Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 69.6% → 99.5%

Time: 35.9s

Alternatives: 21

Speedup: 4.7×

• 47.7% 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: 69.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

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

   4. Taylor expanded in x1 around inf 100.0%

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

      1. *-commutative 100.0%

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

   6. Simplified 100.0%

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

      1. metadata-eval 100.0%

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

   8. Applied egg-rr 100.0%

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

4. Final simplification 99.8%

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

Alternative 2: 99.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

function code(x1, x2)
	t_0 = Float64(Float64(fma(Float64(x1 * 3.0), x1, Float64(2.0 * x2)) - x1) / fma(x1, x1, 1.0))
	t_1 = Float64(x1 * Float64(x1 * x1))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(t_2 + Float64(2.0 * x2))
	t_4 = Float64(Float64(x1 * x1) + 1.0)
	t_5 = Float64(Float64(x1 - t_3) / t_4)
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_4 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_5) * Float64(3.0 + t_5)) - Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_5))))) + Float64(t_2 * Float64(Float64(t_3 - x1) / t_4))) + t_1)) + Float64(3.0 * Float64(Float64(x1 - Float64(t_2 - Float64(2.0 * x2))) / Float64(-1.0 - Float64(x1 * x1)))))) <= Inf)
		tmp = Float64(x1 + Float64(Float64(t_1 + fma(fma(Float64(Float64(x1 * 2.0) * t_0), Float64(-3.0 + t_0), Float64(Float64(x1 * x1) * fma(4.0, t_0, -6.0))), fma(x1, x1, 1.0), Float64(t_2 * t_0))) + Float64(x1 - Float64(3.0 * Float64(Float64(Float64(x1 + Float64(2.0 * x2)) - t_2) / fma(x1, x1, 1.0))))));
	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[(N[(x1 * 3.0), $MachinePrecision] * x1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 - t$95$3), $MachinePrecision] / t$95$4), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$4 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$5), $MachinePrecision] * N[(3.0 + t$95$5), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * N[(N[(t$95$3 - x1), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x1 - N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(N[(t$95$1 + N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$0), $MachinePrecision] * N[(-3.0 + t$95$0), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(4.0 * t$95$0 + -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x1 * x1 + 1.0), $MachinePrecision] + N[(t$95$2 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 - N[(3.0 * N[(N[(N[(x1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] / N[(x1 * x1 + 1.0), $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 99.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around inf 100.0%

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

      1. *-commutative 100.0%

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

   6. Simplified 100.0%

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

      1. metadata-eval 100.0%

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

   8. Applied egg-rr 100.0%

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

4. Final simplification 99.6%

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

Alternative 3: 99.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := t\_1 + 2 \cdot x2\\ t_3 := x1 - \left(t\_1 - 2 \cdot x2\right)\\ t_4 := -1 - x1 \cdot x1\\ t_5 := x1 \cdot x1 + 1\\ t_6 := t\_1 \cdot \frac{t\_2 - x1}{t\_5}\\ t_7 := \frac{x1 - t\_2}{t\_5}\\ t_8 := \left(x1 \cdot 2\right) \cdot t\_7\\ t_9 := \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_7\right)\\ \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(t\_5 \cdot \left(t\_8 \cdot \left(3 + t\_7\right) - t\_9\right) + t\_6\right) + t\_0\right)\right) + 3 \cdot \frac{t\_3}{t\_4}\right) \leq \infty:\\ \;\;\;\;x1 - \left(3 \cdot \frac{t\_3}{t\_5} - \left(x1 + \left(t\_0 + \left(t\_6 - \left(t\_8 \cdot \left(3 + \frac{1}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(x1 - \mathsf{fma}\left(3, {x1}^{2}, 2 \cdot x2\right)\right)\right) - t\_9\right) \cdot t\_4\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ t_1 (* 2.0 x2)))
        (t_3 (- x1 (- t_1 (* 2.0 x2))))
        (t_4 (- -1.0 (* x1 x1)))
        (t_5 (+ (* x1 x1) 1.0))
        (t_6 (* t_1 (/ (- t_2 x1) t_5)))
        (t_7 (/ (- x1 t_2) t_5))
        (t_8 (* (* x1 2.0) t_7))
        (t_9 (* (* x1 x1) (+ 6.0 (* 4.0 t_7)))))
   (if (<=
        (+
         x1
         (+
          (+ x1 (+ (+ (* t_5 (- (* t_8 (+ 3.0 t_7)) t_9)) t_6) t_0))
          (* 3.0 (/ t_3 t_4))))
        INFINITY)
     (-
      x1
      (-
       (* 3.0 (/ t_3 t_5))
       (+
        x1
        (+
         t_0
         (-
          t_6
          (*
           (-
            (*
             t_8
             (+
              3.0
              (*
               (/ 1.0 (fma x1 x1 1.0))
               (- x1 (fma 3.0 (pow x1 2.0) (* 2.0 x2))))))
            t_9)
           t_4))))))
     (+ 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 * 3.0);
	double t_2 = t_1 + (2.0 * x2);
	double t_3 = x1 - (t_1 - (2.0 * x2));
	double t_4 = -1.0 - (x1 * x1);
	double t_5 = (x1 * x1) + 1.0;
	double t_6 = t_1 * ((t_2 - x1) / t_5);
	double t_7 = (x1 - t_2) / t_5;
	double t_8 = (x1 * 2.0) * t_7;
	double t_9 = (x1 * x1) * (6.0 + (4.0 * t_7));
	double tmp;
	if ((x1 + ((x1 + (((t_5 * ((t_8 * (3.0 + t_7)) - t_9)) + t_6) + t_0)) + (3.0 * (t_3 / t_4)))) <= ((double) INFINITY)) {
		tmp = x1 - ((3.0 * (t_3 / t_5)) - (x1 + (t_0 + (t_6 - (((t_8 * (3.0 + ((1.0 / fma(x1, x1, 1.0)) * (x1 - fma(3.0, pow(x1, 2.0), (2.0 * x2)))))) - t_9) * t_4)))));
	} else {
		tmp = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + 9.0);
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(t_1 + Float64(2.0 * x2))
	t_3 = Float64(x1 - Float64(t_1 - Float64(2.0 * x2)))
	t_4 = Float64(-1.0 - Float64(x1 * x1))
	t_5 = Float64(Float64(x1 * x1) + 1.0)
	t_6 = Float64(t_1 * Float64(Float64(t_2 - x1) / t_5))
	t_7 = Float64(Float64(x1 - t_2) / t_5)
	t_8 = Float64(Float64(x1 * 2.0) * t_7)
	t_9 = Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_7)))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_5 * Float64(Float64(t_8 * Float64(3.0 + t_7)) - t_9)) + t_6) + t_0)) + Float64(3.0 * Float64(t_3 / t_4)))) <= Inf)
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(t_3 / t_5)) - Float64(x1 + Float64(t_0 + Float64(t_6 - Float64(Float64(Float64(t_8 * Float64(3.0 + Float64(Float64(1.0 / fma(x1, x1, 1.0)) * Float64(x1 - fma(3.0, (x1 ^ 2.0), Float64(2.0 * x2)))))) - t_9) * t_4))))));
	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[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 - N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$1 * N[(N[(t$95$2 - x1), $MachinePrecision] / t$95$5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x1 - t$95$2), $MachinePrecision] / t$95$5), $MachinePrecision]}, Block[{t$95$8 = N[(N[(x1 * 2.0), $MachinePrecision] * t$95$7), $MachinePrecision]}, Block[{t$95$9 = N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$5 * N[(N[(t$95$8 * N[(3.0 + t$95$7), $MachinePrecision]), $MachinePrecision] - t$95$9), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(t$95$3 / t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 - N[(N[(3.0 * N[(t$95$3 / t$95$5), $MachinePrecision]), $MachinePrecision] - N[(x1 + N[(t$95$0 + N[(t$95$6 - N[(N[(N[(t$95$8 * N[(3.0 + N[(N[(1.0 / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] * N[(x1 - N[(3.0 * N[Power[x1, 2.0], $MachinePrecision] + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$9), $MachinePrecision] * t$95$4), $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. Step-by-step derivation

      1. fma-define 99.4%

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

      2. div-inv 99.4%

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

      3. associate-*r* 99.4%

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

      4. fma-define 99.4%

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

      5. pow2 99.4%

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

   4. Applied egg-rr 99.4%

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

   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 0.0%

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

   4. Taylor expanded in x1 around inf 100.0%

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

      1. *-commutative 100.0%

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

   6. Simplified 100.0%

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

      1. metadata-eval 100.0%

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

   8. Applied egg-rr 100.0%

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

4. Final simplification 99.6%

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

Alternative 4: 99.3% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ t_0 (* 2.0 x2)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (/ (- x1 t_1) t_2))
        (t_4
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               t_2
               (-
                (* (* (* x1 2.0) t_3) (+ 3.0 t_3))
                (* (* x1 x1) (+ 6.0 (* 4.0 t_3)))))
              (* t_0 (/ (- t_1 x1) t_2)))
             (* x1 (* x1 x1))))
           (* 3.0 (/ (- x1 (- t_0 (* 2.0 x2))) (- -1.0 (* x1 x1))))))))
   (if (<= t_4 INFINITY) t_4 (+ 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 = t_0 + (2.0 * x2);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = (x1 - t_1) / t_2;
	double t_4 = x1 + ((x1 + (((t_2 * ((((x1 * 2.0) * t_3) * (3.0 + t_3)) - ((x1 * x1) * (6.0 + (4.0 * t_3))))) + (t_0 * ((t_1 - x1) / t_2))) + (x1 * (x1 * x1)))) + (3.0 * ((x1 - (t_0 - (2.0 * x2))) / (-1.0 - (x1 * x1)))));
	double tmp;
	if (t_4 <= ((double) INFINITY)) {
		tmp = t_4;
	} 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 = t_0 + (2.0 * x2);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = (x1 - t_1) / t_2;
	double t_4 = x1 + ((x1 + (((t_2 * ((((x1 * 2.0) * t_3) * (3.0 + t_3)) - ((x1 * x1) * (6.0 + (4.0 * t_3))))) + (t_0 * ((t_1 - x1) / t_2))) + (x1 * (x1 * x1)))) + (3.0 * ((x1 - (t_0 - (2.0 * x2))) / (-1.0 - (x1 * x1)))));
	double tmp;
	if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} 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 = t_0 + (2.0 * x2)
	t_2 = (x1 * x1) + 1.0
	t_3 = (x1 - t_1) / t_2
	t_4 = x1 + ((x1 + (((t_2 * ((((x1 * 2.0) * t_3) * (3.0 + t_3)) - ((x1 * x1) * (6.0 + (4.0 * t_3))))) + (t_0 * ((t_1 - x1) / t_2))) + (x1 * (x1 * x1)))) + (3.0 * ((x1 - (t_0 - (2.0 * x2))) / (-1.0 - (x1 * x1)))))
	tmp = 0
	if t_4 <= math.inf:
		tmp = t_4
	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(t_0 + Float64(2.0 * x2))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(x1 - t_1) / t_2)
	t_4 = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_2 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(3.0 + t_3)) - Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_3))))) + Float64(t_0 * Float64(Float64(t_1 - x1) / t_2))) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(x1 - Float64(t_0 - Float64(2.0 * x2))) / Float64(-1.0 - Float64(x1 * x1))))))
	tmp = 0.0
	if (t_4 <= Inf)
		tmp = t_4;
	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 = t_0 + (2.0 * x2);
	t_2 = (x1 * x1) + 1.0;
	t_3 = (x1 - t_1) / t_2;
	t_4 = x1 + ((x1 + (((t_2 * ((((x1 * 2.0) * t_3) * (3.0 + t_3)) - ((x1 * x1) * (6.0 + (4.0 * t_3))))) + (t_0 * ((t_1 - x1) / t_2))) + (x1 * (x1 * x1)))) + (3.0 * ((x1 - (t_0 - (2.0 * x2))) / (-1.0 - (x1 * x1)))));
	tmp = 0.0;
	if (t_4 <= Inf)
		tmp = t_4;
	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[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 - t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$2 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(3.0 + t$95$3), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(N[(t$95$1 - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x1 - N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, Infinity], t$95$4, 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 0.0%

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

   4. Taylor expanded in x1 around inf 100.0%

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

      1. *-commutative 100.0%

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

   6. Simplified 100.0%

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

      1. metadata-eval 100.0%

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

   8. Applied egg-rr 100.0%

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

4. Final simplification 99.6%

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

Alternative 5: 95.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot \left(2 - x1 \cdot 9\right)\\ t_3 := t\_1 + 2 \cdot x2\\ t_4 := \frac{x1 - t\_3}{t\_0}\\ t_5 := x1 + \left(9 - \left(\left(\left(t\_1 \cdot t\_4 + t\_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_4\right) + \left(\frac{t\_3 - x1}{t\_0} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot t\_4\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+115}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{t\_2}{x2}\right)\\ \mathbf{elif}\;x1 \leq -0.0025:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{-18}:\\ \;\;\;\;x2 \cdot -6 + \left(x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+150}:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;x1 - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (* x1 (- 2.0 (* x1 9.0))))
        (t_3 (+ t_1 (* 2.0 x2)))
        (t_4 (/ (- x1 t_3) t_0))
        (t_5
         (+
          x1
          (-
           9.0
           (-
            (-
             (+
              (* t_1 t_4)
              (*
               t_0
               (+
                (* (* x1 x1) (+ 6.0 (* 4.0 t_4)))
                (* (- (/ (- t_3 x1) t_0) 3.0) (* (* x1 2.0) t_4)))))
             (* x1 (* x1 x1)))
            x1)))))
   (if (<= x1 -9.5e+115)
     (- x1 (* x2 (+ 6.0 (/ t_2 x2))))
     (if (<= x1 -0.0025)
       t_5
       (if (<= x1 4e-18)
         (+
          (* x2 -6.0)
          (+
           (* x1 (+ -1.0 (* x1 9.0)))
           (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 12.0) 12.0))))))
         (if (<= x1 4e+150) t_5 (- x1 t_2)))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = x1 * (2.0 - (x1 * 9.0));
	double t_3 = t_1 + (2.0 * x2);
	double t_4 = (x1 - t_3) / t_0;
	double t_5 = x1 + (9.0 - ((((t_1 * t_4) + (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_4))) + ((((t_3 - x1) / t_0) - 3.0) * ((x1 * 2.0) * t_4))))) - (x1 * (x1 * x1))) - x1));
	double tmp;
	if (x1 <= -9.5e+115) {
		tmp = x1 - (x2 * (6.0 + (t_2 / x2)));
	} else if (x1 <= -0.0025) {
		tmp = t_5;
	} else if (x1 <= 4e-18) {
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))));
	} else if (x1 <= 4e+150) {
		tmp = t_5;
	} else {
		tmp = x1 - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = x1 * (2.0d0 - (x1 * 9.0d0))
    t_3 = t_1 + (2.0d0 * x2)
    t_4 = (x1 - t_3) / t_0
    t_5 = x1 + (9.0d0 - ((((t_1 * t_4) + (t_0 * (((x1 * x1) * (6.0d0 + (4.0d0 * t_4))) + ((((t_3 - x1) / t_0) - 3.0d0) * ((x1 * 2.0d0) * t_4))))) - (x1 * (x1 * x1))) - x1))
    if (x1 <= (-9.5d+115)) then
        tmp = x1 - (x2 * (6.0d0 + (t_2 / x2)))
    else if (x1 <= (-0.0025d0)) then
        tmp = t_5
    else if (x1 <= 4d-18) then
        tmp = (x2 * (-6.0d0)) + ((x1 * ((-1.0d0) + (x1 * 9.0d0))) + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 12.0d0) - 12.0d0)))))
    else if (x1 <= 4d+150) then
        tmp = t_5
    else
        tmp = x1 - t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = x1 * (2.0 - (x1 * 9.0));
	double t_3 = t_1 + (2.0 * x2);
	double t_4 = (x1 - t_3) / t_0;
	double t_5 = x1 + (9.0 - ((((t_1 * t_4) + (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_4))) + ((((t_3 - x1) / t_0) - 3.0) * ((x1 * 2.0) * t_4))))) - (x1 * (x1 * x1))) - x1));
	double tmp;
	if (x1 <= -9.5e+115) {
		tmp = x1 - (x2 * (6.0 + (t_2 / x2)));
	} else if (x1 <= -0.0025) {
		tmp = t_5;
	} else if (x1 <= 4e-18) {
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))));
	} else if (x1 <= 4e+150) {
		tmp = t_5;
	} else {
		tmp = x1 - t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = x1 * (2.0 - (x1 * 9.0))
	t_3 = t_1 + (2.0 * x2)
	t_4 = (x1 - t_3) / t_0
	t_5 = x1 + (9.0 - ((((t_1 * t_4) + (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_4))) + ((((t_3 - x1) / t_0) - 3.0) * ((x1 * 2.0) * t_4))))) - (x1 * (x1 * x1))) - x1))
	tmp = 0
	if x1 <= -9.5e+115:
		tmp = x1 - (x2 * (6.0 + (t_2 / x2)))
	elif x1 <= -0.0025:
		tmp = t_5
	elif x1 <= 4e-18:
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))))
	elif x1 <= 4e+150:
		tmp = t_5
	else:
		tmp = x1 - t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(x1 * Float64(2.0 - Float64(x1 * 9.0)))
	t_3 = Float64(t_1 + Float64(2.0 * x2))
	t_4 = Float64(Float64(x1 - t_3) / t_0)
	t_5 = Float64(x1 + Float64(9.0 - Float64(Float64(Float64(Float64(t_1 * t_4) + Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_4))) + Float64(Float64(Float64(Float64(t_3 - x1) / t_0) - 3.0) * Float64(Float64(x1 * 2.0) * t_4))))) - Float64(x1 * Float64(x1 * x1))) - x1)))
	tmp = 0.0
	if (x1 <= -9.5e+115)
		tmp = Float64(x1 - Float64(x2 * Float64(6.0 + Float64(t_2 / x2))));
	elseif (x1 <= -0.0025)
		tmp = t_5;
	elseif (x1 <= 4e-18)
		tmp = Float64(Float64(x2 * -6.0) + Float64(Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))) + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 12.0) - 12.0))))));
	elseif (x1 <= 4e+150)
		tmp = t_5;
	else
		tmp = Float64(x1 - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * 3.0);
	t_2 = x1 * (2.0 - (x1 * 9.0));
	t_3 = t_1 + (2.0 * x2);
	t_4 = (x1 - t_3) / t_0;
	t_5 = x1 + (9.0 - ((((t_1 * t_4) + (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_4))) + ((((t_3 - x1) / t_0) - 3.0) * ((x1 * 2.0) * t_4))))) - (x1 * (x1 * x1))) - x1));
	tmp = 0.0;
	if (x1 <= -9.5e+115)
		tmp = x1 - (x2 * (6.0 + (t_2 / x2)));
	elseif (x1 <= -0.0025)
		tmp = t_5;
	elseif (x1 <= 4e-18)
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))));
	elseif (x1 <= 4e+150)
		tmp = t_5;
	else
		tmp = x1 - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 - t$95$3), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(9.0 - N[(N[(N[(N[(t$95$1 * t$95$4), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(t$95$3 - x1), $MachinePrecision] / t$95$0), $MachinePrecision] - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -9.5e+115], N[(x1 - N[(x2 * N[(6.0 + N[(t$95$2 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -0.0025], t$95$5, If[LessEqual[x1, 4e-18], N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 12.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4e+150], t$95$5, N[(x1 - t$95$2), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -9.4999999999999997e115

   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 32.5%

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

   5. Taylor expanded in x1 around 0 44.8%

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

   6. Taylor expanded in x2 around 0 70.2%

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

   7. Taylor expanded in x2 around inf 95.4%

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

   if -9.4999999999999997e115 < x1 < -0.00250000000000000005 or 4.0000000000000003e-18 < x1 < 3.99999999999999992e150

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around inf 98.4%

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

      1. metadata-eval 73.7%

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

   5. Applied egg-rr 98.4%

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

   if -0.00250000000000000005 < x1 < 4.0000000000000003e-18

   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 89.4%

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

   5. Taylor expanded in x1 around 0 89.5%

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

   6. Taylor expanded in x2 around 0 99.9%

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

   if 3.99999999999999992e150 < 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%

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

   5. Taylor expanded in x1 around 0 70.7%

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

   6. Taylor expanded in x2 around 0 100.0%

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

   7. Taylor expanded in x2 around 0 100.0%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+115}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \mathbf{elif}\;x1 \leq -0.0025:\\ \;\;\;\;x1 + \left(9 - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{-18}:\\ \;\;\;\;x2 \cdot -6 + \left(x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+150}:\\ \;\;\;\;x1 + \left(9 - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - x1 \cdot \left(2 - x1 \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \frac{x1 - \left(t\_2 + 2 \cdot x2\right)}{t\_1}\\ t_4 := 3 + t\_3\\ t_5 := \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_3\right)\\ \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+115}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{-18}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(t\_2 - 2 \cdot x2\right)}{-1 - x1 \cdot x1} - \left(\left(\left(t\_2 \cdot t\_3 + t\_1 \cdot \left(t\_5 + \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right) \cdot t\_4\right)\right) - t\_0\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+150}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(t\_0 + \left(t\_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_3\right) \cdot t\_4 - t\_5\right) + t\_2 \cdot \left(3 + \frac{-1 - \frac{3 - 2 \cdot x2}{x1}}{x1}\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - x1 \cdot \left(2 - x1 \cdot 9\right)\\ \end{array} \end{array} \]

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 (/ (- x1 (+ t_2 (* 2.0 x2))) t_1))
        (t_4 (+ 3.0 t_3))
        (t_5 (* (* x1 x1) (+ 6.0 (* 4.0 t_3)))))
   (if (<= x1 -9.5e+115)
     (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) 9.0))
     (if (<= x1 4e-18)
       (+
        x1
        (-
         (* 3.0 (/ (- x1 (- t_2 (* 2.0 x2))) (- -1.0 (* x1 x1))))
         (-
          (-
           (+
            (* t_2 t_3)
            (* t_1 (+ t_5 (* (* (* x1 2.0) (- (* 2.0 x2) x1)) t_4))))
           t_0)
          x1)))
       (if (<= x1 4e+150)
         (+
          x1
          (+
           9.0
           (+
            x1
            (+
             t_0
             (+
              (* t_1 (- (* (* (* x1 2.0) t_3) t_4) t_5))
              (* t_2 (+ 3.0 (/ (- -1.0 (/ (- 3.0 (* 2.0 x2)) x1)) x1))))))))
         (- x1 (* x1 (- 2.0 (* x1 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 = (x1 - (t_2 + (2.0 * x2))) / t_1;
	double t_4 = 3.0 + t_3;
	double t_5 = (x1 * x1) * (6.0 + (4.0 * t_3));
	double tmp;
	if (x1 <= -9.5e+115) {
		tmp = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + 9.0);
	} else if (x1 <= 4e-18) {
		tmp = x1 + ((3.0 * ((x1 - (t_2 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) - ((((t_2 * t_3) + (t_1 * (t_5 + (((x1 * 2.0) * ((2.0 * x2) - x1)) * t_4)))) - t_0) - x1));
	} else if (x1 <= 4e+150) {
		tmp = x1 + (9.0 + (x1 + (t_0 + ((t_1 * ((((x1 * 2.0) * t_3) * t_4) - t_5)) + (t_2 * (3.0 + ((-1.0 - ((3.0 - (2.0 * x2)) / x1)) / x1)))))));
	} else {
		tmp = x1 - (x1 * (2.0 - (x1 * 9.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = x1 * (x1 * x1)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = (x1 - (t_2 + (2.0d0 * x2))) / t_1
    t_4 = 3.0d0 + t_3
    t_5 = (x1 * x1) * (6.0d0 + (4.0d0 * t_3))
    if (x1 <= (-9.5d+115)) then
        tmp = x1 + ((x1 + (6.0d0 * (x1 ** 4.0d0))) + 9.0d0)
    else if (x1 <= 4d-18) then
        tmp = x1 + ((3.0d0 * ((x1 - (t_2 - (2.0d0 * x2))) / ((-1.0d0) - (x1 * x1)))) - ((((t_2 * t_3) + (t_1 * (t_5 + (((x1 * 2.0d0) * ((2.0d0 * x2) - x1)) * t_4)))) - t_0) - x1))
    else if (x1 <= 4d+150) then
        tmp = x1 + (9.0d0 + (x1 + (t_0 + ((t_1 * ((((x1 * 2.0d0) * t_3) * t_4) - t_5)) + (t_2 * (3.0d0 + (((-1.0d0) - ((3.0d0 - (2.0d0 * x2)) / x1)) / x1)))))))
    else
        tmp = x1 - (x1 * (2.0d0 - (x1 * 9.0d0)))
    end if
    code = tmp
end function

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 = (x1 - (t_2 + (2.0 * x2))) / t_1;
	double t_4 = 3.0 + t_3;
	double t_5 = (x1 * x1) * (6.0 + (4.0 * t_3));
	double tmp;
	if (x1 <= -9.5e+115) {
		tmp = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + 9.0);
	} else if (x1 <= 4e-18) {
		tmp = x1 + ((3.0 * ((x1 - (t_2 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) - ((((t_2 * t_3) + (t_1 * (t_5 + (((x1 * 2.0) * ((2.0 * x2) - x1)) * t_4)))) - t_0) - x1));
	} else if (x1 <= 4e+150) {
		tmp = x1 + (9.0 + (x1 + (t_0 + ((t_1 * ((((x1 * 2.0) * t_3) * t_4) - t_5)) + (t_2 * (3.0 + ((-1.0 - ((3.0 - (2.0 * x2)) / x1)) / x1)))))));
	} else {
		tmp = x1 - (x1 * (2.0 - (x1 * 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 = (x1 - (t_2 + (2.0 * x2))) / t_1
	t_4 = 3.0 + t_3
	t_5 = (x1 * x1) * (6.0 + (4.0 * t_3))
	tmp = 0
	if x1 <= -9.5e+115:
		tmp = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + 9.0)
	elif x1 <= 4e-18:
		tmp = x1 + ((3.0 * ((x1 - (t_2 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) - ((((t_2 * t_3) + (t_1 * (t_5 + (((x1 * 2.0) * ((2.0 * x2) - x1)) * t_4)))) - t_0) - x1))
	elif x1 <= 4e+150:
		tmp = x1 + (9.0 + (x1 + (t_0 + ((t_1 * ((((x1 * 2.0) * t_3) * t_4) - t_5)) + (t_2 * (3.0 + ((-1.0 - ((3.0 - (2.0 * x2)) / x1)) / x1)))))))
	else:
		tmp = x1 - (x1 * (2.0 - (x1 * 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(x1 - Float64(t_2 + Float64(2.0 * x2))) / t_1)
	t_4 = Float64(3.0 + t_3)
	t_5 = Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_3)))
	tmp = 0.0
	if (x1 <= -9.5e+115)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + 9.0));
	elseif (x1 <= 4e-18)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 - Float64(t_2 - Float64(2.0 * x2))) / Float64(-1.0 - Float64(x1 * x1)))) - Float64(Float64(Float64(Float64(t_2 * t_3) + Float64(t_1 * Float64(t_5 + Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(2.0 * x2) - x1)) * t_4)))) - t_0) - x1)));
	elseif (x1 <= 4e+150)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_0 + Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_3) * t_4) - t_5)) + Float64(t_2 * Float64(3.0 + Float64(Float64(-1.0 - Float64(Float64(3.0 - Float64(2.0 * x2)) / x1)) / x1))))))));
	else
		tmp = Float64(x1 - Float64(x1 * Float64(2.0 - Float64(x1 * 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 = (x1 - (t_2 + (2.0 * x2))) / t_1;
	t_4 = 3.0 + t_3;
	t_5 = (x1 * x1) * (6.0 + (4.0 * t_3));
	tmp = 0.0;
	if (x1 <= -9.5e+115)
		tmp = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + 9.0);
	elseif (x1 <= 4e-18)
		tmp = x1 + ((3.0 * ((x1 - (t_2 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) - ((((t_2 * t_3) + (t_1 * (t_5 + (((x1 * 2.0) * ((2.0 * x2) - x1)) * t_4)))) - t_0) - x1));
	elseif (x1 <= 4e+150)
		tmp = x1 + (9.0 + (x1 + (t_0 + ((t_1 * ((((x1 * 2.0) * t_3) * t_4) - t_5)) + (t_2 * (3.0 + ((-1.0 - ((3.0 - (2.0 * x2)) / x1)) / x1)))))));
	else
		tmp = x1 - (x1 * (2.0 - (x1 * 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[(x1 - N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 + t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -9.5e+115], N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4e-18], N[(x1 + N[(N[(3.0 * N[(N[(x1 - N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(t$95$2 * t$95$3), $MachinePrecision] + N[(t$95$1 * N[(t$95$5 + N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4e+150], N[(x1 + N[(9.0 + N[(x1 + N[(t$95$0 + N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * t$95$4), $MachinePrecision] - t$95$5), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * N[(3.0 + N[(N[(-1.0 - N[(N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 - N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -9.4999999999999997e115

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around inf 100.0%

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

      1. *-commutative 100.0%

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

   6. Simplified 100.0%

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

      1. metadata-eval 100.0%

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

   8. Applied egg-rr 100.0%

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

   if -9.4999999999999997e115 < x1 < 4.0000000000000003e-18

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around 0 97.6%

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

      1. +-commutative 97.6%

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

      2. mul-1-neg 97.6%

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

      3. unsub-neg 97.6%

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

   5. Simplified 97.6%

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

   if 4.0000000000000003e-18 < x1 < 3.99999999999999992e150

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around inf 98.0%

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

   4. Taylor expanded in x1 around -inf 99.4%

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

   if 3.99999999999999992e150 < 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%

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

   5. Taylor expanded in x1 around 0 70.7%

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

   6. Taylor expanded in x2 around 0 100.0%

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

   7. Taylor expanded in x2 around 0 100.0%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+115}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{-18}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) + \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+150}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 + \frac{-1 - \frac{3 - 2 \cdot x2}{x1}}{x1}\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - x1 \cdot \left(2 - x1 \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := t\_1 + 2 \cdot x2\\ t_3 := \frac{x1 - t\_2}{t\_0}\\ \mathbf{if}\;x1 \leq -2.1 \cdot 10^{+14}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{-18}:\\ \;\;\;\;x2 \cdot -6 + \left(x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+150}:\\ \;\;\;\;x1 + \left(9 - \left(\left(\left(t\_1 \cdot t\_3 + t\_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_3\right) + \left(\frac{t\_2 - x1}{t\_0} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot t\_3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - x1 \cdot \left(2 - x1 \cdot 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ t_1 (* 2.0 x2)))
        (t_3 (/ (- x1 t_2) t_0)))
   (if (<= x1 -2.1e+14)
     (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) 9.0))
     (if (<= x1 4e-18)
       (+
        (* x2 -6.0)
        (+
         (* x1 (+ -1.0 (* x1 9.0)))
         (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 12.0) 12.0))))))
       (if (<= x1 4e+150)
         (+
          x1
          (-
           9.0
           (-
            (-
             (+
              (* t_1 t_3)
              (*
               t_0
               (+
                (* (* x1 x1) (+ 6.0 (* 4.0 t_3)))
                (* (- (/ (- t_2 x1) t_0) 3.0) (* (* x1 2.0) t_3)))))
             (* x1 (* x1 x1)))
            x1)))
         (- x1 (* x1 (- 2.0 (* x1 9.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = t_1 + (2.0 * x2);
	double t_3 = (x1 - t_2) / t_0;
	double tmp;
	if (x1 <= -2.1e+14) {
		tmp = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + 9.0);
	} else if (x1 <= 4e-18) {
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))));
	} else if (x1 <= 4e+150) {
		tmp = x1 + (9.0 - ((((t_1 * t_3) + (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_3))) + ((((t_2 - x1) / t_0) - 3.0) * ((x1 * 2.0) * t_3))))) - (x1 * (x1 * x1))) - x1));
	} else {
		tmp = x1 - (x1 * (2.0 - (x1 * 9.0)));
	}
	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) + 1.0d0
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = t_1 + (2.0d0 * x2)
    t_3 = (x1 - t_2) / t_0
    if (x1 <= (-2.1d+14)) then
        tmp = x1 + ((x1 + (6.0d0 * (x1 ** 4.0d0))) + 9.0d0)
    else if (x1 <= 4d-18) then
        tmp = (x2 * (-6.0d0)) + ((x1 * ((-1.0d0) + (x1 * 9.0d0))) + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 12.0d0) - 12.0d0)))))
    else if (x1 <= 4d+150) then
        tmp = x1 + (9.0d0 - ((((t_1 * t_3) + (t_0 * (((x1 * x1) * (6.0d0 + (4.0d0 * t_3))) + ((((t_2 - x1) / t_0) - 3.0d0) * ((x1 * 2.0d0) * t_3))))) - (x1 * (x1 * x1))) - x1))
    else
        tmp = x1 - (x1 * (2.0d0 - (x1 * 9.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = t_1 + (2.0 * x2);
	double t_3 = (x1 - t_2) / t_0;
	double tmp;
	if (x1 <= -2.1e+14) {
		tmp = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + 9.0);
	} else if (x1 <= 4e-18) {
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))));
	} else if (x1 <= 4e+150) {
		tmp = x1 + (9.0 - ((((t_1 * t_3) + (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_3))) + ((((t_2 - x1) / t_0) - 3.0) * ((x1 * 2.0) * t_3))))) - (x1 * (x1 * x1))) - x1));
	} else {
		tmp = x1 - (x1 * (2.0 - (x1 * 9.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = t_1 + (2.0 * x2)
	t_3 = (x1 - t_2) / t_0
	tmp = 0
	if x1 <= -2.1e+14:
		tmp = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + 9.0)
	elif x1 <= 4e-18:
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))))
	elif x1 <= 4e+150:
		tmp = x1 + (9.0 - ((((t_1 * t_3) + (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_3))) + ((((t_2 - x1) / t_0) - 3.0) * ((x1 * 2.0) * t_3))))) - (x1 * (x1 * x1))) - x1))
	else:
		tmp = x1 - (x1 * (2.0 - (x1 * 9.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(t_1 + Float64(2.0 * x2))
	t_3 = Float64(Float64(x1 - t_2) / t_0)
	tmp = 0.0
	if (x1 <= -2.1e+14)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + 9.0));
	elseif (x1 <= 4e-18)
		tmp = Float64(Float64(x2 * -6.0) + Float64(Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))) + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 12.0) - 12.0))))));
	elseif (x1 <= 4e+150)
		tmp = Float64(x1 + Float64(9.0 - Float64(Float64(Float64(Float64(t_1 * t_3) + Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_3))) + Float64(Float64(Float64(Float64(t_2 - x1) / t_0) - 3.0) * Float64(Float64(x1 * 2.0) * t_3))))) - Float64(x1 * Float64(x1 * x1))) - x1)));
	else
		tmp = Float64(x1 - Float64(x1 * Float64(2.0 - Float64(x1 * 9.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * 3.0);
	t_2 = t_1 + (2.0 * x2);
	t_3 = (x1 - t_2) / t_0;
	tmp = 0.0;
	if (x1 <= -2.1e+14)
		tmp = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + 9.0);
	elseif (x1 <= 4e-18)
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))));
	elseif (x1 <= 4e+150)
		tmp = x1 + (9.0 - ((((t_1 * t_3) + (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_3))) + ((((t_2 - x1) / t_0) - 3.0) * ((x1 * 2.0) * t_3))))) - (x1 * (x1 * x1))) - x1));
	else
		tmp = x1 - (x1 * (2.0 - (x1 * 9.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 - t$95$2), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[LessEqual[x1, -2.1e+14], N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4e-18], N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 12.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4e+150], N[(x1 + N[(9.0 - N[(N[(N[(N[(t$95$1 * t$95$3), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(t$95$2 - x1), $MachinePrecision] / t$95$0), $MachinePrecision] - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 - N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.1e14

   1. Initial program 30.8%

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

   3. Taylor expanded in x1 around inf 30.8%

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

   4. Taylor expanded in x1 around inf 95.0%

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

      1. *-commutative 95.0%

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

   6. Simplified 95.0%

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

      1. metadata-eval 95.0%

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

   8. Applied egg-rr 95.0%

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

   if -2.1e14 < x1 < 4.0000000000000003e-18

   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 89.7%

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

   5. Taylor expanded in x1 around 0 89.0%

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

   6. Taylor expanded in x2 around 0 99.1%

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

   if 4.0000000000000003e-18 < x1 < 3.99999999999999992e150

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around inf 98.0%

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

      1. metadata-eval 73.9%

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

   5. Applied egg-rr 98.0%

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

   if 3.99999999999999992e150 < 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%

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

   5. Taylor expanded in x1 around 0 70.7%

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

   6. Taylor expanded in x2 around 0 100.0%

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

   7. Taylor expanded in x2 around 0 100.0%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.1 \cdot 10^{+14}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{-18}:\\ \;\;\;\;x2 \cdot -6 + \left(x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+150}:\\ \;\;\;\;x1 + \left(9 - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - x1 \cdot \left(2 - x1 \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 96.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(2 - x1 \cdot 9\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := t\_2 + 2 \cdot x2\\ t_4 := \frac{x1 - t\_3}{t\_0}\\ t_5 := x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_2 \cdot \frac{t\_3 - x1}{t\_0} - t\_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_4\right) + \frac{2 \cdot \frac{x2}{x1} + \left(-1 - \frac{3}{x1}\right)}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot t\_4\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+115}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{t\_1}{x2}\right)\\ \mathbf{elif}\;x1 \leq -0.86:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x1 \leq 0.72:\\ \;\;\;\;x2 \cdot -6 + \left(x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;x1 - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (- 2.0 (* x1 9.0))))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (+ t_2 (* 2.0 x2)))
        (t_4 (/ (- x1 t_3) t_0))
        (t_5
         (+
          x1
          (+
           9.0
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (-
              (* t_2 (/ (- t_3 x1) t_0))
              (*
               t_0
               (+
                (* (* x1 x1) (+ 6.0 (* 4.0 t_4)))
                (*
                 (/ (+ (* 2.0 (/ x2 x1)) (- -1.0 (/ 3.0 x1))) x1)
                 (* (* x1 2.0) t_4)))))))))))
   (if (<= x1 -9.5e+115)
     (- x1 (* x2 (+ 6.0 (/ t_1 x2))))
     (if (<= x1 -0.86)
       t_5
       (if (<= x1 0.72)
         (+
          (* x2 -6.0)
          (+
           (* x1 (+ -1.0 (* x1 9.0)))
           (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 12.0) 12.0))))))
         (if (<= x1 5e+153) t_5 (- x1 t_1)))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (2.0 - (x1 * 9.0));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = t_2 + (2.0 * x2);
	double t_4 = (x1 - t_3) / t_0;
	double t_5 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * ((t_3 - x1) / t_0)) - (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_4))) + ((((2.0 * (x2 / x1)) + (-1.0 - (3.0 / x1))) / x1) * ((x1 * 2.0) * t_4))))))));
	double tmp;
	if (x1 <= -9.5e+115) {
		tmp = x1 - (x2 * (6.0 + (t_1 / x2)));
	} else if (x1 <= -0.86) {
		tmp = t_5;
	} else if (x1 <= 0.72) {
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))));
	} else if (x1 <= 5e+153) {
		tmp = t_5;
	} else {
		tmp = x1 - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * (2.0d0 - (x1 * 9.0d0))
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = t_2 + (2.0d0 * x2)
    t_4 = (x1 - t_3) / t_0
    t_5 = x1 + (9.0d0 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * ((t_3 - x1) / t_0)) - (t_0 * (((x1 * x1) * (6.0d0 + (4.0d0 * t_4))) + ((((2.0d0 * (x2 / x1)) + ((-1.0d0) - (3.0d0 / x1))) / x1) * ((x1 * 2.0d0) * t_4))))))))
    if (x1 <= (-9.5d+115)) then
        tmp = x1 - (x2 * (6.0d0 + (t_1 / x2)))
    else if (x1 <= (-0.86d0)) then
        tmp = t_5
    else if (x1 <= 0.72d0) then
        tmp = (x2 * (-6.0d0)) + ((x1 * ((-1.0d0) + (x1 * 9.0d0))) + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 12.0d0) - 12.0d0)))))
    else if (x1 <= 5d+153) then
        tmp = t_5
    else
        tmp = x1 - t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (2.0 - (x1 * 9.0));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = t_2 + (2.0 * x2);
	double t_4 = (x1 - t_3) / t_0;
	double t_5 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * ((t_3 - x1) / t_0)) - (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_4))) + ((((2.0 * (x2 / x1)) + (-1.0 - (3.0 / x1))) / x1) * ((x1 * 2.0) * t_4))))))));
	double tmp;
	if (x1 <= -9.5e+115) {
		tmp = x1 - (x2 * (6.0 + (t_1 / x2)));
	} else if (x1 <= -0.86) {
		tmp = t_5;
	} else if (x1 <= 0.72) {
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))));
	} else if (x1 <= 5e+153) {
		tmp = t_5;
	} else {
		tmp = x1 - t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (2.0 - (x1 * 9.0))
	t_2 = x1 * (x1 * 3.0)
	t_3 = t_2 + (2.0 * x2)
	t_4 = (x1 - t_3) / t_0
	t_5 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * ((t_3 - x1) / t_0)) - (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_4))) + ((((2.0 * (x2 / x1)) + (-1.0 - (3.0 / x1))) / x1) * ((x1 * 2.0) * t_4))))))))
	tmp = 0
	if x1 <= -9.5e+115:
		tmp = x1 - (x2 * (6.0 + (t_1 / x2)))
	elif x1 <= -0.86:
		tmp = t_5
	elif x1 <= 0.72:
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))))
	elif x1 <= 5e+153:
		tmp = t_5
	else:
		tmp = x1 - t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(2.0 - Float64(x1 * 9.0)))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(t_2 + Float64(2.0 * x2))
	t_4 = Float64(Float64(x1 - t_3) / t_0)
	t_5 = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_2 * Float64(Float64(t_3 - x1) / t_0)) - Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_4))) + Float64(Float64(Float64(Float64(2.0 * Float64(x2 / x1)) + Float64(-1.0 - Float64(3.0 / x1))) / x1) * Float64(Float64(x1 * 2.0) * t_4)))))))))
	tmp = 0.0
	if (x1 <= -9.5e+115)
		tmp = Float64(x1 - Float64(x2 * Float64(6.0 + Float64(t_1 / x2))));
	elseif (x1 <= -0.86)
		tmp = t_5;
	elseif (x1 <= 0.72)
		tmp = Float64(Float64(x2 * -6.0) + Float64(Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))) + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 12.0) - 12.0))))));
	elseif (x1 <= 5e+153)
		tmp = t_5;
	else
		tmp = Float64(x1 - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (2.0 - (x1 * 9.0));
	t_2 = x1 * (x1 * 3.0);
	t_3 = t_2 + (2.0 * x2);
	t_4 = (x1 - t_3) / t_0;
	t_5 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * ((t_3 - x1) / t_0)) - (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_4))) + ((((2.0 * (x2 / x1)) + (-1.0 - (3.0 / x1))) / x1) * ((x1 * 2.0) * t_4))))))));
	tmp = 0.0;
	if (x1 <= -9.5e+115)
		tmp = x1 - (x2 * (6.0 + (t_1 / x2)));
	elseif (x1 <= -0.86)
		tmp = t_5;
	elseif (x1 <= 0.72)
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))));
	elseif (x1 <= 5e+153)
		tmp = t_5;
	else
		tmp = x1 - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 - t$95$3), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(9.0 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(N[(t$95$3 - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] - N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(2.0 * N[(x2 / x1), $MachinePrecision]), $MachinePrecision] + N[(-1.0 - N[(3.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -9.5e+115], N[(x1 - N[(x2 * N[(6.0 + N[(t$95$1 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -0.86], t$95$5, If[LessEqual[x1, 0.72], N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 12.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], t$95$5, N[(x1 - t$95$1), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -9.4999999999999997e115

   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 32.5%

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

   5. Taylor expanded in x1 around 0 44.8%

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

   6. Taylor expanded in x2 around 0 70.2%

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

   7. Taylor expanded in x2 around inf 95.4%

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

   if -9.4999999999999997e115 < x1 < -0.859999999999999987 or 0.71999999999999997 < x1 < 5.00000000000000018e153

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around inf 98.4%

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

   4. Taylor expanded in x1 around inf 97.9%

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

      1. associate-*r/ 97.9%

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

      2. metadata-eval 97.9%

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

   6. Simplified 97.9%

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

   if -0.859999999999999987 < x1 < 0.71999999999999997

   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 89.6%

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

   5. Taylor expanded in x1 around 0 89.7%

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

   6. Taylor expanded in x2 around 0 99.9%

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

   if 5.00000000000000018e153 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 70.7%

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

   6. Taylor expanded in x2 around 0 100.0%

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

   7. Taylor expanded in x2 around 0 100.0%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+115}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \mathbf{elif}\;x1 \leq -0.86:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) + \frac{2 \cdot \frac{x2}{x1} + \left(-1 - \frac{3}{x1}\right)}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.72:\\ \;\;\;\;x2 \cdot -6 + \left(x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) + \frac{2 \cdot \frac{x2}{x1} + \left(-1 - \frac{3}{x1}\right)}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - x1 \cdot \left(2 - x1 \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 95.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{x1 - \left(t\_0 + 2 \cdot x2\right)}{t\_1}\\ \mathbf{if}\;x1 \leq -62000000000000:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{-18}:\\ \;\;\;\;x2 \cdot -6 + \left(x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+150}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(3 + t\_2\right) - \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_2\right)\right) + t\_0 \cdot \left(3 + \frac{-1 - \frac{3 - 2 \cdot x2}{x1}}{x1}\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - x1 \cdot \left(2 - x1 \cdot 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- x1 (+ t_0 (* 2.0 x2))) t_1)))
   (if (<= x1 -62000000000000.0)
     (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) 9.0))
     (if (<= x1 4e-18)
       (+
        (* x2 -6.0)
        (+
         (* x1 (+ -1.0 (* x1 9.0)))
         (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 12.0) 12.0))))))
       (if (<= x1 4e+150)
         (+
          x1
          (+
           9.0
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (*
               t_1
               (-
                (* (* (* x1 2.0) t_2) (+ 3.0 t_2))
                (* (* x1 x1) (+ 6.0 (* 4.0 t_2)))))
              (* t_0 (+ 3.0 (/ (- -1.0 (/ (- 3.0 (* 2.0 x2)) x1)) x1))))))))
         (- x1 (* x1 (- 2.0 (* x1 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 = (x1 - (t_0 + (2.0 * x2))) / t_1;
	double tmp;
	if (x1 <= -62000000000000.0) {
		tmp = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + 9.0);
	} else if (x1 <= 4e-18) {
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))));
	} else if (x1 <= 4e+150) {
		tmp = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (3.0 + t_2)) - ((x1 * x1) * (6.0 + (4.0 * t_2))))) + (t_0 * (3.0 + ((-1.0 - ((3.0 - (2.0 * x2)) / x1)) / x1)))))));
	} else {
		tmp = x1 - (x1 * (2.0 - (x1 * 9.0)));
	}
	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 = (x1 - (t_0 + (2.0d0 * x2))) / t_1
    if (x1 <= (-62000000000000.0d0)) then
        tmp = x1 + ((x1 + (6.0d0 * (x1 ** 4.0d0))) + 9.0d0)
    else if (x1 <= 4d-18) then
        tmp = (x2 * (-6.0d0)) + ((x1 * ((-1.0d0) + (x1 * 9.0d0))) + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 12.0d0) - 12.0d0)))))
    else if (x1 <= 4d+150) then
        tmp = x1 + (9.0d0 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0d0) * t_2) * (3.0d0 + t_2)) - ((x1 * x1) * (6.0d0 + (4.0d0 * t_2))))) + (t_0 * (3.0d0 + (((-1.0d0) - ((3.0d0 - (2.0d0 * x2)) / x1)) / x1)))))))
    else
        tmp = x1 - (x1 * (2.0d0 - (x1 * 9.0d0)))
    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 = (x1 - (t_0 + (2.0 * x2))) / t_1;
	double tmp;
	if (x1 <= -62000000000000.0) {
		tmp = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + 9.0);
	} else if (x1 <= 4e-18) {
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))));
	} else if (x1 <= 4e+150) {
		tmp = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (3.0 + t_2)) - ((x1 * x1) * (6.0 + (4.0 * t_2))))) + (t_0 * (3.0 + ((-1.0 - ((3.0 - (2.0 * x2)) / x1)) / x1)))))));
	} else {
		tmp = x1 - (x1 * (2.0 - (x1 * 9.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = (x1 - (t_0 + (2.0 * x2))) / t_1
	tmp = 0
	if x1 <= -62000000000000.0:
		tmp = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + 9.0)
	elif x1 <= 4e-18:
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))))
	elif x1 <= 4e+150:
		tmp = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (3.0 + t_2)) - ((x1 * x1) * (6.0 + (4.0 * t_2))))) + (t_0 * (3.0 + ((-1.0 - ((3.0 - (2.0 * x2)) / x1)) / x1)))))))
	else:
		tmp = x1 - (x1 * (2.0 - (x1 * 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(x1 - Float64(t_0 + Float64(2.0 * x2))) / t_1)
	tmp = 0.0
	if (x1 <= -62000000000000.0)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + 9.0));
	elseif (x1 <= 4e-18)
		tmp = Float64(Float64(x2 * -6.0) + Float64(Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))) + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 12.0) - 12.0))))));
	elseif (x1 <= 4e+150)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(3.0 + t_2)) - Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_2))))) + Float64(t_0 * Float64(3.0 + Float64(Float64(-1.0 - Float64(Float64(3.0 - Float64(2.0 * x2)) / x1)) / x1))))))));
	else
		tmp = Float64(x1 - Float64(x1 * Float64(2.0 - Float64(x1 * 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 = (x1 - (t_0 + (2.0 * x2))) / t_1;
	tmp = 0.0;
	if (x1 <= -62000000000000.0)
		tmp = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + 9.0);
	elseif (x1 <= 4e-18)
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))));
	elseif (x1 <= 4e+150)
		tmp = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (3.0 + t_2)) - ((x1 * x1) * (6.0 + (4.0 * t_2))))) + (t_0 * (3.0 + ((-1.0 - ((3.0 - (2.0 * x2)) / x1)) / x1)))))));
	else
		tmp = x1 - (x1 * (2.0 - (x1 * 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[(x1 - N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[x1, -62000000000000.0], N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4e-18], N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 12.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4e+150], N[(x1 + N[(9.0 + 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[(3.0 + t$95$2), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(3.0 + N[(N[(-1.0 - N[(N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 - N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -6.2e13

   1. Initial program 30.8%

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

   3. Taylor expanded in x1 around inf 30.8%

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

   4. Taylor expanded in x1 around inf 95.0%

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

      1. *-commutative 95.0%

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

   6. Simplified 95.0%

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

      1. metadata-eval 95.0%

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

   8. Applied egg-rr 95.0%

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

   if -6.2e13 < x1 < 4.0000000000000003e-18

   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 89.7%

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

   5. Taylor expanded in x1 around 0 89.0%

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

   6. Taylor expanded in x2 around 0 99.1%

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

   if 4.0000000000000003e-18 < x1 < 3.99999999999999992e150

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around inf 98.0%

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

   4. Taylor expanded in x1 around -inf 99.4%

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

   if 3.99999999999999992e150 < 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%

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

   5. Taylor expanded in x1 around 0 70.7%

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

   6. Taylor expanded in x2 around 0 100.0%

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

   7. Taylor expanded in x2 around 0 100.0%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -62000000000000:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{-18}:\\ \;\;\;\;x2 \cdot -6 + \left(x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+150}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 + \frac{-1 - \frac{3 - 2 \cdot x2}{x1}}{x1}\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - x1 \cdot \left(2 - x1 \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 93.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := \frac{x1 - \left(t\_0 + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\\ t_2 := x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(\left(\left(x1 \cdot 2\right) \cdot t\_1\right) \cdot \left(3 + t\_1\right) - \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \left(\frac{1 + \frac{3 - 2 \cdot x2}{x1}}{x1} - 3\right)\right)\right) \cdot \left(-1 - x1 \cdot x1\right) - t\_0 \cdot \left(2 \cdot x2\right)\right)\right)\right)\right)\\ t_3 := x1 \cdot \left(2 - x1 \cdot 9\right)\\ \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+115}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{t\_3}{x2}\right)\\ \mathbf{elif}\;x1 \leq -0.15:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{-18}:\\ \;\;\;\;x2 \cdot -6 + \left(x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.4 \cdot 10^{+153}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x1 - t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (/ (- x1 (+ t_0 (* 2.0 x2))) (+ (* x1 x1) 1.0)))
        (t_2
         (+
          x1
          (+
           9.0
           (+
            x1
            (-
             (* x1 (* x1 x1))
             (-
              (*
               (-
                (* (* (* x1 2.0) t_1) (+ 3.0 t_1))
                (*
                 (* x1 x1)
                 (+
                  6.0
                  (* 4.0 (- (/ (+ 1.0 (/ (- 3.0 (* 2.0 x2)) x1)) x1) 3.0)))))
               (- -1.0 (* x1 x1)))
              (* t_0 (* 2.0 x2))))))))
        (t_3 (* x1 (- 2.0 (* x1 9.0)))))
   (if (<= x1 -9.5e+115)
     (- x1 (* x2 (+ 6.0 (/ t_3 x2))))
     (if (<= x1 -0.15)
       t_2
       (if (<= x1 4e-18)
         (+
          (* x2 -6.0)
          (+
           (* x1 (+ -1.0 (* x1 9.0)))
           (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 12.0) 12.0))))))
         (if (<= x1 4.4e+153) t_2 (- x1 t_3)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 - (t_0 + (2.0 * x2))) / ((x1 * x1) + 1.0);
	double t_2 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) - ((((((x1 * 2.0) * t_1) * (3.0 + t_1)) - ((x1 * x1) * (6.0 + (4.0 * (((1.0 + ((3.0 - (2.0 * x2)) / x1)) / x1) - 3.0))))) * (-1.0 - (x1 * x1))) - (t_0 * (2.0 * x2))))));
	double t_3 = x1 * (2.0 - (x1 * 9.0));
	double tmp;
	if (x1 <= -9.5e+115) {
		tmp = x1 - (x2 * (6.0 + (t_3 / x2)));
	} else if (x1 <= -0.15) {
		tmp = t_2;
	} else if (x1 <= 4e-18) {
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))));
	} else if (x1 <= 4.4e+153) {
		tmp = t_2;
	} else {
		tmp = x1 - t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 - (t_0 + (2.0d0 * x2))) / ((x1 * x1) + 1.0d0)
    t_2 = x1 + (9.0d0 + (x1 + ((x1 * (x1 * x1)) - ((((((x1 * 2.0d0) * t_1) * (3.0d0 + t_1)) - ((x1 * x1) * (6.0d0 + (4.0d0 * (((1.0d0 + ((3.0d0 - (2.0d0 * x2)) / x1)) / x1) - 3.0d0))))) * ((-1.0d0) - (x1 * x1))) - (t_0 * (2.0d0 * x2))))))
    t_3 = x1 * (2.0d0 - (x1 * 9.0d0))
    if (x1 <= (-9.5d+115)) then
        tmp = x1 - (x2 * (6.0d0 + (t_3 / x2)))
    else if (x1 <= (-0.15d0)) then
        tmp = t_2
    else if (x1 <= 4d-18) then
        tmp = (x2 * (-6.0d0)) + ((x1 * ((-1.0d0) + (x1 * 9.0d0))) + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 12.0d0) - 12.0d0)))))
    else if (x1 <= 4.4d+153) then
        tmp = t_2
    else
        tmp = x1 - t_3
    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 - (t_0 + (2.0 * x2))) / ((x1 * x1) + 1.0);
	double t_2 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) - ((((((x1 * 2.0) * t_1) * (3.0 + t_1)) - ((x1 * x1) * (6.0 + (4.0 * (((1.0 + ((3.0 - (2.0 * x2)) / x1)) / x1) - 3.0))))) * (-1.0 - (x1 * x1))) - (t_0 * (2.0 * x2))))));
	double t_3 = x1 * (2.0 - (x1 * 9.0));
	double tmp;
	if (x1 <= -9.5e+115) {
		tmp = x1 - (x2 * (6.0 + (t_3 / x2)));
	} else if (x1 <= -0.15) {
		tmp = t_2;
	} else if (x1 <= 4e-18) {
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))));
	} else if (x1 <= 4.4e+153) {
		tmp = t_2;
	} else {
		tmp = x1 - t_3;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 - (t_0 + (2.0 * x2))) / ((x1 * x1) + 1.0)
	t_2 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) - ((((((x1 * 2.0) * t_1) * (3.0 + t_1)) - ((x1 * x1) * (6.0 + (4.0 * (((1.0 + ((3.0 - (2.0 * x2)) / x1)) / x1) - 3.0))))) * (-1.0 - (x1 * x1))) - (t_0 * (2.0 * x2))))))
	t_3 = x1 * (2.0 - (x1 * 9.0))
	tmp = 0
	if x1 <= -9.5e+115:
		tmp = x1 - (x2 * (6.0 + (t_3 / x2)))
	elif x1 <= -0.15:
		tmp = t_2
	elif x1 <= 4e-18:
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))))
	elif x1 <= 4.4e+153:
		tmp = t_2
	else:
		tmp = x1 - t_3
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 - Float64(t_0 + Float64(2.0 * x2))) / Float64(Float64(x1 * x1) + 1.0))
	t_2 = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) - Float64(Float64(Float64(Float64(Float64(Float64(x1 * 2.0) * t_1) * Float64(3.0 + t_1)) - Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * Float64(Float64(Float64(1.0 + Float64(Float64(3.0 - Float64(2.0 * x2)) / x1)) / x1) - 3.0))))) * Float64(-1.0 - Float64(x1 * x1))) - Float64(t_0 * Float64(2.0 * x2)))))))
	t_3 = Float64(x1 * Float64(2.0 - Float64(x1 * 9.0)))
	tmp = 0.0
	if (x1 <= -9.5e+115)
		tmp = Float64(x1 - Float64(x2 * Float64(6.0 + Float64(t_3 / x2))));
	elseif (x1 <= -0.15)
		tmp = t_2;
	elseif (x1 <= 4e-18)
		tmp = Float64(Float64(x2 * -6.0) + Float64(Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))) + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 12.0) - 12.0))))));
	elseif (x1 <= 4.4e+153)
		tmp = t_2;
	else
		tmp = Float64(x1 - t_3);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 - (t_0 + (2.0 * x2))) / ((x1 * x1) + 1.0);
	t_2 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) - ((((((x1 * 2.0) * t_1) * (3.0 + t_1)) - ((x1 * x1) * (6.0 + (4.0 * (((1.0 + ((3.0 - (2.0 * x2)) / x1)) / x1) - 3.0))))) * (-1.0 - (x1 * x1))) - (t_0 * (2.0 * x2))))));
	t_3 = x1 * (2.0 - (x1 * 9.0));
	tmp = 0.0;
	if (x1 <= -9.5e+115)
		tmp = x1 - (x2 * (6.0 + (t_3 / x2)));
	elseif (x1 <= -0.15)
		tmp = t_2;
	elseif (x1 <= 4e-18)
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))));
	elseif (x1 <= 4.4e+153)
		tmp = t_2;
	else
		tmp = x1 - t_3;
	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 - N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(9.0 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$1), $MachinePrecision] * N[(3.0 + t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * N[(N[(N[(1.0 + N[(N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$0 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -9.5e+115], N[(x1 - N[(x2 * N[(6.0 + N[(t$95$3 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -0.15], t$95$2, If[LessEqual[x1, 4e-18], N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 12.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.4e+153], t$95$2, N[(x1 - t$95$3), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -9.4999999999999997e115

   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 32.5%

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

   5. Taylor expanded in x1 around 0 44.8%

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

   6. Taylor expanded in x2 around 0 70.2%

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

   7. Taylor expanded in x2 around inf 95.4%

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

   if -9.4999999999999997e115 < x1 < -0.149999999999999994 or 4.0000000000000003e-18 < x1 < 4.3999999999999999e153

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around inf 98.4%

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

   4. Taylor expanded in x1 around 0 92.3%

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

   5. Taylor expanded in x1 around -inf 92.4%

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

   if -0.149999999999999994 < x1 < 4.0000000000000003e-18

   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 89.4%

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

   5. Taylor expanded in x1 around 0 89.5%

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

   6. Taylor expanded in x2 around 0 99.9%

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

   if 4.3999999999999999e153 < 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%

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

   5. Taylor expanded in x1 around 0 70.7%

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

   6. Taylor expanded in x2 around 0 100.0%

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

   7. Taylor expanded in x2 around 0 100.0%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+115}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \mathbf{elif}\;x1 \leq -0.15:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(\left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \left(\frac{1 + \frac{3 - 2 \cdot x2}{x1}}{x1} - 3\right)\right)\right) \cdot \left(-1 - x1 \cdot x1\right) - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{-18}:\\ \;\;\;\;x2 \cdot -6 + \left(x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(\left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \left(\frac{1 + \frac{3 - 2 \cdot x2}{x1}}{x1} - 3\right)\right)\right) \cdot \left(-1 - x1 \cdot x1\right) - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - x1 \cdot \left(2 - x1 \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 93.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{x1 - \left(t\_0 + 2 \cdot x2\right)}{t\_1}\\ t_3 := x1 + \left(9 - \left(\left(\left(t\_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_2\right) + \frac{2 \cdot \frac{x2}{x1} + \left(-1 - \frac{3}{x1}\right)}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot t\_2\right)\right) - t\_0 \cdot \left(2 \cdot x2\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ t_4 := x1 \cdot \left(2 - x1 \cdot 9\right)\\ \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+115}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{t\_4}{x2}\right)\\ \mathbf{elif}\;x1 \leq -0.82:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x1 \leq 0.7:\\ \;\;\;\;x2 \cdot -6 + \left(x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.4 \cdot 10^{+153}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;x1 - t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- x1 (+ t_0 (* 2.0 x2))) t_1))
        (t_3
         (+
          x1
          (-
           9.0
           (-
            (-
             (-
              (*
               t_1
               (+
                (* (* x1 x1) (+ 6.0 (* 4.0 t_2)))
                (*
                 (/ (+ (* 2.0 (/ x2 x1)) (- -1.0 (/ 3.0 x1))) x1)
                 (* (* x1 2.0) t_2))))
              (* t_0 (* 2.0 x2)))
             (* x1 (* x1 x1)))
            x1))))
        (t_4 (* x1 (- 2.0 (* x1 9.0)))))
   (if (<= x1 -9.5e+115)
     (- x1 (* x2 (+ 6.0 (/ t_4 x2))))
     (if (<= x1 -0.82)
       t_3
       (if (<= x1 0.7)
         (+
          (* x2 -6.0)
          (+
           (* x1 (+ -1.0 (* x1 9.0)))
           (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 12.0) 12.0))))))
         (if (<= x1 4.4e+153) t_3 (- x1 t_4)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = (x1 - (t_0 + (2.0 * x2))) / t_1;
	double t_3 = x1 + (9.0 - ((((t_1 * (((x1 * x1) * (6.0 + (4.0 * t_2))) + ((((2.0 * (x2 / x1)) + (-1.0 - (3.0 / x1))) / x1) * ((x1 * 2.0) * t_2)))) - (t_0 * (2.0 * x2))) - (x1 * (x1 * x1))) - x1));
	double t_4 = x1 * (2.0 - (x1 * 9.0));
	double tmp;
	if (x1 <= -9.5e+115) {
		tmp = x1 - (x2 * (6.0 + (t_4 / x2)));
	} else if (x1 <= -0.82) {
		tmp = t_3;
	} else if (x1 <= 0.7) {
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))));
	} else if (x1 <= 4.4e+153) {
		tmp = t_3;
	} else {
		tmp = x1 - t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = (x1 - (t_0 + (2.0d0 * x2))) / t_1
    t_3 = x1 + (9.0d0 - ((((t_1 * (((x1 * x1) * (6.0d0 + (4.0d0 * t_2))) + ((((2.0d0 * (x2 / x1)) + ((-1.0d0) - (3.0d0 / x1))) / x1) * ((x1 * 2.0d0) * t_2)))) - (t_0 * (2.0d0 * x2))) - (x1 * (x1 * x1))) - x1))
    t_4 = x1 * (2.0d0 - (x1 * 9.0d0))
    if (x1 <= (-9.5d+115)) then
        tmp = x1 - (x2 * (6.0d0 + (t_4 / x2)))
    else if (x1 <= (-0.82d0)) then
        tmp = t_3
    else if (x1 <= 0.7d0) then
        tmp = (x2 * (-6.0d0)) + ((x1 * ((-1.0d0) + (x1 * 9.0d0))) + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 12.0d0) - 12.0d0)))))
    else if (x1 <= 4.4d+153) then
        tmp = t_3
    else
        tmp = x1 - t_4
    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 = (x1 - (t_0 + (2.0 * x2))) / t_1;
	double t_3 = x1 + (9.0 - ((((t_1 * (((x1 * x1) * (6.0 + (4.0 * t_2))) + ((((2.0 * (x2 / x1)) + (-1.0 - (3.0 / x1))) / x1) * ((x1 * 2.0) * t_2)))) - (t_0 * (2.0 * x2))) - (x1 * (x1 * x1))) - x1));
	double t_4 = x1 * (2.0 - (x1 * 9.0));
	double tmp;
	if (x1 <= -9.5e+115) {
		tmp = x1 - (x2 * (6.0 + (t_4 / x2)));
	} else if (x1 <= -0.82) {
		tmp = t_3;
	} else if (x1 <= 0.7) {
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))));
	} else if (x1 <= 4.4e+153) {
		tmp = t_3;
	} else {
		tmp = x1 - t_4;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = (x1 - (t_0 + (2.0 * x2))) / t_1
	t_3 = x1 + (9.0 - ((((t_1 * (((x1 * x1) * (6.0 + (4.0 * t_2))) + ((((2.0 * (x2 / x1)) + (-1.0 - (3.0 / x1))) / x1) * ((x1 * 2.0) * t_2)))) - (t_0 * (2.0 * x2))) - (x1 * (x1 * x1))) - x1))
	t_4 = x1 * (2.0 - (x1 * 9.0))
	tmp = 0
	if x1 <= -9.5e+115:
		tmp = x1 - (x2 * (6.0 + (t_4 / x2)))
	elif x1 <= -0.82:
		tmp = t_3
	elif x1 <= 0.7:
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))))
	elif x1 <= 4.4e+153:
		tmp = t_3
	else:
		tmp = x1 - t_4
	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(x1 - Float64(t_0 + Float64(2.0 * x2))) / t_1)
	t_3 = Float64(x1 + Float64(9.0 - Float64(Float64(Float64(Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_2))) + Float64(Float64(Float64(Float64(2.0 * Float64(x2 / x1)) + Float64(-1.0 - Float64(3.0 / x1))) / x1) * Float64(Float64(x1 * 2.0) * t_2)))) - Float64(t_0 * Float64(2.0 * x2))) - Float64(x1 * Float64(x1 * x1))) - x1)))
	t_4 = Float64(x1 * Float64(2.0 - Float64(x1 * 9.0)))
	tmp = 0.0
	if (x1 <= -9.5e+115)
		tmp = Float64(x1 - Float64(x2 * Float64(6.0 + Float64(t_4 / x2))));
	elseif (x1 <= -0.82)
		tmp = t_3;
	elseif (x1 <= 0.7)
		tmp = Float64(Float64(x2 * -6.0) + Float64(Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))) + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 12.0) - 12.0))))));
	elseif (x1 <= 4.4e+153)
		tmp = t_3;
	else
		tmp = Float64(x1 - t_4);
	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 = (x1 - (t_0 + (2.0 * x2))) / t_1;
	t_3 = x1 + (9.0 - ((((t_1 * (((x1 * x1) * (6.0 + (4.0 * t_2))) + ((((2.0 * (x2 / x1)) + (-1.0 - (3.0 / x1))) / x1) * ((x1 * 2.0) * t_2)))) - (t_0 * (2.0 * x2))) - (x1 * (x1 * x1))) - x1));
	t_4 = x1 * (2.0 - (x1 * 9.0));
	tmp = 0.0;
	if (x1 <= -9.5e+115)
		tmp = x1 - (x2 * (6.0 + (t_4 / x2)));
	elseif (x1 <= -0.82)
		tmp = t_3;
	elseif (x1 <= 0.7)
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))));
	elseif (x1 <= 4.4e+153)
		tmp = t_3;
	else
		tmp = x1 - t_4;
	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[(x1 - N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(9.0 - N[(N[(N[(N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(2.0 * N[(x2 / x1), $MachinePrecision]), $MachinePrecision] + N[(-1.0 - N[(3.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$0 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -9.5e+115], N[(x1 - N[(x2 * N[(6.0 + N[(t$95$4 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -0.82], t$95$3, If[LessEqual[x1, 0.7], N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 12.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.4e+153], t$95$3, N[(x1 - t$95$4), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -9.4999999999999997e115

   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 32.5%

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

   5. Taylor expanded in x1 around 0 44.8%

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

   6. Taylor expanded in x2 around 0 70.2%

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

   7. Taylor expanded in x2 around inf 95.4%

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

   if -9.4999999999999997e115 < x1 < -0.819999999999999951 or 0.69999999999999996 < x1 < 4.3999999999999999e153

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around inf 98.4%

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

   4. Taylor expanded in x1 around 0 92.1%

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

   5. Taylor expanded in x1 around inf 92.1%

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

      1. associate-*r/ 97.9%

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

      2. metadata-eval 97.9%

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

   7. Simplified 92.1%

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

   if -0.819999999999999951 < x1 < 0.69999999999999996

   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 89.6%

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

   5. Taylor expanded in x1 around 0 89.7%

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

   6. Taylor expanded in x2 around 0 99.9%

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

   if 4.3999999999999999e153 < 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%

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

   5. Taylor expanded in x1 around 0 70.7%

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

   6. Taylor expanded in x2 around 0 100.0%

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

   7. Taylor expanded in x2 around 0 100.0%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+115}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \mathbf{elif}\;x1 \leq -0.82:\\ \;\;\;\;x1 + \left(9 - \left(\left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) + \frac{2 \cdot \frac{x2}{x1} + \left(-1 - \frac{3}{x1}\right)}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right) - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 0.7:\\ \;\;\;\;x2 \cdot -6 + \left(x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 - \left(\left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) + \frac{2 \cdot \frac{x2}{x1} + \left(-1 - \frac{3}{x1}\right)}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right) - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - x1 \cdot \left(2 - x1 \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 90.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := x1 \cdot \left(2 - x1 \cdot 9\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := t\_3 + 2 \cdot x2\\ t_5 := t\_3 \cdot \left(2 \cdot x2\right)\\ t_6 := \frac{x1 - t\_4}{t\_0}\\ t_7 := \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_6\right)\\ \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+115}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{t\_2}{x2}\right)\\ \mathbf{elif}\;x1 \leq -550:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(t\_1 + \left(t\_5 - t\_0 \cdot \left(t\_7 + \frac{-1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot t\_6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{-18}:\\ \;\;\;\;x2 \cdot -6 + \left(x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(t\_1 + \left(t\_5 + t\_0 \cdot \left(\left(\frac{t\_4 - x1}{t\_0} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2\right)\right) - t\_7\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 x1)))
        (t_2 (* x1 (- 2.0 (* x1 9.0))))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (+ t_3 (* 2.0 x2)))
        (t_5 (* t_3 (* 2.0 x2)))
        (t_6 (/ (- x1 t_4) t_0))
        (t_7 (* (* x1 x1) (+ 6.0 (* 4.0 t_6)))))
   (if (<= x1 -9.5e+115)
     (- x1 (* x2 (+ 6.0 (/ t_2 x2))))
     (if (<= x1 -550.0)
       (+
        x1
        (+
         9.0
         (+
          x1
          (+ t_1 (- t_5 (* t_0 (+ t_7 (* (/ -1.0 x1) (* (* x1 2.0) t_6)))))))))
       (if (<= x1 4e-18)
         (+
          (* x2 -6.0)
          (+
           (* x1 (+ -1.0 (* x1 9.0)))
           (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 12.0) 12.0))))))
         (if (<= x1 4.4e+153)
           (+
            x1
            (+
             9.0
             (+
              x1
              (+
               t_1
               (+
                t_5
                (*
                 t_0
                 (-
                  (* (- (/ (- t_4 x1) t_0) 3.0) (* (* x1 2.0) (* 2.0 x2)))
                  t_7)))))))
           (- x1 t_2)))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * x1);
	double t_2 = x1 * (2.0 - (x1 * 9.0));
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = t_3 + (2.0 * x2);
	double t_5 = t_3 * (2.0 * x2);
	double t_6 = (x1 - t_4) / t_0;
	double t_7 = (x1 * x1) * (6.0 + (4.0 * t_6));
	double tmp;
	if (x1 <= -9.5e+115) {
		tmp = x1 - (x2 * (6.0 + (t_2 / x2)));
	} else if (x1 <= -550.0) {
		tmp = x1 + (9.0 + (x1 + (t_1 + (t_5 - (t_0 * (t_7 + ((-1.0 / x1) * ((x1 * 2.0) * t_6))))))));
	} else if (x1 <= 4e-18) {
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))));
	} else if (x1 <= 4.4e+153) {
		tmp = x1 + (9.0 + (x1 + (t_1 + (t_5 + (t_0 * (((((t_4 - x1) / t_0) - 3.0) * ((x1 * 2.0) * (2.0 * x2))) - t_7))))));
	} else {
		tmp = x1 - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * (x1 * x1)
    t_2 = x1 * (2.0d0 - (x1 * 9.0d0))
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = t_3 + (2.0d0 * x2)
    t_5 = t_3 * (2.0d0 * x2)
    t_6 = (x1 - t_4) / t_0
    t_7 = (x1 * x1) * (6.0d0 + (4.0d0 * t_6))
    if (x1 <= (-9.5d+115)) then
        tmp = x1 - (x2 * (6.0d0 + (t_2 / x2)))
    else if (x1 <= (-550.0d0)) then
        tmp = x1 + (9.0d0 + (x1 + (t_1 + (t_5 - (t_0 * (t_7 + (((-1.0d0) / x1) * ((x1 * 2.0d0) * t_6))))))))
    else if (x1 <= 4d-18) then
        tmp = (x2 * (-6.0d0)) + ((x1 * ((-1.0d0) + (x1 * 9.0d0))) + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 12.0d0) - 12.0d0)))))
    else if (x1 <= 4.4d+153) then
        tmp = x1 + (9.0d0 + (x1 + (t_1 + (t_5 + (t_0 * (((((t_4 - x1) / t_0) - 3.0d0) * ((x1 * 2.0d0) * (2.0d0 * x2))) - t_7))))))
    else
        tmp = x1 - t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * x1);
	double t_2 = x1 * (2.0 - (x1 * 9.0));
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = t_3 + (2.0 * x2);
	double t_5 = t_3 * (2.0 * x2);
	double t_6 = (x1 - t_4) / t_0;
	double t_7 = (x1 * x1) * (6.0 + (4.0 * t_6));
	double tmp;
	if (x1 <= -9.5e+115) {
		tmp = x1 - (x2 * (6.0 + (t_2 / x2)));
	} else if (x1 <= -550.0) {
		tmp = x1 + (9.0 + (x1 + (t_1 + (t_5 - (t_0 * (t_7 + ((-1.0 / x1) * ((x1 * 2.0) * t_6))))))));
	} else if (x1 <= 4e-18) {
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))));
	} else if (x1 <= 4.4e+153) {
		tmp = x1 + (9.0 + (x1 + (t_1 + (t_5 + (t_0 * (((((t_4 - x1) / t_0) - 3.0) * ((x1 * 2.0) * (2.0 * x2))) - t_7))))));
	} else {
		tmp = x1 - t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * x1)
	t_2 = x1 * (2.0 - (x1 * 9.0))
	t_3 = x1 * (x1 * 3.0)
	t_4 = t_3 + (2.0 * x2)
	t_5 = t_3 * (2.0 * x2)
	t_6 = (x1 - t_4) / t_0
	t_7 = (x1 * x1) * (6.0 + (4.0 * t_6))
	tmp = 0
	if x1 <= -9.5e+115:
		tmp = x1 - (x2 * (6.0 + (t_2 / x2)))
	elif x1 <= -550.0:
		tmp = x1 + (9.0 + (x1 + (t_1 + (t_5 - (t_0 * (t_7 + ((-1.0 / x1) * ((x1 * 2.0) * t_6))))))))
	elif x1 <= 4e-18:
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))))
	elif x1 <= 4.4e+153:
		tmp = x1 + (9.0 + (x1 + (t_1 + (t_5 + (t_0 * (((((t_4 - x1) / t_0) - 3.0) * ((x1 * 2.0) * (2.0 * x2))) - t_7))))))
	else:
		tmp = x1 - t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(x1 * x1))
	t_2 = Float64(x1 * Float64(2.0 - Float64(x1 * 9.0)))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(t_3 + Float64(2.0 * x2))
	t_5 = Float64(t_3 * Float64(2.0 * x2))
	t_6 = Float64(Float64(x1 - t_4) / t_0)
	t_7 = Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_6)))
	tmp = 0.0
	if (x1 <= -9.5e+115)
		tmp = Float64(x1 - Float64(x2 * Float64(6.0 + Float64(t_2 / x2))));
	elseif (x1 <= -550.0)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_1 + Float64(t_5 - Float64(t_0 * Float64(t_7 + Float64(Float64(-1.0 / x1) * Float64(Float64(x1 * 2.0) * t_6)))))))));
	elseif (x1 <= 4e-18)
		tmp = Float64(Float64(x2 * -6.0) + Float64(Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))) + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 12.0) - 12.0))))));
	elseif (x1 <= 4.4e+153)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_1 + Float64(t_5 + Float64(t_0 * Float64(Float64(Float64(Float64(Float64(t_4 - x1) / t_0) - 3.0) * Float64(Float64(x1 * 2.0) * Float64(2.0 * x2))) - t_7)))))));
	else
		tmp = Float64(x1 - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * x1);
	t_2 = x1 * (2.0 - (x1 * 9.0));
	t_3 = x1 * (x1 * 3.0);
	t_4 = t_3 + (2.0 * x2);
	t_5 = t_3 * (2.0 * x2);
	t_6 = (x1 - t_4) / t_0;
	t_7 = (x1 * x1) * (6.0 + (4.0 * t_6));
	tmp = 0.0;
	if (x1 <= -9.5e+115)
		tmp = x1 - (x2 * (6.0 + (t_2 / x2)));
	elseif (x1 <= -550.0)
		tmp = x1 + (9.0 + (x1 + (t_1 + (t_5 - (t_0 * (t_7 + ((-1.0 / x1) * ((x1 * 2.0) * t_6))))))));
	elseif (x1 <= 4e-18)
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))));
	elseif (x1 <= 4.4e+153)
		tmp = x1 + (9.0 + (x1 + (t_1 + (t_5 + (t_0 * (((((t_4 - x1) / t_0) - 3.0) * ((x1 * 2.0) * (2.0 * x2))) - t_7))))));
	else
		tmp = x1 - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$3 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 - t$95$4), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -9.5e+115], N[(x1 - N[(x2 * N[(6.0 + N[(t$95$2 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -550.0], N[(x1 + N[(9.0 + N[(x1 + N[(t$95$1 + N[(t$95$5 - N[(t$95$0 * N[(t$95$7 + N[(N[(-1.0 / x1), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4e-18], N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 12.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.4e+153], N[(x1 + N[(9.0 + N[(x1 + N[(t$95$1 + N[(t$95$5 + N[(t$95$0 * N[(N[(N[(N[(N[(t$95$4 - x1), $MachinePrecision] / t$95$0), $MachinePrecision] - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 - t$95$2), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -9.4999999999999997e115

   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 32.5%

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

   5. Taylor expanded in x1 around 0 44.8%

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

   6. Taylor expanded in x2 around 0 70.2%

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

   7. Taylor expanded in x2 around inf 95.4%

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

   if -9.4999999999999997e115 < x1 < -550

   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 99.2%

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

   4. Taylor expanded in x1 around 0 91.0%

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

   5. Taylor expanded in x1 around inf 88.9%

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

   if -550 < x1 < 4.0000000000000003e-18

   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 89.4%

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

   5. Taylor expanded in x1 around 0 89.5%

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

   6. Taylor expanded in x2 around 0 99.9%

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

   if 4.0000000000000003e-18 < x1 < 4.3999999999999999e153

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around inf 98.0%

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

   4. Taylor expanded in x1 around 0 93.0%

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

   5. Taylor expanded in x1 around 0 86.6%

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

   if 4.3999999999999999e153 < 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%

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

   5. Taylor expanded in x1 around 0 70.7%

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

   6. Taylor expanded in x2 around 0 100.0%

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

   7. Taylor expanded in x2 around 0 100.0%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+115}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \mathbf{elif}\;x1 \leq -550:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right) - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) + \frac{-1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{-18}:\\ \;\;\;\;x2 \cdot -6 + \left(x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2\right)\right) - \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - x1 \cdot \left(2 - x1 \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 91.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(2 - x1 \cdot 9\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \frac{x1 - \left(t\_2 + 2 \cdot x2\right)}{t\_0}\\ t_4 := x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_2 \cdot \left(2 \cdot x2\right) - t\_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_3\right) + \frac{-1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot t\_3\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+115}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{t\_1}{x2}\right)\\ \mathbf{elif}\;x1 \leq -400:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x1 \leq 450000:\\ \;\;\;\;x2 \cdot -6 + \left(x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.4 \cdot 10^{+153}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;x1 - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (- 2.0 (* x1 9.0))))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (/ (- x1 (+ t_2 (* 2.0 x2))) t_0))
        (t_4
         (+
          x1
          (+
           9.0
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (-
              (* t_2 (* 2.0 x2))
              (*
               t_0
               (+
                (* (* x1 x1) (+ 6.0 (* 4.0 t_3)))
                (* (/ -1.0 x1) (* (* x1 2.0) t_3)))))))))))
   (if (<= x1 -9.5e+115)
     (- x1 (* x2 (+ 6.0 (/ t_1 x2))))
     (if (<= x1 -400.0)
       t_4
       (if (<= x1 450000.0)
         (+
          (* x2 -6.0)
          (+
           (* x1 (+ -1.0 (* x1 9.0)))
           (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 12.0) 12.0))))))
         (if (<= x1 4.4e+153) t_4 (- x1 t_1)))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (2.0 - (x1 * 9.0));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = (x1 - (t_2 + (2.0 * x2))) / t_0;
	double t_4 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * (2.0 * x2)) - (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_3))) + ((-1.0 / x1) * ((x1 * 2.0) * t_3))))))));
	double tmp;
	if (x1 <= -9.5e+115) {
		tmp = x1 - (x2 * (6.0 + (t_1 / x2)));
	} else if (x1 <= -400.0) {
		tmp = t_4;
	} else if (x1 <= 450000.0) {
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))));
	} else if (x1 <= 4.4e+153) {
		tmp = t_4;
	} else {
		tmp = x1 - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * (2.0d0 - (x1 * 9.0d0))
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = (x1 - (t_2 + (2.0d0 * x2))) / t_0
    t_4 = x1 + (9.0d0 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * (2.0d0 * x2)) - (t_0 * (((x1 * x1) * (6.0d0 + (4.0d0 * t_3))) + (((-1.0d0) / x1) * ((x1 * 2.0d0) * t_3))))))))
    if (x1 <= (-9.5d+115)) then
        tmp = x1 - (x2 * (6.0d0 + (t_1 / x2)))
    else if (x1 <= (-400.0d0)) then
        tmp = t_4
    else if (x1 <= 450000.0d0) then
        tmp = (x2 * (-6.0d0)) + ((x1 * ((-1.0d0) + (x1 * 9.0d0))) + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 12.0d0) - 12.0d0)))))
    else if (x1 <= 4.4d+153) then
        tmp = t_4
    else
        tmp = x1 - t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (2.0 - (x1 * 9.0));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = (x1 - (t_2 + (2.0 * x2))) / t_0;
	double t_4 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * (2.0 * x2)) - (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_3))) + ((-1.0 / x1) * ((x1 * 2.0) * t_3))))))));
	double tmp;
	if (x1 <= -9.5e+115) {
		tmp = x1 - (x2 * (6.0 + (t_1 / x2)));
	} else if (x1 <= -400.0) {
		tmp = t_4;
	} else if (x1 <= 450000.0) {
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))));
	} else if (x1 <= 4.4e+153) {
		tmp = t_4;
	} else {
		tmp = x1 - t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (2.0 - (x1 * 9.0))
	t_2 = x1 * (x1 * 3.0)
	t_3 = (x1 - (t_2 + (2.0 * x2))) / t_0
	t_4 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * (2.0 * x2)) - (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_3))) + ((-1.0 / x1) * ((x1 * 2.0) * t_3))))))))
	tmp = 0
	if x1 <= -9.5e+115:
		tmp = x1 - (x2 * (6.0 + (t_1 / x2)))
	elif x1 <= -400.0:
		tmp = t_4
	elif x1 <= 450000.0:
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))))
	elif x1 <= 4.4e+153:
		tmp = t_4
	else:
		tmp = x1 - t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(2.0 - Float64(x1 * 9.0)))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(x1 - Float64(t_2 + Float64(2.0 * x2))) / t_0)
	t_4 = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_2 * Float64(2.0 * x2)) - Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_3))) + Float64(Float64(-1.0 / x1) * Float64(Float64(x1 * 2.0) * t_3)))))))))
	tmp = 0.0
	if (x1 <= -9.5e+115)
		tmp = Float64(x1 - Float64(x2 * Float64(6.0 + Float64(t_1 / x2))));
	elseif (x1 <= -400.0)
		tmp = t_4;
	elseif (x1 <= 450000.0)
		tmp = Float64(Float64(x2 * -6.0) + Float64(Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))) + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 12.0) - 12.0))))));
	elseif (x1 <= 4.4e+153)
		tmp = t_4;
	else
		tmp = Float64(x1 - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (2.0 - (x1 * 9.0));
	t_2 = x1 * (x1 * 3.0);
	t_3 = (x1 - (t_2 + (2.0 * x2))) / t_0;
	t_4 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * (2.0 * x2)) - (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_3))) + ((-1.0 / x1) * ((x1 * 2.0) * t_3))))))));
	tmp = 0.0;
	if (x1 <= -9.5e+115)
		tmp = x1 - (x2 * (6.0 + (t_1 / x2)));
	elseif (x1 <= -400.0)
		tmp = t_4;
	elseif (x1 <= 450000.0)
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 12.0) - 12.0)))));
	elseif (x1 <= 4.4e+153)
		tmp = t_4;
	else
		tmp = x1 - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 - N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(9.0 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-1.0 / x1), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -9.5e+115], N[(x1 - N[(x2 * N[(6.0 + N[(t$95$1 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -400.0], t$95$4, If[LessEqual[x1, 450000.0], N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 12.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.4e+153], t$95$4, N[(x1 - t$95$1), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -9.4999999999999997e115

   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 32.5%

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

   5. Taylor expanded in x1 around 0 44.8%

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

   6. Taylor expanded in x2 around 0 70.2%

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

   7. Taylor expanded in x2 around inf 95.4%

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

   if -9.4999999999999997e115 < x1 < -400 or 4.5e5 < x1 < 4.3999999999999999e153

   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 99.3%

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

   4. Taylor expanded in x1 around 0 93.6%

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

   5. Taylor expanded in x1 around inf 87.4%

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

   if -400 < x1 < 4.5e5

   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 89.8%

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

   5. Taylor expanded in x1 around 0 88.5%

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

   6. Taylor expanded in x2 around 0 98.4%

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

   if 4.3999999999999999e153 < 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%

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

   5. Taylor expanded in x1 around 0 70.7%

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

   6. Taylor expanded in x2 around 0 100.0%

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

   7. Taylor expanded in x2 around 0 100.0%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+115}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \mathbf{elif}\;x1 \leq -400:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right) - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) + \frac{-1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 450000:\\ \;\;\;\;x2 \cdot -6 + \left(x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 12 - 12\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right) - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) + \frac{-1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - x1 \cdot \left(2 - x1 \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 82.2% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.7 \cdot 10^{+34} \lor \neg \left(x1 \leq 2.95 \cdot 10^{+116}\right):\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot -12\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -1.7e+34) (not (<= x1 2.95e+116)))
   (- x1 (* x2 (+ 6.0 (/ (* x1 (- 2.0 (* x1 9.0))) x2))))
   (+
    x1
    (+
     (* x2 -6.0)
     (+
      (* x1 (- (* x1 9.0) 2.0))
      (* x2 (+ (* 8.0 (* x1 x2)) (* x1 -12.0))))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -1.7e+34) || !(x1 <= 2.95e+116)) {
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	} else {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * -12.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-1.7d+34)) .or. (.not. (x1 <= 2.95d+116))) then
        tmp = x1 - (x2 * (6.0d0 + ((x1 * (2.0d0 - (x1 * 9.0d0))) / x2)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + ((x1 * ((x1 * 9.0d0) - 2.0d0)) + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * (-12.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -1.7e+34) || !(x1 <= 2.95e+116)) {
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	} else {
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * -12.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -1.7e+34) or not (x1 <= 2.95e+116):
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)))
	else:
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * -12.0)))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -1.7e+34) || !(x1 <= 2.95e+116))
		tmp = Float64(x1 - Float64(x2 * Float64(6.0 + Float64(Float64(x1 * Float64(2.0 - Float64(x1 * 9.0))) / x2))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0)) + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * -12.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -1.7e+34) || ~((x1 <= 2.95e+116)))
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	else
		tmp = x1 + ((x2 * -6.0) + ((x1 * ((x1 * 9.0) - 2.0)) + (x2 * ((8.0 * (x1 * x2)) + (x1 * -12.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -1.7e+34], N[Not[LessEqual[x1, 2.95e+116]], $MachinePrecision]], N[(x1 - N[(x2 * N[(6.0 + N[(N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.7e34 or 2.95e116 < x1

   1. Initial program 24.2%

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

   3. Simplified 36.4%

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

   5. Taylor expanded in x1 around 0 46.0%

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

   6. Taylor expanded in x2 around 0 66.0%

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

   7. Taylor expanded in x2 around inf 84.9%

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

   if -1.7e34 < x1 < 2.95e116

   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 91.5%

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

   5. Taylor expanded in x1 around 0 76.7%

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

   6. Taylor expanded in x2 around inf 76.7%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + \color{blue}{x2 \cdot \left(9 \cdot \frac{x1}{x2} + 12 \cdot x1\right)}\right) - 2\right)\right) \]

   7. Taylor expanded in x2 around 0 76.8%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + x2 \cdot \color{blue}{\left(9 \cdot \frac{x1}{x2}\right)}\right) - 2\right)\right) \]
   8. Step-by-step derivation

      1. associate-*r/ 76.8%

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

      2. *-commutative 76.8%

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

      3. associate-*r/ 76.8%

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

   9. Simplified 76.8%

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

   10. Taylor expanded in x2 around 0 84.9%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.7 \cdot 10^{+34} \lor \neg \left(x1 \leq 2.95 \cdot 10^{+116}\right):\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot -12\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 75.2% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -7 \cdot 10^{+15} \lor \neg \left(x1 \leq 3.6 \cdot 10^{+114}\right):\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -7e+15) (not (<= x1 3.6e+114)))
   (- x1 (* x2 (+ 6.0 (/ (* x1 (- 2.0 (* x1 9.0))) x2))))
   (- (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))) -1.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -7e+15) || !(x1 <= 3.6e+114)) {
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	} else {
		tmp = (x2 * -6.0) - (x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - -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 ((x1 <= (-7d+15)) .or. (.not. (x1 <= 3.6d+114))) then
        tmp = x1 - (x2 * (6.0d0 + ((x1 * (2.0d0 - (x1 * 9.0d0))) / x2)))
    else
        tmp = (x2 * (-6.0d0)) - (x1 * ((4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))) - (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -7e+15) || !(x1 <= 3.6e+114)) {
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	} else {
		tmp = (x2 * -6.0) - (x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - -1.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -7e+15) or not (x1 <= 3.6e+114):
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)))
	else:
		tmp = (x2 * -6.0) - (x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - -1.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -7e+15) || !(x1 <= 3.6e+114))
		tmp = Float64(x1 - Float64(x2 * Float64(6.0 + Float64(Float64(x1 * Float64(2.0 - Float64(x1 * 9.0))) / x2))));
	else
		tmp = Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))) - -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -7e+15) || ~((x1 <= 3.6e+114)))
		tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
	else
		tmp = (x2 * -6.0) - (x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -7e+15], N[Not[LessEqual[x1, 3.6e+114]], $MachinePrecision]], N[(x1 - N[(x2 * N[(6.0 + N[(N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -7e15 or 3.6000000000000001e114 < x1

   1. Initial program 25.6%

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

   3. Simplified 37.5%

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

   5. Taylor expanded in x1 around 0 45.3%

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

   6. Taylor expanded in x2 around 0 64.9%

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

   7. Taylor expanded in x2 around inf 83.5%

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

   if -7e15 < x1 < 3.6000000000000001e114

   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 99.4%

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

   5. Taylor expanded in x1 around 0 76.8%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7 \cdot 10^{+15} \lor \neg \left(x1 \leq 3.6 \cdot 10^{+114}\right):\\ \;\;\;\;x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 62.7% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.8 \cdot 10^{-14} \lor \neg \left(x1 \leq 6 \cdot 10^{-16}\right):\\ \;\;\;\;x1 - x1 \cdot \left(2 - x1 \cdot 9\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -2.8e-14) (not (<= x1 6e-16)))
   (- x1 (* x1 (- 2.0 (* x1 9.0))))
   (- (* x2 -6.0) x1)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -2.8e-14) || !(x1 <= 6e-16)) {
		tmp = x1 - (x1 * (2.0 - (x1 * 9.0)));
	} else {
		tmp = (x2 * -6.0) - x1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-2.8d-14)) .or. (.not. (x1 <= 6d-16))) then
        tmp = x1 - (x1 * (2.0d0 - (x1 * 9.0d0)))
    else
        tmp = (x2 * (-6.0d0)) - x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -2.8e-14) || !(x1 <= 6e-16)) {
		tmp = x1 - (x1 * (2.0 - (x1 * 9.0)));
	} else {
		tmp = (x2 * -6.0) - x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -2.8e-14) or not (x1 <= 6e-16):
		tmp = x1 - (x1 * (2.0 - (x1 * 9.0)))
	else:
		tmp = (x2 * -6.0) - x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -2.8e-14) || !(x1 <= 6e-16))
		tmp = Float64(x1 - Float64(x1 * Float64(2.0 - Float64(x1 * 9.0))));
	else
		tmp = Float64(Float64(x2 * -6.0) - x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -2.8e-14) || ~((x1 <= 6e-16)))
		tmp = x1 - (x1 * (2.0 - (x1 * 9.0)));
	else
		tmp = (x2 * -6.0) - x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -2.8e-14], N[Not[LessEqual[x1, 6e-16]], $MachinePrecision]], N[(x1 - N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -2.8000000000000001e-14 or 5.99999999999999987e-16 < x1

   1. Initial program 41.9%

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

   3. Simplified 51.2%

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

   5. Taylor expanded in x1 around 0 42.8%

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

   6. Taylor expanded in x2 around 0 53.1%

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

   7. Taylor expanded in x2 around 0 53.2%

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

   if -2.8000000000000001e-14 < x1 < 5.99999999999999987e-16

   1. Initial program 99.5%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in x1 around 0 89.4%

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

   6. Taylor expanded in x2 around 0 76.7%

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

   7. Taylor expanded in x1 around 0 76.7%

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

      1. *-commutative 76.7%

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

      2. mul-1-neg 76.7%

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

      3. unsub-neg 76.7%

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

   9. Simplified 76.7%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.8 \cdot 10^{-14} \lor \neg \left(x1 \leq 6 \cdot 10^{-16}\right):\\ \;\;\;\;x1 - x1 \cdot \left(2 - x1 \cdot 9\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 67.3% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right) \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (- x1 (* x2 (+ 6.0 (/ (* x1 (- 2.0 (* x1 9.0))) x2)))))

C

double code(double x1, double x2) {
	return x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x1 - (x2 * (6.0d0 + ((x1 * (2.0d0 - (x1 * 9.0d0))) / x2)))
end function

Java

public static double code(double x1, double x2) {
	return x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
}

Python

def code(x1, x2):
	return x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)))

Julia

function code(x1, x2)
	return Float64(x1 - Float64(x2 * Float64(6.0 + Float64(Float64(x1 * Float64(2.0 - Float64(x1 * 9.0))) / x2))))
end

MATLAB

function tmp = code(x1, x2)
	tmp = x1 - (x2 * (6.0 + ((x1 * (2.0 - (x1 * 9.0))) / x2)));
end

Wolfram

code[x1_, x2_] := N[(x1 - N[(x2 * N[(6.0 + N[(N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 68.0%

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

3. Simplified 68.5%

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

5. Taylor expanded in x1 around 0 63.9%

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

6. Taylor expanded in x2 around 0 63.8%

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

7. Taylor expanded in x2 around inf 71.7%

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

8. Final simplification 71.7%

   \[\leadsto x1 - x2 \cdot \left(6 + \frac{x1 \cdot \left(2 - x1 \cdot 9\right)}{x2}\right) \]
9. Add Preprocessing

Alternative 18: 62.8% accurate, 11.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.0%

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

3. Simplified 68.5%

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

5. Taylor expanded in x1 around 0 63.9%

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

6. Taylor expanded in x2 around 0 63.8%

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

7. Taylor expanded in x1 around 0 63.8%

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

8. Final simplification 63.8%

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

Alternative 19: 36.9% 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 68.0%

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

3. Simplified 68.5%

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

5. Taylor expanded in x1 around 0 63.9%

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

6. Taylor expanded in x2 around 0 63.8%

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

7. Taylor expanded in x1 around 0 36.9%

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

   1. *-commutative 36.9%

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

   2. mul-1-neg 36.9%

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

   3. unsub-neg 36.9%

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

9. Simplified 36.9%

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

Alternative 20: 25.5% 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 68.0%

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

3. Simplified 68.0%

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

5. Taylor expanded in x1 around 0 25.5%

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

   1. *-commutative 25.5%

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

7. Simplified 25.5%

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

Alternative 21: 3.4% accurate, 127.0× speedup

Math

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

FPCore

(FPCore (x1 x2) :precision binary64 9.0)

C

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

Fortran

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

Java

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

Python

def code(x1, x2):
	return 9.0

Julia

function code(x1, x2)
	return 9.0
end

MATLAB

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

Wolfram

code[x1_, x2_] := 9.0

Derivation

1. Initial program 68.0%

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

3. Taylor expanded in x1 around inf 34.5%

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

4. Taylor expanded in x1 around inf 50.1%

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

   1. *-commutative 50.1%

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

6. Simplified 50.1%

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

7. Taylor expanded in x1 around 0 3.7%

   \[\leadsto \color{blue}{9} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024157 
(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))))))