Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.7% → 99.5%

Time: 33.0s

Alternatives: 23

Speedup: 5.1×

• 46.7% 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: 70.7% 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

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

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))))))
     (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) 9.0)))))

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 = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + 9.0);
	}
	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(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + 9.0));
	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[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

   3. Simplified 99.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 11.1%

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

   4. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.8%

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

Alternative 2: 99.4% accurate, 0.2× speedup

Math

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

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (/ (- (+ t_2 (* 2.0 x2)) x1) t_1))
        (t_4 (* t_2 t_3))
        (t_5 (* (* (* x1 2.0) t_3) (- t_3 3.0)))
        (t_6 (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_1)))
        (t_7 (+ 1.0 (pow x1 2.0))))
   (if (<=
        (+
         x1
         (+
          (+
           x1
           (+ (+ (* t_1 (+ t_5 (* (* x1 x1) (- (* t_3 4.0) 6.0)))) t_4) t_0))
          t_6))
        INFINITY)
     (+
      x1
      (+
       t_6
       (+
        x1
        (+
         t_0
         (+
          t_4
          (*
           t_1
           (+
            t_5
            (*
             (* x1 x1)
             (-
              (*
               4.0
               (+
                (+ (* 2.0 (/ x2 t_7)) (* 3.0 (/ (pow x1 2.0) t_7)))
                (/ x1 (- -1.0 (pow x1 2.0)))))
              6.0)))))))))
     (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) 9.0)))))

C

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

Java

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = (x1 * x1) + 1.0;
	t_2 = x1 * (x1 * 3.0);
	t_3 = ((t_2 + (2.0 * x2)) - x1) / t_1;
	t_4 = t_2 * t_3;
	t_5 = ((x1 * 2.0) * t_3) * (t_3 - 3.0);
	t_6 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_1);
	t_7 = 1.0 + (x1 ^ 2.0);
	tmp = 0.0;
	if ((x1 + ((x1 + (((t_1 * (t_5 + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + t_4) + t_0)) + t_6)) <= Inf)
		tmp = x1 + (t_6 + (x1 + (t_0 + (t_4 + (t_1 * (t_5 + ((x1 * x1) * ((4.0 * (((2.0 * (x2 / t_7)) + (3.0 * ((x1 ^ 2.0) / t_7))) + (x1 / (-1.0 - (x1 ^ 2.0))))) - 6.0))))))));
	else
		tmp = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + 9.0);
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

   3. Taylor expanded in x2 around 0 99.5%

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

   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 11.1%

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

   4. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.6%

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

Alternative 3: 99.3% accurate, 0.5× speedup

Math

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

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))
        (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 (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) 9.0)))))

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 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 = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + 9.0);
	}
	return tmp;
}

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / 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 = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + 9.0);
	}
	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
	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 = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + 9.0)
	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)
	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(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + 9.0));
	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;
	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 + ((x1 + (6.0 * (x1 ^ 4.0))) + 9.0);
	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]}, 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[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 11.1%

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

   4. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.6%

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

Alternative 4: 98.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot \left(x1 \cdot 9 + -1\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := 3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_2}\\ t_4 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_2}\\ t_5 := x1 + \left(t\_3 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_0 + t\_2 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_4\right) \cdot \left(t\_4 - 3\right) + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(x1 \cdot 6 - 4\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(t\_3 + \left(x1 + \left(x2 \cdot -4 + \left(x2 \cdot 8 + x1 \cdot \left(2 + x1 \cdot \left(x2 \cdot -4 + \left(x1 \cdot -2 + \left(-2 \cdot \left(3 - 2 \cdot x2\right) + \left(x2 \cdot 8 + x2 \cdot 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -0.026:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x1 \leq 0.038:\\ \;\;\;\;t\_1 + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right) - 6\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+152}:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (* x1 (+ (* x1 9.0) -1.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_2)))
        (t_4 (/ (- (+ t_0 (* 2.0 x2)) x1) t_2))
        (t_5
         (+
          x1
          (+
           t_3
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* 3.0 t_0)
              (*
               t_2
               (+
                (* (* (* x1 2.0) t_4) (- t_4 3.0))
                (+
                 (* 4.0 (- (* 2.0 x2) 3.0))
                 (* x1 (- (* x1 6.0) 4.0))))))))))))
   (if (<= x1 -4.4e+153)
     t_1
     (if (<= x1 -5.6e+102)
       (+
        x1
        (+
         t_3
         (+
          x1
          (+
           (* x2 -4.0)
           (+
            (* x2 8.0)
            (*
             x1
             (+
              2.0
              (*
               x1
               (+
                (* x2 -4.0)
                (+
                 (* x1 -2.0)
                 (+
                  (* -2.0 (- 3.0 (* 2.0 x2)))
                  (+ (* x2 8.0) (* x2 6.0)))))))))))))
       (if (<= x1 -0.026)
         t_5
         (if (<= x1 0.038)
           (+
            t_1
            (* x2 (- (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 12.0) 12.0))) 6.0)))
           (if (<= x1 2e+152) t_5 t_1)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * ((x1 * 9.0) + -1.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2);
	double t_4 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	double t_5 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_2 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((4.0 * ((2.0 * x2) - 3.0)) + (x1 * ((x1 * 6.0) - 4.0)))))))));
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = t_1;
	} else if (x1 <= -5.6e+102) {
		tmp = x1 + (t_3 + (x1 + ((x2 * -4.0) + ((x2 * 8.0) + (x1 * (2.0 + (x1 * ((x2 * -4.0) + ((x1 * -2.0) + ((-2.0 * (3.0 - (2.0 * x2))) + ((x2 * 8.0) + (x2 * 6.0))))))))))));
	} else if (x1 <= -0.026) {
		tmp = t_5;
	} else if (x1 <= 0.038) {
		tmp = t_1 + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0));
	} else if (x1 <= 2e+152) {
		tmp = t_5;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = x1 * ((x1 * 9.0d0) + (-1.0d0))
    t_2 = (x1 * x1) + 1.0d0
    t_3 = 3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_2)
    t_4 = ((t_0 + (2.0d0 * x2)) - x1) / t_2
    t_5 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_0) + (t_2 * ((((x1 * 2.0d0) * t_4) * (t_4 - 3.0d0)) + ((4.0d0 * ((2.0d0 * x2) - 3.0d0)) + (x1 * ((x1 * 6.0d0) - 4.0d0)))))))))
    if (x1 <= (-4.4d+153)) then
        tmp = t_1
    else if (x1 <= (-5.6d+102)) then
        tmp = x1 + (t_3 + (x1 + ((x2 * (-4.0d0)) + ((x2 * 8.0d0) + (x1 * (2.0d0 + (x1 * ((x2 * (-4.0d0)) + ((x1 * (-2.0d0)) + (((-2.0d0) * (3.0d0 - (2.0d0 * x2))) + ((x2 * 8.0d0) + (x2 * 6.0d0))))))))))))
    else if (x1 <= (-0.026d0)) then
        tmp = t_5
    else if (x1 <= 0.038d0) then
        tmp = t_1 + (x2 * (((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 12.0d0) - 12.0d0))) - 6.0d0))
    else if (x1 <= 2d+152) then
        tmp = t_5
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * ((x1 * 9.0) + -1.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2);
	double t_4 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	double t_5 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_2 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((4.0 * ((2.0 * x2) - 3.0)) + (x1 * ((x1 * 6.0) - 4.0)))))))));
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = t_1;
	} else if (x1 <= -5.6e+102) {
		tmp = x1 + (t_3 + (x1 + ((x2 * -4.0) + ((x2 * 8.0) + (x1 * (2.0 + (x1 * ((x2 * -4.0) + ((x1 * -2.0) + ((-2.0 * (3.0 - (2.0 * x2))) + ((x2 * 8.0) + (x2 * 6.0))))))))))));
	} else if (x1 <= -0.026) {
		tmp = t_5;
	} else if (x1 <= 0.038) {
		tmp = t_1 + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0));
	} else if (x1 <= 2e+152) {
		tmp = t_5;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = x1 * ((x1 * 9.0) + -1.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)
	t_4 = ((t_0 + (2.0 * x2)) - x1) / t_2
	t_5 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_2 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((4.0 * ((2.0 * x2) - 3.0)) + (x1 * ((x1 * 6.0) - 4.0)))))))))
	tmp = 0
	if x1 <= -4.4e+153:
		tmp = t_1
	elif x1 <= -5.6e+102:
		tmp = x1 + (t_3 + (x1 + ((x2 * -4.0) + ((x2 * 8.0) + (x1 * (2.0 + (x1 * ((x2 * -4.0) + ((x1 * -2.0) + ((-2.0 * (3.0 - (2.0 * x2))) + ((x2 * 8.0) + (x2 * 6.0))))))))))))
	elif x1 <= -0.026:
		tmp = t_5
	elif x1 <= 0.038:
		tmp = t_1 + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0))
	elif x1 <= 2e+152:
		tmp = t_5
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_2))
	t_4 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_2)
	t_5 = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_0) + Float64(t_2 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(t_4 - 3.0)) + Float64(Float64(4.0 * Float64(Float64(2.0 * x2) - 3.0)) + Float64(x1 * Float64(Float64(x1 * 6.0) - 4.0))))))))))
	tmp = 0.0
	if (x1 <= -4.4e+153)
		tmp = t_1;
	elseif (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(Float64(x2 * -4.0) + Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(2.0 + Float64(x1 * Float64(Float64(x2 * -4.0) + Float64(Float64(x1 * -2.0) + Float64(Float64(-2.0 * Float64(3.0 - Float64(2.0 * x2))) + Float64(Float64(x2 * 8.0) + Float64(x2 * 6.0)))))))))))));
	elseif (x1 <= -0.026)
		tmp = t_5;
	elseif (x1 <= 0.038)
		tmp = Float64(t_1 + Float64(x2 * Float64(Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 12.0) - 12.0))) - 6.0)));
	elseif (x1 <= 2e+152)
		tmp = t_5;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = x1 * ((x1 * 9.0) + -1.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2);
	t_4 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	t_5 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_2 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((4.0 * ((2.0 * x2) - 3.0)) + (x1 * ((x1 * 6.0) - 4.0)))))))));
	tmp = 0.0;
	if (x1 <= -4.4e+153)
		tmp = t_1;
	elseif (x1 <= -5.6e+102)
		tmp = x1 + (t_3 + (x1 + ((x2 * -4.0) + ((x2 * 8.0) + (x1 * (2.0 + (x1 * ((x2 * -4.0) + ((x1 * -2.0) + ((-2.0 * (3.0 - (2.0 * x2))) + ((x2 * 8.0) + (x2 * 6.0))))))))))));
	elseif (x1 <= -0.026)
		tmp = t_5;
	elseif (x1 <= 0.038)
		tmp = t_1 + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0));
	elseif (x1 <= 2e+152)
		tmp = t_5;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(t$95$3 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$0), $MachinePrecision] + N[(t$95$2 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(4.0 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.4e+153], t$95$1, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(t$95$3 + N[(x1 + N[(N[(x2 * -4.0), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(2.0 + N[(x1 * N[(N[(x2 * -4.0), $MachinePrecision] + N[(N[(x1 * -2.0), $MachinePrecision] + N[(N[(-2.0 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -0.026], t$95$5, If[LessEqual[x1, 0.038], N[(t$95$1 + N[(x2 * N[(N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 12.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+152], t$95$5, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.3999999999999999e153 or 2.0000000000000001e152 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 73.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in x2 around inf 100.0%

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

   10. Taylor expanded in x2 around 0 100.0%

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

   if -4.3999999999999999e153 < 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%

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

   4. Taylor expanded in x2 around inf 0.0%

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

      1. *-commutative 0.0%

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

   6. Simplified 0.0%

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

   7. Taylor expanded in x1 around inf 0.0%

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

   8. Taylor expanded in x1 around 0 100.0%

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

   if -5.60000000000000037e102 < x1 < -0.0259999999999999988 or 0.0379999999999999991 < x1 < 2.0000000000000001e152

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around -inf 98.4%

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

   4. Taylor expanded in x1 around 0 98.6%

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

   5. Taylor expanded in x1 around inf 98.7%

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

   if -0.0259999999999999988 < x1 < 0.0379999999999999991

   1. Initial program 99.4%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x1 around 0 86.9%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 86.9%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{\left(9 \cdot x1 + x2 \cdot \left(\left(8 \cdot x2 + 12 \cdot x1\right) - 12\right)\right)} - 1\right) \]

   7. Taylor expanded in x2 around 0 99.8%

      \[\leadsto \color{blue}{x1 \cdot \left(9 \cdot x1 - 1\right) + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9 + -1\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 + \left(x2 \cdot -4 + \left(x2 \cdot 8 + x1 \cdot \left(2 + x1 \cdot \left(x2 \cdot -4 + \left(x1 \cdot -2 + \left(-2 \cdot \left(3 - 2 \cdot x2\right) + \left(x2 \cdot 8 + x2 \cdot 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -0.026:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(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(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(x1 \cdot 6 - 4\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.038:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9 + -1\right) + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right) - 6\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\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(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(x1 \cdot 6 - 4\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ \mathbf{if}\;x1 \leq -8.5 \cdot 10^{+72}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t\_2 \cdot 4 - 6\right)\right) + 3 \cdot t\_0\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \end{array} \]

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 (<= x1 -8.5e+72)
     (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) 9.0))
     (if (<= x1 2e+152)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))
         (+
          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))))))
       (* x1 (+ (* x1 9.0) -1.0))))))

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 <= -8.5e+72) {
		tmp = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + 9.0);
	} else if (x1 <= 2e+152) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (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)))));
	} else {
		tmp = x1 * ((x1 * 9.0) + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: 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 <= (-8.5d+72)) then
        tmp = x1 + ((x1 + (6.0d0 * (x1 ** 4.0d0))) + 9.0d0)
    else if (x1 <= 2d+152) then
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)) + (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)))))
    else
        tmp = x1 * ((x1 * 9.0d0) + (-1.0d0))
    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 <= -8.5e+72) {
		tmp = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + 9.0);
	} else if (x1 <= 2e+152) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (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)))));
	} else {
		tmp = x1 * ((x1 * 9.0) + -1.0);
	}
	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 <= -8.5e+72:
		tmp = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + 9.0)
	elif x1 <= 2e+152:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (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)))))
	else:
		tmp = x1 * ((x1 * 9.0) + -1.0)
	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 <= -8.5e+72)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + 9.0));
	elseif (x1 <= 2e+152)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_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))))));
	else
		tmp = Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0));
	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 <= -8.5e+72)
		tmp = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + 9.0);
	elseif (x1 <= 2e+152)
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (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)))));
	else
		tmp = x1 * ((x1 * 9.0) + -1.0);
	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[LessEqual[x1, -8.5e+72], N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+152], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$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]), $MachinePrecision]), $MachinePrecision], N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -8.5000000000000004e72

   1. Initial program 8.3%

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

   3. Taylor expanded in x1 around inf 25.0%

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

   4. Taylor expanded in x1 around inf 100.0%

      \[\leadsto x1 + \left(\left(6 \cdot {x1}^{4} + x1\right) + \color{blue}{9}\right) \]

   if -8.5000000000000004e72 < x1 < 2.0000000000000001e152

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around inf 99.0%

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

   if 2.0000000000000001e152 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 80.0%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in x2 around inf 100.0%

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

   10. Taylor expanded in x2 around 0 100.0%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -8.5 \cdot 10^{+72}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 94.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot \left(x1 \cdot 9 + -1\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := 3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_2}\\ t_4 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_2}\\ t_5 := x1 + \left(t\_3 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_0 + t\_2 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t\_4 \cdot 4 - 6\right) + \left(t\_4 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -2 \cdot 10^{+155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(t\_3 + \left(x1 + \left(x2 \cdot -4 + \left(x2 \cdot 8 + x1 \cdot \left(2 + x1 \cdot \left(x2 \cdot -4 + \left(x1 \cdot -2 + \left(-2 \cdot \left(3 - 2 \cdot x2\right) + \left(x2 \cdot 8 + x2 \cdot 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -62:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x1 \leq 8 \cdot 10^{+24}:\\ \;\;\;\;t\_1 + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right) - 6\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+152}:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (* x1 (+ (* x1 9.0) -1.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_2)))
        (t_4 (/ (- (+ t_0 (* 2.0 x2)) x1) t_2))
        (t_5
         (+
          x1
          (+
           t_3
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* 3.0 t_0)
              (*
               t_2
               (+
                (* (* x1 x1) (- (* t_4 4.0) 6.0))
                (* (- t_4 3.0) (* (* x1 2.0) 3.0)))))))))))
   (if (<= x1 -2e+155)
     t_1
     (if (<= x1 -5e+102)
       (+
        x1
        (+
         t_3
         (+
          x1
          (+
           (* x2 -4.0)
           (+
            (* x2 8.0)
            (*
             x1
             (+
              2.0
              (*
               x1
               (+
                (* x2 -4.0)
                (+
                 (* x1 -2.0)
                 (+
                  (* -2.0 (- 3.0 (* 2.0 x2)))
                  (+ (* x2 8.0) (* x2 6.0)))))))))))))
       (if (<= x1 -62.0)
         t_5
         (if (<= x1 8e+24)
           (+
            t_1
            (* x2 (- (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 12.0) 12.0))) 6.0)))
           (if (<= x1 2e+152) t_5 t_1)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * ((x1 * 9.0) + -1.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2);
	double t_4 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	double t_5 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_2 * (((x1 * x1) * ((t_4 * 4.0) - 6.0)) + ((t_4 - 3.0) * ((x1 * 2.0) * 3.0))))))));
	double tmp;
	if (x1 <= -2e+155) {
		tmp = t_1;
	} else if (x1 <= -5e+102) {
		tmp = x1 + (t_3 + (x1 + ((x2 * -4.0) + ((x2 * 8.0) + (x1 * (2.0 + (x1 * ((x2 * -4.0) + ((x1 * -2.0) + ((-2.0 * (3.0 - (2.0 * x2))) + ((x2 * 8.0) + (x2 * 6.0))))))))))));
	} else if (x1 <= -62.0) {
		tmp = t_5;
	} else if (x1 <= 8e+24) {
		tmp = t_1 + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0));
	} else if (x1 <= 2e+152) {
		tmp = t_5;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = x1 * ((x1 * 9.0d0) + (-1.0d0))
    t_2 = (x1 * x1) + 1.0d0
    t_3 = 3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_2)
    t_4 = ((t_0 + (2.0d0 * x2)) - x1) / t_2
    t_5 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_0) + (t_2 * (((x1 * x1) * ((t_4 * 4.0d0) - 6.0d0)) + ((t_4 - 3.0d0) * ((x1 * 2.0d0) * 3.0d0))))))))
    if (x1 <= (-2d+155)) then
        tmp = t_1
    else if (x1 <= (-5d+102)) then
        tmp = x1 + (t_3 + (x1 + ((x2 * (-4.0d0)) + ((x2 * 8.0d0) + (x1 * (2.0d0 + (x1 * ((x2 * (-4.0d0)) + ((x1 * (-2.0d0)) + (((-2.0d0) * (3.0d0 - (2.0d0 * x2))) + ((x2 * 8.0d0) + (x2 * 6.0d0))))))))))))
    else if (x1 <= (-62.0d0)) then
        tmp = t_5
    else if (x1 <= 8d+24) then
        tmp = t_1 + (x2 * (((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 12.0d0) - 12.0d0))) - 6.0d0))
    else if (x1 <= 2d+152) then
        tmp = t_5
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * ((x1 * 9.0) + -1.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2);
	double t_4 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	double t_5 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_2 * (((x1 * x1) * ((t_4 * 4.0) - 6.0)) + ((t_4 - 3.0) * ((x1 * 2.0) * 3.0))))))));
	double tmp;
	if (x1 <= -2e+155) {
		tmp = t_1;
	} else if (x1 <= -5e+102) {
		tmp = x1 + (t_3 + (x1 + ((x2 * -4.0) + ((x2 * 8.0) + (x1 * (2.0 + (x1 * ((x2 * -4.0) + ((x1 * -2.0) + ((-2.0 * (3.0 - (2.0 * x2))) + ((x2 * 8.0) + (x2 * 6.0))))))))))));
	} else if (x1 <= -62.0) {
		tmp = t_5;
	} else if (x1 <= 8e+24) {
		tmp = t_1 + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0));
	} else if (x1 <= 2e+152) {
		tmp = t_5;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = x1 * ((x1 * 9.0) + -1.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)
	t_4 = ((t_0 + (2.0 * x2)) - x1) / t_2
	t_5 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_2 * (((x1 * x1) * ((t_4 * 4.0) - 6.0)) + ((t_4 - 3.0) * ((x1 * 2.0) * 3.0))))))))
	tmp = 0
	if x1 <= -2e+155:
		tmp = t_1
	elif x1 <= -5e+102:
		tmp = x1 + (t_3 + (x1 + ((x2 * -4.0) + ((x2 * 8.0) + (x1 * (2.0 + (x1 * ((x2 * -4.0) + ((x1 * -2.0) + ((-2.0 * (3.0 - (2.0 * x2))) + ((x2 * 8.0) + (x2 * 6.0))))))))))))
	elif x1 <= -62.0:
		tmp = t_5
	elif x1 <= 8e+24:
		tmp = t_1 + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0))
	elif x1 <= 2e+152:
		tmp = t_5
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_2))
	t_4 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_2)
	t_5 = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_0) + Float64(t_2 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_4 * 4.0) - 6.0)) + Float64(Float64(t_4 - 3.0) * Float64(Float64(x1 * 2.0) * 3.0)))))))))
	tmp = 0.0
	if (x1 <= -2e+155)
		tmp = t_1;
	elseif (x1 <= -5e+102)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(Float64(x2 * -4.0) + Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(2.0 + Float64(x1 * Float64(Float64(x2 * -4.0) + Float64(Float64(x1 * -2.0) + Float64(Float64(-2.0 * Float64(3.0 - Float64(2.0 * x2))) + Float64(Float64(x2 * 8.0) + Float64(x2 * 6.0)))))))))))));
	elseif (x1 <= -62.0)
		tmp = t_5;
	elseif (x1 <= 8e+24)
		tmp = Float64(t_1 + Float64(x2 * Float64(Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 12.0) - 12.0))) - 6.0)));
	elseif (x1 <= 2e+152)
		tmp = t_5;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = x1 * ((x1 * 9.0) + -1.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2);
	t_4 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	t_5 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_2 * (((x1 * x1) * ((t_4 * 4.0) - 6.0)) + ((t_4 - 3.0) * ((x1 * 2.0) * 3.0))))))));
	tmp = 0.0;
	if (x1 <= -2e+155)
		tmp = t_1;
	elseif (x1 <= -5e+102)
		tmp = x1 + (t_3 + (x1 + ((x2 * -4.0) + ((x2 * 8.0) + (x1 * (2.0 + (x1 * ((x2 * -4.0) + ((x1 * -2.0) + ((-2.0 * (3.0 - (2.0 * x2))) + ((x2 * 8.0) + (x2 * 6.0))))))))))));
	elseif (x1 <= -62.0)
		tmp = t_5;
	elseif (x1 <= 8e+24)
		tmp = t_1 + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0));
	elseif (x1 <= 2e+152)
		tmp = t_5;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(t$95$3 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$0), $MachinePrecision] + N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$4 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$4 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2e+155], t$95$1, If[LessEqual[x1, -5e+102], N[(x1 + N[(t$95$3 + N[(x1 + N[(N[(x2 * -4.0), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(2.0 + N[(x1 * N[(N[(x2 * -4.0), $MachinePrecision] + N[(N[(x1 * -2.0), $MachinePrecision] + N[(N[(-2.0 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -62.0], t$95$5, If[LessEqual[x1, 8e+24], N[(t$95$1 + N[(x2 * N[(N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 12.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+152], t$95$5, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.00000000000000001e155 or 2.0000000000000001e152 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 73.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in x2 around inf 100.0%

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

   10. Taylor expanded in x2 around 0 100.0%

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

   if -2.00000000000000001e155 < x1 < -5e102

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around -inf 0.0%

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

   4. Taylor expanded in x2 around inf 0.0%

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

      1. *-commutative 0.0%

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

   6. Simplified 0.0%

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

   7. Taylor expanded in x1 around inf 0.0%

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

   8. Taylor expanded in x1 around 0 100.0%

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

   if -5e102 < x1 < -62 or 7.9999999999999999e24 < x1 < 2.0000000000000001e152

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around inf 90.5%

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

   4. Taylor expanded in x1 around inf 90.5%

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

   if -62 < x1 < 7.9999999999999999e24

   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 99.8%

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

   5. Taylor expanded in x1 around 0 85.2%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 85.2%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{\left(9 \cdot x1 + x2 \cdot \left(\left(8 \cdot x2 + 12 \cdot x1\right) - 12\right)\right)} - 1\right) \]

   7. Taylor expanded in x2 around 0 97.6%

      \[\leadsto \color{blue}{x1 \cdot \left(9 \cdot x1 - 1\right) + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2 \cdot 10^{+155}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \mathbf{elif}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x2 \cdot -4 + \left(x2 \cdot 8 + x1 \cdot \left(2 + x1 \cdot \left(x2 \cdot -4 + \left(x1 \cdot -2 + \left(-2 \cdot \left(3 - 2 \cdot x2\right) + \left(x2 \cdot 8 + x2 \cdot 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -62:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(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(\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 3\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8 \cdot 10^{+24}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9 + -1\right) + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right) - 6\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ \mathbf{if}\;x1 \leq -7.3 \cdot 10^{+40} \lor \neg \left(x1 \leq 5.2 \cdot 10^{+51}\right):\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_0 \cdot t\_2 + t\_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (if (or (<= x1 -7.3e+40) (not (<= x1 5.2e+51)))
     (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) 9.0))
     (+
      x1
      (+
       (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (* t_0 t_2)
          (*
           t_1
           (+ (* (* (* x1 2.0) t_2) (- t_2 3.0)) (* (* x1 x1) 6.0)))))))))))

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 <= -7.3e+40) || !(x1 <= 5.2e+51)) {
		tmp = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + 9.0);
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	}
	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 <= (-7.3d+40)) .or. (.not. (x1 <= 5.2d+51))) then
        tmp = x1 + ((x1 + (6.0d0 * (x1 ** 4.0d0))) + 9.0d0)
    else
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * 6.0d0)))))))
    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 <= -7.3e+40) || !(x1 <= 5.2e+51)) {
		tmp = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + 9.0);
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	}
	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 <= -7.3e+40) or not (x1 <= 5.2e+51):
		tmp = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + 9.0)
	else:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))))
	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 <= -7.3e+40) || !(x1 <= 5.2e+51))
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + 9.0));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * t_2) + Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * 6.0))))))));
	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 <= -7.3e+40) || ~((x1 <= 5.2e+51)))
		tmp = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + 9.0);
	else
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	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, -7.3e+40], N[Not[LessEqual[x1, 5.2e+51]], $MachinePrecision]], N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * t$95$2), $MachinePrecision] + 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] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -7.3000000000000005e40 or 5.2000000000000002e51 < x1

   1. Initial program 26.1%

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

   3. Taylor expanded in x1 around inf 32.0%

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

   4. Taylor expanded in x1 around inf 97.6%

      \[\leadsto x1 + \left(\left(6 \cdot {x1}^{4} + x1\right) + \color{blue}{9}\right) \]

   if -7.3000000000000005e40 < x1 < 5.2000000000000002e51

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around inf 96.5%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.3 \cdot 10^{+40} \lor \neg \left(x1 \leq 5.2 \cdot 10^{+51}\right):\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 92.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot \left(x1 \cdot 9 + -1\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := 3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_2}\\ t_4 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_2}\\ t_5 := x1 + \left(t\_3 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_0 \cdot t\_4 + t\_2 \cdot \left(\left(x1 \cdot x1\right) \cdot 6 + \left(t\_4 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -4.5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(t\_3 + \left(x1 + \left(x2 \cdot -4 + \left(x2 \cdot 8 + x1 \cdot \left(2 + x1 \cdot \left(x2 \cdot -4 + \left(x1 \cdot -2 + \left(-2 \cdot \left(3 - 2 \cdot x2\right) + \left(x2 \cdot 8 + x2 \cdot 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -75:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x1 \leq 2.8 \cdot 10^{+24}:\\ \;\;\;\;t\_1 + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right) - 6\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+152}:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (* x1 (+ (* x1 9.0) -1.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_2)))
        (t_4 (/ (- (+ t_0 (* 2.0 x2)) x1) t_2))
        (t_5
         (+
          x1
          (+
           t_3
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* t_0 t_4)
              (*
               t_2
               (+ (* (* x1 x1) 6.0) (* (- t_4 3.0) (* (* x1 2.0) 3.0)))))))))))
   (if (<= x1 -4.4e+153)
     t_1
     (if (<= x1 -4.5e+102)
       (+
        x1
        (+
         t_3
         (+
          x1
          (+
           (* x2 -4.0)
           (+
            (* x2 8.0)
            (*
             x1
             (+
              2.0
              (*
               x1
               (+
                (* x2 -4.0)
                (+
                 (* x1 -2.0)
                 (+
                  (* -2.0 (- 3.0 (* 2.0 x2)))
                  (+ (* x2 8.0) (* x2 6.0)))))))))))))
       (if (<= x1 -75.0)
         t_5
         (if (<= x1 2.8e+24)
           (+
            t_1
            (* x2 (- (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 12.0) 12.0))) 6.0)))
           (if (<= x1 2e+152) t_5 t_1)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * ((x1 * 9.0) + -1.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2);
	double t_4 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	double t_5 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_4) + (t_2 * (((x1 * x1) * 6.0) + ((t_4 - 3.0) * ((x1 * 2.0) * 3.0))))))));
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = t_1;
	} else if (x1 <= -4.5e+102) {
		tmp = x1 + (t_3 + (x1 + ((x2 * -4.0) + ((x2 * 8.0) + (x1 * (2.0 + (x1 * ((x2 * -4.0) + ((x1 * -2.0) + ((-2.0 * (3.0 - (2.0 * x2))) + ((x2 * 8.0) + (x2 * 6.0))))))))))));
	} else if (x1 <= -75.0) {
		tmp = t_5;
	} else if (x1 <= 2.8e+24) {
		tmp = t_1 + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0));
	} else if (x1 <= 2e+152) {
		tmp = t_5;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = x1 * ((x1 * 9.0d0) + (-1.0d0))
    t_2 = (x1 * x1) + 1.0d0
    t_3 = 3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_2)
    t_4 = ((t_0 + (2.0d0 * x2)) - x1) / t_2
    t_5 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_4) + (t_2 * (((x1 * x1) * 6.0d0) + ((t_4 - 3.0d0) * ((x1 * 2.0d0) * 3.0d0))))))))
    if (x1 <= (-4.4d+153)) then
        tmp = t_1
    else if (x1 <= (-4.5d+102)) then
        tmp = x1 + (t_3 + (x1 + ((x2 * (-4.0d0)) + ((x2 * 8.0d0) + (x1 * (2.0d0 + (x1 * ((x2 * (-4.0d0)) + ((x1 * (-2.0d0)) + (((-2.0d0) * (3.0d0 - (2.0d0 * x2))) + ((x2 * 8.0d0) + (x2 * 6.0d0))))))))))))
    else if (x1 <= (-75.0d0)) then
        tmp = t_5
    else if (x1 <= 2.8d+24) then
        tmp = t_1 + (x2 * (((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 12.0d0) - 12.0d0))) - 6.0d0))
    else if (x1 <= 2d+152) then
        tmp = t_5
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * ((x1 * 9.0) + -1.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2);
	double t_4 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	double t_5 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_4) + (t_2 * (((x1 * x1) * 6.0) + ((t_4 - 3.0) * ((x1 * 2.0) * 3.0))))))));
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = t_1;
	} else if (x1 <= -4.5e+102) {
		tmp = x1 + (t_3 + (x1 + ((x2 * -4.0) + ((x2 * 8.0) + (x1 * (2.0 + (x1 * ((x2 * -4.0) + ((x1 * -2.0) + ((-2.0 * (3.0 - (2.0 * x2))) + ((x2 * 8.0) + (x2 * 6.0))))))))))));
	} else if (x1 <= -75.0) {
		tmp = t_5;
	} else if (x1 <= 2.8e+24) {
		tmp = t_1 + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0));
	} else if (x1 <= 2e+152) {
		tmp = t_5;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = x1 * ((x1 * 9.0) + -1.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)
	t_4 = ((t_0 + (2.0 * x2)) - x1) / t_2
	t_5 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_4) + (t_2 * (((x1 * x1) * 6.0) + ((t_4 - 3.0) * ((x1 * 2.0) * 3.0))))))))
	tmp = 0
	if x1 <= -4.4e+153:
		tmp = t_1
	elif x1 <= -4.5e+102:
		tmp = x1 + (t_3 + (x1 + ((x2 * -4.0) + ((x2 * 8.0) + (x1 * (2.0 + (x1 * ((x2 * -4.0) + ((x1 * -2.0) + ((-2.0 * (3.0 - (2.0 * x2))) + ((x2 * 8.0) + (x2 * 6.0))))))))))))
	elif x1 <= -75.0:
		tmp = t_5
	elif x1 <= 2.8e+24:
		tmp = t_1 + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0))
	elif x1 <= 2e+152:
		tmp = t_5
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_2))
	t_4 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_2)
	t_5 = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * t_4) + Float64(t_2 * Float64(Float64(Float64(x1 * x1) * 6.0) + Float64(Float64(t_4 - 3.0) * Float64(Float64(x1 * 2.0) * 3.0)))))))))
	tmp = 0.0
	if (x1 <= -4.4e+153)
		tmp = t_1;
	elseif (x1 <= -4.5e+102)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(Float64(x2 * -4.0) + Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(2.0 + Float64(x1 * Float64(Float64(x2 * -4.0) + Float64(Float64(x1 * -2.0) + Float64(Float64(-2.0 * Float64(3.0 - Float64(2.0 * x2))) + Float64(Float64(x2 * 8.0) + Float64(x2 * 6.0)))))))))))));
	elseif (x1 <= -75.0)
		tmp = t_5;
	elseif (x1 <= 2.8e+24)
		tmp = Float64(t_1 + Float64(x2 * Float64(Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 12.0) - 12.0))) - 6.0)));
	elseif (x1 <= 2e+152)
		tmp = t_5;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = x1 * ((x1 * 9.0) + -1.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2);
	t_4 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	t_5 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_4) + (t_2 * (((x1 * x1) * 6.0) + ((t_4 - 3.0) * ((x1 * 2.0) * 3.0))))))));
	tmp = 0.0;
	if (x1 <= -4.4e+153)
		tmp = t_1;
	elseif (x1 <= -4.5e+102)
		tmp = x1 + (t_3 + (x1 + ((x2 * -4.0) + ((x2 * 8.0) + (x1 * (2.0 + (x1 * ((x2 * -4.0) + ((x1 * -2.0) + ((-2.0 * (3.0 - (2.0 * x2))) + ((x2 * 8.0) + (x2 * 6.0))))))))))));
	elseif (x1 <= -75.0)
		tmp = t_5;
	elseif (x1 <= 2.8e+24)
		tmp = t_1 + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0));
	elseif (x1 <= 2e+152)
		tmp = t_5;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(t$95$3 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * t$95$4), $MachinePrecision] + N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision] + N[(N[(t$95$4 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.4e+153], t$95$1, If[LessEqual[x1, -4.5e+102], N[(x1 + N[(t$95$3 + N[(x1 + N[(N[(x2 * -4.0), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(2.0 + N[(x1 * N[(N[(x2 * -4.0), $MachinePrecision] + N[(N[(x1 * -2.0), $MachinePrecision] + N[(N[(-2.0 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -75.0], t$95$5, If[LessEqual[x1, 2.8e+24], N[(t$95$1 + N[(x2 * N[(N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 12.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+152], t$95$5, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.3999999999999999e153 or 2.0000000000000001e152 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 73.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in x2 around inf 100.0%

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

   10. Taylor expanded in x2 around 0 100.0%

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

   if -4.3999999999999999e153 < x1 < -4.50000000000000021e102

   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%

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

   4. Taylor expanded in x2 around inf 0.0%

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

      1. *-commutative 0.0%

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

   6. Simplified 0.0%

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

   7. Taylor expanded in x1 around inf 0.0%

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

   8. Taylor expanded in x1 around 0 100.0%

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

   if -4.50000000000000021e102 < x1 < -75 or 2.8000000000000002e24 < x1 < 2.0000000000000001e152

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around inf 90.5%

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

   4. Taylor expanded in x1 around inf 81.6%

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

   if -75 < x1 < 2.8000000000000002e24

   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 99.8%

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

   5. Taylor expanded in x1 around 0 85.2%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 85.2%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{\left(9 \cdot x1 + x2 \cdot \left(\left(8 \cdot x2 + 12 \cdot x1\right) - 12\right)\right)} - 1\right) \]

   7. Taylor expanded in x2 around 0 97.6%

      \[\leadsto \color{blue}{x1 \cdot \left(9 \cdot x1 - 1\right) + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \mathbf{elif}\;x1 \leq -4.5 \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 + \left(x2 \cdot -4 + \left(x2 \cdot 8 + x1 \cdot \left(2 + x1 \cdot \left(x2 \cdot -4 + \left(x1 \cdot -2 + \left(-2 \cdot \left(3 - 2 \cdot x2\right) + \left(x2 \cdot 8 + x2 \cdot 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -75:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{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 3\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.8 \cdot 10^{+24}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9 + -1\right) + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right) - 6\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{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 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 95.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 9 + -1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{\left(t\_1 + 2 \cdot x2\right) - x1}{t\_2}\\ \mathbf{if}\;x1 \leq -130:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{elif}\;x1 \leq 0.014:\\ \;\;\;\;t\_0 + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right) - 6\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_1 - 2 \cdot x2\right) - x1}{t\_2} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_1 + t\_2 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_3\right) \cdot \left(t\_3 - 3\right) + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(x1 \cdot 6 - 4\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ (* x1 9.0) -1.0)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (/ (- (+ t_1 (* 2.0 x2)) x1) t_2)))
   (if (<= x1 -130.0)
     (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) 9.0))
     (if (<= x1 0.014)
       (+ t_0 (* x2 (- (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 12.0) 12.0))) 6.0)))
       (if (<= x1 2e+152)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2))
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* 3.0 t_1)
              (*
               t_2
               (+
                (* (* (* x1 2.0) t_3) (- t_3 3.0))
                (+ (* 4.0 (- (* 2.0 x2) 3.0)) (* x1 (- (* x1 6.0) 4.0))))))))))
         t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 9.0) + -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 tmp;
	if (x1 <= -130.0) {
		tmp = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + 9.0);
	} else if (x1 <= 0.014) {
		tmp = t_0 + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0));
	} else if (x1 <= 2e+152) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((4.0 * ((2.0 * x2) - 3.0)) + (x1 * ((x1 * 6.0) - 4.0)))))))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x1 * ((x1 * 9.0d0) + (-1.0d0))
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = ((t_1 + (2.0d0 * x2)) - x1) / t_2
    if (x1 <= (-130.0d0)) then
        tmp = x1 + ((x1 + (6.0d0 * (x1 ** 4.0d0))) + 9.0d0)
    else if (x1 <= 0.014d0) then
        tmp = t_0 + (x2 * (((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 12.0d0) - 12.0d0))) - 6.0d0))
    else if (x1 <= 2d+152) then
        tmp = x1 + ((3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_2)) + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_1) + (t_2 * ((((x1 * 2.0d0) * t_3) * (t_3 - 3.0d0)) + ((4.0d0 * ((2.0d0 * x2) - 3.0d0)) + (x1 * ((x1 * 6.0d0) - 4.0d0)))))))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 9.0) + -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 tmp;
	if (x1 <= -130.0) {
		tmp = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + 9.0);
	} else if (x1 <= 0.014) {
		tmp = t_0 + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0));
	} else if (x1 <= 2e+152) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((4.0 * ((2.0 * x2) - 3.0)) + (x1 * ((x1 * 6.0) - 4.0)))))))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((x1 * 9.0) + -1.0)
	t_1 = x1 * (x1 * 3.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2
	tmp = 0
	if x1 <= -130.0:
		tmp = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + 9.0)
	elif x1 <= 0.014:
		tmp = t_0 + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0))
	elif x1 <= 2e+152:
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((4.0 * ((2.0 * x2) - 3.0)) + (x1 * ((x1 * 6.0) - 4.0)))))))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(x1 * 9.0) + -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)
	tmp = 0.0
	if (x1 <= -130.0)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + 9.0));
	elseif (x1 <= 0.014)
		tmp = Float64(t_0 + Float64(x2 * Float64(Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 12.0) - 12.0))) - 6.0)));
	elseif (x1 <= 2e+152)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_1) + Float64(t_2 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(t_3 - 3.0)) + Float64(Float64(4.0 * Float64(Float64(2.0 * x2) - 3.0)) + Float64(x1 * Float64(Float64(x1 * 6.0) - 4.0))))))))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((x1 * 9.0) + -1.0);
	t_1 = x1 * (x1 * 3.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	tmp = 0.0;
	if (x1 <= -130.0)
		tmp = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + 9.0);
	elseif (x1 <= 0.014)
		tmp = t_0 + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0));
	elseif (x1 <= 2e+152)
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((4.0 * ((2.0 * x2) - 3.0)) + (x1 * ((x1 * 6.0) - 4.0)))))))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -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]}, If[LessEqual[x1, -130.0], N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.014], N[(t$95$0 + N[(x2 * N[(N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 12.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+152], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$1), $MachinePrecision] + 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[(4.0 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -130

   1. Initial program 24.4%

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

   3. Taylor expanded in x1 around inf 32.8%

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

   4. Taylor expanded in x1 around inf 94.3%

      \[\leadsto x1 + \left(\left(6 \cdot {x1}^{4} + x1\right) + \color{blue}{9}\right) \]

   if -130 < x1 < 0.0140000000000000003

   1. Initial program 99.4%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x1 around 0 86.9%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 86.9%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{\left(9 \cdot x1 + x2 \cdot \left(\left(8 \cdot x2 + 12 \cdot x1\right) - 12\right)\right)} - 1\right) \]

   7. Taylor expanded in x2 around 0 99.8%

      \[\leadsto \color{blue}{x1 \cdot \left(9 \cdot x1 - 1\right) + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)} \]

   if 0.0140000000000000003 < x1 < 2.0000000000000001e152

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around -inf 99.6%

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

   4. Taylor expanded in x1 around 0 99.6%

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

   5. Taylor expanded in x1 around inf 99.6%

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

   if 2.0000000000000001e152 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 80.0%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in x2 around inf 100.0%

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

   10. Taylor expanded in x2 around 0 100.0%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -130:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{elif}\;x1 \leq 0.014:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9 + -1\right) + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right) - 6\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(x1 \cdot 6 - 4\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 86.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot x2 - 3\\ t_1 := x1 \cdot \left(x1 \cdot 9 + -1\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := 6 \cdot t\_0\\ t_4 := x1 \cdot \left(x1 \cdot 3\right)\\ t_5 := \frac{\left(t\_4 + 2 \cdot x2\right) - x1}{t\_2}\\ t_6 := 3 \cdot \frac{\left(t\_4 - 2 \cdot x2\right) - x1}{t\_2}\\ t_7 := x1 \cdot \left(x1 \cdot x1\right)\\ \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -6.2 \cdot 10^{+23}:\\ \;\;\;\;x1 + \left(t\_6 + \left(x1 + x1 \cdot \left(t\_3 + x1 \cdot \left(\left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(t\_3 + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 6\right)\right)\right) - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.027:\\ \;\;\;\;t\_1 + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right) - 6\right)\\ \mathbf{elif}\;x1 \leq 10^{+86}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(t\_7 + \left(t\_4 \cdot t\_5 + t\_2 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_5\right) \cdot \left(t\_5 - 3\right) + x2 \cdot 8\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(t\_6 + \left(x1 + \left(t\_7 + \left(x2 \cdot 8 + 4 \cdot \left(x1 \cdot \left(x2 \cdot t\_0\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* 2.0 x2) 3.0))
        (t_1 (* x1 (+ (* x1 9.0) -1.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* 6.0 t_0))
        (t_4 (* x1 (* x1 3.0)))
        (t_5 (/ (- (+ t_4 (* 2.0 x2)) x1) t_2))
        (t_6 (* 3.0 (/ (- (- t_4 (* 2.0 x2)) x1) t_2)))
        (t_7 (* x1 (* x1 x1))))
   (if (<= x1 -4.4e+153)
     t_1
     (if (<= x1 -6.2e+23)
       (+
        x1
        (+
         t_6
         (+
          x1
          (*
           x1
           (+
            t_3
            (*
             x1
             (-
              (+
               (* x2 6.0)
               (+
                (* x2 8.0)
                (* x1 (- (+ t_3 (* 6.0 (+ 3.0 (* x2 -2.0)))) 6.0))))
              12.0)))))))
       (if (<= x1 0.027)
         (+
          t_1
          (* x2 (- (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 12.0) 12.0))) 6.0)))
         (if (<= x1 1e+86)
           (+
            x1
            (+
             9.0
             (+
              x1
              (+
               t_7
               (+
                (* t_4 t_5)
                (* t_2 (+ (* (* (* x1 2.0) t_5) (- t_5 3.0)) (* x2 8.0))))))))
           (if (<= x1 2e+152)
             (+
              x1
              (+ t_6 (+ x1 (+ t_7 (+ (* x2 8.0) (* 4.0 (* x1 (* x2 t_0))))))))
             t_1)))))))

C

double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = x1 * ((x1 * 9.0) + -1.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 6.0 * t_0;
	double t_4 = x1 * (x1 * 3.0);
	double t_5 = ((t_4 + (2.0 * x2)) - x1) / t_2;
	double t_6 = 3.0 * (((t_4 - (2.0 * x2)) - x1) / t_2);
	double t_7 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = t_1;
	} else if (x1 <= -6.2e+23) {
		tmp = x1 + (t_6 + (x1 + (x1 * (t_3 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_3 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))));
	} else if (x1 <= 0.027) {
		tmp = t_1 + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0));
	} else if (x1 <= 1e+86) {
		tmp = x1 + (9.0 + (x1 + (t_7 + ((t_4 * t_5) + (t_2 * ((((x1 * 2.0) * t_5) * (t_5 - 3.0)) + (x2 * 8.0)))))));
	} else if (x1 <= 2e+152) {
		tmp = x1 + (t_6 + (x1 + (t_7 + ((x2 * 8.0) + (4.0 * (x1 * (x2 * 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) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = (2.0d0 * x2) - 3.0d0
    t_1 = x1 * ((x1 * 9.0d0) + (-1.0d0))
    t_2 = (x1 * x1) + 1.0d0
    t_3 = 6.0d0 * t_0
    t_4 = x1 * (x1 * 3.0d0)
    t_5 = ((t_4 + (2.0d0 * x2)) - x1) / t_2
    t_6 = 3.0d0 * (((t_4 - (2.0d0 * x2)) - x1) / t_2)
    t_7 = x1 * (x1 * x1)
    if (x1 <= (-4.4d+153)) then
        tmp = t_1
    else if (x1 <= (-6.2d+23)) then
        tmp = x1 + (t_6 + (x1 + (x1 * (t_3 + (x1 * (((x2 * 6.0d0) + ((x2 * 8.0d0) + (x1 * ((t_3 + (6.0d0 * (3.0d0 + (x2 * (-2.0d0))))) - 6.0d0)))) - 12.0d0))))))
    else if (x1 <= 0.027d0) then
        tmp = t_1 + (x2 * (((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 12.0d0) - 12.0d0))) - 6.0d0))
    else if (x1 <= 1d+86) then
        tmp = x1 + (9.0d0 + (x1 + (t_7 + ((t_4 * t_5) + (t_2 * ((((x1 * 2.0d0) * t_5) * (t_5 - 3.0d0)) + (x2 * 8.0d0)))))))
    else if (x1 <= 2d+152) then
        tmp = x1 + (t_6 + (x1 + (t_7 + ((x2 * 8.0d0) + (4.0d0 * (x1 * (x2 * t_0)))))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = x1 * ((x1 * 9.0) + -1.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 6.0 * t_0;
	double t_4 = x1 * (x1 * 3.0);
	double t_5 = ((t_4 + (2.0 * x2)) - x1) / t_2;
	double t_6 = 3.0 * (((t_4 - (2.0 * x2)) - x1) / t_2);
	double t_7 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = t_1;
	} else if (x1 <= -6.2e+23) {
		tmp = x1 + (t_6 + (x1 + (x1 * (t_3 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_3 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))));
	} else if (x1 <= 0.027) {
		tmp = t_1 + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0));
	} else if (x1 <= 1e+86) {
		tmp = x1 + (9.0 + (x1 + (t_7 + ((t_4 * t_5) + (t_2 * ((((x1 * 2.0) * t_5) * (t_5 - 3.0)) + (x2 * 8.0)))))));
	} else if (x1 <= 2e+152) {
		tmp = x1 + (t_6 + (x1 + (t_7 + ((x2 * 8.0) + (4.0 * (x1 * (x2 * t_0)))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (2.0 * x2) - 3.0
	t_1 = x1 * ((x1 * 9.0) + -1.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = 6.0 * t_0
	t_4 = x1 * (x1 * 3.0)
	t_5 = ((t_4 + (2.0 * x2)) - x1) / t_2
	t_6 = 3.0 * (((t_4 - (2.0 * x2)) - x1) / t_2)
	t_7 = x1 * (x1 * x1)
	tmp = 0
	if x1 <= -4.4e+153:
		tmp = t_1
	elif x1 <= -6.2e+23:
		tmp = x1 + (t_6 + (x1 + (x1 * (t_3 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_3 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))))
	elif x1 <= 0.027:
		tmp = t_1 + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0))
	elif x1 <= 1e+86:
		tmp = x1 + (9.0 + (x1 + (t_7 + ((t_4 * t_5) + (t_2 * ((((x1 * 2.0) * t_5) * (t_5 - 3.0)) + (x2 * 8.0)))))))
	elif x1 <= 2e+152:
		tmp = x1 + (t_6 + (x1 + (t_7 + ((x2 * 8.0) + (4.0 * (x1 * (x2 * t_0)))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(2.0 * x2) - 3.0)
	t_1 = Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(6.0 * t_0)
	t_4 = Float64(x1 * Float64(x1 * 3.0))
	t_5 = Float64(Float64(Float64(t_4 + Float64(2.0 * x2)) - x1) / t_2)
	t_6 = Float64(3.0 * Float64(Float64(Float64(t_4 - Float64(2.0 * x2)) - x1) / t_2))
	t_7 = Float64(x1 * Float64(x1 * x1))
	tmp = 0.0
	if (x1 <= -4.4e+153)
		tmp = t_1;
	elseif (x1 <= -6.2e+23)
		tmp = Float64(x1 + Float64(t_6 + Float64(x1 + Float64(x1 * Float64(t_3 + Float64(x1 * Float64(Float64(Float64(x2 * 6.0) + Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_3 + Float64(6.0 * Float64(3.0 + Float64(x2 * -2.0)))) - 6.0)))) - 12.0)))))));
	elseif (x1 <= 0.027)
		tmp = Float64(t_1 + Float64(x2 * Float64(Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 12.0) - 12.0))) - 6.0)));
	elseif (x1 <= 1e+86)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_7 + Float64(Float64(t_4 * t_5) + Float64(t_2 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_5) * Float64(t_5 - 3.0)) + Float64(x2 * 8.0))))))));
	elseif (x1 <= 2e+152)
		tmp = Float64(x1 + Float64(t_6 + Float64(x1 + Float64(t_7 + Float64(Float64(x2 * 8.0) + Float64(4.0 * Float64(x1 * Float64(x2 * t_0))))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (2.0 * x2) - 3.0;
	t_1 = x1 * ((x1 * 9.0) + -1.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = 6.0 * t_0;
	t_4 = x1 * (x1 * 3.0);
	t_5 = ((t_4 + (2.0 * x2)) - x1) / t_2;
	t_6 = 3.0 * (((t_4 - (2.0 * x2)) - x1) / t_2);
	t_7 = x1 * (x1 * x1);
	tmp = 0.0;
	if (x1 <= -4.4e+153)
		tmp = t_1;
	elseif (x1 <= -6.2e+23)
		tmp = x1 + (t_6 + (x1 + (x1 * (t_3 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_3 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))));
	elseif (x1 <= 0.027)
		tmp = t_1 + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0));
	elseif (x1 <= 1e+86)
		tmp = x1 + (9.0 + (x1 + (t_7 + ((t_4 * t_5) + (t_2 * ((((x1 * 2.0) * t_5) * (t_5 - 3.0)) + (x2 * 8.0)))))));
	elseif (x1 <= 2e+152)
		tmp = x1 + (t_6 + (x1 + (t_7 + ((x2 * 8.0) + (4.0 * (x1 * (x2 * t_0)))))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(6.0 * t$95$0), $MachinePrecision]}, Block[{t$95$4 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(t$95$4 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$6 = N[(3.0 * N[(N[(N[(t$95$4 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.4e+153], t$95$1, If[LessEqual[x1, -6.2e+23], N[(x1 + N[(t$95$6 + N[(x1 + N[(x1 * N[(t$95$3 + N[(x1 * N[(N[(N[(x2 * 6.0), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$3 + N[(6.0 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.027], N[(t$95$1 + N[(x2 * N[(N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 12.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1e+86], N[(x1 + N[(9.0 + N[(x1 + N[(t$95$7 + N[(N[(t$95$4 * t$95$5), $MachinePrecision] + N[(t$95$2 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$5), $MachinePrecision] * N[(t$95$5 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+152], N[(x1 + N[(t$95$6 + N[(x1 + N[(t$95$7 + N[(N[(x2 * 8.0), $MachinePrecision] + N[(4.0 * N[(x1 * N[(x2 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -4.3999999999999999e153 or 2.0000000000000001e152 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 73.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in x2 around inf 100.0%

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

   10. Taylor expanded in x2 around 0 100.0%

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

   if -4.3999999999999999e153 < x1 < -6.19999999999999941e23

   1. Initial program 59.5%

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

   3. Taylor expanded in x1 around inf 59.5%

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

   4. Taylor expanded in x1 around 0 48.8%

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

   if -6.19999999999999941e23 < x1 < 0.0269999999999999997

   1. Initial program 99.4%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x1 around 0 85.0%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 85.0%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{\left(9 \cdot x1 + x2 \cdot \left(\left(8 \cdot x2 + 12 \cdot x1\right) - 12\right)\right)} - 1\right) \]

   7. Taylor expanded in x2 around 0 97.6%

      \[\leadsto \color{blue}{x1 \cdot \left(9 \cdot x1 - 1\right) + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)} \]

   if 0.0269999999999999997 < x1 < 1e86

   1. Initial program 99.0%

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

   3. Taylor expanded in x1 around -inf 99.1%

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

   4. Taylor expanded in x2 around inf 48.2%

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

      1. *-commutative 48.2%

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

   6. Simplified 48.2%

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

   7. Taylor expanded in x1 around inf 48.2%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + x2 \cdot 8\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + \color{blue}{9}\right) \]

   if 1e86 < x1 < 2.0000000000000001e152

   1. Initial program 100.0%

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

   3. Taylor expanded in x1 around -inf 100.0%

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

   4. Taylor expanded in x2 around inf 48.5%

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

      1. *-commutative 48.5%

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

   6. Simplified 48.5%

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

   7. Taylor expanded in x1 around 0 81.8%

      \[\leadsto x1 + \left(\left(\left(\color{blue}{\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 8 \cdot x2\right)} + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \mathbf{elif}\;x1 \leq -6.2 \cdot 10^{+23}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + x1 \cdot \left(6 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(\left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(6 \cdot \left(2 \cdot x2 - 3\right) + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 6\right)\right)\right) - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.027:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9 + -1\right) + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right) - 6\right)\\ \mathbf{elif}\;x1 \leq 10^{+86}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + x2 \cdot 8\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(x2 \cdot 8 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 83.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(2 \cdot x2 - 3\right)\\ t_1 := x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -6.2 \cdot 10^{+23}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + x1 \cdot \left(t\_0 + x1 \cdot \left(\left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(t\_0 + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 6\right)\right)\right) - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.5 \cdot 10^{+98}:\\ \;\;\;\;t\_1 + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot 9\right)}{x2} - 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 6.0 (- (* 2.0 x2) 3.0))) (t_1 (* x1 (+ (* x1 9.0) -1.0))))
   (if (<= x1 -4.4e+153)
     t_1
     (if (<= x1 -6.2e+23)
       (+
        x1
        (+
         (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
         (+
          x1
          (*
           x1
           (+
            t_0
            (*
             x1
             (-
              (+
               (* x2 6.0)
               (+
                (* x2 8.0)
                (* x1 (- (+ t_0 (* 6.0 (+ 3.0 (* x2 -2.0)))) 6.0))))
              12.0)))))))
       (if (<= x1 3.5e+98)
         (+
          t_1
          (* x2 (- (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 12.0) 12.0))) 6.0)))
         (* x2 (- (/ (* x1 (* x1 9.0)) x2) 6.0)))))))

C

double code(double x1, double x2) {
	double t_0 = 6.0 * ((2.0 * x2) - 3.0);
	double t_1 = x1 * ((x1 * 9.0) + -1.0);
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = t_1;
	} else if (x1 <= -6.2e+23) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (x1 * (t_0 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_0 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))));
	} else if (x1 <= 3.5e+98) {
		tmp = t_1 + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0));
	} else {
		tmp = x2 * (((x1 * (x1 * 9.0)) / x2) - 6.0);
	}
	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 = 6.0d0 * ((2.0d0 * x2) - 3.0d0)
    t_1 = x1 * ((x1 * 9.0d0) + (-1.0d0))
    if (x1 <= (-4.4d+153)) then
        tmp = t_1
    else if (x1 <= (-6.2d+23)) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0))) + (x1 + (x1 * (t_0 + (x1 * (((x2 * 6.0d0) + ((x2 * 8.0d0) + (x1 * ((t_0 + (6.0d0 * (3.0d0 + (x2 * (-2.0d0))))) - 6.0d0)))) - 12.0d0))))))
    else if (x1 <= 3.5d+98) then
        tmp = t_1 + (x2 * (((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 12.0d0) - 12.0d0))) - 6.0d0))
    else
        tmp = x2 * (((x1 * (x1 * 9.0d0)) / x2) - 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 6.0 * ((2.0 * x2) - 3.0);
	double t_1 = x1 * ((x1 * 9.0) + -1.0);
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = t_1;
	} else if (x1 <= -6.2e+23) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (x1 * (t_0 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_0 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))));
	} else if (x1 <= 3.5e+98) {
		tmp = t_1 + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0));
	} else {
		tmp = x2 * (((x1 * (x1 * 9.0)) / x2) - 6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 6.0 * ((2.0 * x2) - 3.0)
	t_1 = x1 * ((x1 * 9.0) + -1.0)
	tmp = 0
	if x1 <= -4.4e+153:
		tmp = t_1
	elif x1 <= -6.2e+23:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (x1 * (t_0 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_0 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))))
	elif x1 <= 3.5e+98:
		tmp = t_1 + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0))
	else:
		tmp = x2 * (((x1 * (x1 * 9.0)) / x2) - 6.0)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(6.0 * Float64(Float64(2.0 * x2) - 3.0))
	t_1 = Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0))
	tmp = 0.0
	if (x1 <= -4.4e+153)
		tmp = t_1;
	elseif (x1 <= -6.2e+23)
		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(x1 * Float64(t_0 + Float64(x1 * Float64(Float64(Float64(x2 * 6.0) + Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_0 + Float64(6.0 * Float64(3.0 + Float64(x2 * -2.0)))) - 6.0)))) - 12.0)))))));
	elseif (x1 <= 3.5e+98)
		tmp = Float64(t_1 + Float64(x2 * Float64(Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 12.0) - 12.0))) - 6.0)));
	else
		tmp = Float64(x2 * Float64(Float64(Float64(x1 * Float64(x1 * 9.0)) / x2) - 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 6.0 * ((2.0 * x2) - 3.0);
	t_1 = x1 * ((x1 * 9.0) + -1.0);
	tmp = 0.0;
	if (x1 <= -4.4e+153)
		tmp = t_1;
	elseif (x1 <= -6.2e+23)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (x1 * (t_0 + (x1 * (((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_0 + (6.0 * (3.0 + (x2 * -2.0)))) - 6.0)))) - 12.0))))));
	elseif (x1 <= 3.5e+98)
		tmp = t_1 + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0));
	else
		tmp = x2 * (((x1 * (x1 * 9.0)) / x2) - 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(6.0 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.4e+153], t$95$1, If[LessEqual[x1, -6.2e+23], 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[(x1 * N[(t$95$0 + N[(x1 * N[(N[(N[(x2 * 6.0), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$0 + N[(6.0 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.5e+98], N[(t$95$1 + N[(x2 * N[(N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 12.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * N[(N[(N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.3999999999999999e153

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 68.9%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in x2 around inf 100.0%

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

   10. Taylor expanded in x2 around 0 100.0%

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

   if -4.3999999999999999e153 < x1 < -6.19999999999999941e23

   1. Initial program 59.5%

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

   3. Taylor expanded in x1 around inf 59.5%

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

   4. Taylor expanded in x1 around 0 48.8%

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

   if -6.19999999999999941e23 < x1 < 3.5e98

   1. Initial program 99.4%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x1 around 0 75.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 76.5%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{\left(9 \cdot x1 + x2 \cdot \left(\left(8 \cdot x2 + 12 \cdot x1\right) - 12\right)\right)} - 1\right) \]

   7. Taylor expanded in x2 around 0 87.2%

      \[\leadsto \color{blue}{x1 \cdot \left(9 \cdot x1 - 1\right) + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)} \]

   if 3.5e98 < x1

   1. Initial program 22.2%

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

   3. Simplified 22.2%

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

   5. Taylor expanded in x1 around 0 69.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 79.3%

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

      1. *-commutative 79.3%

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

   8. Simplified 79.3%

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

   9. Taylor expanded in x2 around inf 89.7%

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

   10. Taylor expanded in x1 around inf 89.7%

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

       1. *-commutative 89.7%

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

   12. Simplified 89.7%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \mathbf{elif}\;x1 \leq -6.2 \cdot 10^{+23}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + x1 \cdot \left(6 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(\left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(6 \cdot \left(2 \cdot x2 - 3\right) + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 6\right)\right)\right) - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.5 \cdot 10^{+98}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9 + -1\right) + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot 9\right)}{x2} - 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 83.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -1.15 \cdot 10^{+24}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x2 \cdot -4 + \left(x2 \cdot 8 + x1 \cdot \left(2 + x1 \cdot \left(x2 \cdot -4 + \left(x1 \cdot -2 + \left(-2 \cdot \left(3 - 2 \cdot x2\right) + \left(x2 \cdot 8 + x2 \cdot 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6.2 \cdot 10^{+96}:\\ \;\;\;\;t\_0 + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot 9\right)}{x2} - 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ (* x1 9.0) -1.0))))
   (if (<= x1 -4.4e+153)
     t_0
     (if (<= x1 -1.15e+24)
       (+
        x1
        (+
         (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
         (+
          x1
          (+
           (* x2 -4.0)
           (+
            (* x2 8.0)
            (*
             x1
             (+
              2.0
              (*
               x1
               (+
                (* x2 -4.0)
                (+
                 (* x1 -2.0)
                 (+
                  (* -2.0 (- 3.0 (* 2.0 x2)))
                  (+ (* x2 8.0) (* x2 6.0)))))))))))))
       (if (<= x1 6.2e+96)
         (+
          t_0
          (* x2 (- (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 12.0) 12.0))) 6.0)))
         (* x2 (- (/ (* x1 (* x1 9.0)) x2) 6.0)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 9.0) + -1.0);
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = t_0;
	} else if (x1 <= -1.15e+24) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + ((x2 * -4.0) + ((x2 * 8.0) + (x1 * (2.0 + (x1 * ((x2 * -4.0) + ((x1 * -2.0) + ((-2.0 * (3.0 - (2.0 * x2))) + ((x2 * 8.0) + (x2 * 6.0))))))))))));
	} else if (x1 <= 6.2e+96) {
		tmp = t_0 + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0));
	} else {
		tmp = x2 * (((x1 * (x1 * 9.0)) / x2) - 6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 * ((x1 * 9.0d0) + (-1.0d0))
    if (x1 <= (-4.4d+153)) then
        tmp = t_0
    else if (x1 <= (-1.15d+24)) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0))) + (x1 + ((x2 * (-4.0d0)) + ((x2 * 8.0d0) + (x1 * (2.0d0 + (x1 * ((x2 * (-4.0d0)) + ((x1 * (-2.0d0)) + (((-2.0d0) * (3.0d0 - (2.0d0 * x2))) + ((x2 * 8.0d0) + (x2 * 6.0d0))))))))))))
    else if (x1 <= 6.2d+96) then
        tmp = t_0 + (x2 * (((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 12.0d0) - 12.0d0))) - 6.0d0))
    else
        tmp = x2 * (((x1 * (x1 * 9.0d0)) / x2) - 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 9.0) + -1.0);
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = t_0;
	} else if (x1 <= -1.15e+24) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + ((x2 * -4.0) + ((x2 * 8.0) + (x1 * (2.0 + (x1 * ((x2 * -4.0) + ((x1 * -2.0) + ((-2.0 * (3.0 - (2.0 * x2))) + ((x2 * 8.0) + (x2 * 6.0))))))))))));
	} else if (x1 <= 6.2e+96) {
		tmp = t_0 + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0));
	} else {
		tmp = x2 * (((x1 * (x1 * 9.0)) / x2) - 6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((x1 * 9.0) + -1.0)
	tmp = 0
	if x1 <= -4.4e+153:
		tmp = t_0
	elif x1 <= -1.15e+24:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + ((x2 * -4.0) + ((x2 * 8.0) + (x1 * (2.0 + (x1 * ((x2 * -4.0) + ((x1 * -2.0) + ((-2.0 * (3.0 - (2.0 * x2))) + ((x2 * 8.0) + (x2 * 6.0))))))))))))
	elif x1 <= 6.2e+96:
		tmp = t_0 + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0))
	else:
		tmp = x2 * (((x1 * (x1 * 9.0)) / x2) - 6.0)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0))
	tmp = 0.0
	if (x1 <= -4.4e+153)
		tmp = t_0;
	elseif (x1 <= -1.15e+24)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))) + Float64(x1 + Float64(Float64(x2 * -4.0) + Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(2.0 + Float64(x1 * Float64(Float64(x2 * -4.0) + Float64(Float64(x1 * -2.0) + Float64(Float64(-2.0 * Float64(3.0 - Float64(2.0 * x2))) + Float64(Float64(x2 * 8.0) + Float64(x2 * 6.0)))))))))))));
	elseif (x1 <= 6.2e+96)
		tmp = Float64(t_0 + Float64(x2 * Float64(Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 12.0) - 12.0))) - 6.0)));
	else
		tmp = Float64(x2 * Float64(Float64(Float64(x1 * Float64(x1 * 9.0)) / x2) - 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((x1 * 9.0) + -1.0);
	tmp = 0.0;
	if (x1 <= -4.4e+153)
		tmp = t_0;
	elseif (x1 <= -1.15e+24)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + ((x2 * -4.0) + ((x2 * 8.0) + (x1 * (2.0 + (x1 * ((x2 * -4.0) + ((x1 * -2.0) + ((-2.0 * (3.0 - (2.0 * x2))) + ((x2 * 8.0) + (x2 * 6.0))))))))))));
	elseif (x1 <= 6.2e+96)
		tmp = t_0 + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0));
	else
		tmp = x2 * (((x1 * (x1 * 9.0)) / x2) - 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.4e+153], t$95$0, If[LessEqual[x1, -1.15e+24], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x2 * -4.0), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(2.0 + N[(x1 * N[(N[(x2 * -4.0), $MachinePrecision] + N[(N[(x1 * -2.0), $MachinePrecision] + N[(N[(-2.0 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6.2e+96], N[(t$95$0 + N[(x2 * N[(N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 12.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * N[(N[(N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.3999999999999999e153

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 68.9%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in x2 around inf 100.0%

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

   10. Taylor expanded in x2 around 0 100.0%

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

   if -4.3999999999999999e153 < x1 < -1.15e24

   1. Initial program 59.5%

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

   3. Taylor expanded in x1 around -inf 59.6%

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

   4. Taylor expanded in x2 around inf 9.5%

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

      1. *-commutative 9.5%

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

   6. Simplified 9.5%

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

   7. Taylor expanded in x1 around inf 9.5%

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

   8. Taylor expanded in x1 around 0 48.8%

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

   if -1.15e24 < x1 < 6.1999999999999996e96

   1. Initial program 99.4%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x1 around 0 75.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 76.5%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{\left(9 \cdot x1 + x2 \cdot \left(\left(8 \cdot x2 + 12 \cdot x1\right) - 12\right)\right)} - 1\right) \]

   7. Taylor expanded in x2 around 0 87.2%

      \[\leadsto \color{blue}{x1 \cdot \left(9 \cdot x1 - 1\right) + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)} \]

   if 6.1999999999999996e96 < x1

   1. Initial program 22.2%

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

   3. Simplified 22.2%

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

   5. Taylor expanded in x1 around 0 69.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 79.3%

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

      1. *-commutative 79.3%

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

   8. Simplified 79.3%

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

   9. Taylor expanded in x2 around inf 89.7%

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

   10. Taylor expanded in x1 around inf 89.7%

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

       1. *-commutative 89.7%

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

   12. Simplified 89.7%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \mathbf{elif}\;x1 \leq -1.15 \cdot 10^{+24}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x2 \cdot -4 + \left(x2 \cdot 8 + x1 \cdot \left(2 + x1 \cdot \left(x2 \cdot -4 + \left(x1 \cdot -2 + \left(-2 \cdot \left(3 - 2 \cdot x2\right) + \left(x2 \cdot 8 + x2 \cdot 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6.2 \cdot 10^{+96}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9 + -1\right) + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot 9\right)}{x2} - 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 81.7% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.3 \cdot 10^{+44} \lor \neg \left(x1 \leq 1.05 \cdot 10^{+97}\right):\\ \;\;\;\;x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot 9\right)}{x2} - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9 + -1\right) + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right) - 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -2.3e+44) (not (<= x1 1.05e+97)))
   (* x2 (- (/ (* x1 (* x1 9.0)) x2) 6.0))
   (+
    (* x1 (+ (* x1 9.0) -1.0))
    (* x2 (- (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 12.0) 12.0))) 6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -2.3e+44) || !(x1 <= 1.05e+97)) {
		tmp = x2 * (((x1 * (x1 * 9.0)) / x2) - 6.0);
	} else {
		tmp = (x1 * ((x1 * 9.0) + -1.0)) + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 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 <= (-2.3d+44)) .or. (.not. (x1 <= 1.05d+97))) then
        tmp = x2 * (((x1 * (x1 * 9.0d0)) / x2) - 6.0d0)
    else
        tmp = (x1 * ((x1 * 9.0d0) + (-1.0d0))) + (x2 * (((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 12.0d0) - 12.0d0))) - 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -2.3e+44) || !(x1 <= 1.05e+97)) {
		tmp = x2 * (((x1 * (x1 * 9.0)) / x2) - 6.0);
	} else {
		tmp = (x1 * ((x1 * 9.0) + -1.0)) + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -2.3e+44) or not (x1 <= 1.05e+97):
		tmp = x2 * (((x1 * (x1 * 9.0)) / x2) - 6.0)
	else:
		tmp = (x1 * ((x1 * 9.0) + -1.0)) + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -2.3e+44) || !(x1 <= 1.05e+97))
		tmp = Float64(x2 * Float64(Float64(Float64(x1 * Float64(x1 * 9.0)) / x2) - 6.0));
	else
		tmp = Float64(Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0)) + Float64(x2 * Float64(Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 12.0) - 12.0))) - 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -2.3e+44) || ~((x1 <= 1.05e+97)))
		tmp = x2 * (((x1 * (x1 * 9.0)) / x2) - 6.0);
	else
		tmp = (x1 * ((x1 * 9.0) + -1.0)) + (x2 * (((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0))) - 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -2.3e+44], N[Not[LessEqual[x1, 1.05e+97]], $MachinePrecision]], N[(x2 * N[(N[(N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision], N[(N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 12.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -2.30000000000000004e44 or 1.05000000000000006e97 < x1

   1. Initial program 19.6%

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

   3. Simplified 19.6%

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

   5. Taylor expanded in x1 around 0 57.3%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 73.2%

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

      1. *-commutative 73.2%

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

   8. Simplified 73.2%

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

   9. Taylor expanded in x2 around inf 83.3%

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

   10. Taylor expanded in x1 around inf 83.3%

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

       1. *-commutative 83.3%

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

   12. Simplified 83.3%

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

   if -2.30000000000000004e44 < x1 < 1.05000000000000006e97

   1. Initial program 99.4%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x1 around 0 74.4%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 75.1%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{\left(9 \cdot x1 + x2 \cdot \left(\left(8 \cdot x2 + 12 \cdot x1\right) - 12\right)\right)} - 1\right) \]

   7. Taylor expanded in x2 around 0 85.5%

      \[\leadsto \color{blue}{x1 \cdot \left(9 \cdot x1 - 1\right) + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.3 \cdot 10^{+44} \lor \neg \left(x1 \leq 1.05 \cdot 10^{+97}\right):\\ \;\;\;\;x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot 9\right)}{x2} - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9 + -1\right) + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right) - 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 72.5% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq 6.4 \cdot 10^{-161}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot \left(9 \cdot \frac{x1}{x2} + \frac{-1}{x2}\right) - 6\right)\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{+96}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(\left(x1 \cdot 9 + x2 \cdot \left(\left(x1 \cdot 12 + x2 \cdot 8\right) - 12\right)\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot 9\right)}{x2} - 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 6.4e-161)
   (* x2 (- (* x1 (+ (* 9.0 (/ x1 x2)) (/ -1.0 x2))) 6.0))
   (if (<= x1 3.9e+96)
     (+
      (* x2 -6.0)
      (*
       x1
       (+ (+ (* x1 9.0) (* x2 (- (+ (* x1 12.0) (* x2 8.0)) 12.0))) -1.0)))
     (* x2 (- (/ (* x1 (* x1 9.0)) x2) 6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= 6.4e-161) {
		tmp = x2 * ((x1 * ((9.0 * (x1 / x2)) + (-1.0 / x2))) - 6.0);
	} else if (x1 <= 3.9e+96) {
		tmp = (x2 * -6.0) + (x1 * (((x1 * 9.0) + (x2 * (((x1 * 12.0) + (x2 * 8.0)) - 12.0))) + -1.0));
	} else {
		tmp = x2 * (((x1 * (x1 * 9.0)) / 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 <= 6.4d-161) then
        tmp = x2 * ((x1 * ((9.0d0 * (x1 / x2)) + ((-1.0d0) / x2))) - 6.0d0)
    else if (x1 <= 3.9d+96) then
        tmp = (x2 * (-6.0d0)) + (x1 * (((x1 * 9.0d0) + (x2 * (((x1 * 12.0d0) + (x2 * 8.0d0)) - 12.0d0))) + (-1.0d0)))
    else
        tmp = x2 * (((x1 * (x1 * 9.0d0)) / x2) - 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= 6.4e-161) {
		tmp = x2 * ((x1 * ((9.0 * (x1 / x2)) + (-1.0 / x2))) - 6.0);
	} else if (x1 <= 3.9e+96) {
		tmp = (x2 * -6.0) + (x1 * (((x1 * 9.0) + (x2 * (((x1 * 12.0) + (x2 * 8.0)) - 12.0))) + -1.0));
	} else {
		tmp = x2 * (((x1 * (x1 * 9.0)) / x2) - 6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= 6.4e-161:
		tmp = x2 * ((x1 * ((9.0 * (x1 / x2)) + (-1.0 / x2))) - 6.0)
	elif x1 <= 3.9e+96:
		tmp = (x2 * -6.0) + (x1 * (((x1 * 9.0) + (x2 * (((x1 * 12.0) + (x2 * 8.0)) - 12.0))) + -1.0))
	else:
		tmp = x2 * (((x1 * (x1 * 9.0)) / x2) - 6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= 6.4e-161)
		tmp = Float64(x2 * Float64(Float64(x1 * Float64(Float64(9.0 * Float64(x1 / x2)) + Float64(-1.0 / x2))) - 6.0));
	elseif (x1 <= 3.9e+96)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(x1 * 9.0) + Float64(x2 * Float64(Float64(Float64(x1 * 12.0) + Float64(x2 * 8.0)) - 12.0))) + -1.0)));
	else
		tmp = Float64(x2 * Float64(Float64(Float64(x1 * Float64(x1 * 9.0)) / x2) - 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= 6.4e-161)
		tmp = x2 * ((x1 * ((9.0 * (x1 / x2)) + (-1.0 / x2))) - 6.0);
	elseif (x1 <= 3.9e+96)
		tmp = (x2 * -6.0) + (x1 * (((x1 * 9.0) + (x2 * (((x1 * 12.0) + (x2 * 8.0)) - 12.0))) + -1.0));
	else
		tmp = x2 * (((x1 * (x1 * 9.0)) / x2) - 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, 6.4e-161], N[(x2 * N[(N[(x1 * N[(N[(9.0 * N[(x1 / x2), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.9e+96], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(x1 * 9.0), $MachinePrecision] + N[(x2 * N[(N[(N[(x1 * 12.0), $MachinePrecision] + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * N[(N[(N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < 6.39999999999999971e-161

   1. Initial program 64.5%

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

   3. Simplified 64.7%

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

   5. Taylor expanded in x1 around 0 66.2%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 76.3%

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

      1. *-commutative 76.3%

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

   8. Simplified 76.3%

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

   9. Taylor expanded in x2 around inf 80.5%

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

   10. Taylor expanded in x1 around 0 80.5%

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

   if 6.39999999999999971e-161 < x1 < 3.9e96

   1. Initial program 99.4%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x1 around 0 66.6%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 68.4%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{\left(9 \cdot x1 + x2 \cdot \left(\left(8 \cdot x2 + 12 \cdot x1\right) - 12\right)\right)} - 1\right) \]

   if 3.9e96 < x1

   1. Initial program 22.2%

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

   3. Simplified 22.2%

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

   5. Taylor expanded in x1 around 0 69.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 79.3%

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

      1. *-commutative 79.3%

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

   8. Simplified 79.3%

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

   9. Taylor expanded in x2 around inf 89.7%

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

   10. Taylor expanded in x1 around inf 89.7%

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

       1. *-commutative 89.7%

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

   12. Simplified 89.7%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq 6.4 \cdot 10^{-161}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot \left(9 \cdot \frac{x1}{x2} + \frac{-1}{x2}\right) - 6\right)\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{+96}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(\left(x1 \cdot 9 + x2 \cdot \left(\left(x1 \cdot 12 + x2 \cdot 8\right) - 12\right)\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot 9\right)}{x2} - 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 72.1% accurate, 5.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq 6.2 \cdot 10^{-161}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot \left(9 \cdot \frac{x1}{x2} + \frac{-1}{x2}\right) - 6\right)\\ \mathbf{elif}\;x1 \leq 3 \cdot 10^{+97}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot \left(x2 \cdot 8 - 12\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot 9\right)}{x2} - 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 6.2e-161)
   (* x2 (- (* x1 (+ (* 9.0 (/ x1 x2)) (/ -1.0 x2))) 6.0))
   (if (<= x1 3e+97)
     (+ (* x2 -6.0) (* x1 (+ (* x2 (- (* x2 8.0) 12.0)) -1.0)))
     (* x2 (- (/ (* x1 (* x1 9.0)) x2) 6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= 6.2e-161) {
		tmp = x2 * ((x1 * ((9.0 * (x1 / x2)) + (-1.0 / x2))) - 6.0);
	} else if (x1 <= 3e+97) {
		tmp = (x2 * -6.0) + (x1 * ((x2 * ((x2 * 8.0) - 12.0)) + -1.0));
	} else {
		tmp = x2 * (((x1 * (x1 * 9.0)) / 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 <= 6.2d-161) then
        tmp = x2 * ((x1 * ((9.0d0 * (x1 / x2)) + ((-1.0d0) / x2))) - 6.0d0)
    else if (x1 <= 3d+97) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((x2 * ((x2 * 8.0d0) - 12.0d0)) + (-1.0d0)))
    else
        tmp = x2 * (((x1 * (x1 * 9.0d0)) / x2) - 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= 6.2e-161) {
		tmp = x2 * ((x1 * ((9.0 * (x1 / x2)) + (-1.0 / x2))) - 6.0);
	} else if (x1 <= 3e+97) {
		tmp = (x2 * -6.0) + (x1 * ((x2 * ((x2 * 8.0) - 12.0)) + -1.0));
	} else {
		tmp = x2 * (((x1 * (x1 * 9.0)) / x2) - 6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= 6.2e-161:
		tmp = x2 * ((x1 * ((9.0 * (x1 / x2)) + (-1.0 / x2))) - 6.0)
	elif x1 <= 3e+97:
		tmp = (x2 * -6.0) + (x1 * ((x2 * ((x2 * 8.0) - 12.0)) + -1.0))
	else:
		tmp = x2 * (((x1 * (x1 * 9.0)) / x2) - 6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= 6.2e-161)
		tmp = Float64(x2 * Float64(Float64(x1 * Float64(Float64(9.0 * Float64(x1 / x2)) + Float64(-1.0 / x2))) - 6.0));
	elseif (x1 <= 3e+97)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x2 * Float64(Float64(x2 * 8.0) - 12.0)) + -1.0)));
	else
		tmp = Float64(x2 * Float64(Float64(Float64(x1 * Float64(x1 * 9.0)) / x2) - 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= 6.2e-161)
		tmp = x2 * ((x1 * ((9.0 * (x1 / x2)) + (-1.0 / x2))) - 6.0);
	elseif (x1 <= 3e+97)
		tmp = (x2 * -6.0) + (x1 * ((x2 * ((x2 * 8.0) - 12.0)) + -1.0));
	else
		tmp = x2 * (((x1 * (x1 * 9.0)) / x2) - 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, 6.2e-161], N[(x2 * N[(N[(x1 * N[(N[(9.0 * N[(x1 / x2), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3e+97], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x2 * N[(N[(x2 * 8.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * N[(N[(N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < 6.1999999999999997e-161

   1. Initial program 64.5%

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

   3. Simplified 64.7%

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

   5. Taylor expanded in x1 around 0 66.2%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 76.3%

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

      1. *-commutative 76.3%

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

   8. Simplified 76.3%

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

   9. Taylor expanded in x2 around inf 80.5%

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

   10. Taylor expanded in x1 around 0 80.5%

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

   if 6.1999999999999997e-161 < x1 < 2.9999999999999998e97

   1. Initial program 99.4%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x1 around 0 66.6%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 68.4%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{\left(9 \cdot x1 + x2 \cdot \left(\left(8 \cdot x2 + 12 \cdot x1\right) - 12\right)\right)} - 1\right) \]

   7. Taylor expanded in x1 around 0 67.2%

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

   if 2.9999999999999998e97 < x1

   1. Initial program 22.2%

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

   3. Simplified 22.2%

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

   5. Taylor expanded in x1 around 0 69.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 79.3%

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

      1. *-commutative 79.3%

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

   8. Simplified 79.3%

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

   9. Taylor expanded in x2 around inf 89.7%

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

   10. Taylor expanded in x1 around inf 89.7%

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

       1. *-commutative 89.7%

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

   12. Simplified 89.7%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq 6.2 \cdot 10^{-161}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot \left(9 \cdot \frac{x1}{x2} + \frac{-1}{x2}\right) - 6\right)\\ \mathbf{elif}\;x1 \leq 3 \cdot 10^{+97}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot \left(x2 \cdot 8 - 12\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot 9\right)}{x2} - 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 67.8% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -3.7 \cdot 10^{+52} \lor \neg \left(x1 \leq 1.9 \cdot 10^{+51}\right):\\ \;\;\;\;x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot 9\right)}{x2} - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9 + -1\right) + x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -3.7e+52) (not (<= x1 1.9e+51)))
   (* x2 (- (/ (* x1 (* x1 9.0)) x2) 6.0))
   (+ (* x1 (+ (* x1 9.0) -1.0)) (* x2 -6.0))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -3.7e+52) || !(x1 <= 1.9e+51)) {
		tmp = x2 * (((x1 * (x1 * 9.0)) / x2) - 6.0);
	} else {
		tmp = (x1 * ((x1 * 9.0) + -1.0)) + (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 <= (-3.7d+52)) .or. (.not. (x1 <= 1.9d+51))) then
        tmp = x2 * (((x1 * (x1 * 9.0d0)) / x2) - 6.0d0)
    else
        tmp = (x1 * ((x1 * 9.0d0) + (-1.0d0))) + (x2 * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -3.7e+52) || !(x1 <= 1.9e+51)) {
		tmp = x2 * (((x1 * (x1 * 9.0)) / x2) - 6.0);
	} else {
		tmp = (x1 * ((x1 * 9.0) + -1.0)) + (x2 * -6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -3.7e+52) or not (x1 <= 1.9e+51):
		tmp = x2 * (((x1 * (x1 * 9.0)) / x2) - 6.0)
	else:
		tmp = (x1 * ((x1 * 9.0) + -1.0)) + (x2 * -6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -3.7e+52) || !(x1 <= 1.9e+51))
		tmp = Float64(x2 * Float64(Float64(Float64(x1 * Float64(x1 * 9.0)) / x2) - 6.0));
	else
		tmp = Float64(Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0)) + Float64(x2 * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -3.7e+52) || ~((x1 <= 1.9e+51)))
		tmp = x2 * (((x1 * (x1 * 9.0)) / x2) - 6.0);
	else
		tmp = (x1 * ((x1 * 9.0) + -1.0)) + (x2 * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -3.7e+52], N[Not[LessEqual[x1, 1.9e+51]], $MachinePrecision]], N[(x2 * N[(N[(N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision], N[(N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -3.7e52 or 1.8999999999999999e51 < x1

   1. Initial program 24.3%

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

   3. Simplified 24.3%

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

   5. Taylor expanded in x1 around 0 55.7%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 69.1%

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

      1. *-commutative 69.1%

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

   8. Simplified 69.1%

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

   9. Taylor expanded in x2 around inf 78.6%

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

   10. Taylor expanded in x1 around inf 78.6%

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

       1. *-commutative 78.6%

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

   12. Simplified 78.6%

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

   if -3.7e52 < x1 < 1.8999999999999999e51

   1. Initial program 99.4%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x1 around 0 76.6%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 68.4%

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

      1. *-commutative 68.4%

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

   8. Simplified 68.4%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.7 \cdot 10^{+52} \lor \neg \left(x1 \leq 1.9 \cdot 10^{+51}\right):\\ \;\;\;\;x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot 9\right)}{x2} - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9 + -1\right) + x2 \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 67.3% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.18 \cdot 10^{+24} \lor \neg \left(x1 \leq 1.5 \cdot 10^{-12}\right):\\ \;\;\;\;x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot 9\right)}{x2} - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -1.18e+24) (not (<= x1 1.5e-12)))
   (* x2 (- (/ (* x1 (* x1 9.0)) x2) 6.0))
   (- (* x2 -6.0) x1)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -1.18e+24) || !(x1 <= 1.5e-12)) {
		tmp = x2 * (((x1 * (x1 * 9.0)) / x2) - 6.0);
	} 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 <= (-1.18d+24)) .or. (.not. (x1 <= 1.5d-12))) then
        tmp = x2 * (((x1 * (x1 * 9.0d0)) / x2) - 6.0d0)
    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 <= -1.18e+24) || !(x1 <= 1.5e-12)) {
		tmp = x2 * (((x1 * (x1 * 9.0)) / x2) - 6.0);
	} else {
		tmp = (x2 * -6.0) - x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -1.18e+24) or not (x1 <= 1.5e-12):
		tmp = x2 * (((x1 * (x1 * 9.0)) / x2) - 6.0)
	else:
		tmp = (x2 * -6.0) - x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -1.18e+24) || !(x1 <= 1.5e-12))
		tmp = Float64(x2 * Float64(Float64(Float64(x1 * Float64(x1 * 9.0)) / x2) - 6.0));
	else
		tmp = Float64(Float64(x2 * -6.0) - x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -1.18e+24) || ~((x1 <= 1.5e-12)))
		tmp = x2 * (((x1 * (x1 * 9.0)) / x2) - 6.0);
	else
		tmp = (x2 * -6.0) - x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -1.18e+24], N[Not[LessEqual[x1, 1.5e-12]], $MachinePrecision]], N[(x2 * N[(N[(N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.17999999999999997e24 or 1.5000000000000001e-12 < x1

   1. Initial program 34.1%

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

   3. Simplified 34.1%

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

   5. Taylor expanded in x1 around 0 51.9%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 60.6%

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

      1. *-commutative 60.6%

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

   8. Simplified 60.6%

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

   9. Taylor expanded in x2 around inf 68.9%

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

   10. Taylor expanded in x1 around inf 68.9%

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

       1. *-commutative 68.9%

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

   12. Simplified 68.9%

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

   if -1.17999999999999997e24 < x1 < 1.5000000000000001e-12

   1. Initial program 99.4%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x1 around 0 84.1%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 78.0%

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

      1. *-commutative 78.0%

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

   8. Simplified 78.0%

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

   9. Taylor expanded in x1 around 0 77.7%

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

       1. *-commutative 77.7%

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

       2. mul-1-neg 77.7%

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

       3. unsub-neg 77.7%

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

   11. Simplified 77.7%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.18 \cdot 10^{+24} \lor \neg \left(x1 \leq 1.5 \cdot 10^{-12}\right):\\ \;\;\;\;x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot 9\right)}{x2} - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 70.2% accurate, 6.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq 1.2 \cdot 10^{+45}:\\ \;\;\;\;x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot 9 + -1\right)}{x2} - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x2 \cdot 12\right) + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 1.2e+45)
   (* x2 (- (/ (* x1 (+ (* x1 9.0) -1.0)) x2) 6.0))
   (+ (* x2 -6.0) (* x1 (+ (* x1 (+ 9.0 (* x2 12.0))) -1.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= 1.2e+45) {
		tmp = x2 * (((x1 * ((x1 * 9.0) + -1.0)) / x2) - 6.0);
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x2 * 12.0))) + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x2 <= 1.2d+45) then
        tmp = x2 * (((x1 * ((x1 * 9.0d0) + (-1.0d0))) / x2) - 6.0d0)
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * (9.0d0 + (x2 * 12.0d0))) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x2 <= 1.2e+45) {
		tmp = x2 * (((x1 * ((x1 * 9.0) + -1.0)) / x2) - 6.0);
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x2 * 12.0))) + -1.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= 1.2e+45:
		tmp = x2 * (((x1 * ((x1 * 9.0) + -1.0)) / x2) - 6.0)
	else:
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x2 * 12.0))) + -1.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= 1.2e+45)
		tmp = Float64(x2 * Float64(Float64(Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0)) / x2) - 6.0));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(x2 * 12.0))) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= 1.2e+45)
		tmp = x2 * (((x1 * ((x1 * 9.0) + -1.0)) / x2) - 6.0);
	else
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x2 * 12.0))) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, 1.2e+45], N[(x2 * N[(N[(N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(9.0 + N[(x2 * 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < 1.19999999999999995e45

   1. Initial program 65.2%

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

   3. Simplified 65.4%

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

   5. Taylor expanded in x1 around 0 67.5%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 73.5%

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

      1. *-commutative 73.5%

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

   8. Simplified 73.5%

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

   9. Taylor expanded in x2 around inf 79.2%

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

   if 1.19999999999999995e45 < x2

   1. Initial program 62.0%

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

   3. Simplified 62.0%

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

   5. Taylor expanded in x1 around 0 64.9%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 70.1%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{\left(9 \cdot x1 + x2 \cdot \left(\left(8 \cdot x2 + 12 \cdot x1\right) - 12\right)\right)} - 1\right) \]

   7. Taylor expanded in x1 around inf 66.1%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + 12 \cdot x2\right)} - 1\right) \]
   8. Step-by-step derivation

      1. *-commutative 66.1%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x2 \cdot 12}\right) - 1\right) \]

   9. Simplified 66.1%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x2 \cdot 12\right)} - 1\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq 1.2 \cdot 10^{+45}:\\ \;\;\;\;x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot 9 + -1\right)}{x2} - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x2 \cdot 12\right) + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 63.7% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -3.4 \cdot 10^{+132} \lor \neg \left(x1 \leq 1.15 \cdot 10^{-19}\right):\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\left(-6\right) - \frac{x1}{x2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -3.4e+132) (not (<= x1 1.15e-19)))
   (* x1 (+ (* x1 9.0) -1.0))
   (* x2 (- (- 6.0) (/ x1 x2)))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -3.4e+132) || !(x1 <= 1.15e-19)) {
		tmp = x1 * ((x1 * 9.0) + -1.0);
	} else {
		tmp = x2 * (-6.0 - (x1 / x2));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-3.4d+132)) .or. (.not. (x1 <= 1.15d-19))) then
        tmp = x1 * ((x1 * 9.0d0) + (-1.0d0))
    else
        tmp = x2 * (-6.0d0 - (x1 / x2))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -3.4e+132) || !(x1 <= 1.15e-19)) {
		tmp = x1 * ((x1 * 9.0) + -1.0);
	} else {
		tmp = x2 * (-6.0 - (x1 / x2));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -3.4e+132) or not (x1 <= 1.15e-19):
		tmp = x1 * ((x1 * 9.0) + -1.0)
	else:
		tmp = x2 * (-6.0 - (x1 / x2))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -3.4e+132) || !(x1 <= 1.15e-19))
		tmp = Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0));
	else
		tmp = Float64(x2 * Float64(Float64(-6.0) - Float64(x1 / x2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -3.4e+132) || ~((x1 <= 1.15e-19)))
		tmp = x1 * ((x1 * 9.0) + -1.0);
	else
		tmp = x2 * (-6.0 - (x1 / x2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -3.4e+132], N[Not[LessEqual[x1, 1.15e-19]], $MachinePrecision]], N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(x2 * N[((-6.0) - N[(x1 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -3.40000000000000025e132 or 1.1499999999999999e-19 < x1

   1. Initial program 29.5%

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

   3. Simplified 29.5%

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

   5. Taylor expanded in x1 around 0 61.3%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 70.3%

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

      1. *-commutative 70.3%

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

   8. Simplified 70.3%

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

   9. Taylor expanded in x2 around inf 74.3%

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

   10. Taylor expanded in x2 around 0 70.4%

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

   if -3.40000000000000025e132 < x1 < 1.1499999999999999e-19

   1. Initial program 94.3%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in x1 around 0 71.7%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 67.3%

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

      1. *-commutative 67.3%

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

   8. Simplified 67.3%

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

   9. Taylor expanded in x1 around 0 67.0%

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

       1. *-commutative 67.0%

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

       2. mul-1-neg 67.0%

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

       3. unsub-neg 67.0%

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

   11. Simplified 67.0%

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

   12. Taylor expanded in x2 around -inf 69.8%

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

       1. mul-1-neg 69.8%

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

       2. *-commutative 69.8%

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

       3. distribute-rgt-neg-in 69.8%

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

   14. Simplified 69.8%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.4 \cdot 10^{+132} \lor \neg \left(x1 \leq 1.15 \cdot 10^{-19}\right):\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\left(-6\right) - \frac{x1}{x2}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 63.2% accurate, 7.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.55 \cdot 10^{+23} \lor \neg \left(x1 \leq 1.15 \cdot 10^{-19}\right):\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -2.55e+23) (not (<= x1 1.15e-19)))
   (* x1 (+ (* x1 9.0) -1.0))
   (- (* x2 -6.0) x1)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -2.55e+23) || !(x1 <= 1.15e-19)) {
		tmp = x1 * ((x1 * 9.0) + -1.0);
	} 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 <= (-2.55d+23)) .or. (.not. (x1 <= 1.15d-19))) then
        tmp = x1 * ((x1 * 9.0d0) + (-1.0d0))
    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 <= -2.55e+23) || !(x1 <= 1.15e-19)) {
		tmp = x1 * ((x1 * 9.0) + -1.0);
	} else {
		tmp = (x2 * -6.0) - x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -2.55e+23) or not (x1 <= 1.15e-19):
		tmp = x1 * ((x1 * 9.0) + -1.0)
	else:
		tmp = (x2 * -6.0) - x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -2.55e+23) || !(x1 <= 1.15e-19))
		tmp = Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0));
	else
		tmp = Float64(Float64(x2 * -6.0) - x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -2.55e+23) || ~((x1 <= 1.15e-19)))
		tmp = x1 * ((x1 * 9.0) + -1.0);
	else
		tmp = (x2 * -6.0) - x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -2.55e+23], N[Not[LessEqual[x1, 1.15e-19]], $MachinePrecision]], N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -2.5500000000000001e23 or 1.1499999999999999e-19 < x1

   1. Initial program 35.5%

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

   3. Simplified 35.5%

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

   5. Taylor expanded in x1 around 0 52.3%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 60.1%

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

      1. *-commutative 60.1%

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

   8. Simplified 60.1%

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

   9. Taylor expanded in x2 around inf 68.2%

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

   10. Taylor expanded in x2 around 0 60.2%

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

   if -2.5500000000000001e23 < x1 < 1.1499999999999999e-19

   1. Initial program 99.4%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x1 around 0 84.5%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 79.1%

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

      1. *-commutative 79.1%

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

   8. Simplified 79.1%

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

   9. Taylor expanded in x1 around 0 79.1%

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

       1. *-commutative 79.1%

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

       2. mul-1-neg 79.1%

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

       3. unsub-neg 79.1%

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

   11. Simplified 79.1%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.55 \cdot 10^{+23} \lor \neg \left(x1 \leq 1.15 \cdot 10^{-19}\right):\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 67.8% accurate, 9.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 64.5%

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

3. Simplified 64.6%

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

5. Taylor expanded in x1 around 0 66.9%

   \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

6. Taylor expanded in x2 around 0 68.7%

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

   1. *-commutative 68.7%

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

8. Simplified 68.7%

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

9. Taylor expanded in x2 around inf 73.1%

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

10. Final simplification 73.1%

    \[\leadsto x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot 9 + -1\right)}{x2} - 6\right) \]
11. Add Preprocessing

Alternative 22: 38.2% 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 64.5%

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

3. Simplified 64.6%

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

5. Taylor expanded in x1 around 0 66.9%

   \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

6. Taylor expanded in x2 around 0 68.7%

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

   1. *-commutative 68.7%

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

8. Simplified 68.7%

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

9. Taylor expanded in x1 around 0 37.9%

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

    1. *-commutative 37.9%

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

    2. mul-1-neg 37.9%

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

    3. unsub-neg 37.9%

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

11. Simplified 37.9%

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

Alternative 23: 26.0% accurate, 42.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 64.5%

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

3. Simplified 64.6%

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

5. Taylor expanded in x1 around 0 28.9%

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

   1. *-commutative 28.9%

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

7. Simplified 28.9%

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

Reproduce

herbie shell --seed 2024137 
(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))))))