Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.0% → 99.5%

Time: 23.7s

Alternatives: 16

Speedup: 4.4×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 70.0% 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, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ t_3 := x1 + \left(\left(x1 + \left(\left(t\_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t\_2 \cdot 4 - 6\right)\right) + t\_0 \cdot t\_2\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_1}\right)\\ \mathbf{if}\;t\_3 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;{x1}^{4} \cdot \left(6 + \frac{\frac{15 + \left(-4 \cdot \left(3 - 2 \cdot x2\right) - 6\right)}{x1} - 3}{x1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1))
        (t_3
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               t_1
               (+
                (* (* (* x1 2.0) t_2) (- t_2 3.0))
                (* (* x1 x1) (- (* t_2 4.0) 6.0))))
              (* t_0 t_2))
             (* x1 (* x1 x1))))
           (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))))))
   (if (<= t_3 INFINITY)
     t_3
     (*
      (pow x1 4.0)
      (+
       6.0
       (/ (- (/ (+ 15.0 (- (* -4.0 (- 3.0 (* 2.0 x2))) 6.0)) x1) 3.0) x1))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double t_3 = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)));
	double tmp;
	if (t_3 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = pow(x1, 4.0) * (6.0 + ((((15.0 + ((-4.0 * (3.0 - (2.0 * x2))) - 6.0)) / x1) - 3.0) / x1));
	}
	return tmp;
}

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double t_3 = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)));
	double tmp;
	if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = Math.pow(x1, 4.0) * (6.0 + ((((15.0 + ((-4.0 * (3.0 - (2.0 * x2))) - 6.0)) / x1) - 3.0) / x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1
	t_3 = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)))
	tmp = 0
	if t_3 <= math.inf:
		tmp = t_3
	else:
		tmp = math.pow(x1, 4.0) * (6.0 + ((((15.0 + ((-4.0 * (3.0 - (2.0 * x2))) - 6.0)) / x1) - 3.0) / x1))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	t_3 = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)))) + Float64(t_0 * t_2)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1))))
	tmp = 0.0
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = Float64((x1 ^ 4.0) * Float64(6.0 + Float64(Float64(Float64(Float64(15.0 + Float64(Float64(-4.0 * Float64(3.0 - Float64(2.0 * x2))) - 6.0)) / x1) - 3.0) / x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	t_3 = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)));
	tmp = 0.0;
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = (x1 ^ 4.0) * (6.0 + ((((15.0 + ((-4.0 * (3.0 - (2.0 * x2))) - 6.0)) / x1) - 3.0) / x1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, Infinity], t$95$3, N[(N[Power[x1, 4.0], $MachinePrecision] * N[(6.0 + N[(N[(N[(N[(15.0 + N[(N[(-4.0 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision] - 3.0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

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

   1. Initial program 0.0%

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

   3. Simplified 18.1%

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

   5. Taylor expanded in x1 around -inf 100.0%

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(6 + -4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.5%

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

Alternative 2: 99.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

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

   1. Initial program 0.0%

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

   3. Simplified 18.1%

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

   5. Taylor expanded in x1 around inf 95.8%

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

      1. associate-*r/ 95.8%

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

      2. metadata-eval 95.8%

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

   7. Simplified 95.8%

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

4. Final simplification 98.4%

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

Alternative 3: 97.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := {x1}^{4} \cdot \left(6 - \frac{3}{x1}\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \left(t\_2 + 2 \cdot x2\right) - x1\\ t_4 := \frac{t\_3}{-1 - x1 \cdot x1}\\ t_5 := \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_4\right)\\ t_6 := x1 \cdot x1 + 1\\ t_7 := \frac{t\_3}{t\_6}\\ \mathbf{if}\;x1 \leq -4 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{-5}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 - \left(\left(t\_2 \cdot \left(\frac{1}{x1} - 3\right) + t\_6 \cdot \left(t\_5 + \left(\left(x1 \cdot 2\right) \cdot t\_7\right) \cdot \left(3 + t\_4\right)\right)\right) - t\_0\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{+119}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_2 - 2 \cdot x2\right) - x1}{t\_6} + \left(x1 + \left(t\_0 + \left(t\_2 \cdot t\_7 - t\_6 \cdot \left(t\_5 + \left(t\_7 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x1 - 2 \cdot x2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (* (pow x1 4.0) (- 6.0 (/ 3.0 x1))))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (- (+ t_2 (* 2.0 x2)) x1))
        (t_4 (/ t_3 (- -1.0 (* x1 x1))))
        (t_5 (* (* x1 x1) (+ 6.0 (* 4.0 t_4))))
        (t_6 (+ (* x1 x1) 1.0))
        (t_7 (/ t_3 t_6)))
   (if (<= x1 -4e+104)
     t_1
     (if (<= x1 -5.6e-5)
       (+
        x1
        (+
         (* 3.0 (- (* x2 -2.0) x1))
         (-
          x1
          (-
           (+
            (* t_2 (- (/ 1.0 x1) 3.0))
            (* t_6 (+ t_5 (* (* (* x1 2.0) t_7) (+ 3.0 t_4)))))
           t_0))))
       (if (<= x1 1e+119)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_6))
           (+
            x1
            (+
             t_0
             (-
              (* t_2 t_7)
              (*
               t_6
               (+ t_5 (* (- t_7 3.0) (* (* x1 2.0) (- x1 (* 2.0 x2)))))))))))
         t_1)))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = pow(x1, 4.0) * (6.0 - (3.0 / x1));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = (t_2 + (2.0 * x2)) - x1;
	double t_4 = t_3 / (-1.0 - (x1 * x1));
	double t_5 = (x1 * x1) * (6.0 + (4.0 * t_4));
	double t_6 = (x1 * x1) + 1.0;
	double t_7 = t_3 / t_6;
	double tmp;
	if (x1 <= -4e+104) {
		tmp = t_1;
	} else if (x1 <= -5.6e-5) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 - (((t_2 * ((1.0 / x1) - 3.0)) + (t_6 * (t_5 + (((x1 * 2.0) * t_7) * (3.0 + t_4))))) - t_0)));
	} else if (x1 <= 1e+119) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_6)) + (x1 + (t_0 + ((t_2 * t_7) - (t_6 * (t_5 + ((t_7 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = x1 * (x1 * x1)
    t_1 = (x1 ** 4.0d0) * (6.0d0 - (3.0d0 / x1))
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = (t_2 + (2.0d0 * x2)) - x1
    t_4 = t_3 / ((-1.0d0) - (x1 * x1))
    t_5 = (x1 * x1) * (6.0d0 + (4.0d0 * t_4))
    t_6 = (x1 * x1) + 1.0d0
    t_7 = t_3 / t_6
    if (x1 <= (-4d+104)) then
        tmp = t_1
    else if (x1 <= (-5.6d-5)) then
        tmp = x1 + ((3.0d0 * ((x2 * (-2.0d0)) - x1)) + (x1 - (((t_2 * ((1.0d0 / x1) - 3.0d0)) + (t_6 * (t_5 + (((x1 * 2.0d0) * t_7) * (3.0d0 + t_4))))) - t_0)))
    else if (x1 <= 1d+119) then
        tmp = x1 + ((3.0d0 * (((t_2 - (2.0d0 * x2)) - x1) / t_6)) + (x1 + (t_0 + ((t_2 * t_7) - (t_6 * (t_5 + ((t_7 - 3.0d0) * ((x1 * 2.0d0) * (x1 - (2.0d0 * x2))))))))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = Math.pow(x1, 4.0) * (6.0 - (3.0 / x1));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = (t_2 + (2.0 * x2)) - x1;
	double t_4 = t_3 / (-1.0 - (x1 * x1));
	double t_5 = (x1 * x1) * (6.0 + (4.0 * t_4));
	double t_6 = (x1 * x1) + 1.0;
	double t_7 = t_3 / t_6;
	double tmp;
	if (x1 <= -4e+104) {
		tmp = t_1;
	} else if (x1 <= -5.6e-5) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 - (((t_2 * ((1.0 / x1) - 3.0)) + (t_6 * (t_5 + (((x1 * 2.0) * t_7) * (3.0 + t_4))))) - t_0)));
	} else if (x1 <= 1e+119) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_6)) + (x1 + (t_0 + ((t_2 * t_7) - (t_6 * (t_5 + ((t_7 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = math.pow(x1, 4.0) * (6.0 - (3.0 / x1))
	t_2 = x1 * (x1 * 3.0)
	t_3 = (t_2 + (2.0 * x2)) - x1
	t_4 = t_3 / (-1.0 - (x1 * x1))
	t_5 = (x1 * x1) * (6.0 + (4.0 * t_4))
	t_6 = (x1 * x1) + 1.0
	t_7 = t_3 / t_6
	tmp = 0
	if x1 <= -4e+104:
		tmp = t_1
	elif x1 <= -5.6e-5:
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 - (((t_2 * ((1.0 / x1) - 3.0)) + (t_6 * (t_5 + (((x1 * 2.0) * t_7) * (3.0 + t_4))))) - t_0)))
	elif x1 <= 1e+119:
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_6)) + (x1 + (t_0 + ((t_2 * t_7) - (t_6 * (t_5 + ((t_7 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64((x1 ^ 4.0) * Float64(6.0 - Float64(3.0 / x1)))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(t_2 + Float64(2.0 * x2)) - x1)
	t_4 = Float64(t_3 / Float64(-1.0 - Float64(x1 * x1)))
	t_5 = Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_4)))
	t_6 = Float64(Float64(x1 * x1) + 1.0)
	t_7 = Float64(t_3 / t_6)
	tmp = 0.0
	if (x1 <= -4e+104)
		tmp = t_1;
	elseif (x1 <= -5.6e-5)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - x1)) + Float64(x1 - Float64(Float64(Float64(t_2 * Float64(Float64(1.0 / x1) - 3.0)) + Float64(t_6 * Float64(t_5 + Float64(Float64(Float64(x1 * 2.0) * t_7) * Float64(3.0 + t_4))))) - t_0))));
	elseif (x1 <= 1e+119)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_6)) + Float64(x1 + Float64(t_0 + Float64(Float64(t_2 * t_7) - Float64(t_6 * Float64(t_5 + Float64(Float64(t_7 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(x1 - Float64(2.0 * x2)))))))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = (x1 ^ 4.0) * (6.0 - (3.0 / x1));
	t_2 = x1 * (x1 * 3.0);
	t_3 = (t_2 + (2.0 * x2)) - x1;
	t_4 = t_3 / (-1.0 - (x1 * x1));
	t_5 = (x1 * x1) * (6.0 + (4.0 * t_4));
	t_6 = (x1 * x1) + 1.0;
	t_7 = t_3 / t_6;
	tmp = 0.0;
	if (x1 <= -4e+104)
		tmp = t_1;
	elseif (x1 <= -5.6e-5)
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 - (((t_2 * ((1.0 / x1) - 3.0)) + (t_6 * (t_5 + (((x1 * 2.0) * t_7) * (3.0 + t_4))))) - t_0)));
	elseif (x1 <= 1e+119)
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_6)) + (x1 + (t_0 + ((t_2 * t_7) - (t_6 * (t_5 + ((t_7 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Power[x1, 4.0], $MachinePrecision] * N[(6.0 - N[(3.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$3 / t$95$6), $MachinePrecision]}, If[LessEqual[x1, -4e+104], t$95$1, If[LessEqual[x1, -5.6e-5], N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] + N[(x1 - N[(N[(N[(t$95$2 * N[(N[(1.0 / x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$6 * N[(t$95$5 + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$7), $MachinePrecision] * N[(3.0 + t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1e+119], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$6), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$0 + N[(N[(t$95$2 * t$95$7), $MachinePrecision] - N[(t$95$6 * N[(t$95$5 + N[(N[(t$95$7 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(x1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4e104 or 9.99999999999999944e118 < x1

   1. Initial program 10.1%

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

   3. Simplified 25.3%

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

   5. Taylor expanded in x1 around inf 97.5%

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

      1. associate-*r/ 97.5%

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

      2. metadata-eval 97.5%

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

   7. Simplified 97.5%

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

   if -4e104 < x1 < -5.59999999999999992e-5

   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 99.5%

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

      1. mul-1-neg 99.5%

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

      2. unsub-neg 99.5%

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

      3. *-commutative 99.5%

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

   5. Simplified 99.5%

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

   6. Taylor expanded in x1 around inf 99.5%

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

   if -5.59999999999999992e-5 < x1 < 9.99999999999999944e118

   1. Initial program 98.6%

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

   3. Taylor expanded in x1 around 0 97.2%

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

      1. +-commutative 97.2%

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

      2. mul-1-neg 97.2%

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

      3. unsub-neg 97.2%

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

   5. Simplified 97.2%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+104}:\\ \;\;\;\;{x1}^{4} \cdot \left(6 - \frac{3}{x1}\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{-5}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 - \left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(\frac{1}{x1} - 3\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{+119}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x1 - 2 \cdot x2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{x1}^{4} \cdot \left(6 - \frac{3}{x1}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102} \lor \neg \left(x1 \leq 2.7 \cdot 10^{+73}\right):\\ \;\;\;\;{x1}^{4} \cdot \left(6 - \frac{3}{x1}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t\_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t\_2 \cdot 4 - 6\right)\right) + t\_0 \cdot t\_2\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (if (or (<= x1 -5.6e+102) (not (<= x1 2.7e+73)))
     (* (pow x1 4.0) (- 6.0 (/ 3.0 x1)))
     (+
      x1
      (+
       (+
        x1
        (+
         (+
          (*
           t_1
           (+
            (* (* (* x1 2.0) t_2) (- t_2 3.0))
            (* (* x1 x1) (- (* t_2 4.0) 6.0))))
          (* t_0 t_2))
         (* x1 (* x1 x1))))
       (* 3.0 (- (* x2 -2.0) x1)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -5.6e+102) || !(x1 <= 2.7e+73)) {
		tmp = pow(x1, 4.0) * (6.0 - (3.0 / x1));
	} else {
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    if ((x1 <= (-5.6d+102)) .or. (.not. (x1 <= 2.7d+73))) then
        tmp = (x1 ** 4.0d0) * (6.0d0 - (3.0d0 / x1))
    else
        tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * ((t_2 * 4.0d0) - 6.0d0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0d0 * ((x2 * (-2.0d0)) - x1)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -5.6e+102) || !(x1 <= 2.7e+73)) {
		tmp = Math.pow(x1, 4.0) * (6.0 - (3.0 / x1));
	} else {
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1
	tmp = 0
	if (x1 <= -5.6e+102) or not (x1 <= 2.7e+73):
		tmp = math.pow(x1, 4.0) * (6.0 - (3.0 / x1))
	else:
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if ((x1 <= -5.6e+102) || !(x1 <= 2.7e+73))
		tmp = Float64((x1 ^ 4.0) * Float64(6.0 - Float64(3.0 / x1)));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)))) + Float64(t_0 * t_2)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	tmp = 0.0;
	if ((x1 <= -5.6e+102) || ~((x1 <= 2.7e+73)))
		tmp = (x1 ^ 4.0) * (6.0 - (3.0 / x1));
	else
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[x1, -5.6e+102], N[Not[LessEqual[x1, 2.7e+73]], $MachinePrecision]], N[(N[Power[x1, 4.0], $MachinePrecision] * N[(6.0 - N[(3.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -5.60000000000000037e102 or 2.6999999999999999e73 < x1

   1. Initial program 18.2%

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

   3. Simplified 33.0%

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

   5. Taylor expanded in x1 around inf 96.6%

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

      1. associate-*r/ 96.6%

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

      2. metadata-eval 96.6%

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

   7. Simplified 96.6%

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

   if -5.60000000000000037e102 < x1 < 2.6999999999999999e73

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 98.9%

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

      1. mul-1-neg 98.9%

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

      2. unsub-neg 98.9%

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

      3. *-commutative 98.9%

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

   5. Simplified 98.9%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102} \lor \neg \left(x1 \leq 2.7 \cdot 10^{+73}\right):\\ \;\;\;\;{x1}^{4} \cdot \left(6 - \frac{3}{x1}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 \cdot \left(x2 \cdot -2 - x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := {x1}^{4} \cdot \left(6 - \frac{3}{x1}\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := \left(t\_3 + 2 \cdot x2\right) - x1\\ t_5 := \frac{t\_4}{-1 - x1 \cdot x1}\\ t_6 := \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_5\right)\\ t_7 := x1 \cdot x1 + 1\\ t_8 := \frac{t\_4}{t\_7}\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq -1 \cdot 10^{-5}:\\ \;\;\;\;x1 + \left(t\_0 + \left(x1 - \left(\left(t\_3 \cdot \left(\frac{1}{x1} - 3\right) + t\_7 \cdot \left(t\_6 + \left(\left(x1 \cdot 2\right) \cdot t\_8\right) \cdot \left(3 + t\_5\right)\right)\right) - t\_1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{+118}:\\ \;\;\;\;x1 + \left(t\_0 + \left(x1 + \left(t\_1 + \left(t\_3 \cdot t\_8 - t\_7 \cdot \left(t\_6 + \left(t\_8 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x1 - 2 \cdot x2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 3.0 (- (* x2 -2.0) x1)))
        (t_1 (* x1 (* x1 x1)))
        (t_2 (* (pow x1 4.0) (- 6.0 (/ 3.0 x1))))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (- (+ t_3 (* 2.0 x2)) x1))
        (t_5 (/ t_4 (- -1.0 (* x1 x1))))
        (t_6 (* (* x1 x1) (+ 6.0 (* 4.0 t_5))))
        (t_7 (+ (* x1 x1) 1.0))
        (t_8 (/ t_4 t_7)))
   (if (<= x1 -5e+102)
     t_2
     (if (<= x1 -1e-5)
       (+
        x1
        (+
         t_0
         (-
          x1
          (-
           (+
            (* t_3 (- (/ 1.0 x1) 3.0))
            (* t_7 (+ t_6 (* (* (* x1 2.0) t_8) (+ 3.0 t_5)))))
           t_1))))
       (if (<= x1 6e+118)
         (+
          x1
          (+
           t_0
           (+
            x1
            (+
             t_1
             (-
              (* t_3 t_8)
              (*
               t_7
               (+ t_6 (* (- t_8 3.0) (* (* x1 2.0) (- x1 (* 2.0 x2)))))))))))
         t_2)))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 * ((x2 * -2.0) - x1);
	double t_1 = x1 * (x1 * x1);
	double t_2 = pow(x1, 4.0) * (6.0 - (3.0 / x1));
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = (t_3 + (2.0 * x2)) - x1;
	double t_5 = t_4 / (-1.0 - (x1 * x1));
	double t_6 = (x1 * x1) * (6.0 + (4.0 * t_5));
	double t_7 = (x1 * x1) + 1.0;
	double t_8 = t_4 / t_7;
	double tmp;
	if (x1 <= -5e+102) {
		tmp = t_2;
	} else if (x1 <= -1e-5) {
		tmp = x1 + (t_0 + (x1 - (((t_3 * ((1.0 / x1) - 3.0)) + (t_7 * (t_6 + (((x1 * 2.0) * t_8) * (3.0 + t_5))))) - t_1)));
	} else if (x1 <= 6e+118) {
		tmp = x1 + (t_0 + (x1 + (t_1 + ((t_3 * t_8) - (t_7 * (t_6 + ((t_8 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: tmp
    t_0 = 3.0d0 * ((x2 * (-2.0d0)) - x1)
    t_1 = x1 * (x1 * x1)
    t_2 = (x1 ** 4.0d0) * (6.0d0 - (3.0d0 / x1))
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = (t_3 + (2.0d0 * x2)) - x1
    t_5 = t_4 / ((-1.0d0) - (x1 * x1))
    t_6 = (x1 * x1) * (6.0d0 + (4.0d0 * t_5))
    t_7 = (x1 * x1) + 1.0d0
    t_8 = t_4 / t_7
    if (x1 <= (-5d+102)) then
        tmp = t_2
    else if (x1 <= (-1d-5)) then
        tmp = x1 + (t_0 + (x1 - (((t_3 * ((1.0d0 / x1) - 3.0d0)) + (t_7 * (t_6 + (((x1 * 2.0d0) * t_8) * (3.0d0 + t_5))))) - t_1)))
    else if (x1 <= 6d+118) then
        tmp = x1 + (t_0 + (x1 + (t_1 + ((t_3 * t_8) - (t_7 * (t_6 + ((t_8 - 3.0d0) * ((x1 * 2.0d0) * (x1 - (2.0d0 * x2))))))))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 * ((x2 * -2.0) - x1);
	double t_1 = x1 * (x1 * x1);
	double t_2 = Math.pow(x1, 4.0) * (6.0 - (3.0 / x1));
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = (t_3 + (2.0 * x2)) - x1;
	double t_5 = t_4 / (-1.0 - (x1 * x1));
	double t_6 = (x1 * x1) * (6.0 + (4.0 * t_5));
	double t_7 = (x1 * x1) + 1.0;
	double t_8 = t_4 / t_7;
	double tmp;
	if (x1 <= -5e+102) {
		tmp = t_2;
	} else if (x1 <= -1e-5) {
		tmp = x1 + (t_0 + (x1 - (((t_3 * ((1.0 / x1) - 3.0)) + (t_7 * (t_6 + (((x1 * 2.0) * t_8) * (3.0 + t_5))))) - t_1)));
	} else if (x1 <= 6e+118) {
		tmp = x1 + (t_0 + (x1 + (t_1 + ((t_3 * t_8) - (t_7 * (t_6 + ((t_8 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 * ((x2 * -2.0) - x1)
	t_1 = x1 * (x1 * x1)
	t_2 = math.pow(x1, 4.0) * (6.0 - (3.0 / x1))
	t_3 = x1 * (x1 * 3.0)
	t_4 = (t_3 + (2.0 * x2)) - x1
	t_5 = t_4 / (-1.0 - (x1 * x1))
	t_6 = (x1 * x1) * (6.0 + (4.0 * t_5))
	t_7 = (x1 * x1) + 1.0
	t_8 = t_4 / t_7
	tmp = 0
	if x1 <= -5e+102:
		tmp = t_2
	elif x1 <= -1e-5:
		tmp = x1 + (t_0 + (x1 - (((t_3 * ((1.0 / x1) - 3.0)) + (t_7 * (t_6 + (((x1 * 2.0) * t_8) * (3.0 + t_5))))) - t_1)))
	elif x1 <= 6e+118:
		tmp = x1 + (t_0 + (x1 + (t_1 + ((t_3 * t_8) - (t_7 * (t_6 + ((t_8 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))
	t_1 = Float64(x1 * Float64(x1 * x1))
	t_2 = Float64((x1 ^ 4.0) * Float64(6.0 - Float64(3.0 / x1)))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(Float64(t_3 + Float64(2.0 * x2)) - x1)
	t_5 = Float64(t_4 / Float64(-1.0 - Float64(x1 * x1)))
	t_6 = Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_5)))
	t_7 = Float64(Float64(x1 * x1) + 1.0)
	t_8 = Float64(t_4 / t_7)
	tmp = 0.0
	if (x1 <= -5e+102)
		tmp = t_2;
	elseif (x1 <= -1e-5)
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 - Float64(Float64(Float64(t_3 * Float64(Float64(1.0 / x1) - 3.0)) + Float64(t_7 * Float64(t_6 + Float64(Float64(Float64(x1 * 2.0) * t_8) * Float64(3.0 + t_5))))) - t_1))));
	elseif (x1 <= 6e+118)
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(t_1 + Float64(Float64(t_3 * t_8) - Float64(t_7 * Float64(t_6 + Float64(Float64(t_8 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(x1 - Float64(2.0 * x2)))))))))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 * ((x2 * -2.0) - x1);
	t_1 = x1 * (x1 * x1);
	t_2 = (x1 ^ 4.0) * (6.0 - (3.0 / x1));
	t_3 = x1 * (x1 * 3.0);
	t_4 = (t_3 + (2.0 * x2)) - x1;
	t_5 = t_4 / (-1.0 - (x1 * x1));
	t_6 = (x1 * x1) * (6.0 + (4.0 * t_5));
	t_7 = (x1 * x1) + 1.0;
	t_8 = t_4 / t_7;
	tmp = 0.0;
	if (x1 <= -5e+102)
		tmp = t_2;
	elseif (x1 <= -1e-5)
		tmp = x1 + (t_0 + (x1 - (((t_3 * ((1.0 / x1) - 3.0)) + (t_7 * (t_6 + (((x1 * 2.0) * t_8) * (3.0 + t_5))))) - t_1)));
	elseif (x1 <= 6e+118)
		tmp = x1 + (t_0 + (x1 + (t_1 + ((t_3 * t_8) - (t_7 * (t_6 + ((t_8 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Power[x1, 4.0], $MachinePrecision] * N[(6.0 - N[(3.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$4 / t$95$7), $MachinePrecision]}, If[LessEqual[x1, -5e+102], t$95$2, If[LessEqual[x1, -1e-5], N[(x1 + N[(t$95$0 + N[(x1 - N[(N[(N[(t$95$3 * N[(N[(1.0 / x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$7 * N[(t$95$6 + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$8), $MachinePrecision] * N[(3.0 + t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6e+118], N[(x1 + N[(t$95$0 + N[(x1 + N[(t$95$1 + N[(N[(t$95$3 * t$95$8), $MachinePrecision] - N[(t$95$7 * N[(t$95$6 + N[(N[(t$95$8 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(x1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5e102 or 6e118 < x1

   1. Initial program 10.1%

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

   3. Simplified 25.3%

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

   5. Taylor expanded in x1 around inf 97.5%

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

      1. associate-*r/ 97.5%

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

      2. metadata-eval 97.5%

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

   7. Simplified 97.5%

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

   if -5e102 < x1 < -1.00000000000000008e-5

   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 99.5%

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

      1. mul-1-neg 99.5%

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

      2. unsub-neg 99.5%

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

      3. *-commutative 99.5%

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

   5. Simplified 99.5%

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

   6. Taylor expanded in x1 around inf 99.5%

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

   if -1.00000000000000008e-5 < x1 < 6e118

   1. Initial program 98.6%

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

   3. Taylor expanded in x1 around 0 98.2%

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

      1. mul-1-neg 98.2%

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

      2. unsub-neg 98.2%

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

      3. *-commutative 98.2%

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

   5. Simplified 98.2%

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

   6. Taylor expanded in x1 around 0 96.7%

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

      1. +-commutative 97.2%

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

      2. mul-1-neg 97.2%

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

      3. unsub-neg 97.2%

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

   8. Simplified 96.7%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;{x1}^{4} \cdot \left(6 - \frac{3}{x1}\right)\\ \mathbf{elif}\;x1 \leq -1 \cdot 10^{-5}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 - \left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(\frac{1}{x1} - 3\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{+118}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x1 - 2 \cdot x2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{x1}^{4} \cdot \left(6 - \frac{3}{x1}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 - x1 \cdot x1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\left(t\_1 + 2 \cdot x2\right) - x1}{t\_0}\\ t_3 := x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(t\_1 \cdot t\_2 - t\_0 \cdot \left(\left(x1 \cdot \left(6 + \frac{-2}{x1}\right)\right) \cdot \left(3 + t\_2\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_2\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x1 \cdot \left(12 + x1 \cdot 24\right)\right) - x1 \cdot \left(9 + x1 \cdot -19\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq -3100:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x1 \leq 12000:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{elif}\;x1 \leq 5.2 \cdot 10^{+141}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 12\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- -1.0 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (/ (- (+ t_1 (* 2.0 x2)) x1) t_0))
        (t_3
         (+
          x1
          (+
           (* 3.0 (- (* x2 -2.0) x1))
           (+
            x1
            (-
             (* x1 (* x1 x1))
             (-
              (* t_1 t_2)
              (*
               t_0
               (+
                (* (* x1 (+ 6.0 (/ -2.0 x1))) (+ 3.0 t_2))
                (* (* x1 x1) (+ 6.0 (* 4.0 t_2))))))))))))
   (if (<= x1 -5.6e+102)
     (-
      (* x2 -6.0)
      (*
       x1
       (-
        (-
         (* x2 (- 12.0 (* x1 (+ 12.0 (* x1 24.0)))))
         (* x1 (+ 9.0 (* x1 -19.0))))
        -1.0)))
     (if (<= x1 -3100.0)
       t_3
       (if (<= x1 12000.0)
         (- (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0)) x1)
         (if (<= x1 5.2e+141)
           t_3
           (+
            (* x2 -6.0)
            (* x1 (+ -1.0 (+ (* x2 -12.0) (* x1 (+ 9.0 (* x2 12.0)))))))))))))

C

double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0;
	double t_3 = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + ((x1 * (x1 * x1)) - ((t_1 * t_2) - (t_0 * (((x1 * (6.0 + (-2.0 / x1))) * (3.0 + t_2)) + ((x1 * x1) * (6.0 + (4.0 * t_2)))))))));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x1 * (12.0 + (x1 * 24.0))))) - (x1 * (9.0 + (x1 * -19.0)))) - -1.0));
	} else if (x1 <= -3100.0) {
		tmp = t_3;
	} else if (x1 <= 12000.0) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else if (x1 <= 5.2e+141) {
		tmp = t_3;
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * -12.0) + (x1 * (9.0 + (x2 * 12.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = (-1.0d0) - (x1 * x1)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = ((t_1 + (2.0d0 * x2)) - x1) / t_0
    t_3 = x1 + ((3.0d0 * ((x2 * (-2.0d0)) - x1)) + (x1 + ((x1 * (x1 * x1)) - ((t_1 * t_2) - (t_0 * (((x1 * (6.0d0 + ((-2.0d0) / x1))) * (3.0d0 + t_2)) + ((x1 * x1) * (6.0d0 + (4.0d0 * t_2)))))))))
    if (x1 <= (-5.6d+102)) then
        tmp = (x2 * (-6.0d0)) - (x1 * (((x2 * (12.0d0 - (x1 * (12.0d0 + (x1 * 24.0d0))))) - (x1 * (9.0d0 + (x1 * (-19.0d0))))) - (-1.0d0)))
    else if (x1 <= (-3100.0d0)) then
        tmp = t_3
    else if (x1 <= 12000.0d0) then
        tmp = (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)) - x1
    else if (x1 <= 5.2d+141) then
        tmp = t_3
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + ((x2 * (-12.0d0)) + (x1 * (9.0d0 + (x2 * 12.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0;
	double t_3 = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + ((x1 * (x1 * x1)) - ((t_1 * t_2) - (t_0 * (((x1 * (6.0 + (-2.0 / x1))) * (3.0 + t_2)) + ((x1 * x1) * (6.0 + (4.0 * t_2)))))))));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x1 * (12.0 + (x1 * 24.0))))) - (x1 * (9.0 + (x1 * -19.0)))) - -1.0));
	} else if (x1 <= -3100.0) {
		tmp = t_3;
	} else if (x1 <= 12000.0) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else if (x1 <= 5.2e+141) {
		tmp = t_3;
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * -12.0) + (x1 * (9.0 + (x2 * 12.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = -1.0 - (x1 * x1)
	t_1 = x1 * (x1 * 3.0)
	t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0
	t_3 = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + ((x1 * (x1 * x1)) - ((t_1 * t_2) - (t_0 * (((x1 * (6.0 + (-2.0 / x1))) * (3.0 + t_2)) + ((x1 * x1) * (6.0 + (4.0 * t_2)))))))))
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x1 * (12.0 + (x1 * 24.0))))) - (x1 * (9.0 + (x1 * -19.0)))) - -1.0))
	elif x1 <= -3100.0:
		tmp = t_3
	elif x1 <= 12000.0:
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1
	elif x1 <= 5.2e+141:
		tmp = t_3
	else:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * -12.0) + (x1 * (9.0 + (x2 * 12.0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(-1.0 - Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_0)
	t_3 = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - x1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) - Float64(Float64(t_1 * t_2) - Float64(t_0 * Float64(Float64(Float64(x1 * Float64(6.0 + Float64(-2.0 / x1))) * Float64(3.0 + t_2)) + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_2))))))))))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(Float64(Float64(x2 * Float64(12.0 - Float64(x1 * Float64(12.0 + Float64(x1 * 24.0))))) - Float64(x1 * Float64(9.0 + Float64(x1 * -19.0)))) - -1.0)));
	elseif (x1 <= -3100.0)
		tmp = t_3;
	elseif (x1 <= 12000.0)
		tmp = Float64(Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0)) - x1);
	elseif (x1 <= 5.2e+141)
		tmp = t_3;
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(Float64(x2 * -12.0) + Float64(x1 * Float64(9.0 + Float64(x2 * 12.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = -1.0 - (x1 * x1);
	t_1 = x1 * (x1 * 3.0);
	t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0;
	t_3 = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + ((x1 * (x1 * x1)) - ((t_1 * t_2) - (t_0 * (((x1 * (6.0 + (-2.0 / x1))) * (3.0 + t_2)) + ((x1 * x1) * (6.0 + (4.0 * t_2)))))))));
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x1 * (12.0 + (x1 * 24.0))))) - (x1 * (9.0 + (x1 * -19.0)))) - -1.0));
	elseif (x1 <= -3100.0)
		tmp = t_3;
	elseif (x1 <= 12000.0)
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	elseif (x1 <= 5.2e+141)
		tmp = t_3;
	else
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * -12.0) + (x1 * (9.0 + (x2 * 12.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$1 * t$95$2), $MachinePrecision] - N[(t$95$0 * N[(N[(N[(x1 * N[(6.0 + N[(-2.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(3.0 + t$95$2), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(N[(N[(x2 * N[(12.0 - N[(x1 * N[(12.0 + N[(x1 * 24.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -3100.0], t$95$3, If[LessEqual[x1, 12000.0], N[(N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 5.2e+141], t$95$3, N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(N[(x2 * -12.0), $MachinePrecision] + N[(x1 * N[(9.0 + N[(x2 * 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   3. Simplified 27.8%

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

   5. Taylor expanded in x1 around 0 55.6%

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

   6. Taylor expanded in x2 around 0 61.1%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) + x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right)} - 1\right) \]

   if -5.60000000000000037e102 < x1 < -3100 or 12000 < x1 < 5.1999999999999999e141

   1. Initial program 95.8%

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

      1. add-cube-cbrt 95.7%

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

      2. pow3 95.7%

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

   4. Applied egg-rr 95.7%

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

   5. Taylor expanded in x1 around 0 95.7%

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

      1. mul-1-neg 95.8%

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

      2. unsub-neg 95.8%

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

      3. *-commutative 95.8%

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

   7. Simplified 95.7%

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

   8. Taylor expanded in x1 around inf 81.9%

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

      1. rem-cube-cbrt 81.9%

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

      2. associate-*r/ 81.9%

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

      3. metadata-eval 81.9%

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

      4. rem-cube-cbrt 81.9%

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

      5. metadata-eval 81.9%

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

   10. Simplified 81.9%

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

   if -3100 < x1 < 12000

   1. Initial program 99.3%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in x1 around 0 84.6%

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

      1. fma-define 84.7%

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

      2. metadata-eval 84.7%

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

      3. cancel-sign-sub-inv 84.7%

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

      4. associate-*r* 84.7%

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

      5. fmm-def 84.7%

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

      6. *-commutative 84.7%

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

      7. cancel-sign-sub-inv 84.7%

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

      8. metadata-eval 84.7%

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

      9. *-commutative 84.7%

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

      10. metadata-eval 84.7%

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

   7. Simplified 84.7%

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

   8. Taylor expanded in x2 around 0 97.5%

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

   if 5.1999999999999999e141 < x1

   1. Initial program 8.1%

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

   3. Simplified 10.8%

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

   5. Taylor expanded in x1 around 0 78.6%

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

   6. Taylor expanded in x2 around 0 70.5%

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

   7. Taylor expanded in x1 around 0 81.3%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x1 \cdot \left(12 + x1 \cdot 24\right)\right) - x1 \cdot \left(9 + x1 \cdot -19\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq -3100:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(x1 \cdot \left(6 + \frac{-2}{x1}\right)\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 12000:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{elif}\;x1 \leq 5.2 \cdot 10^{+141}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(x1 \cdot \left(6 + \frac{-2}{x1}\right)\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 12\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := \left(t\_0 + 2 \cdot x2\right) - x1\\ t_2 := \frac{t\_1}{-1 - x1 \cdot x1}\\ t_3 := x1 \cdot x1 + 1\\ t_4 := \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_2\right)\\ t_5 := x1 \cdot \left(x1 \cdot x1\right)\\ t_6 := 3 \cdot \left(x2 \cdot -2 - x1\right)\\ t_7 := \frac{t\_1}{t\_3}\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x1 \cdot \left(12 + x1 \cdot 24\right)\right) - x1 \cdot \left(9 + x1 \cdot -19\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq -4.2 \cdot 10^{-5}:\\ \;\;\;\;x1 + \left(t\_6 + \left(x1 - \left(\left(t\_0 \cdot \left(\frac{1}{x1} - 3\right) + t\_3 \cdot \left(t\_4 + \left(\left(x1 \cdot 2\right) \cdot t\_7\right) \cdot \left(3 + t\_2\right)\right)\right) - t\_5\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5.2 \cdot 10^{+141}:\\ \;\;\;\;x1 + \left(t\_6 + \left(x1 + \left(t\_5 + \left(t\_0 \cdot t\_7 - t\_3 \cdot \left(t\_4 + \left(t\_7 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x1 - 2 \cdot x2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 12\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (- (+ t_0 (* 2.0 x2)) x1))
        (t_2 (/ t_1 (- -1.0 (* x1 x1))))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (* (* x1 x1) (+ 6.0 (* 4.0 t_2))))
        (t_5 (* x1 (* x1 x1)))
        (t_6 (* 3.0 (- (* x2 -2.0) x1)))
        (t_7 (/ t_1 t_3)))
   (if (<= x1 -5.6e+102)
     (-
      (* x2 -6.0)
      (*
       x1
       (-
        (-
         (* x2 (- 12.0 (* x1 (+ 12.0 (* x1 24.0)))))
         (* x1 (+ 9.0 (* x1 -19.0))))
        -1.0)))
     (if (<= x1 -4.2e-5)
       (+
        x1
        (+
         t_6
         (-
          x1
          (-
           (+
            (* t_0 (- (/ 1.0 x1) 3.0))
            (* t_3 (+ t_4 (* (* (* x1 2.0) t_7) (+ 3.0 t_2)))))
           t_5))))
       (if (<= x1 5.2e+141)
         (+
          x1
          (+
           t_6
           (+
            x1
            (+
             t_5
             (-
              (* t_0 t_7)
              (*
               t_3
               (+ t_4 (* (- t_7 3.0) (* (* x1 2.0) (- x1 (* 2.0 x2)))))))))))
         (+
          (* x2 -6.0)
          (* x1 (+ -1.0 (+ (* x2 -12.0) (* x1 (+ 9.0 (* x2 12.0))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (t_0 + (2.0 * x2)) - x1;
	double t_2 = t_1 / (-1.0 - (x1 * x1));
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = (x1 * x1) * (6.0 + (4.0 * t_2));
	double t_5 = x1 * (x1 * x1);
	double t_6 = 3.0 * ((x2 * -2.0) - x1);
	double t_7 = t_1 / t_3;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x1 * (12.0 + (x1 * 24.0))))) - (x1 * (9.0 + (x1 * -19.0)))) - -1.0));
	} else if (x1 <= -4.2e-5) {
		tmp = x1 + (t_6 + (x1 - (((t_0 * ((1.0 / x1) - 3.0)) + (t_3 * (t_4 + (((x1 * 2.0) * t_7) * (3.0 + t_2))))) - t_5)));
	} else if (x1 <= 5.2e+141) {
		tmp = x1 + (t_6 + (x1 + (t_5 + ((t_0 * t_7) - (t_3 * (t_4 + ((t_7 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * -12.0) + (x1 * (9.0 + (x2 * 12.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (t_0 + (2.0d0 * x2)) - x1
    t_2 = t_1 / ((-1.0d0) - (x1 * x1))
    t_3 = (x1 * x1) + 1.0d0
    t_4 = (x1 * x1) * (6.0d0 + (4.0d0 * t_2))
    t_5 = x1 * (x1 * x1)
    t_6 = 3.0d0 * ((x2 * (-2.0d0)) - x1)
    t_7 = t_1 / t_3
    if (x1 <= (-5.6d+102)) then
        tmp = (x2 * (-6.0d0)) - (x1 * (((x2 * (12.0d0 - (x1 * (12.0d0 + (x1 * 24.0d0))))) - (x1 * (9.0d0 + (x1 * (-19.0d0))))) - (-1.0d0)))
    else if (x1 <= (-4.2d-5)) then
        tmp = x1 + (t_6 + (x1 - (((t_0 * ((1.0d0 / x1) - 3.0d0)) + (t_3 * (t_4 + (((x1 * 2.0d0) * t_7) * (3.0d0 + t_2))))) - t_5)))
    else if (x1 <= 5.2d+141) then
        tmp = x1 + (t_6 + (x1 + (t_5 + ((t_0 * t_7) - (t_3 * (t_4 + ((t_7 - 3.0d0) * ((x1 * 2.0d0) * (x1 - (2.0d0 * x2))))))))))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + ((x2 * (-12.0d0)) + (x1 * (9.0d0 + (x2 * 12.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (t_0 + (2.0 * x2)) - x1;
	double t_2 = t_1 / (-1.0 - (x1 * x1));
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = (x1 * x1) * (6.0 + (4.0 * t_2));
	double t_5 = x1 * (x1 * x1);
	double t_6 = 3.0 * ((x2 * -2.0) - x1);
	double t_7 = t_1 / t_3;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x1 * (12.0 + (x1 * 24.0))))) - (x1 * (9.0 + (x1 * -19.0)))) - -1.0));
	} else if (x1 <= -4.2e-5) {
		tmp = x1 + (t_6 + (x1 - (((t_0 * ((1.0 / x1) - 3.0)) + (t_3 * (t_4 + (((x1 * 2.0) * t_7) * (3.0 + t_2))))) - t_5)));
	} else if (x1 <= 5.2e+141) {
		tmp = x1 + (t_6 + (x1 + (t_5 + ((t_0 * t_7) - (t_3 * (t_4 + ((t_7 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * -12.0) + (x1 * (9.0 + (x2 * 12.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (t_0 + (2.0 * x2)) - x1
	t_2 = t_1 / (-1.0 - (x1 * x1))
	t_3 = (x1 * x1) + 1.0
	t_4 = (x1 * x1) * (6.0 + (4.0 * t_2))
	t_5 = x1 * (x1 * x1)
	t_6 = 3.0 * ((x2 * -2.0) - x1)
	t_7 = t_1 / t_3
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x1 * (12.0 + (x1 * 24.0))))) - (x1 * (9.0 + (x1 * -19.0)))) - -1.0))
	elif x1 <= -4.2e-5:
		tmp = x1 + (t_6 + (x1 - (((t_0 * ((1.0 / x1) - 3.0)) + (t_3 * (t_4 + (((x1 * 2.0) * t_7) * (3.0 + t_2))))) - t_5)))
	elif x1 <= 5.2e+141:
		tmp = x1 + (t_6 + (x1 + (t_5 + ((t_0 * t_7) - (t_3 * (t_4 + ((t_7 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))))
	else:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * -12.0) + (x1 * (9.0 + (x2 * 12.0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(t_0 + Float64(2.0 * x2)) - x1)
	t_2 = Float64(t_1 / Float64(-1.0 - Float64(x1 * x1)))
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_2)))
	t_5 = Float64(x1 * Float64(x1 * x1))
	t_6 = Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))
	t_7 = Float64(t_1 / t_3)
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(Float64(Float64(x2 * Float64(12.0 - Float64(x1 * Float64(12.0 + Float64(x1 * 24.0))))) - Float64(x1 * Float64(9.0 + Float64(x1 * -19.0)))) - -1.0)));
	elseif (x1 <= -4.2e-5)
		tmp = Float64(x1 + Float64(t_6 + Float64(x1 - Float64(Float64(Float64(t_0 * Float64(Float64(1.0 / x1) - 3.0)) + Float64(t_3 * Float64(t_4 + Float64(Float64(Float64(x1 * 2.0) * t_7) * Float64(3.0 + t_2))))) - t_5))));
	elseif (x1 <= 5.2e+141)
		tmp = Float64(x1 + Float64(t_6 + Float64(x1 + Float64(t_5 + Float64(Float64(t_0 * t_7) - Float64(t_3 * Float64(t_4 + Float64(Float64(t_7 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(x1 - Float64(2.0 * x2)))))))))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(Float64(x2 * -12.0) + Float64(x1 * Float64(9.0 + Float64(x2 * 12.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (t_0 + (2.0 * x2)) - x1;
	t_2 = t_1 / (-1.0 - (x1 * x1));
	t_3 = (x1 * x1) + 1.0;
	t_4 = (x1 * x1) * (6.0 + (4.0 * t_2));
	t_5 = x1 * (x1 * x1);
	t_6 = 3.0 * ((x2 * -2.0) - x1);
	t_7 = t_1 / t_3;
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x1 * (12.0 + (x1 * 24.0))))) - (x1 * (9.0 + (x1 * -19.0)))) - -1.0));
	elseif (x1 <= -4.2e-5)
		tmp = x1 + (t_6 + (x1 - (((t_0 * ((1.0 / x1) - 3.0)) + (t_3 * (t_4 + (((x1 * 2.0) * t_7) * (3.0 + t_2))))) - t_5)));
	elseif (x1 <= 5.2e+141)
		tmp = x1 + (t_6 + (x1 + (t_5 + ((t_0 * t_7) - (t_3 * (t_4 + ((t_7 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))));
	else
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * -12.0) + (x1 * (9.0 + (x2 * 12.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$1 / t$95$3), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(N[(N[(x2 * N[(12.0 - N[(x1 * N[(12.0 + N[(x1 * 24.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -4.2e-5], N[(x1 + N[(t$95$6 + N[(x1 - N[(N[(N[(t$95$0 * N[(N[(1.0 / x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 * N[(t$95$4 + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$7), $MachinePrecision] * N[(3.0 + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.2e+141], N[(x1 + N[(t$95$6 + N[(x1 + N[(t$95$5 + N[(N[(t$95$0 * t$95$7), $MachinePrecision] - N[(t$95$3 * N[(t$95$4 + N[(N[(t$95$7 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(x1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(N[(x2 * -12.0), $MachinePrecision] + N[(x1 * N[(9.0 + N[(x2 * 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   3. Simplified 27.8%

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

   5. Taylor expanded in x1 around 0 55.6%

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

   6. Taylor expanded in x2 around 0 61.1%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) + x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right)} - 1\right) \]

   if -5.60000000000000037e102 < x1 < -4.19999999999999977e-5

   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 99.5%

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

      1. mul-1-neg 99.5%

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

      2. unsub-neg 99.5%

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

      3. *-commutative 99.5%

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

   5. Simplified 99.5%

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

   6. Taylor expanded in x1 around inf 99.5%

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

   if -4.19999999999999977e-5 < x1 < 5.1999999999999999e141

   1. Initial program 98.0%

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

   3. Taylor expanded in x1 around 0 97.6%

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

      1. mul-1-neg 97.6%

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

      2. unsub-neg 97.6%

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

      3. *-commutative 97.6%

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

   5. Simplified 97.6%

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

   6. Taylor expanded in x1 around 0 96.2%

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

      1. +-commutative 96.6%

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

      2. mul-1-neg 96.6%

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

      3. unsub-neg 96.6%

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

   8. Simplified 96.2%

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

   if 5.1999999999999999e141 < x1

   1. Initial program 8.1%

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

   3. Simplified 10.8%

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

   5. Taylor expanded in x1 around 0 78.6%

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

   6. Taylor expanded in x2 around 0 70.5%

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

   7. Taylor expanded in x1 around 0 81.3%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x1 \cdot \left(12 + x1 \cdot 24\right)\right) - x1 \cdot \left(9 + x1 \cdot -19\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq -4.2 \cdot 10^{-5}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 - \left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(\frac{1}{x1} - 3\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5.2 \cdot 10^{+141}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x1 - 2 \cdot x2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 12\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \left(t\_1 + 2 \cdot x2\right) - x1\\ t_3 := \frac{t\_2}{t\_0}\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x1 \cdot \left(12 + x1 \cdot 24\right)\right) - x1 \cdot \left(9 + x1 \cdot -19\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq 5.2 \cdot 10^{+141}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_1 \cdot t\_3 - t\_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{t\_2}{-1 - x1 \cdot x1}\right) + \left(t\_3 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x1 - 2 \cdot x2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 12\right)\right)\right)\\ \end{array} \end{array} \]

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)) x1))
        (t_3 (/ t_2 t_0)))
   (if (<= x1 -5.6e+102)
     (-
      (* x2 -6.0)
      (*
       x1
       (-
        (-
         (* x2 (- 12.0 (* x1 (+ 12.0 (* x1 24.0)))))
         (* x1 (+ 9.0 (* x1 -19.0))))
        -1.0)))
     (if (<= x1 5.2e+141)
       (+
        x1
        (+
         (* 3.0 (- (* x2 -2.0) x1))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (-
            (* t_1 t_3)
            (*
             t_0
             (+
              (* (* x1 x1) (+ 6.0 (* 4.0 (/ t_2 (- -1.0 (* x1 x1))))))
              (* (- t_3 3.0) (* (* x1 2.0) (- x1 (* 2.0 x2)))))))))))
       (+
        (* x2 -6.0)
        (* x1 (+ -1.0 (+ (* x2 -12.0) (* x1 (+ 9.0 (* x2 12.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (t_1 + (2.0 * x2)) - x1;
	double t_3 = t_2 / t_0;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x1 * (12.0 + (x1 * 24.0))))) - (x1 * (9.0 + (x1 * -19.0)))) - -1.0));
	} else if (x1 <= 5.2e+141) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_3) - (t_0 * (((x1 * x1) * (6.0 + (4.0 * (t_2 / (-1.0 - (x1 * x1)))))) + ((t_3 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * -12.0) + (x1 * (9.0 + (x2 * 12.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (t_1 + (2.0d0 * x2)) - x1
    t_3 = t_2 / t_0
    if (x1 <= (-5.6d+102)) then
        tmp = (x2 * (-6.0d0)) - (x1 * (((x2 * (12.0d0 - (x1 * (12.0d0 + (x1 * 24.0d0))))) - (x1 * (9.0d0 + (x1 * (-19.0d0))))) - (-1.0d0)))
    else if (x1 <= 5.2d+141) then
        tmp = x1 + ((3.0d0 * ((x2 * (-2.0d0)) - x1)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_3) - (t_0 * (((x1 * x1) * (6.0d0 + (4.0d0 * (t_2 / ((-1.0d0) - (x1 * x1)))))) + ((t_3 - 3.0d0) * ((x1 * 2.0d0) * (x1 - (2.0d0 * x2))))))))))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + ((x2 * (-12.0d0)) + (x1 * (9.0d0 + (x2 * 12.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (t_1 + (2.0 * x2)) - x1;
	double t_3 = t_2 / t_0;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x1 * (12.0 + (x1 * 24.0))))) - (x1 * (9.0 + (x1 * -19.0)))) - -1.0));
	} else if (x1 <= 5.2e+141) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_3) - (t_0 * (((x1 * x1) * (6.0 + (4.0 * (t_2 / (-1.0 - (x1 * x1)))))) + ((t_3 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * -12.0) + (x1 * (9.0 + (x2 * 12.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = (t_1 + (2.0 * x2)) - x1
	t_3 = t_2 / t_0
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x1 * (12.0 + (x1 * 24.0))))) - (x1 * (9.0 + (x1 * -19.0)))) - -1.0))
	elif x1 <= 5.2e+141:
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_3) - (t_0 * (((x1 * x1) * (6.0 + (4.0 * (t_2 / (-1.0 - (x1 * x1)))))) + ((t_3 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))))
	else:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * -12.0) + (x1 * (9.0 + (x2 * 12.0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(t_1 + Float64(2.0 * x2)) - x1)
	t_3 = Float64(t_2 / t_0)
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(Float64(Float64(x2 * Float64(12.0 - Float64(x1 * Float64(12.0 + Float64(x1 * 24.0))))) - Float64(x1 * Float64(9.0 + Float64(x1 * -19.0)))) - -1.0)));
	elseif (x1 <= 5.2e+141)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - x1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * t_3) - Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * Float64(t_2 / Float64(-1.0 - Float64(x1 * x1)))))) + Float64(Float64(t_3 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(x1 - Float64(2.0 * x2)))))))))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(Float64(x2 * -12.0) + Float64(x1 * Float64(9.0 + Float64(x2 * 12.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * 3.0);
	t_2 = (t_1 + (2.0 * x2)) - x1;
	t_3 = t_2 / t_0;
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x1 * (12.0 + (x1 * 24.0))))) - (x1 * (9.0 + (x1 * -19.0)))) - -1.0));
	elseif (x1 <= 5.2e+141)
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_3) - (t_0 * (((x1 * x1) * (6.0 + (4.0 * (t_2 / (-1.0 - (x1 * x1)))))) + ((t_3 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))));
	else
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * -12.0) + (x1 * (9.0 + (x2 * 12.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / t$95$0), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(N[(N[(x2 * N[(12.0 - N[(x1 * N[(12.0 + N[(x1 * 24.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.2e+141], N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * t$95$3), $MachinePrecision] - N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * N[(t$95$2 / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$3 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(x1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(N[(x2 * -12.0), $MachinePrecision] + N[(x1 * N[(9.0 + N[(x2 * 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   3. Simplified 27.8%

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

   5. Taylor expanded in x1 around 0 55.6%

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

   6. Taylor expanded in x2 around 0 61.1%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) + x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right)} - 1\right) \]

   if -5.60000000000000037e102 < x1 < 5.1999999999999999e141

   1. Initial program 98.3%

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

   3. Taylor expanded in x1 around 0 97.9%

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

      1. mul-1-neg 97.9%

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

      2. unsub-neg 97.9%

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

      3. *-commutative 97.9%

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

   5. Simplified 97.9%

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

   6. Taylor expanded in x1 around 0 94.3%

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

      1. +-commutative 94.7%

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

      2. mul-1-neg 94.7%

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

      3. unsub-neg 94.7%

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

   8. Simplified 94.3%

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

   if 5.1999999999999999e141 < x1

   1. Initial program 8.1%

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

   3. Simplified 10.8%

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

   5. Taylor expanded in x1 around 0 78.6%

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

   6. Taylor expanded in x2 around 0 70.5%

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

   7. Taylor expanded in x1 around 0 81.3%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x1 \cdot \left(12 + x1 \cdot 24\right)\right) - x1 \cdot \left(9 + x1 \cdot -19\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq 5.2 \cdot 10^{+141}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x1 - 2 \cdot x2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 12\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := -1 - x1 \cdot x1\\ \mathbf{if}\;x1 \leq -4.8 \cdot 10^{+74}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x1 \cdot \left(12 + x1 \cdot 24\right)\right) - x1 \cdot \left(9 + x1 \cdot -19\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq 850:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{elif}\;x1 \leq 5.4 \cdot 10^{+118}:\\ \;\;\;\;x1 - \left(\left(\left(\left(t\_0 \cdot \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1} + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - x1 \cdot \left(6 - \left(2 \cdot \left(x2 \cdot -2 + \left(3 - 2 \cdot x2\right)\right) + x2 \cdot 8\right)\right)\right)\right) \cdot t\_1\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right) + 3 \cdot \left(x1 - x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 12\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0))) (t_1 (- -1.0 (* x1 x1))))
   (if (<= x1 -4.8e+74)
     (-
      (* x2 -6.0)
      (*
       x1
       (-
        (-
         (* x2 (- 12.0 (* x1 (+ 12.0 (* x1 24.0)))))
         (* x1 (+ 9.0 (* x1 -19.0))))
        -1.0)))
     (if (<= x1 850.0)
       (- (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0)) x1)
       (if (<= x1 5.4e+118)
         (-
          x1
          (+
           (-
            (-
             (+
              (* t_0 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1))
              (*
               (*
                x1
                (-
                 (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))
                 (*
                  x1
                  (-
                   6.0
                   (+
                    (* 2.0 (+ (* x2 -2.0) (- 3.0 (* 2.0 x2))))
                    (* x2 8.0))))))
               t_1))
             (* x1 (* x1 x1)))
            x1)
           (* 3.0 (- x1 (* x2 -2.0)))))
         (+
          (* x2 -6.0)
          (* x1 (+ -1.0 (+ (* x2 -12.0) (* x1 (+ 9.0 (* x2 12.0))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = -1.0 - (x1 * x1);
	double tmp;
	if (x1 <= -4.8e+74) {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x1 * (12.0 + (x1 * 24.0))))) - (x1 * (9.0 + (x1 * -19.0)))) - -1.0));
	} else if (x1 <= 850.0) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else if (x1 <= 5.4e+118) {
		tmp = x1 - (((((t_0 * (((t_0 + (2.0 * x2)) - x1) / t_1)) + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - (x1 * (6.0 - ((2.0 * ((x2 * -2.0) + (3.0 - (2.0 * x2)))) + (x2 * 8.0)))))) * t_1)) - (x1 * (x1 * x1))) - x1) + (3.0 * (x1 - (x2 * -2.0))));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * -12.0) + (x1 * (9.0 + (x2 * 12.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (-1.0d0) - (x1 * x1)
    if (x1 <= (-4.8d+74)) then
        tmp = (x2 * (-6.0d0)) - (x1 * (((x2 * (12.0d0 - (x1 * (12.0d0 + (x1 * 24.0d0))))) - (x1 * (9.0d0 + (x1 * (-19.0d0))))) - (-1.0d0)))
    else if (x1 <= 850.0d0) then
        tmp = (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)) - x1
    else if (x1 <= 5.4d+118) then
        tmp = x1 - (((((t_0 * (((t_0 + (2.0d0 * x2)) - x1) / t_1)) + ((x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - (x1 * (6.0d0 - ((2.0d0 * ((x2 * (-2.0d0)) + (3.0d0 - (2.0d0 * x2)))) + (x2 * 8.0d0)))))) * t_1)) - (x1 * (x1 * x1))) - x1) + (3.0d0 * (x1 - (x2 * (-2.0d0)))))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + ((x2 * (-12.0d0)) + (x1 * (9.0d0 + (x2 * 12.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = -1.0 - (x1 * x1);
	double tmp;
	if (x1 <= -4.8e+74) {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x1 * (12.0 + (x1 * 24.0))))) - (x1 * (9.0 + (x1 * -19.0)))) - -1.0));
	} else if (x1 <= 850.0) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else if (x1 <= 5.4e+118) {
		tmp = x1 - (((((t_0 * (((t_0 + (2.0 * x2)) - x1) / t_1)) + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - (x1 * (6.0 - ((2.0 * ((x2 * -2.0) + (3.0 - (2.0 * x2)))) + (x2 * 8.0)))))) * t_1)) - (x1 * (x1 * x1))) - x1) + (3.0 * (x1 - (x2 * -2.0))));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * -12.0) + (x1 * (9.0 + (x2 * 12.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = -1.0 - (x1 * x1)
	tmp = 0
	if x1 <= -4.8e+74:
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x1 * (12.0 + (x1 * 24.0))))) - (x1 * (9.0 + (x1 * -19.0)))) - -1.0))
	elif x1 <= 850.0:
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1
	elif x1 <= 5.4e+118:
		tmp = x1 - (((((t_0 * (((t_0 + (2.0 * x2)) - x1) / t_1)) + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - (x1 * (6.0 - ((2.0 * ((x2 * -2.0) + (3.0 - (2.0 * x2)))) + (x2 * 8.0)))))) * t_1)) - (x1 * (x1 * x1))) - x1) + (3.0 * (x1 - (x2 * -2.0))))
	else:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * -12.0) + (x1 * (9.0 + (x2 * 12.0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(-1.0 - Float64(x1 * x1))
	tmp = 0.0
	if (x1 <= -4.8e+74)
		tmp = Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(Float64(Float64(x2 * Float64(12.0 - Float64(x1 * Float64(12.0 + Float64(x1 * 24.0))))) - Float64(x1 * Float64(9.0 + Float64(x1 * -19.0)))) - -1.0)));
	elseif (x1 <= 850.0)
		tmp = Float64(Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0)) - x1);
	elseif (x1 <= 5.4e+118)
		tmp = Float64(x1 - Float64(Float64(Float64(Float64(Float64(t_0 * Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)) + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - Float64(x1 * Float64(6.0 - Float64(Float64(2.0 * Float64(Float64(x2 * -2.0) + Float64(3.0 - Float64(2.0 * x2)))) + Float64(x2 * 8.0)))))) * t_1)) - Float64(x1 * Float64(x1 * x1))) - x1) + Float64(3.0 * Float64(x1 - Float64(x2 * -2.0)))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(Float64(x2 * -12.0) + Float64(x1 * Float64(9.0 + Float64(x2 * 12.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = -1.0 - (x1 * x1);
	tmp = 0.0;
	if (x1 <= -4.8e+74)
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x1 * (12.0 + (x1 * 24.0))))) - (x1 * (9.0 + (x1 * -19.0)))) - -1.0));
	elseif (x1 <= 850.0)
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	elseif (x1 <= 5.4e+118)
		tmp = x1 - (((((t_0 * (((t_0 + (2.0 * x2)) - x1) / t_1)) + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - (x1 * (6.0 - ((2.0 * ((x2 * -2.0) + (3.0 - (2.0 * x2)))) + (x2 * 8.0)))))) * t_1)) - (x1 * (x1 * x1))) - x1) + (3.0 * (x1 - (x2 * -2.0))));
	else
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * -12.0) + (x1 * (9.0 + (x2 * 12.0))))));
	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[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.8e+74], N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(N[(N[(x2 * N[(12.0 - N[(x1 * N[(12.0 + N[(x1 * 24.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 850.0], N[(N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 5.4e+118], N[(x1 - N[(N[(N[(N[(N[(t$95$0 * N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(6.0 - N[(N[(2.0 * N[(N[(x2 * -2.0), $MachinePrecision] + N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] + N[(3.0 * N[(x1 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(N[(x2 * -12.0), $MachinePrecision] + N[(x1 * N[(9.0 + N[(x2 * 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.80000000000000017e74

   1. Initial program 10.0%

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

   3. Simplified 35.0%

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

   5. Taylor expanded in x1 around 0 50.8%

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

   6. Taylor expanded in x2 around 0 55.8%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) + x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right)} - 1\right) \]

   if -4.80000000000000017e74 < x1 < 850

   1. Initial program 99.3%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in x1 around 0 76.1%

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

      1. fma-define 76.2%

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

      2. metadata-eval 76.2%

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

      3. cancel-sign-sub-inv 76.2%

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

      4. associate-*r* 76.2%

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

      5. fmm-def 76.2%

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

      6. *-commutative 76.2%

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

      7. cancel-sign-sub-inv 76.2%

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

      8. metadata-eval 76.2%

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

      9. *-commutative 76.2%

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

      10. metadata-eval 76.2%

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

   7. Simplified 76.2%

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

   8. Taylor expanded in x2 around 0 87.2%

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

   if 850 < x1 < 5.4e118

   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 99.6%

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

      1. mul-1-neg 99.6%

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

      2. unsub-neg 99.6%

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

      3. *-commutative 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in x1 around 0 52.1%

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

   if 5.4e118 < x1

   1. Initial program 18.2%

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

   3. Simplified 25.0%

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

   5. Taylor expanded in x1 around 0 68.7%

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

   6. Taylor expanded in x2 around 0 66.5%

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

   7. Taylor expanded in x1 around 0 75.6%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.8 \cdot 10^{+74}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x1 \cdot \left(12 + x1 \cdot 24\right)\right) - x1 \cdot \left(9 + x1 \cdot -19\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq 850:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{elif}\;x1 \leq 5.4 \cdot 10^{+118}:\\ \;\;\;\;x1 - \left(\left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - x1 \cdot \left(6 - \left(2 \cdot \left(x2 \cdot -2 + \left(3 - 2 \cdot x2\right)\right) + x2 \cdot 8\right)\right)\right)\right) \cdot \left(-1 - x1 \cdot x1\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right) + 3 \cdot \left(x1 - x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 12\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 72.7% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.08 \cdot 10^{+79}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x1 \cdot \left(12 + x1 \cdot 24\right)\right) - x1 \cdot \left(9 + x1 \cdot -19\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq 5.2 \cdot 10^{+110}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 12\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.08e+79)
   (-
    (* x2 -6.0)
    (*
     x1
     (-
      (-
       (* x2 (- 12.0 (* x1 (+ 12.0 (* x1 24.0)))))
       (* x1 (+ 9.0 (* x1 -19.0))))
      -1.0)))
   (if (<= x1 5.2e+110)
     (- (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0)) x1)
     (+
      (* x2 -6.0)
      (* x1 (+ -1.0 (+ (* x2 -12.0) (* x1 (+ 9.0 (* x2 12.0))))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.08e+79) {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x1 * (12.0 + (x1 * 24.0))))) - (x1 * (9.0 + (x1 * -19.0)))) - -1.0));
	} else if (x1 <= 5.2e+110) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * -12.0) + (x1 * (9.0 + (x2 * 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 <= (-1.08d+79)) then
        tmp = (x2 * (-6.0d0)) - (x1 * (((x2 * (12.0d0 - (x1 * (12.0d0 + (x1 * 24.0d0))))) - (x1 * (9.0d0 + (x1 * (-19.0d0))))) - (-1.0d0)))
    else if (x1 <= 5.2d+110) then
        tmp = (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)) - x1
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + ((x2 * (-12.0d0)) + (x1 * (9.0d0 + (x2 * 12.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.08e+79) {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x1 * (12.0 + (x1 * 24.0))))) - (x1 * (9.0 + (x1 * -19.0)))) - -1.0));
	} else if (x1 <= 5.2e+110) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * -12.0) + (x1 * (9.0 + (x2 * 12.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.08e+79:
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x1 * (12.0 + (x1 * 24.0))))) - (x1 * (9.0 + (x1 * -19.0)))) - -1.0))
	elif x1 <= 5.2e+110:
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1
	else:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * -12.0) + (x1 * (9.0 + (x2 * 12.0))))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.08e+79)
		tmp = Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(Float64(Float64(x2 * Float64(12.0 - Float64(x1 * Float64(12.0 + Float64(x1 * 24.0))))) - Float64(x1 * Float64(9.0 + Float64(x1 * -19.0)))) - -1.0)));
	elseif (x1 <= 5.2e+110)
		tmp = Float64(Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0)) - x1);
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(Float64(x2 * -12.0) + Float64(x1 * Float64(9.0 + Float64(x2 * 12.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -1.08e+79)
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x1 * (12.0 + (x1 * 24.0))))) - (x1 * (9.0 + (x1 * -19.0)))) - -1.0));
	elseif (x1 <= 5.2e+110)
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	else
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * -12.0) + (x1 * (9.0 + (x2 * 12.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.08e+79], N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(N[(N[(x2 * N[(12.0 - N[(x1 * N[(12.0 + N[(x1 * 24.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.2e+110], N[(N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(N[(x2 * -12.0), $MachinePrecision] + N[(x1 * N[(9.0 + N[(x2 * 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.08000000000000002e79

   1. Initial program 10.0%

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

   3. Simplified 35.0%

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

   5. Taylor expanded in x1 around 0 50.8%

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

   6. Taylor expanded in x2 around 0 55.8%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) + x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right)} - 1\right) \]

   if -1.08000000000000002e79 < x1 < 5.2e110

   1. Initial program 99.3%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in x1 around 0 71.7%

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

      1. fma-define 71.8%

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

      2. metadata-eval 71.8%

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

      3. cancel-sign-sub-inv 71.8%

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

      4. associate-*r* 71.8%

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

      5. fmm-def 71.8%

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

      6. *-commutative 71.8%

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

      7. cancel-sign-sub-inv 71.8%

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

      8. metadata-eval 71.8%

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

      9. *-commutative 71.8%

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

      10. metadata-eval 71.8%

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

   7. Simplified 71.8%

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

   8. Taylor expanded in x2 around 0 81.6%

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

   if 5.2e110 < x1

   1. Initial program 23.4%

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

   3. Simplified 29.8%

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

   5. Taylor expanded in x1 around 0 64.7%

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

   6. Taylor expanded in x2 around 0 62.6%

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

   7. Taylor expanded in x1 around 0 71.1%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.08 \cdot 10^{+79}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x1 \cdot \left(12 + x1 \cdot 24\right)\right) - x1 \cdot \left(9 + x1 \cdot -19\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq 5.2 \cdot 10^{+110}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 12\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 73.8% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -3.2 \cdot 10^{+33} \lor \neg \left(x1 \leq 1.3 \cdot 10^{+110}\right):\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 12\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -3.2e+33) (not (<= x1 1.3e+110)))
   (+ (* x2 -6.0) (* x1 (+ -1.0 (+ (* x2 -12.0) (* x1 (+ 9.0 (* x2 12.0)))))))
   (- (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0)) x1)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -3.2e+33) || !(x1 <= 1.3e+110)) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * -12.0) + (x1 * (9.0 + (x2 * 12.0))))));
	} else {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-3.2d+33)) .or. (.not. (x1 <= 1.3d+110))) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + ((x2 * (-12.0d0)) + (x1 * (9.0d0 + (x2 * 12.0d0))))))
    else
        tmp = (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)) - x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -3.2e+33) || !(x1 <= 1.3e+110)) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * -12.0) + (x1 * (9.0 + (x2 * 12.0))))));
	} else {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -3.2e+33) or not (x1 <= 1.3e+110):
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * -12.0) + (x1 * (9.0 + (x2 * 12.0))))))
	else:
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -3.2e+33) || !(x1 <= 1.3e+110))
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(Float64(x2 * -12.0) + Float64(x1 * Float64(9.0 + Float64(x2 * 12.0)))))));
	else
		tmp = Float64(Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0)) - x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -3.2e+33) || ~((x1 <= 1.3e+110)))
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * -12.0) + (x1 * (9.0 + (x2 * 12.0))))));
	else
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -3.2e+33], N[Not[LessEqual[x1, 1.3e+110]], $MachinePrecision]], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(N[(x2 * -12.0), $MachinePrecision] + N[(x1 * N[(9.0 + N[(x2 * 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -3.20000000000000017e33 or 1.3e110 < x1

   1. Initial program 27.1%

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

   3. Simplified 40.3%

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

   5. Taylor expanded in x1 around 0 47.7%

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

   6. Taylor expanded in x2 around 0 50.8%

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

   7. Taylor expanded in x1 around 0 55.8%

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

   if -3.20000000000000017e33 < x1 < 1.3e110

   1. Initial program 99.3%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in x1 around 0 75.1%

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

      1. fma-define 75.2%

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

      2. metadata-eval 75.2%

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

      3. cancel-sign-sub-inv 75.2%

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

      4. associate-*r* 75.2%

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

      5. fmm-def 75.2%

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

      6. *-commutative 75.2%

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

      7. cancel-sign-sub-inv 75.2%

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

      8. metadata-eval 75.2%

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

      9. *-commutative 75.2%

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

      10. metadata-eval 75.2%

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

   7. Simplified 75.2%

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

   8. Taylor expanded in x2 around 0 85.7%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.2 \cdot 10^{+33} \lor \neg \left(x1 \leq 1.3 \cdot 10^{+110}\right):\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 12\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 68.6% accurate, 6.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -4.9 \cdot 10^{+48}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 - \frac{x1}{x2}\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -4.9e+48)
   (* x2 (- (- (* x1 -12.0) (/ x1 x2)) 6.0))
   (- (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0)) x1)))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -4.9e+48) {
		tmp = x2 * (((x1 * -12.0) - (x1 / x2)) - 6.0);
	} else {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-4.9d+48)) then
        tmp = x2 * (((x1 * (-12.0d0)) - (x1 / x2)) - 6.0d0)
    else
        tmp = (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)) - x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -4.9e+48) {
		tmp = x2 * (((x1 * -12.0) - (x1 / x2)) - 6.0);
	} else {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -4.9e+48:
		tmp = x2 * (((x1 * -12.0) - (x1 / x2)) - 6.0)
	else:
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -4.9e+48)
		tmp = Float64(x2 * Float64(Float64(Float64(x1 * -12.0) - Float64(x1 / x2)) - 6.0));
	else
		tmp = Float64(Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0)) - x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -4.9e+48)
		tmp = x2 * (((x1 * -12.0) - (x1 / x2)) - 6.0);
	else
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -4.9e+48], N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] - N[(x1 / x2), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -4.9000000000000003e48

   1. Initial program 23.2%

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

   3. Simplified 44.5%

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

   5. Taylor expanded in x1 around 0 4.5%

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

      1. fma-define 4.5%

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

      2. metadata-eval 4.5%

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

      3. cancel-sign-sub-inv 4.5%

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

      4. associate-*r* 4.5%

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

      5. fmm-def 4.5%

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

      6. *-commutative 4.5%

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

      7. cancel-sign-sub-inv 4.5%

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

      8. metadata-eval 4.5%

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

      9. *-commutative 4.5%

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

      10. metadata-eval 4.5%

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

   7. Simplified 4.5%

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

   8. Taylor expanded in x2 around 0 17.6%

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

   9. Taylor expanded in x2 around inf 35.6%

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

   if -4.9000000000000003e48 < x1

   1. Initial program 82.3%

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

   3. Simplified 75.1%

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

   5. Taylor expanded in x1 around 0 65.2%

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

      1. fma-define 65.3%

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

      2. metadata-eval 65.3%

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

      3. cancel-sign-sub-inv 65.3%

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

      4. associate-*r* 65.3%

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

      5. fmm-def 65.3%

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

      6. *-commutative 65.3%

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

      7. cancel-sign-sub-inv 65.3%

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

      8. metadata-eval 65.3%

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

      9. *-commutative 65.3%

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

      10. metadata-eval 65.3%

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

   7. Simplified 65.3%

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

   8. Taylor expanded in x2 around 0 73.2%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.9 \cdot 10^{+48}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 - \frac{x1}{x2}\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.0% accurate, 6.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -4.9 \cdot 10^{+48}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 - \frac{x1}{x2}\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x2 \cdot \left(x2 \cdot 8 - 12\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -4.9e+48)
   (* x2 (- (- (* x1 -12.0) (/ x1 x2)) 6.0))
   (+ (* x2 -6.0) (* x1 (+ -1.0 (* x2 (- (* x2 8.0) 12.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -4.9e+48) {
		tmp = x2 * (((x1 * -12.0) - (x1 / x2)) - 6.0);
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * ((x2 * 8.0) - 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 <= (-4.9d+48)) then
        tmp = x2 * (((x1 * (-12.0d0)) - (x1 / x2)) - 6.0d0)
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x2 * ((x2 * 8.0d0) - 12.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -4.9e+48) {
		tmp = x2 * (((x1 * -12.0) - (x1 / x2)) - 6.0);
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -4.9e+48:
		tmp = x2 * (((x1 * -12.0) - (x1 / x2)) - 6.0)
	else:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -4.9e+48)
		tmp = Float64(x2 * Float64(Float64(Float64(x1 * -12.0) - Float64(x1 / x2)) - 6.0));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x2 * Float64(Float64(x2 * 8.0) - 12.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -4.9e+48)
		tmp = x2 * (((x1 * -12.0) - (x1 / x2)) - 6.0);
	else
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -4.9e+48], N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] - N[(x1 / x2), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x2 * N[(N[(x2 * 8.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -4.9000000000000003e48

   1. Initial program 23.2%

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

   3. Simplified 44.5%

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

   5. Taylor expanded in x1 around 0 4.5%

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

      1. fma-define 4.5%

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

      2. metadata-eval 4.5%

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

      3. cancel-sign-sub-inv 4.5%

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

      4. associate-*r* 4.5%

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

      5. fmm-def 4.5%

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

      6. *-commutative 4.5%

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

      7. cancel-sign-sub-inv 4.5%

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

      8. metadata-eval 4.5%

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

      9. *-commutative 4.5%

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

      10. metadata-eval 4.5%

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

   7. Simplified 4.5%

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

   8. Taylor expanded in x2 around 0 17.6%

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

   9. Taylor expanded in x2 around inf 35.6%

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

   if -4.9000000000000003e48 < x1

   1. Initial program 82.3%

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

   3. Simplified 75.1%

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

   5. Taylor expanded in x1 around 0 65.2%

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

   6. Taylor expanded in x2 around 0 65.2%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.9 \cdot 10^{+48}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 - \frac{x1}{x2}\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x2 \cdot \left(x2 \cdot 8 - 12\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.9% accurate, 11.5× speedup

Math

\[\begin{array}{l} \\ x2 \cdot \left(\left(x1 \cdot -12 - \frac{x1}{x2}\right) - 6\right) \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (* x2 (- (- (* x1 -12.0) (/ x1 x2)) 6.0)))

C

double code(double x1, double x2) {
	return x2 * (((x1 * -12.0) - (x1 / x2)) - 6.0);
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x2 * (((x1 * (-12.0d0)) - (x1 / x2)) - 6.0d0)
end function

Java

public static double code(double x1, double x2) {
	return x2 * (((x1 * -12.0) - (x1 / x2)) - 6.0);
}

Python

def code(x1, x2):
	return x2 * (((x1 * -12.0) - (x1 / x2)) - 6.0)

Julia

function code(x1, x2)
	return Float64(x2 * Float64(Float64(Float64(x1 * -12.0) - Float64(x1 / x2)) - 6.0))
end

MATLAB

function tmp = code(x1, x2)
	tmp = x2 * (((x1 * -12.0) - (x1 / x2)) - 6.0);
end

Wolfram

code[x1_, x2_] := N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] - N[(x1 / x2), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 71.4%

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

3. Simplified 69.5%

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

5. Taylor expanded in x1 around 0 54.1%

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

   1. fma-define 54.1%

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

   2. metadata-eval 54.1%

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

   3. cancel-sign-sub-inv 54.1%

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

   4. associate-*r* 54.1%

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

   5. fmm-def 54.1%

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

   6. *-commutative 54.1%

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

   7. cancel-sign-sub-inv 54.1%

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

   8. metadata-eval 54.1%

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

   9. *-commutative 54.1%

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

   10. metadata-eval 54.1%

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

7. Simplified 54.1%

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

8. Taylor expanded in x2 around 0 42.8%

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

9. Taylor expanded in x2 around inf 46.1%

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

10. Final simplification 46.1%

    \[\leadsto x2 \cdot \left(\left(x1 \cdot -12 - \frac{x1}{x2}\right) - 6\right) \]
11. Add Preprocessing

Alternative 15: 45.1% accurate, 11.5× speedup

Math

\[\begin{array}{l} \\ x2 \cdot -6 + x1 \cdot \left(-1 + x2 \cdot -12\right) \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (+ (* x2 -6.0) (* x1 (+ -1.0 (* x2 -12.0)))))

C

double code(double x1, double x2) {
	return (x2 * -6.0) + (x1 * (-1.0 + (x2 * -12.0)));
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x2 * (-12.0d0))))
end function

Java

public static double code(double x1, double x2) {
	return (x2 * -6.0) + (x1 * (-1.0 + (x2 * -12.0)));
}

Python

def code(x1, x2):
	return (x2 * -6.0) + (x1 * (-1.0 + (x2 * -12.0)))

Julia

function code(x1, x2)
	return Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x2 * -12.0))))
end

MATLAB

function tmp = code(x1, x2)
	tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * -12.0)));
end

Wolfram

code[x1_, x2_] := N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 71.4%

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

3. Simplified 69.5%

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

5. Taylor expanded in x1 around 0 54.1%

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

   1. fma-define 54.1%

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

   2. metadata-eval 54.1%

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

   3. cancel-sign-sub-inv 54.1%

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

   4. associate-*r* 54.1%

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

   5. fmm-def 54.1%

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

   6. *-commutative 54.1%

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

   7. cancel-sign-sub-inv 54.1%

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

   8. metadata-eval 54.1%

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

   9. *-commutative 54.1%

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

   10. metadata-eval 54.1%

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

7. Simplified 54.1%

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

8. Taylor expanded in x2 around 0 42.8%

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

9. Taylor expanded in x1 around 0 42.8%

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

10. Final simplification 42.8%

    \[\leadsto x2 \cdot -6 + x1 \cdot \left(-1 + x2 \cdot -12\right) \]
11. Add Preprocessing

Alternative 16: 45.2% accurate, 14.1× speedup

Math

\[\begin{array}{l} \\ x2 \cdot \left(x1 \cdot -12 - 6\right) - x1 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (- (* x2 (- (* x1 -12.0) 6.0)) x1))

C

double code(double x1, double x2) {
	return (x2 * ((x1 * -12.0) - 6.0)) - x1;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = (x2 * ((x1 * (-12.0d0)) - 6.0d0)) - x1
end function

Java

public static double code(double x1, double x2) {
	return (x2 * ((x1 * -12.0) - 6.0)) - x1;
}

Python

def code(x1, x2):
	return (x2 * ((x1 * -12.0) - 6.0)) - x1

Julia

function code(x1, x2)
	return Float64(Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)) - x1)
end

MATLAB

function tmp = code(x1, x2)
	tmp = (x2 * ((x1 * -12.0) - 6.0)) - x1;
end

Wolfram

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

Derivation

1. Initial program 71.4%

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

3. Simplified 69.5%

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

5. Taylor expanded in x1 around 0 54.1%

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

   1. fma-define 54.1%

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

   2. metadata-eval 54.1%

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

   3. cancel-sign-sub-inv 54.1%

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

   4. associate-*r* 54.1%

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

   5. fmm-def 54.1%

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

   6. *-commutative 54.1%

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

   7. cancel-sign-sub-inv 54.1%

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

   8. metadata-eval 54.1%

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

   9. *-commutative 54.1%

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

   10. metadata-eval 54.1%

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

7. Simplified 54.1%

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

8. Taylor expanded in x2 around 0 42.8%

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

   1. pow1 42.8%

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

   2. mul-1-neg 42.8%

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

10. Applied egg-rr 42.8%

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

    1. unpow1 42.8%

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

12. Simplified 42.8%

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

13. Taylor expanded in x2 around 0 42.8%

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

14. Final simplification 42.8%

    \[\leadsto x2 \cdot \left(x1 \cdot -12 - 6\right) - x1 \]
15. Add Preprocessing

Reproduce

herbie shell --seed 2024179 
(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))))))