Float64(x2 * -2.0))))) - 6.0))))) - 6.0)))))));
	elseif (x1 <= 1.9e+73)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(Float64(x1 * -3.0) + Float64(2.0 * Float64(x1 * x2))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x1 * t_0))) + Float64(3.0 * Float64(Float64(x2 * -2.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(Float64(x1 + 3.0) - Float64(x2 * -2.0)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x2 * ((2.0 * x2) - 3.0);
	t_1 = 4.0 * t_0;
	tmp = 0.0;
	if (x1 <= -8.5e+150)
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	elseif (x1 <= -5e+89)
		tmp = x1 + (9.0 + (x1 + (x1 * (t_1 + (x1 * (((x2 * -4.0) + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_1 + (4.0 * (x2 * (3.0 + (x2 * -2.0))))) - 6.0))))) - 6.0))))));
	elseif (x1 <= 1.9e+73)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	else
		tmp = x1 + ((x1 + (4.0 * (x1 * t_0))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * ((x1 + 3.0) - (x2 * -2.0))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(4.0 * t$95$0), $MachinePrecision]}, If[LessEqual[x1, -8.5e+150], N[(x1 + N[(x1 + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5e+89], N[(x1 + N[(9.0 + N[(x1 + N[(x1 * N[(t$95$1 + N[(x1 * N[(N[(N[(x2 * -4.0), $MachinePrecision] + N[(N[(x2 * 6.0), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$1 + N[(4.0 * N[(x2 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.9e+73], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x2 * N[(N[(x1 * -3.0), $MachinePrecision] + N[(2.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(4.0 * N[(x1 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(N[(x1 + 3.0), $MachinePrecision] - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -8.4999999999999999e150

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around 0 46.2%

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

   5. Taylor expanded in x2 around 0 96.6%

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

   if -8.4999999999999999e150 < x1 < -4.99999999999999983e89

   1. Initial program 36.4%

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

   3. Taylor expanded in x1 around 0 36.4%

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

   4. Taylor expanded in x1 around inf 36.4%

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

   5. Taylor expanded in x1 around 0 66.1%

      \[\leadsto x1 + \left(\left(\color{blue}{x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(-4 \cdot x2 + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 6\right)\right)\right)\right) - 6\right)\right)} + x1\right) + 9\right) \]

   if -4.99999999999999983e89 < x1 < 1.90000000000000011e73

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 72.0%

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

   4. Taylor expanded in x2 around 0 82.6%

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

   if 1.90000000000000011e73 < x1

   1. Initial program 34.4%

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

   3. Taylor expanded in x1 around 0 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 93.6%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -8.5 \cdot 10^{+150}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{elif}\;x1 \leq -5 \cdot 10^{+89}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(x2 \cdot -4 + \left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + 4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right) - 6\right)\right)\right)\right) - 6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.9 \cdot 10^{+73}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 + x1 \cdot \left(\left(x1 + 3\right) - x2 \cdot -2\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 83.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{elif}\;x1 \leq -2.05 \cdot 10^{+68}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right) + \left(x2 \cdot -6 + x1 \cdot \left(x2 \cdot \left(x1 \cdot 6 + 9 \cdot \frac{x1}{x2}\right) - 3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6.5 \cdot 10^{+72}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 + x1 \cdot \left(\left(x1 + 3\right) - x2 \cdot -2\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -5e+153)
   (+ x1 (+ x1 (* x1 (- (* x1 9.0) 3.0))))
   (if (<= x1 -2.05e+68)
     (+
      x1
      (+
       (+ x1 (* 4.0 (* -3.0 (* x1 x2))))
       (+ (* x2 -6.0) (* x1 (- (* x2 (+ (* x1 6.0) (* 9.0 (/ x1 x2)))) 3.0)))))
     (if (<= x1 6.5e+72)
       (+
        x1
        (+
         (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
         (+ x1 (* 4.0 (* x2 (+ (* x1 -3.0) (* 2.0 (* x1 x2))))))))
       (+
        x1
        (+
         (+ x1 (* 4.0 (* x1 (* x2 (- (* 2.0 x2) 3.0)))))
         (*
          3.0
          (+
           (* x2 -2.0)
           (* x1 (+ -1.0 (* x1 (- (+ x1 3.0) (* x2 -2.0)))))))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -5e+153) {
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	} else if (x1 <= -2.05e+68) {
		tmp = x1 + ((x1 + (4.0 * (-3.0 * (x1 * x2)))) + ((x2 * -6.0) + (x1 * ((x2 * ((x1 * 6.0) + (9.0 * (x1 / x2)))) - 3.0))));
	} else if (x1 <= 6.5e+72) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else {
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * ((x1 + 3.0) - (x2 * -2.0))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-5d+153)) then
        tmp = x1 + (x1 + (x1 * ((x1 * 9.0d0) - 3.0d0)))
    else if (x1 <= (-2.05d+68)) then
        tmp = x1 + ((x1 + (4.0d0 * ((-3.0d0) * (x1 * x2)))) + ((x2 * (-6.0d0)) + (x1 * ((x2 * ((x1 * 6.0d0) + (9.0d0 * (x1 / x2)))) - 3.0d0))))
    else if (x1 <= 6.5d+72) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0))) + (x1 + (4.0d0 * (x2 * ((x1 * (-3.0d0)) + (2.0d0 * (x1 * x2)))))))
    else
        tmp = x1 + ((x1 + (4.0d0 * (x1 * (x2 * ((2.0d0 * x2) - 3.0d0))))) + (3.0d0 * ((x2 * (-2.0d0)) + (x1 * ((-1.0d0) + (x1 * ((x1 + 3.0d0) - (x2 * (-2.0d0)))))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -5e+153) {
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	} else if (x1 <= -2.05e+68) {
		tmp = x1 + ((x1 + (4.0 * (-3.0 * (x1 * x2)))) + ((x2 * -6.0) + (x1 * ((x2 * ((x1 * 6.0) + (9.0 * (x1 / x2)))) - 3.0))));
	} else if (x1 <= 6.5e+72) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else {
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * ((x1 + 3.0) - (x2 * -2.0))))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -5e+153:
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)))
	elif x1 <= -2.05e+68:
		tmp = x1 + ((x1 + (4.0 * (-3.0 * (x1 * x2)))) + ((x2 * -6.0) + (x1 * ((x2 * ((x1 * 6.0) + (9.0 * (x1 / x2)))) - 3.0))))
	elif x1 <= 6.5e+72:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))))
	else:
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * ((x1 + 3.0) - (x2 * -2.0))))))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -5e+153)
		tmp = Float64(x1 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * 9.0) - 3.0))));
	elseif (x1 <= -2.05e+68)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(-3.0 * Float64(x1 * x2)))) + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x2 * Float64(Float64(x1 * 6.0) + Float64(9.0 * Float64(x1 / x2)))) - 3.0)))));
	elseif (x1 <= 6.5e+72)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(Float64(x1 * -3.0) + Float64(2.0 * Float64(x1 * x2))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x1 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))) + Float64(3.0 * Float64(Float64(x2 * -2.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(Float64(x1 + 3.0) - Float64(x2 * -2.0)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -5e+153)
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	elseif (x1 <= -2.05e+68)
		tmp = x1 + ((x1 + (4.0 * (-3.0 * (x1 * x2)))) + ((x2 * -6.0) + (x1 * ((x2 * ((x1 * 6.0) + (9.0 * (x1 / x2)))) - 3.0))));
	elseif (x1 <= 6.5e+72)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	else
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * ((x1 + 3.0) - (x2 * -2.0))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -5e+153], N[(x1 + N[(x1 + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.05e+68], N[(x1 + N[(N[(x1 + N[(4.0 * N[(-3.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x2 * N[(N[(x1 * 6.0), $MachinePrecision] + N[(9.0 * N[(x1 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6.5e+72], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x2 * N[(N[(x1 * -3.0), $MachinePrecision] + N[(2.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(4.0 * N[(x1 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(N[(x1 + 3.0), $MachinePrecision] - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.00000000000000018e153

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around 0 48.0%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -5.00000000000000018e153 < x1 < -2.05e68

   1. Initial program 61.7%

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

   3. Taylor expanded in x1 around 0 9.8%

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

   4. Taylor expanded in x1 around 0 8.3%

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

   5. Taylor expanded in x2 around inf 21.5%

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

   6. Taylor expanded in x2 around 0 35.8%

      \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(-3 \cdot \left(x1 \cdot x2\right)\right)} + x1\right) + \left(-6 \cdot x2 + x1 \cdot \left(x2 \cdot \left(6 \cdot x1 + 9 \cdot \frac{x1}{x2}\right) - 3\right)\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative 35.8%

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

   8. Simplified 35.8%

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

   if -2.05e68 < x1 < 6.5000000000000001e72

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 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 x2 around 0 86.2%

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

   if 6.5000000000000001e72 < x1

   1. Initial program 34.4%

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

   3. Taylor expanded in x1 around 0 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 93.6%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{elif}\;x1 \leq -2.05 \cdot 10^{+68}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right) + \left(x2 \cdot -6 + x1 \cdot \left(x2 \cdot \left(x1 \cdot 6 + 9 \cdot \frac{x1}{x2}\right) - 3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6.5 \cdot 10^{+72}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 + x1 \cdot \left(\left(x1 + 3\right) - x2 \cdot -2\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 83.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{elif}\;x1 \leq -3.4 \cdot 10^{+68}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right) + \left(x2 \cdot -6 + x1 \cdot \left(x2 \cdot \left(x1 \cdot 6 + 9 \cdot \frac{x1}{x2}\right) - 3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.7 \cdot 10^{+74}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 + x1 \cdot \left(\left(x1 + 3\right) - x2 \cdot -2\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -4.4e+153)
   (+ x1 (+ x1 (* x1 (- (* x1 9.0) 3.0))))
   (if (<= x1 -3.4e+68)
     (+
      x1
      (+
       (+ x1 (* 4.0 (* -3.0 (* x1 x2))))
       (+ (* x2 -6.0) (* x1 (- (* x2 (+ (* x1 6.0) (* 9.0 (/ x1 x2)))) 3.0)))))
     (if (<= x1 1.7e+74)
       (+ x1 (+ (* x1 -2.0) (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0))))
       (+
        x1
        (+
         (+ x1 (* 4.0 (* x1 (* x2 (- (* 2.0 x2) 3.0)))))
         (*
          3.0
          (+
           (* x2 -2.0)
           (* x1 (+ -1.0 (* x1 (- (+ x1 3.0) (* x2 -2.0)))))))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	} else if (x1 <= -3.4e+68) {
		tmp = x1 + ((x1 + (4.0 * (-3.0 * (x1 * x2)))) + ((x2 * -6.0) + (x1 * ((x2 * ((x1 * 6.0) + (9.0 * (x1 / x2)))) - 3.0))));
	} else if (x1 <= 1.7e+74) {
		tmp = x1 + ((x1 * -2.0) + (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)));
	} else {
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * ((x1 + 3.0) - (x2 * -2.0))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-4.4d+153)) then
        tmp = x1 + (x1 + (x1 * ((x1 * 9.0d0) - 3.0d0)))
    else if (x1 <= (-3.4d+68)) then
        tmp = x1 + ((x1 + (4.0d0 * ((-3.0d0) * (x1 * x2)))) + ((x2 * (-6.0d0)) + (x1 * ((x2 * ((x1 * 6.0d0) + (9.0d0 * (x1 / x2)))) - 3.0d0))))
    else if (x1 <= 1.7d+74) then
        tmp = x1 + ((x1 * (-2.0d0)) + (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)))
    else
        tmp = x1 + ((x1 + (4.0d0 * (x1 * (x2 * ((2.0d0 * x2) - 3.0d0))))) + (3.0d0 * ((x2 * (-2.0d0)) + (x1 * ((-1.0d0) + (x1 * ((x1 + 3.0d0) - (x2 * (-2.0d0)))))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	} else if (x1 <= -3.4e+68) {
		tmp = x1 + ((x1 + (4.0 * (-3.0 * (x1 * x2)))) + ((x2 * -6.0) + (x1 * ((x2 * ((x1 * 6.0) + (9.0 * (x1 / x2)))) - 3.0))));
	} else if (x1 <= 1.7e+74) {
		tmp = x1 + ((x1 * -2.0) + (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)));
	} else {
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * ((x1 + 3.0) - (x2 * -2.0))))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -4.4e+153:
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)))
	elif x1 <= -3.4e+68:
		tmp = x1 + ((x1 + (4.0 * (-3.0 * (x1 * x2)))) + ((x2 * -6.0) + (x1 * ((x2 * ((x1 * 6.0) + (9.0 * (x1 / x2)))) - 3.0))))
	elif x1 <= 1.7e+74:
		tmp = x1 + ((x1 * -2.0) + (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)))
	else:
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * ((x1 + 3.0) - (x2 * -2.0))))))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -4.4e+153)
		tmp = Float64(x1 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * 9.0) - 3.0))));
	elseif (x1 <= -3.4e+68)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(-3.0 * Float64(x1 * x2)))) + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x2 * Float64(Float64(x1 * 6.0) + Float64(9.0 * Float64(x1 / x2)))) - 3.0)))));
	elseif (x1 <= 1.7e+74)
		tmp = Float64(x1 + Float64(Float64(x1 * -2.0) + Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x1 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))) + Float64(3.0 * Float64(Float64(x2 * -2.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(Float64(x1 + 3.0) - Float64(x2 * -2.0)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -4.4e+153)
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	elseif (x1 <= -3.4e+68)
		tmp = x1 + ((x1 + (4.0 * (-3.0 * (x1 * x2)))) + ((x2 * -6.0) + (x1 * ((x2 * ((x1 * 6.0) + (9.0 * (x1 / x2)))) - 3.0))));
	elseif (x1 <= 1.7e+74)
		tmp = x1 + ((x1 * -2.0) + (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)));
	else
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * ((x1 + 3.0) - (x2 * -2.0))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -4.4e+153], N[(x1 + N[(x1 + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -3.4e+68], N[(x1 + N[(N[(x1 + N[(4.0 * N[(-3.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x2 * N[(N[(x1 * 6.0), $MachinePrecision] + N[(9.0 * N[(x1 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.7e+74], N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] + N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(4.0 * N[(x1 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(N[(x1 + 3.0), $MachinePrecision] - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.3999999999999999e153

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around 0 48.0%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -4.3999999999999999e153 < x1 < -3.40000000000000015e68

   1. Initial program 61.7%

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

   3. Taylor expanded in x1 around 0 9.8%

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

   4. Taylor expanded in x1 around 0 8.3%

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

   5. Taylor expanded in x2 around inf 21.5%

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

   6. Taylor expanded in x2 around 0 35.8%

      \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(-3 \cdot \left(x1 \cdot x2\right)\right)} + x1\right) + \left(-6 \cdot x2 + x1 \cdot \left(x2 \cdot \left(6 \cdot x1 + 9 \cdot \frac{x1}{x2}\right) - 3\right)\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative 35.8%

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

   8. Simplified 35.8%

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

   if -3.40000000000000015e68 < x1 < 1.7e74

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 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 72.5%

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

   5. Taylor expanded in x1 around 0 74.7%

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

   6. Taylor expanded in x2 around 0 86.0%

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

   if 1.7e74 < x1

   1. Initial program 34.4%

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

   3. Taylor expanded in x1 around 0 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 93.6%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{elif}\;x1 \leq -3.4 \cdot 10^{+68}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right) + \left(x2 \cdot -6 + x1 \cdot \left(x2 \cdot \left(x1 \cdot 6 + 9 \cdot \frac{x1}{x2}\right) - 3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.7 \cdot 10^{+74}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 + x1 \cdot \left(\left(x1 + 3\right) - x2 \cdot -2\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 68.9% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ t_1 := x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ t_2 := x2 \cdot -6 - x1\\ \mathbf{if}\;x1 \leq -3.4 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -2.9 \cdot 10^{-118}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 3.6 \cdot 10^{-149}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{-115}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.4 \cdot 10^{-62}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq 5.4 \cdot 10^{+149}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) -1.0)))
        (t_1 (+ x1 (+ x1 (* x1 (- (* x1 9.0) 3.0)))))
        (t_2 (- (* x2 -6.0) x1)))
   (if (<= x1 -3.4e+89)
     t_1
     (if (<= x1 -2.9e-118)
       t_0
       (if (<= x1 3.6e-149)
         t_2
         (if (<= x1 4.5e-115)
           (+ x1 (+ 9.0 (+ x1 (* x2 (+ (* x1 -12.0) (* 8.0 (* x1 x2)))))))
           (if (<= x1 1.4e-62) t_2 (if (<= x1 5.4e+149) t_0 t_1))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0);
	double t_1 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	double t_2 = (x2 * -6.0) - x1;
	double tmp;
	if (x1 <= -3.4e+89) {
		tmp = t_1;
	} else if (x1 <= -2.9e-118) {
		tmp = t_0;
	} else if (x1 <= 3.6e-149) {
		tmp = t_2;
	} else if (x1 <= 4.5e-115) {
		tmp = x1 + (9.0 + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else if (x1 <= 1.4e-62) {
		tmp = t_2;
	} else if (x1 <= 5.4e+149) {
		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) :: t_2
    real(8) :: tmp
    t_0 = x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + (-1.0d0))
    t_1 = x1 + (x1 + (x1 * ((x1 * 9.0d0) - 3.0d0)))
    t_2 = (x2 * (-6.0d0)) - x1
    if (x1 <= (-3.4d+89)) then
        tmp = t_1
    else if (x1 <= (-2.9d-118)) then
        tmp = t_0
    else if (x1 <= 3.6d-149) then
        tmp = t_2
    else if (x1 <= 4.5d-115) then
        tmp = x1 + (9.0d0 + (x1 + (x2 * ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))))))
    else if (x1 <= 1.4d-62) then
        tmp = t_2
    else if (x1 <= 5.4d+149) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0);
	double t_1 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	double t_2 = (x2 * -6.0) - x1;
	double tmp;
	if (x1 <= -3.4e+89) {
		tmp = t_1;
	} else if (x1 <= -2.9e-118) {
		tmp = t_0;
	} else if (x1 <= 3.6e-149) {
		tmp = t_2;
	} else if (x1 <= 4.5e-115) {
		tmp = x1 + (9.0 + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else if (x1 <= 1.4e-62) {
		tmp = t_2;
	} else if (x1 <= 5.4e+149) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0)
	t_1 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)))
	t_2 = (x2 * -6.0) - x1
	tmp = 0
	if x1 <= -3.4e+89:
		tmp = t_1
	elif x1 <= -2.9e-118:
		tmp = t_0
	elif x1 <= 3.6e-149:
		tmp = t_2
	elif x1 <= 4.5e-115:
		tmp = x1 + (9.0 + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))))
	elif x1 <= 1.4e-62:
		tmp = t_2
	elif x1 <= 5.4e+149:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) + -1.0))
	t_1 = Float64(x1 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * 9.0) - 3.0))))
	t_2 = Float64(Float64(x2 * -6.0) - x1)
	tmp = 0.0
	if (x1 <= -3.4e+89)
		tmp = t_1;
	elseif (x1 <= -2.9e-118)
		tmp = t_0;
	elseif (x1 <= 3.6e-149)
		tmp = t_2;
	elseif (x1 <= 4.5e-115)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2)))))));
	elseif (x1 <= 1.4e-62)
		tmp = t_2;
	elseif (x1 <= 5.4e+149)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0);
	t_1 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	t_2 = (x2 * -6.0) - x1;
	tmp = 0.0;
	if (x1 <= -3.4e+89)
		tmp = t_1;
	elseif (x1 <= -2.9e-118)
		tmp = t_0;
	elseif (x1 <= 3.6e-149)
		tmp = t_2;
	elseif (x1 <= 4.5e-115)
		tmp = x1 + (9.0 + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	elseif (x1 <= 1.4e-62)
		tmp = t_2;
	elseif (x1 <= 5.4e+149)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x1 + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision]}, If[LessEqual[x1, -3.4e+89], t$95$1, If[LessEqual[x1, -2.9e-118], t$95$0, If[LessEqual[x1, 3.6e-149], t$95$2, If[LessEqual[x1, 4.5e-115], N[(x1 + N[(9.0 + N[(x1 + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.4e-62], t$95$2, If[LessEqual[x1, 5.4e+149], t$95$0, t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -3.4000000000000002e89 or 5.4000000000000002e149 < x1

   1. Initial program 7.6%

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

   3. Taylor expanded in x1 around 0 0.2%

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

   4. Taylor expanded in x1 around 0 51.5%

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

   5. Taylor expanded in x2 around 0 84.8%

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

   if -3.4000000000000002e89 < x1 < -2.8999999999999998e-118 or 1.40000000000000001e-62 < x1 < 5.4000000000000002e149

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 56.8%

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

   4. Taylor expanded in x1 around 0 51.9%

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

   5. Taylor expanded in x1 around 0 56.0%

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

   6. Taylor expanded in x1 around inf 52.8%

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

   if -2.8999999999999998e-118 < x1 < 3.6000000000000002e-149 or 4.50000000000000023e-115 < x1 < 1.40000000000000001e-62

   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 99.5%

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

   4. Taylor expanded in x1 around 0 99.5%

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

   5. Taylor expanded in x1 around inf 84.9%

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

      1. associate-*r/ 84.9%

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

      2. metadata-eval 84.9%

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

   7. Simplified 84.9%

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

   8. Taylor expanded in x1 around 0 85.2%

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

   if 3.6000000000000002e-149 < x1 < 4.50000000000000023e-115

   1. Initial program 100.0%

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

   3. Taylor expanded in x1 around 0 59.8%

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

   4. Taylor expanded in x1 around inf 45.8%

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

   5. Taylor expanded in x2 around 0 81.9%

      \[\leadsto x1 + \left(\color{blue}{\left(x1 + x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)} + 9\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.4 \cdot 10^{+89}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{elif}\;x1 \leq -2.9 \cdot 10^{-118}:\\ \;\;\;\;x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{elif}\;x1 \leq 3.6 \cdot 10^{-149}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{-115}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.4 \cdot 10^{-62}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 5.4 \cdot 10^{+149}:\\ \;\;\;\;x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 81.7% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+68}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right) + \left(x2 \cdot -6 + x1 \cdot \left(x2 \cdot \left(x1 \cdot 6 + 9 \cdot \frac{x1}{x2}\right) - 3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5.4 \cdot 10^{+149}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (+ x1 (* x1 (- (* x1 9.0) 3.0))))))
   (if (<= x1 -4.4e+153)
     t_0
     (if (<= x1 -5.6e+68)
       (+
        x1
        (+
         (+ x1 (* 4.0 (* -3.0 (* x1 x2))))
         (+
          (* x2 -6.0)
          (* x1 (- (* x2 (+ (* x1 6.0) (* 9.0 (/ x1 x2)))) 3.0)))))
       (if (<= x1 5.4e+149)
         (+
          x1
          (+ (* x1 -2.0) (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0))))
         t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = t_0;
	} else if (x1 <= -5.6e+68) {
		tmp = x1 + ((x1 + (4.0 * (-3.0 * (x1 * x2)))) + ((x2 * -6.0) + (x1 * ((x2 * ((x1 * 6.0) + (9.0 * (x1 / x2)))) - 3.0))));
	} else if (x1 <= 5.4e+149) {
		tmp = x1 + ((x1 * -2.0) + (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + (x1 + (x1 * ((x1 * 9.0d0) - 3.0d0)))
    if (x1 <= (-4.4d+153)) then
        tmp = t_0
    else if (x1 <= (-5.6d+68)) then
        tmp = x1 + ((x1 + (4.0d0 * ((-3.0d0) * (x1 * x2)))) + ((x2 * (-6.0d0)) + (x1 * ((x2 * ((x1 * 6.0d0) + (9.0d0 * (x1 / x2)))) - 3.0d0))))
    else if (x1 <= 5.4d+149) then
        tmp = x1 + ((x1 * (-2.0d0)) + (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = t_0;
	} else if (x1 <= -5.6e+68) {
		tmp = x1 + ((x1 + (4.0 * (-3.0 * (x1 * x2)))) + ((x2 * -6.0) + (x1 * ((x2 * ((x1 * 6.0) + (9.0 * (x1 / x2)))) - 3.0))));
	} else if (x1 <= 5.4e+149) {
		tmp = x1 + ((x1 * -2.0) + (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)))
	tmp = 0
	if x1 <= -4.4e+153:
		tmp = t_0
	elif x1 <= -5.6e+68:
		tmp = x1 + ((x1 + (4.0 * (-3.0 * (x1 * x2)))) + ((x2 * -6.0) + (x1 * ((x2 * ((x1 * 6.0) + (9.0 * (x1 / x2)))) - 3.0))))
	elif x1 <= 5.4e+149:
		tmp = x1 + ((x1 * -2.0) + (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * 9.0) - 3.0))))
	tmp = 0.0
	if (x1 <= -4.4e+153)
		tmp = t_0;
	elseif (x1 <= -5.6e+68)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(-3.0 * Float64(x1 * x2)))) + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x2 * Float64(Float64(x1 * 6.0) + Float64(9.0 * Float64(x1 / x2)))) - 3.0)))));
	elseif (x1 <= 5.4e+149)
		tmp = Float64(x1 + Float64(Float64(x1 * -2.0) + Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	tmp = 0.0;
	if (x1 <= -4.4e+153)
		tmp = t_0;
	elseif (x1 <= -5.6e+68)
		tmp = x1 + ((x1 + (4.0 * (-3.0 * (x1 * x2)))) + ((x2 * -6.0) + (x1 * ((x2 * ((x1 * 6.0) + (9.0 * (x1 / x2)))) - 3.0))));
	elseif (x1 <= 5.4e+149)
		tmp = x1 + ((x1 * -2.0) + (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.4e+153], t$95$0, If[LessEqual[x1, -5.6e+68], N[(x1 + N[(N[(x1 + N[(4.0 * N[(-3.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x2 * N[(N[(x1 * 6.0), $MachinePrecision] + N[(9.0 * N[(x1 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.4e+149], N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] + N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4.3999999999999999e153 or 5.4000000000000002e149 < x1

   1. Initial program 3.0%

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

   3. Taylor expanded in x1 around 0 0.2%

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

   4. Taylor expanded in x1 around 0 59.9%

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

   5. Taylor expanded in x2 around 0 98.7%

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

   if -4.3999999999999999e153 < x1 < -5.6e68

   1. Initial program 61.7%

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

   3. Taylor expanded in x1 around 0 9.8%

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

   4. Taylor expanded in x1 around 0 8.3%

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

   5. Taylor expanded in x2 around inf 21.5%

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

   6. Taylor expanded in x2 around 0 35.8%

      \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(-3 \cdot \left(x1 \cdot x2\right)\right)} + x1\right) + \left(-6 \cdot x2 + x1 \cdot \left(x2 \cdot \left(6 \cdot x1 + 9 \cdot \frac{x1}{x2}\right) - 3\right)\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative 35.8%

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

   8. Simplified 35.8%

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

   if -5.6e68 < x1 < 5.4000000000000002e149

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 72.1%

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

   4. Taylor expanded in x1 around 0 70.0%

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

   5. Taylor expanded in x1 around 0 71.7%

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

   6. Taylor expanded in x2 around 0 81.7%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+68}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right) + \left(x2 \cdot -6 + x1 \cdot \left(x2 \cdot \left(x1 \cdot 6 + 9 \cdot \frac{x1}{x2}\right) - 3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5.4 \cdot 10^{+149}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 75.6% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ t_1 := x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{if}\;x1 \leq -2.7 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -5.5 \cdot 10^{-221}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 1.15 \cdot 10^{-200}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 5.4 \cdot 10^{+149}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x2 -6.0) (* x1 (+ (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) -1.0))))
        (t_1 (+ x1 (+ x1 (* x1 (- (* x1 9.0) 3.0))))))
   (if (<= x1 -2.7e+89)
     t_1
     (if (<= x1 -5.5e-221)
       t_0
       (if (<= x1 1.15e-200)
         (- (* x2 -6.0) x1)
         (if (<= x1 5.4e+149) t_0 t_1))))))

C

double code(double x1, double x2) {
	double t_0 = (x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0));
	double t_1 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	double tmp;
	if (x1 <= -2.7e+89) {
		tmp = t_1;
	} else if (x1 <= -5.5e-221) {
		tmp = t_0;
	} else if (x1 <= 1.15e-200) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 5.4e+149) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + (-1.0d0)))
    t_1 = x1 + (x1 + (x1 * ((x1 * 9.0d0) - 3.0d0)))
    if (x1 <= (-2.7d+89)) then
        tmp = t_1
    else if (x1 <= (-5.5d-221)) then
        tmp = t_0
    else if (x1 <= 1.15d-200) then
        tmp = (x2 * (-6.0d0)) - x1
    else if (x1 <= 5.4d+149) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0));
	double t_1 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	double tmp;
	if (x1 <= -2.7e+89) {
		tmp = t_1;
	} else if (x1 <= -5.5e-221) {
		tmp = t_0;
	} else if (x1 <= 1.15e-200) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 5.4e+149) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0))
	t_1 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)))
	tmp = 0
	if x1 <= -2.7e+89:
		tmp = t_1
	elif x1 <= -5.5e-221:
		tmp = t_0
	elif x1 <= 1.15e-200:
		tmp = (x2 * -6.0) - x1
	elif x1 <= 5.4e+149:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) + -1.0)))
	t_1 = Float64(x1 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * 9.0) - 3.0))))
	tmp = 0.0
	if (x1 <= -2.7e+89)
		tmp = t_1;
	elseif (x1 <= -5.5e-221)
		tmp = t_0;
	elseif (x1 <= 1.15e-200)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	elseif (x1 <= 5.4e+149)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0));
	t_1 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	tmp = 0.0;
	if (x1 <= -2.7e+89)
		tmp = t_1;
	elseif (x1 <= -5.5e-221)
		tmp = t_0;
	elseif (x1 <= 1.15e-200)
		tmp = (x2 * -6.0) - x1;
	elseif (x1 <= 5.4e+149)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x1 + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.7e+89], t$95$1, If[LessEqual[x1, -5.5e-221], t$95$0, If[LessEqual[x1, 1.15e-200], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 5.4e+149], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.7e89 or 5.4000000000000002e149 < x1

   1. Initial program 7.6%

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

   3. Taylor expanded in x1 around 0 0.2%

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

   4. Taylor expanded in x1 around 0 51.5%

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

   5. Taylor expanded in x2 around 0 84.8%

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

   if -2.7e89 < x1 < -5.49999999999999966e-221 or 1.15000000000000004e-200 < x1 < 5.4000000000000002e149

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 66.1%

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

   4. Taylor expanded in x1 around 0 62.9%

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

   5. Taylor expanded in x1 around 0 65.6%

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

   6. Taylor expanded in x1 around 0 65.6%

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

   if -5.49999999999999966e-221 < x1 < 1.15000000000000004e-200

   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 inf 99.6%

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

   4. Taylor expanded in x1 around 0 99.5%

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

   5. Taylor expanded in x1 around inf 93.8%

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

      1. associate-*r/ 93.8%

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

      2. metadata-eval 93.8%

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

   7. Simplified 93.8%

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

   8. Taylor expanded in x1 around 0 94.0%

      \[\leadsto \color{blue}{-6 \cdot x2 + -1 \cdot x1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.7 \cdot 10^{+89}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{elif}\;x1 \leq -5.5 \cdot 10^{-221}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{elif}\;x1 \leq 1.15 \cdot 10^{-200}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 5.4 \cdot 10^{+149}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 67.0% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ t_1 := x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -7 \cdot 10^{+15}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 4.8 \cdot 10^{-41}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 5.4 \cdot 10^{+149}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ 2.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))))
        (t_1 (+ x1 (+ x1 (* x1 (- (* x1 9.0) 3.0))))))
   (if (<= x1 -5e+89)
     t_1
     (if (<= x1 -7e+15)
       t_0
       (if (<= x1 4.8e-41)
         (- (* x2 -6.0) x1)
         (if (<= x1 5.4e+149) t_0 t_1))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	double t_1 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	double tmp;
	if (x1 <= -5e+89) {
		tmp = t_1;
	} else if (x1 <= -7e+15) {
		tmp = t_0;
	} else if (x1 <= 4.8e-41) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 5.4e+149) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x1 * (2.0d0 + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))))
    t_1 = x1 + (x1 + (x1 * ((x1 * 9.0d0) - 3.0d0)))
    if (x1 <= (-5d+89)) then
        tmp = t_1
    else if (x1 <= (-7d+15)) then
        tmp = t_0
    else if (x1 <= 4.8d-41) then
        tmp = (x2 * (-6.0d0)) - x1
    else if (x1 <= 5.4d+149) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	double t_1 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	double tmp;
	if (x1 <= -5e+89) {
		tmp = t_1;
	} else if (x1 <= -7e+15) {
		tmp = t_0;
	} else if (x1 <= 4.8e-41) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 5.4e+149) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))))
	t_1 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)))
	tmp = 0
	if x1 <= -5e+89:
		tmp = t_1
	elif x1 <= -7e+15:
		tmp = t_0
	elif x1 <= 4.8e-41:
		tmp = (x2 * -6.0) - x1
	elif x1 <= 5.4e+149:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(2.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))))
	t_1 = Float64(x1 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * 9.0) - 3.0))))
	tmp = 0.0
	if (x1 <= -5e+89)
		tmp = t_1;
	elseif (x1 <= -7e+15)
		tmp = t_0;
	elseif (x1 <= 4.8e-41)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	elseif (x1 <= 5.4e+149)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	t_1 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	tmp = 0.0;
	if (x1 <= -5e+89)
		tmp = t_1;
	elseif (x1 <= -7e+15)
		tmp = t_0;
	elseif (x1 <= 4.8e-41)
		tmp = (x2 * -6.0) - x1;
	elseif (x1 <= 5.4e+149)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(2.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x1 + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5e+89], t$95$1, If[LessEqual[x1, -7e+15], t$95$0, If[LessEqual[x1, 4.8e-41], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 5.4e+149], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4.99999999999999983e89 or 5.4000000000000002e149 < x1

   1. Initial program 7.6%

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

   3. Taylor expanded in x1 around 0 0.2%

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

   4. Taylor expanded in x1 around 0 51.5%

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

   5. Taylor expanded in x2 around 0 84.8%

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

   if -4.99999999999999983e89 < x1 < -7e15 or 4.80000000000000044e-41 < x1 < 5.4000000000000002e149

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around 0 48.4%

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

   4. Taylor expanded in x1 around inf 42.3%

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

   5. Taylor expanded in x1 around inf 42.3%

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

   if -7e15 < x1 < 4.80000000000000044e-41

   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 98.7%

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

   4. Taylor expanded in x1 around 0 99.4%

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

   5. Taylor expanded in x1 around inf 74.8%

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

      1. associate-*r/ 74.8%

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

      2. metadata-eval 74.8%

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

   7. Simplified 74.8%

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

   8. Taylor expanded in x1 around 0 73.4%

      \[\leadsto \color{blue}{-6 \cdot x2 + -1 \cdot x1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+89}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{elif}\;x1 \leq -7 \cdot 10^{+15}:\\ \;\;\;\;x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.8 \cdot 10^{-41}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 5.4 \cdot 10^{+149}:\\ \;\;\;\;x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 70.4% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ t_1 := x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -1.92 \cdot 10^{-118}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 1.45 \cdot 10^{-62}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 5.4 \cdot 10^{+149}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) -1.0)))
        (t_1 (+ x1 (+ x1 (* x1 (- (* x1 9.0) 3.0))))))
   (if (<= x1 -5e+89)
     t_1
     (if (<= x1 -1.92e-118)
       t_0
       (if (<= x1 1.45e-62)
         (- (* x2 -6.0) x1)
         (if (<= x1 5.4e+149) t_0 t_1))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0);
	double t_1 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	double tmp;
	if (x1 <= -5e+89) {
		tmp = t_1;
	} else if (x1 <= -1.92e-118) {
		tmp = t_0;
	} else if (x1 <= 1.45e-62) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 5.4e+149) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + (-1.0d0))
    t_1 = x1 + (x1 + (x1 * ((x1 * 9.0d0) - 3.0d0)))
    if (x1 <= (-5d+89)) then
        tmp = t_1
    else if (x1 <= (-1.92d-118)) then
        tmp = t_0
    else if (x1 <= 1.45d-62) then
        tmp = (x2 * (-6.0d0)) - x1
    else if (x1 <= 5.4d+149) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0);
	double t_1 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	double tmp;
	if (x1 <= -5e+89) {
		tmp = t_1;
	} else if (x1 <= -1.92e-118) {
		tmp = t_0;
	} else if (x1 <= 1.45e-62) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 5.4e+149) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0)
	t_1 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)))
	tmp = 0
	if x1 <= -5e+89:
		tmp = t_1
	elif x1 <= -1.92e-118:
		tmp = t_0
	elif x1 <= 1.45e-62:
		tmp = (x2 * -6.0) - x1
	elif x1 <= 5.4e+149:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) + -1.0))
	t_1 = Float64(x1 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * 9.0) - 3.0))))
	tmp = 0.0
	if (x1 <= -5e+89)
		tmp = t_1;
	elseif (x1 <= -1.92e-118)
		tmp = t_0;
	elseif (x1 <= 1.45e-62)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	elseif (x1 <= 5.4e+149)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0);
	t_1 = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	tmp = 0.0;
	if (x1 <= -5e+89)
		tmp = t_1;
	elseif (x1 <= -1.92e-118)
		tmp = t_0;
	elseif (x1 <= 1.45e-62)
		tmp = (x2 * -6.0) - x1;
	elseif (x1 <= 5.4e+149)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x1 + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5e+89], t$95$1, If[LessEqual[x1, -1.92e-118], t$95$0, If[LessEqual[x1, 1.45e-62], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 5.4e+149], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4.99999999999999983e89 or 5.4000000000000002e149 < x1

   1. Initial program 7.6%

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

   3. Taylor expanded in x1 around 0 0.2%

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

   4. Taylor expanded in x1 around 0 51.5%

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

   5. Taylor expanded in x2 around 0 84.8%

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

   if -4.99999999999999983e89 < x1 < -1.92000000000000007e-118 or 1.44999999999999993e-62 < x1 < 5.4000000000000002e149

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 56.8%

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

   4. Taylor expanded in x1 around 0 51.9%

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

   5. Taylor expanded in x1 around 0 56.0%

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

   6. Taylor expanded in x1 around inf 52.8%

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

   if -1.92000000000000007e-118 < x1 < 1.44999999999999993e-62

   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 inf 99.6%

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

   4. Taylor expanded in x1 around 0 99.6%

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

   5. Taylor expanded in x1 around inf 79.7%

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

      1. associate-*r/ 79.7%

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

      2. metadata-eval 79.7%

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

   7. Simplified 79.7%

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

   8. Taylor expanded in x1 around 0 79.9%

      \[\leadsto \color{blue}{-6 \cdot x2 + -1 \cdot x1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+89}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{elif}\;x1 \leq -1.92 \cdot 10^{-118}:\\ \;\;\;\;x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{elif}\;x1 \leq 1.45 \cdot 10^{-62}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 5.4 \cdot 10^{+149}:\\ \;\;\;\;x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 79.4% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -3.3 \cdot 10^{+89} \lor \neg \left(x1 \leq 5.4 \cdot 10^{+149}\right):\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -3.3e+89) (not (<= x1 5.4e+149)))
   (+ x1 (+ x1 (* x1 (- (* x1 9.0) 3.0))))
   (+ x1 (+ (* x1 -2.0) (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -3.3e+89) || !(x1 <= 5.4e+149)) {
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	} else {
		tmp = x1 + ((x1 * -2.0) + (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-3.3d+89)) .or. (.not. (x1 <= 5.4d+149))) then
        tmp = x1 + (x1 + (x1 * ((x1 * 9.0d0) - 3.0d0)))
    else
        tmp = x1 + ((x1 * (-2.0d0)) + (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -3.3e+89) || !(x1 <= 5.4e+149)) {
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	} else {
		tmp = x1 + ((x1 * -2.0) + (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -3.3e+89) or not (x1 <= 5.4e+149):
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)))
	else:
		tmp = x1 + ((x1 * -2.0) + (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -3.3e+89) || !(x1 <= 5.4e+149))
		tmp = Float64(x1 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * 9.0) - 3.0))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 * -2.0) + Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -3.3e+89) || ~((x1 <= 5.4e+149)))
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	else
		tmp = x1 + ((x1 * -2.0) + (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -3.3e+89], N[Not[LessEqual[x1, 5.4e+149]], $MachinePrecision]], N[(x1 + N[(x1 + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] + N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -3.29999999999999974e89 or 5.4000000000000002e149 < x1

   1. Initial program 7.6%

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

   3. Taylor expanded in x1 around 0 0.2%

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

   4. Taylor expanded in x1 around 0 51.5%

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

   5. Taylor expanded in x2 around 0 84.8%

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

   if -3.29999999999999974e89 < x1 < 5.4000000000000002e149

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 69.6%

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

   4. Taylor expanded in x1 around 0 67.1%

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

   5. Taylor expanded in x1 around 0 69.2%

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

   6. Taylor expanded in x2 around 0 78.7%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.3 \cdot 10^{+89} \lor \neg \left(x1 \leq 5.4 \cdot 10^{+149}\right):\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 63.6% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -3.6 \cdot 10^{-15} \lor \neg \left(x1 \leq 7 \cdot 10^{-14}\right):\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -3.6e-15) (not (<= x1 7e-14)))
   (+ x1 (+ x1 (* x1 (- (* x1 9.0) 3.0))))
   (- (* x2 -6.0) x1)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -3.6e-15) || !(x1 <= 7e-14)) {
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	} 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 <= (-3.6d-15)) .or. (.not. (x1 <= 7d-14))) then
        tmp = x1 + (x1 + (x1 * ((x1 * 9.0d0) - 3.0d0)))
    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 <= -3.6e-15) || !(x1 <= 7e-14)) {
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	} else {
		tmp = (x2 * -6.0) - x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -3.6e-15) or not (x1 <= 7e-14):
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)))
	else:
		tmp = (x2 * -6.0) - x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -3.6e-15) || !(x1 <= 7e-14))
		tmp = Float64(x1 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * 9.0) - 3.0))));
	else
		tmp = Float64(Float64(x2 * -6.0) - x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -3.6e-15) || ~((x1 <= 7e-14)))
		tmp = x1 + (x1 + (x1 * ((x1 * 9.0) - 3.0)));
	else
		tmp = (x2 * -6.0) - x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -3.6e-15], N[Not[LessEqual[x1, 7e-14]], $MachinePrecision]], N[(x1 + N[(x1 + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -3.6000000000000001e-15 or 7.0000000000000005e-14 < x1

   1. Initial program 47.9%

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

   3. Taylor expanded in x1 around 0 18.2%

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

   4. Taylor expanded in x1 around 0 43.9%

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

   5. Taylor expanded in x2 around 0 51.3%

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

   if -3.6000000000000001e-15 < x1 < 7.0000000000000005e-14

   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 99.5%

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

   4. Taylor expanded in x1 around 0 99.5%

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

   5. Taylor expanded in x1 around inf 72.8%

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

      1. associate-*r/ 72.8%

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

      2. metadata-eval 72.8%

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

   7. Simplified 72.8%

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

   8. Taylor expanded in x1 around 0 73.1%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.6 \cdot 10^{-15} \lor \neg \left(x1 \leq 7 \cdot 10^{-14}\right):\\ \;\;\;\;x1 + \left(x1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 31.0% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -1.72 \cdot 10^{-109} \lor \neg \left(x2 \leq 5.6 \cdot 10^{-251}\right):\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -1.72e-109) (not (<= x2 5.6e-251))) (+ x1 (* x2 -6.0)) (- x1)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.72e-109) || !(x2 <= 5.6e-251)) {
		tmp = x1 + (x2 * -6.0);
	} else {
		tmp = -x1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-1.72d-109)) .or. (.not. (x2 <= 5.6d-251))) then
        tmp = x1 + (x2 * (-6.0d0))
    else
        tmp = -x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.72e-109) || !(x2 <= 5.6e-251)) {
		tmp = x1 + (x2 * -6.0);
	} else {
		tmp = -x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -1.72e-109) or not (x2 <= 5.6e-251):
		tmp = x1 + (x2 * -6.0)
	else:
		tmp = -x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -1.72e-109) || !(x2 <= 5.6e-251))
		tmp = Float64(x1 + Float64(x2 * -6.0));
	else
		tmp = Float64(-x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -1.72e-109) || ~((x2 <= 5.6e-251)))
		tmp = x1 + (x2 * -6.0);
	else
		tmp = -x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -1.72e-109], N[Not[LessEqual[x2, 5.6e-251]], $MachinePrecision]], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision], (-x1)]

Derivation

1. Split input into 2 regimes

2. if x2 < -1.7200000000000001e-109 or 5.59999999999999978e-251 < x2

   1. Initial program 71.0%

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

   3. Taylor expanded in x1 around 0 47.1%

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

   4. Taylor expanded in x1 around 0 58.5%

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

   5. Taylor expanded in x1 around 0 28.0%

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

      1. *-commutative 28.0%

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

   7. Simplified 28.0%

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

   if -1.7200000000000001e-109 < x2 < 5.59999999999999978e-251

   1. Initial program 71.3%

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

   3. Taylor expanded in x1 around 0 52.6%

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

   4. Taylor expanded in x1 around 0 77.7%

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

   5. Taylor expanded in x1 around 0 52.9%

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

   6. Taylor expanded in x2 around 0 39.8%

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

      1. distribute-rgt1-in 39.8%

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

      2. metadata-eval 39.8%

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

      3. mul-1-neg 39.8%

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

   8. Simplified 39.8%

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

4. Final simplification 30.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.72 \cdot 10^{-109} \lor \neg \left(x2 \leq 5.6 \cdot 10^{-251}\right):\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 39.0% 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 71.1%

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

3. Taylor expanded in x1 around inf 70.6%

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

4. Taylor expanded in x1 around 0 71.1%

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

5. Taylor expanded in x1 around inf 81.6%

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

   1. associate-*r/ 81.6%

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

   2. metadata-eval 81.6%

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

7. Simplified 81.6%

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

8. Taylor expanded in x1 around 0 35.0%

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

9. Final simplification 35.0%

   \[\leadsto x2 \cdot -6 - x1 \]
10. Add Preprocessing

Alternative 23: 14.5% accurate, 63.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x1, x2):
	return -x1

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.1%

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

3. Taylor expanded in x1 around 0 48.1%

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

4. Taylor expanded in x1 around 0 62.3%

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

5. Taylor expanded in x1 around 0 53.9%

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

6. Taylor expanded in x2 around 0 11.9%

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

   1. distribute-rgt1-in 11.9%

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

   2. metadata-eval 11.9%

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

   3. mul-1-neg 11.9%

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

8. Simplified 11.9%

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

9. Final simplification 11.9%

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

Alternative 24: 3.5% accurate, 127.0× speedup

Math

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

FPCore

(FPCore (x1 x2) :precision binary64 9.0)

C

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

Fortran

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

Java

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

Python

def code(x1, x2):
	return 9.0

Julia

function code(x1, x2)
	return 9.0
end

MATLAB

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

Wolfram

code[x1_, x2_] := 9.0

Derivation

1. Initial program 71.1%

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

3. Taylor expanded in x1 around 0 48.1%

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

4. Taylor expanded in x1 around inf 24.8%

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

5. Taylor expanded in x1 around 0 3.4%

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

6. Final simplification 3.4%

   \[\leadsto 9 \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024077 
(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))))))