Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 69.8% → 99.5%

Time: 1.0min

Alternatives: 20

Speedup: 1.3×

• 46.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 69.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right)\\ t_3 := \frac{t_2 - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\\ t_4 := \frac{x1 - t_2}{\mathsf{fma}\left(x1, x1, 1\right)}\\ t_5 := t_0 + 2 \cdot x2\\ t_6 := \frac{t_5 - x1}{t_1}\\ t_7 := 3 \cdot \left(x1 \cdot x1\right)\\ \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(\left(\left(t_6 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - t_5}{t_1}\right) - \left(x1 \cdot x1\right) \cdot \left(t_6 \cdot 4 - 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + t_0 \cdot t_6\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_1}\right) \leq \infty:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{t_7 - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 + \mathsf{fma}\left(\mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot \mathsf{fma}\left(t_3, 4, -6\right), \left(x1 \cdot \left(2 \cdot t_4\right)\right) \cdot \left(t_4 - -3\right)\right), \mathsf{fma}\left(t_7, t_3, {x1}^{3}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (fma x1 (* x1 3.0) (* 2.0 x2)))
        (t_3 (/ (- t_2 x1) (fma x1 x1 1.0)))
        (t_4 (/ (- x1 t_2) (fma x1 x1 1.0)))
        (t_5 (+ t_0 (* 2.0 x2)))
        (t_6 (/ (- t_5 x1) t_1))
        (t_7 (* 3.0 (* x1 x1))))
   (if (<=
        (+
         x1
         (+
          (+
           x1
           (+
            (+
             (*
              (-
               (* (- t_6 3.0) (* (* x1 2.0) (/ (- x1 t_5) t_1)))
               (* (* x1 x1) (- (* t_6 4.0) 6.0)))
              (- -1.0 (* x1 x1)))
             (* t_0 t_6))
            (* x1 (* x1 x1))))
          (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))))
        INFINITY)
     (+
      x1
      (fma
       3.0
       (/ (- t_7 (fma 2.0 x2 x1)) (fma x1 x1 1.0))
       (+
        x1
        (fma
         (fma x1 x1 1.0)
         (fma x1 (* x1 (fma t_3 4.0 -6.0)) (* (* x1 (* 2.0 t_4)) (- t_4 -3.0)))
         (fma t_7 t_3 (pow x1 3.0))))))
     (pow (pow (fma x2 -6.0 x1) 3.0) 0.3333333333333333))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = fma(x1, (x1 * 3.0), (2.0 * x2));
	double t_3 = (t_2 - x1) / fma(x1, x1, 1.0);
	double t_4 = (x1 - t_2) / fma(x1, x1, 1.0);
	double t_5 = t_0 + (2.0 * x2);
	double t_6 = (t_5 - x1) / t_1;
	double t_7 = 3.0 * (x1 * x1);
	double tmp;
	if ((x1 + ((x1 + ((((((t_6 - 3.0) * ((x1 * 2.0) * ((x1 - t_5) / t_1))) - ((x1 * x1) * ((t_6 * 4.0) - 6.0))) * (-1.0 - (x1 * x1))) + (t_0 * t_6)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)))) <= ((double) INFINITY)) {
		tmp = x1 + fma(3.0, ((t_7 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), (x1 + fma(fma(x1, x1, 1.0), fma(x1, (x1 * fma(t_3, 4.0, -6.0)), ((x1 * (2.0 * t_4)) * (t_4 - -3.0))), fma(t_7, t_3, pow(x1, 3.0)))));
	} else {
		tmp = pow(pow(fma(x2, -6.0, x1), 3.0), 0.3333333333333333);
	}
	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 = fma(x1, Float64(x1 * 3.0), Float64(2.0 * x2))
	t_3 = Float64(Float64(t_2 - x1) / fma(x1, x1, 1.0))
	t_4 = Float64(Float64(x1 - t_2) / fma(x1, x1, 1.0))
	t_5 = Float64(t_0 + Float64(2.0 * x2))
	t_6 = Float64(Float64(t_5 - x1) / t_1)
	t_7 = Float64(3.0 * Float64(x1 * x1))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(t_6 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(Float64(x1 - t_5) / t_1))) - Float64(Float64(x1 * x1) * Float64(Float64(t_6 * 4.0) - 6.0))) * Float64(-1.0 - Float64(x1 * x1))) + Float64(t_0 * t_6)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1)))) <= Inf)
		tmp = Float64(x1 + fma(3.0, Float64(Float64(t_7 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), Float64(x1 + fma(fma(x1, x1, 1.0), fma(x1, Float64(x1 * fma(t_3, 4.0, -6.0)), Float64(Float64(x1 * Float64(2.0 * t_4)) * Float64(t_4 - -3.0))), fma(t_7, t_3, (x1 ^ 3.0))))));
	else
		tmp = (fma(x2, -6.0, x1) ^ 3.0) ^ 0.3333333333333333;
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision] + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 - t$95$2), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(t$95$5 - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$7 = N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(N[(N[(N[(t$95$6 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(x1 - t$95$5), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$6 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$6), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(3.0 * N[(N[(t$95$7 - 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$3 * 4.0 + -6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(2.0 * t$95$4), $MachinePrecision]), $MachinePrecision] * N[(t$95$4 - -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$7 * t$95$3 + N[Power[x1, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[N[Power[N[(x2 * -6.0 + x1), $MachinePrecision], 3.0], $MachinePrecision], 0.3333333333333333], $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 2 x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)) 3)) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 4 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) 6))) (+.f64 (*.f64 x1 x1) 1)) (*.f64 (*.f64 (*.f64 3 x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 3 (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))))) < +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 2 x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)) 3)) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 4 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) 6))) (+.f64 (*.f64 x1 x1) 1)) (*.f64 (*.f64 (*.f64 3 x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 3 (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)))))

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around 0 3.0%

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

      1. *-commutative 3.0%

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

   6. Simplified 3.0%

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

      1. add-cbrt-cube 43.1%

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

      2. pow1/3 100.0%

         \[\leadsto \color{blue}{{\left(\left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right) \cdot \left(x1 + x2 \cdot -6\right)\right)}^{0.3333333333333333}} \]

      3. pow3 100.0%

         \[\leadsto {\color{blue}{\left({\left(x1 + x2 \cdot -6\right)}^{3}\right)}}^{0.3333333333333333} \]

      4. +-commutative 100.0%

         \[\leadsto {\left({\color{blue}{\left(x2 \cdot -6 + x1\right)}}^{3}\right)}^{0.3333333333333333} \]

      5. fma-def 100.0%

         \[\leadsto {\left({\color{blue}{\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}}^{3}\right)}^{0.3333333333333333} \]

   8. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{{\left({\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}^{3}\right)}^{0.3333333333333333}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(\left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \leq \infty:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{3 \cdot \left(x1 \cdot x1\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 + \mathsf{fma}\left(\mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, 4, -6\right), \left(x1 \cdot \left(2 \cdot \frac{x1 - \mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right) \cdot \left(\frac{x1 - \mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right)}{\mathsf{fma}\left(x1, x1, 1\right)} - -3\right)\right), \mathsf{fma}\left(3 \cdot \left(x1 \cdot x1\right), \frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, {x1}^{3}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := t_0 + 2 \cdot x2\\ t_2 := \frac{\mathsf{fma}\left(x1 \cdot 3, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\\ t_3 := x1 \cdot \left(x1 \cdot x1\right)\\ t_4 := x1 \cdot x1 + 1\\ t_5 := \frac{t_1 - x1}{t_4}\\ \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(\left(\left(t_5 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - t_1}{t_4}\right) - \left(x1 \cdot x1\right) \cdot \left(t_5 \cdot 4 - 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + t_0 \cdot t_5\right) + t_3\right)\right) + 3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_4}\right) \leq \infty:\\ \;\;\;\;x1 + \left(\left(t_3 + \mathsf{fma}\left(\mathsf{fma}\left(\left(x1 \cdot 2\right) \cdot t_2, -3 + t_2, \left(x1 \cdot x1\right) \cdot \mathsf{fma}\left(4, t_2, -6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), t_0 \cdot t_2\right)\right) + \left(x1 - 3 \cdot \frac{\left(x1 + 2 \cdot x2\right) - t_0}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ t_0 (* 2.0 x2)))
        (t_2 (/ (- (fma (* x1 3.0) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0)))
        (t_3 (* x1 (* x1 x1)))
        (t_4 (+ (* x1 x1) 1.0))
        (t_5 (/ (- t_1 x1) t_4)))
   (if (<=
        (+
         x1
         (+
          (+
           x1
           (+
            (+
             (*
              (-
               (* (- t_5 3.0) (* (* x1 2.0) (/ (- x1 t_1) t_4)))
               (* (* x1 x1) (- (* t_5 4.0) 6.0)))
              (- -1.0 (* x1 x1)))
             (* t_0 t_5))
            t_3))
          (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_4))))
        INFINITY)
     (+
      x1
      (+
       (+
        t_3
        (fma
         (fma (* (* x1 2.0) t_2) (+ -3.0 t_2) (* (* x1 x1) (fma 4.0 t_2 -6.0)))
         (fma x1 x1 1.0)
         (* t_0 t_2)))
       (- x1 (* 3.0 (/ (- (+ x1 (* 2.0 x2)) t_0) (fma x1 x1 1.0))))))
     (pow (pow (fma x2 -6.0 x1) 3.0) 0.3333333333333333))))

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 = (fma((x1 * 3.0), x1, (2.0 * x2)) - x1) / fma(x1, x1, 1.0);
	double t_3 = x1 * (x1 * x1);
	double t_4 = (x1 * x1) + 1.0;
	double t_5 = (t_1 - x1) / t_4;
	double tmp;
	if ((x1 + ((x1 + ((((((t_5 - 3.0) * ((x1 * 2.0) * ((x1 - t_1) / t_4))) - ((x1 * x1) * ((t_5 * 4.0) - 6.0))) * (-1.0 - (x1 * x1))) + (t_0 * t_5)) + t_3)) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_4)))) <= ((double) INFINITY)) {
		tmp = x1 + ((t_3 + fma(fma(((x1 * 2.0) * t_2), (-3.0 + t_2), ((x1 * x1) * fma(4.0, t_2, -6.0))), fma(x1, x1, 1.0), (t_0 * t_2))) + (x1 - (3.0 * (((x1 + (2.0 * x2)) - t_0) / fma(x1, x1, 1.0)))));
	} else {
		tmp = pow(pow(fma(x2, -6.0, x1), 3.0), 0.3333333333333333);
	}
	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(fma(Float64(x1 * 3.0), x1, Float64(2.0 * x2)) - x1) / fma(x1, x1, 1.0))
	t_3 = Float64(x1 * Float64(x1 * x1))
	t_4 = Float64(Float64(x1 * x1) + 1.0)
	t_5 = Float64(Float64(t_1 - x1) / t_4)
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(t_5 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(Float64(x1 - t_1) / t_4))) - Float64(Float64(x1 * x1) * Float64(Float64(t_5 * 4.0) - 6.0))) * Float64(-1.0 - Float64(x1 * x1))) + Float64(t_0 * t_5)) + t_3)) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_4)))) <= Inf)
		tmp = Float64(x1 + Float64(Float64(t_3 + fma(fma(Float64(Float64(x1 * 2.0) * t_2), Float64(-3.0 + t_2), Float64(Float64(x1 * x1) * fma(4.0, t_2, -6.0))), fma(x1, x1, 1.0), Float64(t_0 * t_2))) + Float64(x1 - Float64(3.0 * Float64(Float64(Float64(x1 + Float64(2.0 * x2)) - t_0) / fma(x1, x1, 1.0))))));
	else
		tmp = (fma(x2, -6.0, x1) ^ 3.0) ^ 0.3333333333333333;
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(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$3 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$1 - x1), $MachinePrecision] / t$95$4), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(N[(N[(N[(t$95$5 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(x1 - t$95$1), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$5 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$5), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(N[(t$95$3 + N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(-3.0 + t$95$2), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(4.0 * t$95$2 + -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x1 * x1 + 1.0), $MachinePrecision] + N[(t$95$0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 - N[(3.0 * N[(N[(N[(x1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[N[Power[N[(x2 * -6.0 + x1), $MachinePrecision], 3.0], $MachinePrecision], 0.3333333333333333], $MachinePrecision]]]]]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 2 x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)) 3)) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 4 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) 6))) (+.f64 (*.f64 x1 x1) 1)) (*.f64 (*.f64 (*.f64 3 x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 3 (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))))) < +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 2 x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)) 3)) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 4 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) 6))) (+.f64 (*.f64 x1 x1) 1)) (*.f64 (*.f64 (*.f64 3 x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 3 (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)))))

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around 0 3.0%

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

      1. *-commutative 3.0%

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

   6. Simplified 3.0%

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

      1. add-cbrt-cube 43.1%

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

      2. pow1/3 100.0%

         \[\leadsto \color{blue}{{\left(\left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right) \cdot \left(x1 + x2 \cdot -6\right)\right)}^{0.3333333333333333}} \]

      3. pow3 100.0%

         \[\leadsto {\color{blue}{\left({\left(x1 + x2 \cdot -6\right)}^{3}\right)}}^{0.3333333333333333} \]

      4. +-commutative 100.0%

         \[\leadsto {\left({\color{blue}{\left(x2 \cdot -6 + x1\right)}}^{3}\right)}^{0.3333333333333333} \]

      5. fma-def 100.0%

         \[\leadsto {\left({\color{blue}{\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}}^{3}\right)}^{0.3333333333333333} \]

   8. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{{\left({\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}^{3}\right)}^{0.3333333333333333}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(\left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \leq \infty:\\ \;\;\;\;x1 + \left(\left(x1 \cdot \left(x1 \cdot x1\right) + \mathsf{fma}\left(\mathsf{fma}\left(\left(x1 \cdot 2\right) \cdot \frac{\mathsf{fma}\left(x1 \cdot 3, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, -3 + \frac{\mathsf{fma}\left(x1 \cdot 3, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, \left(x1 \cdot x1\right) \cdot \mathsf{fma}\left(4, \frac{\mathsf{fma}\left(x1 \cdot 3, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, -6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\mathsf{fma}\left(x1 \cdot 3, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right) + \left(x1 - 3 \cdot \frac{\left(x1 + 2 \cdot x2\right) - x1 \cdot \left(x1 \cdot 3\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := t_0 + 2 \cdot x2\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{t_1 - x1}{t_2}\\ t_4 := x1 + \left(\left(x1 + \left(\left(\left(\left(t_3 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - t_1}{t_2}\right) - \left(x1 \cdot x1\right) \cdot \left(t_3 \cdot 4 - 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + t_0 \cdot t_3\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_2}\right)\\ \mathbf{if}\;t_4 \leq \infty:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \end{array} \]

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 (/ (- t_1 x1) t_2))
        (t_4
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               (-
                (* (- t_3 3.0) (* (* x1 2.0) (/ (- x1 t_1) t_2)))
                (* (* x1 x1) (- (* t_3 4.0) 6.0)))
               (- -1.0 (* x1 x1)))
              (* t_0 t_3))
             (* x1 (* x1 x1))))
           (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_2))))))
   (if (<= t_4 INFINITY)
     t_4
     (pow (pow (fma x2 -6.0 x1) 3.0) 0.3333333333333333))))

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 = (t_1 - x1) / t_2;
	double t_4 = x1 + ((x1 + ((((((t_3 - 3.0) * ((x1 * 2.0) * ((x1 - t_1) / t_2))) - ((x1 * x1) * ((t_3 * 4.0) - 6.0))) * (-1.0 - (x1 * x1))) + (t_0 * t_3)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)));
	double tmp;
	if (t_4 <= ((double) INFINITY)) {
		tmp = t_4;
	} else {
		tmp = pow(pow(fma(x2, -6.0, x1), 3.0), 0.3333333333333333);
	}
	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(t_1 - x1) / t_2)
	t_4 = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(t_3 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(Float64(x1 - t_1) / t_2))) - Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0))) * Float64(-1.0 - Float64(x1 * x1))) + Float64(t_0 * t_3)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_2))))
	tmp = 0.0
	if (t_4 <= Inf)
		tmp = t_4;
	else
		tmp = (fma(x2, -6.0, x1) ^ 3.0) ^ 0.3333333333333333;
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$1 - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(N[(x1 + N[(N[(N[(N[(N[(N[(t$95$3 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(x1 - t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, Infinity], t$95$4, N[Power[N[Power[N[(x2 * -6.0 + x1), $MachinePrecision], 3.0], $MachinePrecision], 0.3333333333333333], $MachinePrecision]]]]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 2 x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)) 3)) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 4 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) 6))) (+.f64 (*.f64 x1 x1) 1)) (*.f64 (*.f64 (*.f64 3 x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 3 (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))))) < +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 2 x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)) 3)) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 4 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) 6))) (+.f64 (*.f64 x1 x1) 1)) (*.f64 (*.f64 (*.f64 3 x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 3 (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)))))

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around 0 3.0%

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

      1. *-commutative 3.0%

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

   6. Simplified 3.0%

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

      1. add-cbrt-cube 43.1%

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

      2. pow1/3 100.0%

         \[\leadsto \color{blue}{{\left(\left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right) \cdot \left(x1 + x2 \cdot -6\right)\right)}^{0.3333333333333333}} \]

      3. pow3 100.0%

         \[\leadsto {\color{blue}{\left({\left(x1 + x2 \cdot -6\right)}^{3}\right)}}^{0.3333333333333333} \]

      4. +-commutative 100.0%

         \[\leadsto {\left({\color{blue}{\left(x2 \cdot -6 + x1\right)}}^{3}\right)}^{0.3333333333333333} \]

      5. fma-def 100.0%

         \[\leadsto {\left({\color{blue}{\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}}^{3}\right)}^{0.3333333333333333} \]

   8. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{{\left({\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}^{3}\right)}^{0.3333333333333333}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(\left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \leq \infty:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.4% accurate, 0.5× speedup

Math

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

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

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 = (t_1 - x1) / t_2;
	double t_4 = x1 + ((x1 + ((((((t_3 - 3.0) * ((x1 * 2.0) * ((x1 - t_1) / t_2))) - ((x1 * x1) * ((t_3 * 4.0) - 6.0))) * (-1.0 - (x1 * x1))) + (t_0 * t_3)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)));
	double tmp;
	if (t_4 <= ((double) INFINITY)) {
		tmp = t_4;
	} else {
		tmp = x1 + (((3.0 * (pow(x1, 2.0) * (3.0 - (x2 * -2.0)))) - (x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2))))))) + (x2 * -6.0));
	}
	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 = (t_1 - x1) / t_2;
	double t_4 = x1 + ((x1 + ((((((t_3 - 3.0) * ((x1 * 2.0) * ((x1 - t_1) / t_2))) - ((x1 * x1) * ((t_3 * 4.0) - 6.0))) * (-1.0 - (x1 * x1))) + (t_0 * t_3)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)));
	double tmp;
	if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else {
		tmp = x1 + (((3.0 * (Math.pow(x1, 2.0) * (3.0 - (x2 * -2.0)))) - (x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2))))))) + (x2 * -6.0));
	}
	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 = (t_1 - x1) / t_2
	t_4 = x1 + ((x1 + ((((((t_3 - 3.0) * ((x1 * 2.0) * ((x1 - t_1) / t_2))) - ((x1 * x1) * ((t_3 * 4.0) - 6.0))) * (-1.0 - (x1 * x1))) + (t_0 * t_3)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)))
	tmp = 0
	if t_4 <= math.inf:
		tmp = t_4
	else:
		tmp = x1 + (((3.0 * (math.pow(x1, 2.0) * (3.0 - (x2 * -2.0)))) - (x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2))))))) + (x2 * -6.0))
	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(t_1 - x1) / t_2)
	t_4 = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(t_3 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(Float64(x1 - t_1) / t_2))) - Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0))) * Float64(-1.0 - Float64(x1 * x1))) + Float64(t_0 * t_3)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_2))))
	tmp = 0.0
	if (t_4 <= Inf)
		tmp = t_4;
	else
		tmp = Float64(x1 + Float64(Float64(Float64(3.0 * Float64((x1 ^ 2.0) * Float64(3.0 - Float64(x2 * -2.0)))) - Float64(x1 * Float64(2.0 + Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))))) + Float64(x2 * -6.0)));
	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 = (t_1 - x1) / t_2;
	t_4 = x1 + ((x1 + ((((((t_3 - 3.0) * ((x1 * 2.0) * ((x1 - t_1) / t_2))) - ((x1 * x1) * ((t_3 * 4.0) - 6.0))) * (-1.0 - (x1 * x1))) + (t_0 * t_3)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)));
	tmp = 0.0;
	if (t_4 <= Inf)
		tmp = t_4;
	else
		tmp = x1 + (((3.0 * ((x1 ^ 2.0) * (3.0 - (x2 * -2.0)))) - (x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2))))))) + (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 2 x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)) 3)) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 4 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) 6))) (+.f64 (*.f64 x1 x1) 1)) (*.f64 (*.f64 (*.f64 3 x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 3 (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))))) < +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 2 x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)) 3)) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 4 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) 6))) (+.f64 (*.f64 x1 x1) 1)) (*.f64 (*.f64 (*.f64 3 x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 3 (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)))))

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around 0 62.2%

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

4. Final simplification 90.0%

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

Alternative 5: 75.8% accurate, 0.5× speedup

Math

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

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 (/ (- t_1 x1) t_2))
        (t_4
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               (-
                (* (- t_3 3.0) (* (* x1 2.0) (/ (- x1 t_1) t_2)))
                (* (* x1 x1) (- (* t_3 4.0) 6.0)))
               (- -1.0 (* x1 x1)))
              (* t_0 t_3))
             (* x1 (* x1 x1))))
           (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_2))))))
   (if (<= t_4 INFINITY)
     t_4
     (+ x1 (* x1 (- 1.0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2))))))))))

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 = (t_1 - x1) / t_2;
	double t_4 = x1 + ((x1 + ((((((t_3 - 3.0) * ((x1 * 2.0) * ((x1 - t_1) / t_2))) - ((x1 * x1) * ((t_3 * 4.0) - 6.0))) * (-1.0 - (x1 * x1))) + (t_0 * t_3)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)));
	double tmp;
	if (t_4 <= ((double) INFINITY)) {
		tmp = t_4;
	} else {
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	}
	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 = (t_1 - x1) / t_2;
	double t_4 = x1 + ((x1 + ((((((t_3 - 3.0) * ((x1 * 2.0) * ((x1 - t_1) / t_2))) - ((x1 * x1) * ((t_3 * 4.0) - 6.0))) * (-1.0 - (x1 * x1))) + (t_0 * t_3)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)));
	double tmp;
	if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else {
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	}
	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 = (t_1 - x1) / t_2
	t_4 = x1 + ((x1 + ((((((t_3 - 3.0) * ((x1 * 2.0) * ((x1 - t_1) / t_2))) - ((x1 * x1) * ((t_3 * 4.0) - 6.0))) * (-1.0 - (x1 * x1))) + (t_0 * t_3)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)))
	tmp = 0
	if t_4 <= math.inf:
		tmp = t_4
	else:
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))))
	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(t_1 - x1) / t_2)
	t_4 = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(t_3 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(Float64(x1 - t_1) / t_2))) - Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0))) * Float64(-1.0 - Float64(x1 * x1))) + Float64(t_0 * t_3)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_2))))
	tmp = 0.0
	if (t_4 <= Inf)
		tmp = t_4;
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 - Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))));
	end
	return tmp
end

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 2 x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)) 3)) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 4 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) 6))) (+.f64 (*.f64 x1 x1) 1)) (*.f64 (*.f64 (*.f64 3 x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 3 (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))))) < +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 2 x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)) 3)) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 4 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) 6))) (+.f64 (*.f64 x1 x1) 1)) (*.f64 (*.f64 (*.f64 3 x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 3 (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)))))

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around inf 18.8%

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

4. Final simplification 78.9%

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

Alternative 6: 91.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := t_0 + 2 \cdot x2\\ t_2 := x2 \cdot \left(3 - 2 \cdot x2\right)\\ t_3 := x1 \cdot x1 + 1\\ t_4 := 3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_3}\\ t_5 := \frac{t_1 - x1}{t_3}\\ \mathbf{if}\;x1 \leq -1.32 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right) - x1 \cdot \left(2 + 4 \cdot t_2\right)\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq -8.8 \cdot 10^{+49}:\\ \;\;\;\;x1 + \left(t_4 + \left(x1 + 6 \cdot {x1}^{4}\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{+104}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(\left(t_5 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - t_1}{t_3}\right) - \left(x1 \cdot x1\right) \cdot \left(t_5 \cdot 4 - 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + t_0 \cdot t_5\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + t_4\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 - 4 \cdot \left(x1 \cdot t_2\right)\right) + 3 \cdot \mathsf{fma}\left(x2, -2, {x1}^{2} \cdot \left(x1 + \left(3 + 2 \cdot x2\right)\right) - x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ t_0 (* 2.0 x2)))
        (t_2 (* x2 (- 3.0 (* 2.0 x2))))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_3)))
        (t_5 (/ (- t_1 x1) t_3)))
   (if (<= x1 -1.32e+154)
     (+
      x1
      (+
       (-
        (* 3.0 (* (pow x1 2.0) (- 3.0 (* x2 -2.0))))
        (* x1 (+ 2.0 (* 4.0 t_2))))
       (* x2 -6.0)))
     (if (<= x1 -8.8e+49)
       (+ x1 (+ t_4 (+ x1 (* 6.0 (pow x1 4.0)))))
       (if (<= x1 1e+104)
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               (-
                (* (- t_5 3.0) (* (* x1 2.0) (/ (- x1 t_1) t_3)))
                (* (* x1 x1) (- (* t_5 4.0) 6.0)))
               (- -1.0 (* x1 x1)))
              (* t_0 t_5))
             (* x1 (* x1 x1))))
           t_4))
         (+
          x1
          (+
           (- x1 (* 4.0 (* x1 t_2)))
           (*
            3.0
            (fma
             x2
             -2.0
             (- (* (pow x1 2.0) (+ x1 (+ 3.0 (* 2.0 x2)))) x1))))))))))

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 = x2 * (3.0 - (2.0 * x2));
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3);
	double t_5 = (t_1 - x1) / t_3;
	double tmp;
	if (x1 <= -1.32e+154) {
		tmp = x1 + (((3.0 * (pow(x1, 2.0) * (3.0 - (x2 * -2.0)))) - (x1 * (2.0 + (4.0 * t_2)))) + (x2 * -6.0));
	} else if (x1 <= -8.8e+49) {
		tmp = x1 + (t_4 + (x1 + (6.0 * pow(x1, 4.0))));
	} else if (x1 <= 1e+104) {
		tmp = x1 + ((x1 + ((((((t_5 - 3.0) * ((x1 * 2.0) * ((x1 - t_1) / t_3))) - ((x1 * x1) * ((t_5 * 4.0) - 6.0))) * (-1.0 - (x1 * x1))) + (t_0 * t_5)) + (x1 * (x1 * x1)))) + t_4);
	} else {
		tmp = x1 + ((x1 - (4.0 * (x1 * t_2))) + (3.0 * fma(x2, -2.0, ((pow(x1, 2.0) * (x1 + (3.0 + (2.0 * x2)))) - x1))));
	}
	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(x2 * Float64(3.0 - Float64(2.0 * x2)))
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_3))
	t_5 = Float64(Float64(t_1 - x1) / t_3)
	tmp = 0.0
	if (x1 <= -1.32e+154)
		tmp = Float64(x1 + Float64(Float64(Float64(3.0 * Float64((x1 ^ 2.0) * Float64(3.0 - Float64(x2 * -2.0)))) - Float64(x1 * Float64(2.0 + Float64(4.0 * t_2)))) + Float64(x2 * -6.0)));
	elseif (x1 <= -8.8e+49)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(6.0 * (x1 ^ 4.0)))));
	elseif (x1 <= 1e+104)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(t_5 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(Float64(x1 - t_1) / t_3))) - Float64(Float64(x1 * x1) * Float64(Float64(t_5 * 4.0) - 6.0))) * Float64(-1.0 - Float64(x1 * x1))) + Float64(t_0 * t_5)) + Float64(x1 * Float64(x1 * x1)))) + t_4));
	else
		tmp = Float64(x1 + Float64(Float64(x1 - Float64(4.0 * Float64(x1 * t_2))) + Float64(3.0 * fma(x2, -2.0, Float64(Float64((x1 ^ 2.0) * Float64(x1 + Float64(3.0 + Float64(2.0 * x2)))) - x1)))));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$1 - x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, If[LessEqual[x1, -1.32e+154], N[(x1 + N[(N[(N[(3.0 * N[(N[Power[x1, 2.0], $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(2.0 + N[(4.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -8.8e+49], N[(x1 + N[(t$95$4 + N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1e+104], N[(x1 + N[(N[(x1 + N[(N[(N[(N[(N[(N[(t$95$5 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(x1 - t$95$1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$5 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$5), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 - N[(4.0 * N[(x1 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0 + N[(N[(N[Power[x1, 2.0], $MachinePrecision] * N[(x1 + N[(3.0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.31999999999999998e154

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around 0 56.7%

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

   if -1.31999999999999998e154 < x1 < -8.8000000000000003e49

   1. Initial program 59.4%

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

   3. Taylor expanded in x1 around inf 99.7%

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

      1. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   if -8.8000000000000003e49 < x1 < 1e104

   1. Initial program 98.8%

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

   if 1e104 < x1

   1. Initial program 26.3%

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

   3. Taylor expanded in x1 around 0 6.3%

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

   4. Taylor expanded in x1 around 0 84.2%

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

      1. *-commutative 84.2%

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

      2. fma-def 84.2%

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

      3. +-commutative 84.2%

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

      4. mul-1-neg 84.2%

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

      5. unsub-neg 84.2%

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

      6. +-commutative 84.2%

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

      7. unpow3 84.2%

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

      8. unpow2 84.2%

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

      9. distribute-lft-out 97.4%

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

      10. cancel-sign-sub-inv 97.4%

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

      11. metadata-eval 97.4%

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

   6. Simplified 97.4%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.32 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right) - x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq -8.8 \cdot 10^{+49}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 6 \cdot {x1}^{4}\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{+104}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) + 3 \cdot \mathsf{fma}\left(x2, -2, {x1}^{2} \cdot \left(x1 + \left(3 + 2 \cdot x2\right)\right) - x1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := 3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_0}\\ t_3 := t_1 + 2 \cdot x2\\ t_4 := \frac{t_3 - x1}{t_0}\\ \mathbf{if}\;x1 \leq -8.8 \cdot 10^{+49}:\\ \;\;\;\;x1 + \left(t_2 + \left(x1 + 6 \cdot {x1}^{4}\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(\left(t_4 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - t_3}{t_0}\right) - \left(x1 \cdot x1\right) \cdot \left(t_4 \cdot 4 - 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + t_1 \cdot t_4\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + t_2\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_0)))
        (t_3 (+ t_1 (* 2.0 x2)))
        (t_4 (/ (- t_3 x1) t_0)))
   (if (<= x1 -8.8e+49)
     (+ x1 (+ t_2 (+ x1 (* 6.0 (pow x1 4.0)))))
     (if (<= x1 1.35e+154)
       (+
        x1
        (+
         (+
          x1
          (+
           (+
            (*
             (-
              (* (- t_4 3.0) (* (* x1 2.0) (/ (- x1 t_3) t_0)))
              (* (* x1 x1) (- (* t_4 4.0) 6.0)))
             (- -1.0 (* x1 x1)))
            (* t_1 t_4))
           (* x1 (* x1 x1))))
         t_2))
       (+ x1 (* x1 (- 1.0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0);
	double t_3 = t_1 + (2.0 * x2);
	double t_4 = (t_3 - x1) / t_0;
	double tmp;
	if (x1 <= -8.8e+49) {
		tmp = x1 + (t_2 + (x1 + (6.0 * pow(x1, 4.0))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 + ((((((t_4 - 3.0) * ((x1 * 2.0) * ((x1 - t_3) / t_0))) - ((x1 * x1) * ((t_4 * 4.0) - 6.0))) * (-1.0 - (x1 * x1))) + (t_1 * t_4)) + (x1 * (x1 * x1)))) + t_2);
	} else {
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = 3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_0)
    t_3 = t_1 + (2.0d0 * x2)
    t_4 = (t_3 - x1) / t_0
    if (x1 <= (-8.8d+49)) then
        tmp = x1 + (t_2 + (x1 + (6.0d0 * (x1 ** 4.0d0))))
    else if (x1 <= 1.35d+154) then
        tmp = x1 + ((x1 + ((((((t_4 - 3.0d0) * ((x1 * 2.0d0) * ((x1 - t_3) / t_0))) - ((x1 * x1) * ((t_4 * 4.0d0) - 6.0d0))) * ((-1.0d0) - (x1 * x1))) + (t_1 * t_4)) + (x1 * (x1 * x1)))) + t_2)
    else
        tmp = x1 + (x1 * (1.0d0 - (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2))))))
    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 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0);
	double t_3 = t_1 + (2.0 * x2);
	double t_4 = (t_3 - x1) / t_0;
	double tmp;
	if (x1 <= -8.8e+49) {
		tmp = x1 + (t_2 + (x1 + (6.0 * Math.pow(x1, 4.0))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 + ((((((t_4 - 3.0) * ((x1 * 2.0) * ((x1 - t_3) / t_0))) - ((x1 * x1) * ((t_4 * 4.0) - 6.0))) * (-1.0 - (x1 * x1))) + (t_1 * t_4)) + (x1 * (x1 * x1)))) + t_2);
	} else {
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)
	t_3 = t_1 + (2.0 * x2)
	t_4 = (t_3 - x1) / t_0
	tmp = 0
	if x1 <= -8.8e+49:
		tmp = x1 + (t_2 + (x1 + (6.0 * math.pow(x1, 4.0))))
	elif x1 <= 1.35e+154:
		tmp = x1 + ((x1 + ((((((t_4 - 3.0) * ((x1 * 2.0) * ((x1 - t_3) / t_0))) - ((x1 * x1) * ((t_4 * 4.0) - 6.0))) * (-1.0 - (x1 * x1))) + (t_1 * t_4)) + (x1 * (x1 * x1)))) + t_2)
	else:
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))))
	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(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_0))
	t_3 = Float64(t_1 + Float64(2.0 * x2))
	t_4 = Float64(Float64(t_3 - x1) / t_0)
	tmp = 0.0
	if (x1 <= -8.8e+49)
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(6.0 * (x1 ^ 4.0)))));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(t_4 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(Float64(x1 - t_3) / t_0))) - Float64(Float64(x1 * x1) * Float64(Float64(t_4 * 4.0) - 6.0))) * Float64(-1.0 - Float64(x1 * x1))) + Float64(t_1 * t_4)) + Float64(x1 * Float64(x1 * x1)))) + t_2));
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 - Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))));
	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 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0);
	t_3 = t_1 + (2.0 * x2);
	t_4 = (t_3 - x1) / t_0;
	tmp = 0.0;
	if (x1 <= -8.8e+49)
		tmp = x1 + (t_2 + (x1 + (6.0 * (x1 ^ 4.0))));
	elseif (x1 <= 1.35e+154)
		tmp = x1 + ((x1 + ((((((t_4 - 3.0) * ((x1 * 2.0) * ((x1 - t_3) / t_0))) - ((x1 * x1) * ((t_4 * 4.0) - 6.0))) * (-1.0 - (x1 * x1))) + (t_1 * t_4)) + (x1 * (x1 * x1)))) + t_2);
	else
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	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[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[LessEqual[x1, -8.8e+49], N[(x1 + N[(t$95$2 + N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(N[(x1 + N[(N[(N[(N[(N[(N[(t$95$4 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(x1 - t$95$3), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$4 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * N[(1.0 - N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -8.8000000000000003e49

   1. Initial program 19.8%

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

   3. Taylor expanded in x1 around inf 33.2%

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

      1. *-commutative 33.2%

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

   5. Simplified 33.2%

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

   if -8.8000000000000003e49 < x1 < 1.35000000000000003e154

   1. Initial program 98.9%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around inf 39.9%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -8.8 \cdot 10^{+49}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 6 \cdot {x1}^{4}\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x2 \cdot \left(3 - 2 \cdot x2\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := 3 \cdot \frac{\left(t_2 - 2 \cdot x2\right) - x1}{t_0}\\ t_4 := x1 + \left(t_3 - \left(\left(\left(t_0 \cdot \left(\frac{1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 + \frac{-1}{x1}\right)\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(t_2 + 2 \cdot x2\right)}{t_0}\right)\right) - 3 \cdot t_2\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{if}\;x1 \leq -8 \cdot 10^{+19}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x1 \leq -1.6 \cdot 10^{-207}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 1.25 \cdot 10^{-244}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 2100000000:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 - 4 \cdot \left(x1 \cdot t_1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x2 (- 3.0 (* 2.0 x2))))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_0)))
        (t_4
         (+
          x1
          (-
           t_3
           (-
            (-
             (-
              (*
               t_0
               (+
                (* (/ 1.0 x1) (* (* x1 2.0) (+ 3.0 (/ -1.0 x1))))
                (*
                 (* x1 x1)
                 (+ 6.0 (* 4.0 (/ (- x1 (+ t_2 (* 2.0 x2))) t_0))))))
              (* 3.0 t_2))
             (* x1 (* x1 x1)))
            x1)))))
   (if (<= x1 -8e+19)
     t_4
     (if (<= x1 -1.6e-207)
       (+ x1 (+ (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0)) (* x2 -6.0)))
       (if (<= x1 1.25e-244)
         (- (* x2 -6.0) x1)
         (if (<= x1 2100000000.0)
           (+ x1 (+ t_3 (- x1 (* 4.0 (* x1 t_1)))))
           (if (<= x1 1.35e+154) t_4 (+ x1 (* x1 (- 1.0 (* 4.0 t_1)))))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x2 * (3.0 - (2.0 * x2));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0);
	double t_4 = x1 + (t_3 - ((((t_0 * (((1.0 / x1) * ((x1 * 2.0) * (3.0 + (-1.0 / x1)))) + ((x1 * x1) * (6.0 + (4.0 * ((x1 - (t_2 + (2.0 * x2))) / t_0)))))) - (3.0 * t_2)) - (x1 * (x1 * x1))) - x1));
	double tmp;
	if (x1 <= -8e+19) {
		tmp = t_4;
	} else if (x1 <= -1.6e-207) {
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0));
	} else if (x1 <= 1.25e-244) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 2100000000.0) {
		tmp = x1 + (t_3 + (x1 - (4.0 * (x1 * t_1))));
	} else if (x1 <= 1.35e+154) {
		tmp = t_4;
	} else {
		tmp = x1 + (x1 * (1.0 - (4.0 * 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 = x2 * (3.0d0 - (2.0d0 * x2))
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = 3.0d0 * (((t_2 - (2.0d0 * x2)) - x1) / t_0)
    t_4 = x1 + (t_3 - ((((t_0 * (((1.0d0 / x1) * ((x1 * 2.0d0) * (3.0d0 + ((-1.0d0) / x1)))) + ((x1 * x1) * (6.0d0 + (4.0d0 * ((x1 - (t_2 + (2.0d0 * x2))) / t_0)))))) - (3.0d0 * t_2)) - (x1 * (x1 * x1))) - x1))
    if (x1 <= (-8d+19)) then
        tmp = t_4
    else if (x1 <= (-1.6d-207)) then
        tmp = x1 + ((x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)) + (x2 * (-6.0d0)))
    else if (x1 <= 1.25d-244) then
        tmp = (x2 * (-6.0d0)) - x1
    else if (x1 <= 2100000000.0d0) then
        tmp = x1 + (t_3 + (x1 - (4.0d0 * (x1 * t_1))))
    else if (x1 <= 1.35d+154) then
        tmp = t_4
    else
        tmp = x1 + (x1 * (1.0d0 - (4.0d0 * 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 = x2 * (3.0 - (2.0 * x2));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0);
	double t_4 = x1 + (t_3 - ((((t_0 * (((1.0 / x1) * ((x1 * 2.0) * (3.0 + (-1.0 / x1)))) + ((x1 * x1) * (6.0 + (4.0 * ((x1 - (t_2 + (2.0 * x2))) / t_0)))))) - (3.0 * t_2)) - (x1 * (x1 * x1))) - x1));
	double tmp;
	if (x1 <= -8e+19) {
		tmp = t_4;
	} else if (x1 <= -1.6e-207) {
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0));
	} else if (x1 <= 1.25e-244) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 2100000000.0) {
		tmp = x1 + (t_3 + (x1 - (4.0 * (x1 * t_1))));
	} else if (x1 <= 1.35e+154) {
		tmp = t_4;
	} else {
		tmp = x1 + (x1 * (1.0 - (4.0 * t_1)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x2 * (3.0 - (2.0 * x2))
	t_2 = x1 * (x1 * 3.0)
	t_3 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)
	t_4 = x1 + (t_3 - ((((t_0 * (((1.0 / x1) * ((x1 * 2.0) * (3.0 + (-1.0 / x1)))) + ((x1 * x1) * (6.0 + (4.0 * ((x1 - (t_2 + (2.0 * x2))) / t_0)))))) - (3.0 * t_2)) - (x1 * (x1 * x1))) - x1))
	tmp = 0
	if x1 <= -8e+19:
		tmp = t_4
	elif x1 <= -1.6e-207:
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0))
	elif x1 <= 1.25e-244:
		tmp = (x2 * -6.0) - x1
	elif x1 <= 2100000000.0:
		tmp = x1 + (t_3 + (x1 - (4.0 * (x1 * t_1))))
	elif x1 <= 1.35e+154:
		tmp = t_4
	else:
		tmp = x1 + (x1 * (1.0 - (4.0 * t_1)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_0))
	t_4 = Float64(x1 + Float64(t_3 - Float64(Float64(Float64(Float64(t_0 * Float64(Float64(Float64(1.0 / x1) * Float64(Float64(x1 * 2.0) * Float64(3.0 + Float64(-1.0 / x1)))) + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * Float64(Float64(x1 - Float64(t_2 + Float64(2.0 * x2))) / t_0)))))) - Float64(3.0 * t_2)) - Float64(x1 * Float64(x1 * x1))) - x1)))
	tmp = 0.0
	if (x1 <= -8e+19)
		tmp = t_4;
	elseif (x1 <= -1.6e-207)
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0)) + Float64(x2 * -6.0)));
	elseif (x1 <= 1.25e-244)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	elseif (x1 <= 2100000000.0)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 - Float64(4.0 * Float64(x1 * t_1)))));
	elseif (x1 <= 1.35e+154)
		tmp = t_4;
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 - Float64(4.0 * t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x2 * (3.0 - (2.0 * x2));
	t_2 = x1 * (x1 * 3.0);
	t_3 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0);
	t_4 = x1 + (t_3 - ((((t_0 * (((1.0 / x1) * ((x1 * 2.0) * (3.0 + (-1.0 / x1)))) + ((x1 * x1) * (6.0 + (4.0 * ((x1 - (t_2 + (2.0 * x2))) / t_0)))))) - (3.0 * t_2)) - (x1 * (x1 * x1))) - x1));
	tmp = 0.0;
	if (x1 <= -8e+19)
		tmp = t_4;
	elseif (x1 <= -1.6e-207)
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0));
	elseif (x1 <= 1.25e-244)
		tmp = (x2 * -6.0) - x1;
	elseif (x1 <= 2100000000.0)
		tmp = x1 + (t_3 + (x1 - (4.0 * (x1 * t_1))));
	elseif (x1 <= 1.35e+154)
		tmp = t_4;
	else
		tmp = x1 + (x1 * (1.0 - (4.0 * 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[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(t$95$3 - N[(N[(N[(N[(t$95$0 * N[(N[(N[(1.0 / x1), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(3.0 + N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * N[(N[(x1 - N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -8e+19], t$95$4, If[LessEqual[x1, -1.6e-207], N[(x1 + N[(N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.25e-244], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 2100000000.0], N[(x1 + N[(t$95$3 + N[(x1 - N[(4.0 * N[(x1 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], t$95$4, N[(x1 + N[(x1 * N[(1.0 - N[(4.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -8e19 or 2.1e9 < x1 < 1.35000000000000003e154

   1. Initial program 57.3%

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

   3. Taylor expanded in x1 around inf 54.0%

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

   4. Taylor expanded in x1 around inf 54.0%

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

   5. Taylor expanded in x1 around inf 54.0%

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

   if -8e19 < x1 < -1.6000000000000002e-207

   1. Initial program 99.6%

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

   3. Taylor expanded in x1 around 0 87.5%

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

   4. Taylor expanded in x1 around 0 87.9%

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

   if -1.6000000000000002e-207 < x1 < 1.24999999999999999e-244

   1. Initial program 99.3%

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

   3. Taylor expanded in x2 around inf 81.1%

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

      1. associate-/l* 81.1%

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

      2. +-commutative 81.1%

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

      3. unpow2 81.1%

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

      4. fma-udef 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in x1 around 0 81.4%

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

   7. Taylor expanded in x2 around 0 97.5%

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

      1. +-commutative 97.5%

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

      2. *-commutative 97.5%

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

      3. associate-+l+ 97.6%

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

      4. distribute-lft1-in 97.6%

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

      5. metadata-eval 97.6%

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

      6. neg-mul-1 97.6%

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

   9. Simplified 97.6%

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

   if 1.24999999999999999e-244 < x1 < 2.1e9

   1. Initial program 97.6%

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

   3. Taylor expanded in x1 around 0 84.2%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around inf 39.9%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -8 \cdot 10^{+19}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(\left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\frac{1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 + \frac{-1}{x1}\right)\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq -1.6 \cdot 10^{-207}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 1.25 \cdot 10^{-244}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 2100000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(\left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\frac{1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 + \frac{-1}{x1}\right)\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x2 \cdot \left(3 - 2 \cdot x2\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := 3 \cdot \frac{\left(t_2 - 2 \cdot x2\right) - x1}{t_1}\\ t_4 := x1 + \left(t_3 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t_2 - t_1 \cdot \left(\left(\frac{\left(t_2 + 2 \cdot x2\right) - x1}{t_1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right) - \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -3.6 \cdot 10^{+19}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x1 \leq -7.4 \cdot 10^{-208}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 1.6 \cdot 10^{-243}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 25000000000:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 - 4 \cdot \left(x1 \cdot t_0\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot t_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x2 (- 3.0 (* 2.0 x2))))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_1)))
        (t_4
         (+
          x1
          (+
           t_3
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (-
              (* 3.0 t_2)
              (*
               t_1
               (-
                (*
                 (- (/ (- (+ t_2 (* 2.0 x2)) x1) t_1) 3.0)
                 (* (* x1 2.0) (- (/ 1.0 x1) 3.0)))
                (* (* x1 x1) 6.0))))))))))
   (if (<= x1 -3.6e+19)
     t_4
     (if (<= x1 -7.4e-208)
       (+ x1 (+ (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0)) (* x2 -6.0)))
       (if (<= x1 1.6e-243)
         (- (* x2 -6.0) x1)
         (if (<= x1 25000000000.0)
           (+ x1 (+ t_3 (- x1 (* 4.0 (* x1 t_0)))))
           (if (<= x1 1.35e+154) t_4 (+ x1 (* x1 (- 1.0 (* 4.0 t_0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = x2 * (3.0 - (2.0 * x2));
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_1);
	double t_4 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_2) - (t_1 * ((((((t_2 + (2.0 * x2)) - x1) / t_1) - 3.0) * ((x1 * 2.0) * ((1.0 / x1) - 3.0))) - ((x1 * x1) * 6.0)))))));
	double tmp;
	if (x1 <= -3.6e+19) {
		tmp = t_4;
	} else if (x1 <= -7.4e-208) {
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0));
	} else if (x1 <= 1.6e-243) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 25000000000.0) {
		tmp = x1 + (t_3 + (x1 - (4.0 * (x1 * t_0))));
	} else if (x1 <= 1.35e+154) {
		tmp = t_4;
	} else {
		tmp = x1 + (x1 * (1.0 - (4.0 * t_0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = x2 * (3.0d0 - (2.0d0 * x2))
    t_1 = (x1 * x1) + 1.0d0
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = 3.0d0 * (((t_2 - (2.0d0 * x2)) - x1) / t_1)
    t_4 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_2) - (t_1 * ((((((t_2 + (2.0d0 * x2)) - x1) / t_1) - 3.0d0) * ((x1 * 2.0d0) * ((1.0d0 / x1) - 3.0d0))) - ((x1 * x1) * 6.0d0)))))))
    if (x1 <= (-3.6d+19)) then
        tmp = t_4
    else if (x1 <= (-7.4d-208)) then
        tmp = x1 + ((x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)) + (x2 * (-6.0d0)))
    else if (x1 <= 1.6d-243) then
        tmp = (x2 * (-6.0d0)) - x1
    else if (x1 <= 25000000000.0d0) then
        tmp = x1 + (t_3 + (x1 - (4.0d0 * (x1 * t_0))))
    else if (x1 <= 1.35d+154) then
        tmp = t_4
    else
        tmp = x1 + (x1 * (1.0d0 - (4.0d0 * t_0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x2 * (3.0 - (2.0 * x2));
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_1);
	double t_4 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_2) - (t_1 * ((((((t_2 + (2.0 * x2)) - x1) / t_1) - 3.0) * ((x1 * 2.0) * ((1.0 / x1) - 3.0))) - ((x1 * x1) * 6.0)))))));
	double tmp;
	if (x1 <= -3.6e+19) {
		tmp = t_4;
	} else if (x1 <= -7.4e-208) {
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0));
	} else if (x1 <= 1.6e-243) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 25000000000.0) {
		tmp = x1 + (t_3 + (x1 - (4.0 * (x1 * t_0))));
	} else if (x1 <= 1.35e+154) {
		tmp = t_4;
	} else {
		tmp = x1 + (x1 * (1.0 - (4.0 * t_0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x2 * (3.0 - (2.0 * x2))
	t_1 = (x1 * x1) + 1.0
	t_2 = x1 * (x1 * 3.0)
	t_3 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_1)
	t_4 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_2) - (t_1 * ((((((t_2 + (2.0 * x2)) - x1) / t_1) - 3.0) * ((x1 * 2.0) * ((1.0 / x1) - 3.0))) - ((x1 * x1) * 6.0)))))))
	tmp = 0
	if x1 <= -3.6e+19:
		tmp = t_4
	elif x1 <= -7.4e-208:
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0))
	elif x1 <= 1.6e-243:
		tmp = (x2 * -6.0) - x1
	elif x1 <= 25000000000.0:
		tmp = x1 + (t_3 + (x1 - (4.0 * (x1 * t_0))))
	elif x1 <= 1.35e+154:
		tmp = t_4
	else:
		tmp = x1 + (x1 * (1.0 - (4.0 * t_0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_1))
	t_4 = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_2) - Float64(t_1 * Float64(Float64(Float64(Float64(Float64(Float64(t_2 + Float64(2.0 * x2)) - x1) / t_1) - 3.0) * Float64(Float64(x1 * 2.0) * Float64(Float64(1.0 / x1) - 3.0))) - Float64(Float64(x1 * x1) * 6.0))))))))
	tmp = 0.0
	if (x1 <= -3.6e+19)
		tmp = t_4;
	elseif (x1 <= -7.4e-208)
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0)) + Float64(x2 * -6.0)));
	elseif (x1 <= 1.6e-243)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	elseif (x1 <= 25000000000.0)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 - Float64(4.0 * Float64(x1 * t_0)))));
	elseif (x1 <= 1.35e+154)
		tmp = t_4;
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 - Float64(4.0 * t_0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x2 * (3.0 - (2.0 * x2));
	t_1 = (x1 * x1) + 1.0;
	t_2 = x1 * (x1 * 3.0);
	t_3 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_1);
	t_4 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_2) - (t_1 * ((((((t_2 + (2.0 * x2)) - x1) / t_1) - 3.0) * ((x1 * 2.0) * ((1.0 / x1) - 3.0))) - ((x1 * x1) * 6.0)))))));
	tmp = 0.0;
	if (x1 <= -3.6e+19)
		tmp = t_4;
	elseif (x1 <= -7.4e-208)
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0));
	elseif (x1 <= 1.6e-243)
		tmp = (x2 * -6.0) - x1;
	elseif (x1 <= 25000000000.0)
		tmp = x1 + (t_3 + (x1 - (4.0 * (x1 * t_0))));
	elseif (x1 <= 1.35e+154)
		tmp = t_4;
	else
		tmp = x1 + (x1 * (1.0 - (4.0 * t_0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $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[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(t$95$3 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$2), $MachinePrecision] - N[(t$95$1 * N[(N[(N[(N[(N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision] - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(1.0 / x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3.6e+19], t$95$4, If[LessEqual[x1, -7.4e-208], N[(x1 + N[(N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.6e-243], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 25000000000.0], N[(x1 + N[(t$95$3 + N[(x1 - N[(4.0 * N[(x1 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], t$95$4, N[(x1 + N[(x1 * N[(1.0 - N[(4.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -3.6e19 or 2.5e10 < x1 < 1.35000000000000003e154

   1. Initial program 57.3%

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

   3. Taylor expanded in x1 around inf 54.0%

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

   4. Taylor expanded in x1 around inf 54.0%

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

   5. Taylor expanded in x1 around inf 47.5%

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

   if -3.6e19 < x1 < -7.4000000000000004e-208

   1. Initial program 99.6%

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

   3. Taylor expanded in x1 around 0 87.5%

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

   4. Taylor expanded in x1 around 0 87.9%

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

   if -7.4000000000000004e-208 < x1 < 1.5999999999999999e-243

   1. Initial program 99.3%

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

   3. Taylor expanded in x2 around inf 81.1%

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

      1. associate-/l* 81.1%

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

      2. +-commutative 81.1%

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

      3. unpow2 81.1%

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

      4. fma-udef 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in x1 around 0 81.4%

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

   7. Taylor expanded in x2 around 0 97.5%

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

      1. +-commutative 97.5%

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

      2. *-commutative 97.5%

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

      3. associate-+l+ 97.6%

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

      4. distribute-lft1-in 97.6%

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

      5. metadata-eval 97.6%

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

      6. neg-mul-1 97.6%

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

   9. Simplified 97.6%

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

   if 1.5999999999999999e-243 < x1 < 2.5e10

   1. Initial program 97.6%

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

   3. Taylor expanded in x1 around 0 84.2%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around inf 39.9%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.6 \cdot 10^{+19}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right) - \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -7.4 \cdot 10^{-208}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 1.6 \cdot 10^{-243}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 25000000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right) - \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := t_0 + 2 \cdot x2\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{t_1 - x1}{t_2}\\ \mathbf{if}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(\left(t_3 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - t_1}{t_2}\right) - \left(x1 \cdot x1\right) \cdot \left(t_3 \cdot 4 - 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + 3 \cdot t_0\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \end{array} \end{array} \]

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 (/ (- t_1 x1) t_2)))
   (if (<= x1 1.35e+154)
     (+
      x1
      (+
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (*
           (-
            (* (- t_3 3.0) (* (* x1 2.0) (/ (- x1 t_1) t_2)))
            (* (* x1 x1) (- (* t_3 4.0) 6.0)))
           (- -1.0 (* x1 x1)))
          (* 3.0 t_0))))
       (* 3.0 (- (* x2 -2.0) x1))))
     (+ x1 (* x1 (- 1.0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2))))))))))

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 = (t_1 - x1) / t_2;
	double tmp;
	if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + (((((t_3 - 3.0) * ((x1 * 2.0) * ((x1 - t_1) / t_2))) - ((x1 * x1) * ((t_3 * 4.0) - 6.0))) * (-1.0 - (x1 * x1))) + (3.0 * t_0)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = t_0 + (2.0d0 * x2)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = (t_1 - x1) / t_2
    if (x1 <= 1.35d+154) then
        tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + (((((t_3 - 3.0d0) * ((x1 * 2.0d0) * ((x1 - t_1) / t_2))) - ((x1 * x1) * ((t_3 * 4.0d0) - 6.0d0))) * ((-1.0d0) - (x1 * x1))) + (3.0d0 * t_0)))) + (3.0d0 * ((x2 * (-2.0d0)) - x1)))
    else
        tmp = x1 + (x1 * (1.0d0 - (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = t_0 + (2.0 * x2);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = (t_1 - x1) / t_2;
	double tmp;
	if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + (((((t_3 - 3.0) * ((x1 * 2.0) * ((x1 - t_1) / t_2))) - ((x1 * x1) * ((t_3 * 4.0) - 6.0))) * (-1.0 - (x1 * x1))) + (3.0 * t_0)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	}
	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 = (t_1 - x1) / t_2
	tmp = 0
	if x1 <= 1.35e+154:
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + (((((t_3 - 3.0) * ((x1 * 2.0) * ((x1 - t_1) / t_2))) - ((x1 * x1) * ((t_3 * 4.0) - 6.0))) * (-1.0 - (x1 * x1))) + (3.0 * t_0)))) + (3.0 * ((x2 * -2.0) - x1)))
	else:
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))))
	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(t_1 - x1) / t_2)
	tmp = 0.0
	if (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(Float64(Float64(Float64(t_3 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(Float64(x1 - t_1) / t_2))) - Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0))) * Float64(-1.0 - Float64(x1 * x1))) + Float64(3.0 * t_0)))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 - Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = t_0 + (2.0 * x2);
	t_2 = (x1 * x1) + 1.0;
	t_3 = (t_1 - x1) / t_2;
	tmp = 0.0;
	if (x1 <= 1.35e+154)
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + (((((t_3 - 3.0) * ((x1 * 2.0) * ((x1 - t_1) / t_2))) - ((x1 * x1) * ((t_3 * 4.0) - 6.0))) * (-1.0 - (x1 * x1))) + (3.0 * t_0)))) + (3.0 * ((x2 * -2.0) - x1)));
	else
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(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[(t$95$1 - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[x1, 1.35e+154], N[(x1 + N[(N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(N[(t$95$3 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(x1 - t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * N[(1.0 - N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < 1.35000000000000003e154

   1. Initial program 83.3%

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

   3. Taylor expanded in x1 around inf 82.6%

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

   4. Taylor expanded in x1 around 0 83.2%

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

      1. mul-1-neg 83.2%

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

      2. unsub-neg 83.2%

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

      3. *-commutative 83.2%

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

   6. Simplified 83.2%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around inf 39.9%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 73.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := t_1 + 2 \cdot x2\\ \mathbf{if}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_0} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t_1 + \left(\left(\frac{t_2 - x1}{t_0} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - t_2}{t_0}\right) - \left(x1 \cdot x1\right) \cdot 6\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \end{array} \end{array} \]

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))))
   (if (<= x1 1.35e+154)
     (+
      x1
      (+
       (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_0))
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (* 3.0 t_1)
          (*
           (-
            (* (- (/ (- t_2 x1) t_0) 3.0) (* (* x1 2.0) (/ (- x1 t_2) t_0)))
            (* (* x1 x1) 6.0))
           (- -1.0 (* x1 x1))))))))
     (+ x1 (* x1 (- 1.0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2))))))))))

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 tmp;
	if (x1 <= 1.35e+154) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + ((((((t_2 - x1) / t_0) - 3.0) * ((x1 * 2.0) * ((x1 - t_2) / t_0))) - ((x1 * x1) * 6.0)) * (-1.0 - (x1 * x1)))))));
	} else {
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = t_1 + (2.0d0 * x2)
    if (x1 <= 1.35d+154) then
        tmp = x1 + ((3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_1) + ((((((t_2 - x1) / t_0) - 3.0d0) * ((x1 * 2.0d0) * ((x1 - t_2) / t_0))) - ((x1 * x1) * 6.0d0)) * ((-1.0d0) - (x1 * x1)))))))
    else
        tmp = x1 + (x1 * (1.0d0 - (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2))))))
    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 tmp;
	if (x1 <= 1.35e+154) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + ((((((t_2 - x1) / t_0) - 3.0) * ((x1 * 2.0) * ((x1 - t_2) / t_0))) - ((x1 * x1) * 6.0)) * (-1.0 - (x1 * x1)))))));
	} else {
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	}
	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)
	tmp = 0
	if x1 <= 1.35e+154:
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + ((((((t_2 - x1) / t_0) - 3.0) * ((x1 * 2.0) * ((x1 - t_2) / t_0))) - ((x1 * x1) * 6.0)) * (-1.0 - (x1 * x1)))))))
	else:
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))))
	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))
	tmp = 0.0
	if (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_1) + Float64(Float64(Float64(Float64(Float64(Float64(t_2 - x1) / t_0) - 3.0) * Float64(Float64(x1 * 2.0) * Float64(Float64(x1 - t_2) / t_0))) - Float64(Float64(x1 * x1) * 6.0)) * Float64(-1.0 - Float64(x1 * x1))))))));
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 - Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))));
	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);
	tmp = 0.0;
	if (x1 <= 1.35e+154)
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + ((((((t_2 - x1) / t_0) - 3.0) * ((x1 * 2.0) * ((x1 - t_2) / t_0))) - ((x1 * x1) * 6.0)) * (-1.0 - (x1 * x1)))))));
	else
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	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]}, If[LessEqual[x1, 1.35e+154], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$1), $MachinePrecision] + N[(N[(N[(N[(N[(N[(t$95$2 - x1), $MachinePrecision] / t$95$0), $MachinePrecision] - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(x1 - t$95$2), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * N[(1.0 - N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < 1.35000000000000003e154

   1. Initial program 83.3%

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

   3. Taylor expanded in x1 around inf 82.6%

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

   4. Taylor expanded in x1 around inf 79.9%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around inf 39.9%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot 6\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 64.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := 2 \cdot x2 - 3\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := 3 \cdot \frac{\left(t_2 - 2 \cdot x2\right) - x1}{t_0}\\ t_4 := x1 + \left(t_3 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t_2 + t_0 \cdot \left(\left(x1 \cdot x1\right) \cdot 6 + t_1 \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 + \frac{-1}{x1}\right)\right)\right)\right)\right)\right)\right)\\ t_5 := x2 \cdot \left(3 - 2 \cdot x2\right)\\ \mathbf{if}\;x1 \leq -2.4 \cdot 10^{+36}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x1 \leq -3.8 \cdot 10^{-205}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot t_1\right) - 2\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 1.85 \cdot 10^{-244}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 380000000:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 - 4 \cdot \left(x1 \cdot t_5\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot t_5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (- (* 2.0 x2) 3.0))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_0)))
        (t_4
         (+
          x1
          (+
           t_3
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* 3.0 t_2)
              (*
               t_0
               (+
                (* (* x1 x1) 6.0)
                (* t_1 (* (* x1 2.0) (+ 3.0 (/ -1.0 x1))))))))))))
        (t_5 (* x2 (- 3.0 (* 2.0 x2)))))
   (if (<= x1 -2.4e+36)
     t_4
     (if (<= x1 -3.8e-205)
       (+ x1 (+ (* x1 (- (* 4.0 (* x2 t_1)) 2.0)) (* x2 -6.0)))
       (if (<= x1 1.85e-244)
         (- (* x2 -6.0) x1)
         (if (<= x1 380000000.0)
           (+ x1 (+ t_3 (- x1 (* 4.0 (* x1 t_5)))))
           (if (<= x1 1.35e+154) t_4 (+ x1 (* x1 (- 1.0 (* 4.0 t_5)))))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = (2.0 * x2) - 3.0;
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0);
	double t_4 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_2) + (t_0 * (((x1 * x1) * 6.0) + (t_1 * ((x1 * 2.0) * (3.0 + (-1.0 / x1))))))))));
	double t_5 = x2 * (3.0 - (2.0 * x2));
	double tmp;
	if (x1 <= -2.4e+36) {
		tmp = t_4;
	} else if (x1 <= -3.8e-205) {
		tmp = x1 + ((x1 * ((4.0 * (x2 * t_1)) - 2.0)) + (x2 * -6.0));
	} else if (x1 <= 1.85e-244) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 380000000.0) {
		tmp = x1 + (t_3 + (x1 - (4.0 * (x1 * t_5))));
	} else if (x1 <= 1.35e+154) {
		tmp = t_4;
	} else {
		tmp = x1 + (x1 * (1.0 - (4.0 * t_5)));
	}
	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 = (2.0d0 * x2) - 3.0d0
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = 3.0d0 * (((t_2 - (2.0d0 * x2)) - x1) / t_0)
    t_4 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_2) + (t_0 * (((x1 * x1) * 6.0d0) + (t_1 * ((x1 * 2.0d0) * (3.0d0 + ((-1.0d0) / x1))))))))))
    t_5 = x2 * (3.0d0 - (2.0d0 * x2))
    if (x1 <= (-2.4d+36)) then
        tmp = t_4
    else if (x1 <= (-3.8d-205)) then
        tmp = x1 + ((x1 * ((4.0d0 * (x2 * t_1)) - 2.0d0)) + (x2 * (-6.0d0)))
    else if (x1 <= 1.85d-244) then
        tmp = (x2 * (-6.0d0)) - x1
    else if (x1 <= 380000000.0d0) then
        tmp = x1 + (t_3 + (x1 - (4.0d0 * (x1 * t_5))))
    else if (x1 <= 1.35d+154) then
        tmp = t_4
    else
        tmp = x1 + (x1 * (1.0d0 - (4.0d0 * t_5)))
    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 = (2.0 * x2) - 3.0;
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0);
	double t_4 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_2) + (t_0 * (((x1 * x1) * 6.0) + (t_1 * ((x1 * 2.0) * (3.0 + (-1.0 / x1))))))))));
	double t_5 = x2 * (3.0 - (2.0 * x2));
	double tmp;
	if (x1 <= -2.4e+36) {
		tmp = t_4;
	} else if (x1 <= -3.8e-205) {
		tmp = x1 + ((x1 * ((4.0 * (x2 * t_1)) - 2.0)) + (x2 * -6.0));
	} else if (x1 <= 1.85e-244) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 380000000.0) {
		tmp = x1 + (t_3 + (x1 - (4.0 * (x1 * t_5))));
	} else if (x1 <= 1.35e+154) {
		tmp = t_4;
	} else {
		tmp = x1 + (x1 * (1.0 - (4.0 * t_5)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = (2.0 * x2) - 3.0
	t_2 = x1 * (x1 * 3.0)
	t_3 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)
	t_4 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_2) + (t_0 * (((x1 * x1) * 6.0) + (t_1 * ((x1 * 2.0) * (3.0 + (-1.0 / x1))))))))))
	t_5 = x2 * (3.0 - (2.0 * x2))
	tmp = 0
	if x1 <= -2.4e+36:
		tmp = t_4
	elif x1 <= -3.8e-205:
		tmp = x1 + ((x1 * ((4.0 * (x2 * t_1)) - 2.0)) + (x2 * -6.0))
	elif x1 <= 1.85e-244:
		tmp = (x2 * -6.0) - x1
	elif x1 <= 380000000.0:
		tmp = x1 + (t_3 + (x1 - (4.0 * (x1 * t_5))))
	elif x1 <= 1.35e+154:
		tmp = t_4
	else:
		tmp = x1 + (x1 * (1.0 - (4.0 * t_5)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(Float64(2.0 * x2) - 3.0)
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_0))
	t_4 = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_2) + Float64(t_0 * Float64(Float64(Float64(x1 * x1) * 6.0) + Float64(t_1 * Float64(Float64(x1 * 2.0) * Float64(3.0 + Float64(-1.0 / x1)))))))))))
	t_5 = Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))
	tmp = 0.0
	if (x1 <= -2.4e+36)
		tmp = t_4;
	elseif (x1 <= -3.8e-205)
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * t_1)) - 2.0)) + Float64(x2 * -6.0)));
	elseif (x1 <= 1.85e-244)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	elseif (x1 <= 380000000.0)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 - Float64(4.0 * Float64(x1 * t_5)))));
	elseif (x1 <= 1.35e+154)
		tmp = t_4;
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 - Float64(4.0 * t_5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = (2.0 * x2) - 3.0;
	t_2 = x1 * (x1 * 3.0);
	t_3 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0);
	t_4 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_2) + (t_0 * (((x1 * x1) * 6.0) + (t_1 * ((x1 * 2.0) * (3.0 + (-1.0 / x1))))))))));
	t_5 = x2 * (3.0 - (2.0 * x2));
	tmp = 0.0;
	if (x1 <= -2.4e+36)
		tmp = t_4;
	elseif (x1 <= -3.8e-205)
		tmp = x1 + ((x1 * ((4.0 * (x2 * t_1)) - 2.0)) + (x2 * -6.0));
	elseif (x1 <= 1.85e-244)
		tmp = (x2 * -6.0) - x1;
	elseif (x1 <= 380000000.0)
		tmp = x1 + (t_3 + (x1 - (4.0 * (x1 * t_5))));
	elseif (x1 <= 1.35e+154)
		tmp = t_4;
	else
		tmp = x1 + (x1 * (1.0 - (4.0 * t_5)));
	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[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(t$95$3 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$2), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision] + N[(t$95$1 * N[(N[(x1 * 2.0), $MachinePrecision] * N[(3.0 + N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.4e+36], t$95$4, If[LessEqual[x1, -3.8e-205], N[(x1 + N[(N[(x1 * N[(N[(4.0 * N[(x2 * t$95$1), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.85e-244], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 380000000.0], N[(x1 + N[(t$95$3 + N[(x1 - N[(4.0 * N[(x1 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], t$95$4, N[(x1 + N[(x1 * N[(1.0 - N[(4.0 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -2.39999999999999992e36 or 3.8e8 < x1 < 1.35000000000000003e154

   1. Initial program 56.3%

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

   3. Taylor expanded in x1 around inf 52.9%

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

   4. Taylor expanded in x1 around inf 52.9%

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

   5. Taylor expanded in x1 around 0 44.4%

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

   6. Taylor expanded in x1 around inf 44.5%

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

   if -2.39999999999999992e36 < x1 < -3.79999999999999992e-205

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around 0 84.4%

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

   4. Taylor expanded in x1 around 0 84.8%

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

   if -3.79999999999999992e-205 < x1 < 1.8500000000000001e-244

   1. Initial program 99.3%

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

   3. Taylor expanded in x2 around inf 81.1%

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

      1. associate-/l* 81.1%

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

      2. +-commutative 81.1%

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

      3. unpow2 81.1%

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

      4. fma-udef 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in x1 around 0 81.4%

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

   7. Taylor expanded in x2 around 0 97.5%

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

      1. +-commutative 97.5%

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

      2. *-commutative 97.5%

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

      3. associate-+l+ 97.6%

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

      4. distribute-lft1-in 97.6%

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

      5. metadata-eval 97.6%

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

      6. neg-mul-1 97.6%

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

   9. Simplified 97.6%

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

   if 1.8500000000000001e-244 < x1 < 3.8e8

   1. Initial program 97.6%

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

   3. Taylor expanded in x1 around 0 84.2%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around inf 39.9%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.4 \cdot 10^{+36}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6 + \left(2 \cdot x2 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 + \frac{-1}{x1}\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3.8 \cdot 10^{-205}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 1.85 \cdot 10^{-244}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 380000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6 + \left(2 \cdot x2 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 + \frac{-1}{x1}\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.9% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.08 \cdot 10^{+25}:\\ \;\;\;\;x1 + \left(x1 - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \mathbf{elif}\;x1 \leq -5.8 \cdot 10^{-56} \lor \neg \left(x1 \leq 1.8 \cdot 10^{-59}\right):\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.08e+25)
   (+ x1 (- x1 (* x2 (- 6.0 (* x1 -12.0)))))
   (if (or (<= x1 -5.8e-56) (not (<= x1 1.8e-59)))
     (+ x1 (* x1 (- 1.0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))))
     (- (* x2 -6.0) x1))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.08e+25) {
		tmp = x1 + (x1 - (x2 * (6.0 - (x1 * -12.0))));
	} else if ((x1 <= -5.8e-56) || !(x1 <= 1.8e-59)) {
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	} else {
		tmp = (x2 * -6.0) - x1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-1.08d+25)) then
        tmp = x1 + (x1 - (x2 * (6.0d0 - (x1 * (-12.0d0)))))
    else if ((x1 <= (-5.8d-56)) .or. (.not. (x1 <= 1.8d-59))) then
        tmp = x1 + (x1 * (1.0d0 - (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2))))))
    else
        tmp = (x2 * (-6.0d0)) - x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.08e+25) {
		tmp = x1 + (x1 - (x2 * (6.0 - (x1 * -12.0))));
	} else if ((x1 <= -5.8e-56) || !(x1 <= 1.8e-59)) {
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	} else {
		tmp = (x2 * -6.0) - x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.08e+25:
		tmp = x1 + (x1 - (x2 * (6.0 - (x1 * -12.0))))
	elif (x1 <= -5.8e-56) or not (x1 <= 1.8e-59):
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))))
	else:
		tmp = (x2 * -6.0) - x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.08e+25)
		tmp = Float64(x1 + Float64(x1 - Float64(x2 * Float64(6.0 - Float64(x1 * -12.0)))));
	elseif ((x1 <= -5.8e-56) || !(x1 <= 1.8e-59))
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 - Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))));
	else
		tmp = Float64(Float64(x2 * -6.0) - x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -1.08e+25)
		tmp = x1 + (x1 - (x2 * (6.0 - (x1 * -12.0))));
	elseif ((x1 <= -5.8e-56) || ~((x1 <= 1.8e-59)))
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	else
		tmp = (x2 * -6.0) - x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.08e+25], N[(x1 + N[(x1 - N[(x2 * N[(6.0 - N[(x1 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x1, -5.8e-56], N[Not[LessEqual[x1, 1.8e-59]], $MachinePrecision]], N[(x1 + N[(x1 * N[(1.0 - N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.08e25

   1. Initial program 24.8%

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

   3. Taylor expanded in x1 around 0 0.3%

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

      1. add-cube-cbrt 0.3%

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

      2. pow3 0.3%

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

      3. associate-*r* 0.3%

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

      4. fma-neg 0.3%

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

      5. metadata-eval 0.3%

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

   5. Applied egg-rr 0.3%

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

   6. Taylor expanded in x1 around 0 0.3%

      \[\leadsto x1 + \left(\left(4 \cdot {\left(\sqrt[3]{\left(x1 \cdot x2\right) \cdot \mathsf{fma}\left(2, x2, -3\right)}\right)}^{3} + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative 0.3%

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

   8. Simplified 0.3%

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

   9. Taylor expanded in x2 around 0 9.4%

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

   if -1.08e25 < x1 < -5.79999999999999982e-56 or 1.8e-59 < x1

   1. Initial program 72.5%

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

   3. Taylor expanded in x1 around 0 40.4%

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

   4. Taylor expanded in x1 around inf 43.7%

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

   if -5.79999999999999982e-56 < x1 < 1.8e-59

   1. Initial program 99.4%

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

   3. Taylor expanded in x2 around inf 84.5%

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

      1. associate-/l* 84.6%

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

      2. +-commutative 84.6%

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

      3. unpow2 84.6%

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

      4. fma-udef 84.6%

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

   5. Simplified 84.6%

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

   6. Taylor expanded in x1 around 0 84.9%

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

   7. Taylor expanded in x2 around 0 80.3%

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

      1. +-commutative 80.3%

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

      2. *-commutative 80.3%

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

      3. associate-+l+ 80.4%

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

      4. distribute-lft1-in 80.4%

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

      5. metadata-eval 80.4%

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

      6. neg-mul-1 80.4%

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

   9. Simplified 80.4%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.08 \cdot 10^{+25}:\\ \;\;\;\;x1 + \left(x1 - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \mathbf{elif}\;x1 \leq -5.8 \cdot 10^{-56} \lor \neg \left(x1 \leq 1.8 \cdot 10^{-59}\right):\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 54.5% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + x2 \cdot -6\right) \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (+ x1 (+ (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0)) (* x2 -6.0))))

C

double code(double x1, double x2) {
	return x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0));
}

Fortran

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

Java

public static double code(double x1, double x2) {
	return x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0));
}

Python

def code(x1, x2):
	return x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0))

Julia

function code(x1, x2)
	return Float64(x1 + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0)) + Float64(x2 * -6.0)))
end

MATLAB

function tmp = code(x1, x2)
	tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0));
end

Wolfram

code[x1_, x2_] := N[(x1 + N[(N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 74.2%

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

3. Taylor expanded in x1 around 0 50.3%

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

4. Taylor expanded in x1 around 0 54.3%

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

5. Final simplification 54.3%

   \[\leadsto x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + x2 \cdot -6\right) \]
6. Add Preprocessing

Alternative 15: 41.8% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq 1.9:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 1.9) (- (* x2 -6.0) x1) (+ x1 (- x1 (* x2 (- 6.0 (* x1 -12.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= 1.9) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = x1 + (x1 - (x2 * (6.0 - (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 <= 1.9d0) then
        tmp = (x2 * (-6.0d0)) - x1
    else
        tmp = x1 + (x1 - (x2 * (6.0d0 - (x1 * (-12.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= 1.9) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = x1 + (x1 - (x2 * (6.0 - (x1 * -12.0))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= 1.9:
		tmp = (x2 * -6.0) - x1
	else:
		tmp = x1 + (x1 - (x2 * (6.0 - (x1 * -12.0))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= 1.9)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	else
		tmp = Float64(x1 + Float64(x1 - Float64(x2 * Float64(6.0 - Float64(x1 * -12.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= 1.9)
		tmp = (x2 * -6.0) - x1;
	else
		tmp = x1 + (x1 - (x2 * (6.0 - (x1 * -12.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, 1.9], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], N[(x1 + N[(x1 - N[(x2 * N[(6.0 - N[(x1 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < 1.8999999999999999

   1. Initial program 79.6%

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

   3. Taylor expanded in x2 around inf 64.1%

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

      1. associate-/l* 64.1%

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

      2. +-commutative 64.1%

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

      3. unpow2 64.1%

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

      4. fma-udef 64.1%

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

   5. Simplified 64.1%

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

   6. Taylor expanded in x1 around 0 64.6%

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

   7. Taylor expanded in x2 around 0 49.9%

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

      1. +-commutative 49.9%

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

      2. *-commutative 49.9%

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

      3. associate-+l+ 50.0%

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

      4. distribute-lft1-in 50.0%

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

      5. metadata-eval 50.0%

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

      6. neg-mul-1 50.0%

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

   9. Simplified 50.0%

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

   if 1.8999999999999999 < x1

   1. Initial program 59.7%

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

   3. Taylor expanded in x1 around 0 14.0%

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

      1. add-cube-cbrt 14.0%

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

      2. pow3 14.0%

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

      3. associate-*r* 14.0%

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

      4. fma-neg 14.0%

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

      5. metadata-eval 14.0%

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

   5. Applied egg-rr 14.0%

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

   6. Taylor expanded in x1 around 0 30.0%

      \[\leadsto x1 + \left(\left(4 \cdot {\left(\sqrt[3]{\left(x1 \cdot x2\right) \cdot \mathsf{fma}\left(2, x2, -3\right)}\right)}^{3} + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative 30.0%

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

   8. Simplified 30.0%

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

   9. Taylor expanded in x2 around 0 8.3%

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

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq 1.9:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 31.9% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -5 \cdot 10^{-149}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 1.46 \cdot 10^{-92}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 -5e-149)
   (* x2 -6.0)
   (if (<= x2 1.46e-92) (- x1) (+ x1 (* x2 -6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= -5e-149) {
		tmp = x2 * -6.0;
	} else if (x2 <= 1.46e-92) {
		tmp = -x1;
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x2 <= (-5d-149)) then
        tmp = x2 * (-6.0d0)
    else if (x2 <= 1.46d-92) then
        tmp = -x1
    else
        tmp = x1 + (x2 * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x2 <= -5e-149) {
		tmp = x2 * -6.0;
	} else if (x2 <= 1.46e-92) {
		tmp = -x1;
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= -5e-149:
		tmp = x2 * -6.0
	elif x2 <= 1.46e-92:
		tmp = -x1
	else:
		tmp = x1 + (x2 * -6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= -5e-149)
		tmp = Float64(x2 * -6.0);
	elseif (x2 <= 1.46e-92)
		tmp = Float64(-x1);
	else
		tmp = Float64(x1 + Float64(x2 * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= -5e-149)
		tmp = x2 * -6.0;
	elseif (x2 <= 1.46e-92)
		tmp = -x1;
	else
		tmp = x1 + (x2 * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, -5e-149], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x2, 1.46e-92], (-x1), N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -4.99999999999999968e-149

   1. Initial program 68.5%

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

   3. Taylor expanded in x1 around 0 46.4%

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

   4. Taylor expanded in x1 around 0 29.6%

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

      1. *-commutative 29.6%

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

   6. Simplified 29.6%

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

   7. Taylor expanded in x1 around 0 29.9%

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

      1. *-commutative 29.9%

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

   9. Simplified 29.9%

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

   if -4.99999999999999968e-149 < x2 < 1.45999999999999995e-92

   1. Initial program 76.3%

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

   3. Taylor expanded in x2 around inf 51.0%

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

      1. associate-/l* 51.0%

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

      2. +-commutative 51.0%

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

      3. unpow2 51.0%

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

      4. fma-udef 51.0%

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

   5. Simplified 51.0%

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

   6. Taylor expanded in x1 around 0 50.9%

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

   7. Taylor expanded in x2 around 0 36.0%

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

      1. distribute-rgt1-in 36.0%

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

      2. metadata-eval 36.0%

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

      3. neg-mul-1 36.0%

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

   9. Simplified 36.0%

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

   if 1.45999999999999995e-92 < x2

   1. Initial program 79.0%

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

   3. Taylor expanded in x1 around 0 54.3%

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

   4. Taylor expanded in x1 around 0 28.1%

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

      1. *-commutative 28.1%

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

   6. Simplified 28.1%

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

4. Final simplification 31.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -5 \cdot 10^{-149}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 1.46 \cdot 10^{-92}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 31.6% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -4.5 \cdot 10^{-149} \lor \neg \left(x2 \leq 1.46 \cdot 10^{-92}\right):\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -4.5e-149) (not (<= x2 1.46e-92))) (* x2 -6.0) (- x1)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -4.5e-149) || !(x2 <= 1.46e-92)) {
		tmp = x2 * -6.0;
	} else {
		tmp = -x1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-4.5d-149)) .or. (.not. (x2 <= 1.46d-92))) then
        tmp = x2 * (-6.0d0)
    else
        tmp = -x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -4.5e-149) || !(x2 <= 1.46e-92)) {
		tmp = x2 * -6.0;
	} else {
		tmp = -x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -4.5e-149) or not (x2 <= 1.46e-92):
		tmp = x2 * -6.0
	else:
		tmp = -x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -4.5e-149) || !(x2 <= 1.46e-92))
		tmp = Float64(x2 * -6.0);
	else
		tmp = Float64(-x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -4.5e-149) || ~((x2 <= 1.46e-92)))
		tmp = x2 * -6.0;
	else
		tmp = -x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -4.5e-149], N[Not[LessEqual[x2, 1.46e-92]], $MachinePrecision]], N[(x2 * -6.0), $MachinePrecision], (-x1)]

Derivation

1. Split input into 2 regimes

2. if x2 < -4.4999999999999998e-149 or 1.45999999999999995e-92 < x2

   1. Initial program 73.3%

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

   3. Taylor expanded in x1 around 0 50.0%

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

   4. Taylor expanded in x1 around 0 28.9%

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

      1. *-commutative 28.9%

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

   6. Simplified 28.9%

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

   7. Taylor expanded in x1 around 0 28.7%

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

      1. *-commutative 28.7%

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

   9. Simplified 28.7%

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

   if -4.4999999999999998e-149 < x2 < 1.45999999999999995e-92

   1. Initial program 76.3%

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

   3. Taylor expanded in x2 around inf 51.0%

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

      1. associate-/l* 51.0%

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

      2. +-commutative 51.0%

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

      3. unpow2 51.0%

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

      4. fma-udef 51.0%

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

   5. Simplified 51.0%

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

   6. Taylor expanded in x1 around 0 50.9%

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

   7. Taylor expanded in x2 around 0 36.0%

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

      1. distribute-rgt1-in 36.0%

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

      2. metadata-eval 36.0%

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

      3. neg-mul-1 36.0%

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

   9. Simplified 36.0%

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

4. Final simplification 30.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -4.5 \cdot 10^{-149} \lor \neg \left(x2 \leq 1.46 \cdot 10^{-92}\right):\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 38.3% 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 74.2%

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

3. Taylor expanded in x2 around inf 51.4%

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

   1. associate-/l* 50.7%

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

   2. +-commutative 50.7%

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

   3. unpow2 50.7%

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

   4. fma-udef 50.7%

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

5. Simplified 50.7%

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

6. Taylor expanded in x1 around 0 54.3%

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

7. Taylor expanded in x2 around 0 36.5%

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

   1. +-commutative 36.5%

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

   2. *-commutative 36.5%

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

   3. associate-+l+ 36.5%

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

   4. distribute-lft1-in 36.5%

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

   5. metadata-eval 36.5%

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

   6. neg-mul-1 36.5%

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

9. Simplified 36.5%

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

10. Final simplification 36.5%

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

Alternative 19: 14.0% accurate, 63.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x1, x2):
	return -x1

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 74.2%

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

3. Taylor expanded in x2 around inf 51.4%

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

   1. associate-/l* 50.7%

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

   2. +-commutative 50.7%

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

   3. unpow2 50.7%

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

   4. fma-udef 50.7%

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

5. Simplified 50.7%

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

6. Taylor expanded in x1 around 0 54.3%

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

7. Taylor expanded in x2 around 0 13.6%

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

   1. distribute-rgt1-in 13.6%

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

   2. metadata-eval 13.6%

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

   3. neg-mul-1 13.6%

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

9. Simplified 13.6%

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

10. Final simplification 13.6%

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

Alternative 20: 3.3% accurate, 127.0× speedup

Math

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

FPCore

(FPCore (x1 x2) :precision binary64 x1)

C

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

Fortran

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

Java

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

Python

def code(x1, x2):
	return x1

Julia

function code(x1, x2)
	return x1
end

MATLAB

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

Wolfram

code[x1_, x2_] := x1

Derivation

1. Initial program 74.2%

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

3. Taylor expanded in x1 around 0 50.3%

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

4. Taylor expanded in x1 around 0 24.9%

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

   1. *-commutative 24.9%

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

6. Simplified 24.9%

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

7. Taylor expanded in x1 around inf 3.2%

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

8. Final simplification 3.2%

   \[\leadsto x1 \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024020 
(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))))))