Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 69.7% → 99.5%

Time: 22.1s

Alternatives: 23

Speedup: 6.7×

• 47.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 69.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 2 \cdot x2 - x1 \cdot \left(1 - x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_2}\\ \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(t\_2 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_3\right) \cdot \left(t\_3 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t\_3 \cdot 4 - 6\right)\right) + t\_0 \cdot t\_3\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_2}\right) \leq \infty:\\ \;\;\;\;\left(x1 \cdot -3 + x2 \cdot -6\right) + \left(\left(x1 \cdot 2 + t\_2 \cdot \left(\left(x1 \cdot x1\right) \cdot -6 + \frac{x1 \cdot \left(\left(-6 - \frac{t\_1}{\frac{-1 - x1 \cdot x1}{2}}\right) + x1 \cdot 4\right)}{\frac{t\_2}{t\_1}}\right)\right) + x1 \cdot \left(x1 \cdot \left(x1 + 9\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 + \frac{\frac{15 - \left(18 + x2 \cdot -8\right)}{x1} - 3}{x1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (- (* 2.0 x2) (* x1 (- 1.0 (* x1 3.0)))))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (/ (- (+ t_0 (* 2.0 x2)) x1) t_2)))
   (if (<=
        (+
         x1
         (+
          (+
           x1
           (+
            (+
             (*
              t_2
              (+
               (* (* (* x1 2.0) t_3) (- t_3 3.0))
               (* (* x1 x1) (- (* t_3 4.0) 6.0))))
             (* t_0 t_3))
            (* x1 (* x1 x1))))
          (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_2))))
        INFINITY)
     (+
      (+ (* x1 -3.0) (* x2 -6.0))
      (+
       (+
        (* x1 2.0)
        (*
         t_2
         (+
          (* (* x1 x1) -6.0)
          (/
           (* x1 (+ (- -6.0 (/ t_1 (/ (- -1.0 (* x1 x1)) 2.0))) (* x1 4.0)))
           (/ t_2 t_1)))))
       (* x1 (* x1 (+ x1 9.0)))))
     (*
      (* (* x1 x1) (* x1 x1))
      (+ 6.0 (/ (- (/ (- 15.0 (+ 18.0 (* x2 -8.0))) x1) 3.0) x1))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (2.0 * x2) - (x1 * (1.0 - (x1 * 3.0)));
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	double tmp;
	if ((x1 + ((x1 + (((t_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + (t_0 * t_3)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)))) <= ((double) INFINITY)) {
		tmp = ((x1 * -3.0) + (x2 * -6.0)) + (((x1 * 2.0) + (t_2 * (((x1 * x1) * -6.0) + ((x1 * ((-6.0 - (t_1 / ((-1.0 - (x1 * x1)) / 2.0))) + (x1 * 4.0))) / (t_2 / t_1))))) + (x1 * (x1 * (x1 + 9.0))));
	} else {
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 + ((((15.0 - (18.0 + (x2 * -8.0))) / 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 = (2.0 * x2) - (x1 * (1.0 - (x1 * 3.0)));
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	double tmp;
	if ((x1 + ((x1 + (((t_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + (t_0 * t_3)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)))) <= Double.POSITIVE_INFINITY) {
		tmp = ((x1 * -3.0) + (x2 * -6.0)) + (((x1 * 2.0) + (t_2 * (((x1 * x1) * -6.0) + ((x1 * ((-6.0 - (t_1 / ((-1.0 - (x1 * x1)) / 2.0))) + (x1 * 4.0))) / (t_2 / t_1))))) + (x1 * (x1 * (x1 + 9.0))));
	} else {
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 + ((((15.0 - (18.0 + (x2 * -8.0))) / x1) - 3.0) / x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (2.0 * x2) - (x1 * (1.0 - (x1 * 3.0)))
	t_2 = (x1 * x1) + 1.0
	t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2
	tmp = 0
	if (x1 + ((x1 + (((t_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + (t_0 * t_3)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)))) <= math.inf:
		tmp = ((x1 * -3.0) + (x2 * -6.0)) + (((x1 * 2.0) + (t_2 * (((x1 * x1) * -6.0) + ((x1 * ((-6.0 - (t_1 / ((-1.0 - (x1 * x1)) / 2.0))) + (x1 * 4.0))) / (t_2 / t_1))))) + (x1 * (x1 * (x1 + 9.0))))
	else:
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 + ((((15.0 - (18.0 + (x2 * -8.0))) / x1) - 3.0) / x1))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(2.0 * x2) - Float64(x1 * Float64(1.0 - Float64(x1 * 3.0))))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_2)
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_2 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(t_3 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0)))) + Float64(t_0 * t_3)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_2)))) <= Inf)
		tmp = Float64(Float64(Float64(x1 * -3.0) + Float64(x2 * -6.0)) + Float64(Float64(Float64(x1 * 2.0) + Float64(t_2 * Float64(Float64(Float64(x1 * x1) * -6.0) + Float64(Float64(x1 * Float64(Float64(-6.0 - Float64(t_1 / Float64(Float64(-1.0 - Float64(x1 * x1)) / 2.0))) + Float64(x1 * 4.0))) / Float64(t_2 / t_1))))) + Float64(x1 * Float64(x1 * Float64(x1 + 9.0)))));
	else
		tmp = Float64(Float64(Float64(x1 * x1) * Float64(x1 * x1)) * Float64(6.0 + Float64(Float64(Float64(Float64(15.0 - Float64(18.0 + Float64(x2 * -8.0))) / x1) - 3.0) / x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (2.0 * x2) - (x1 * (1.0 - (x1 * 3.0)));
	t_2 = (x1 * x1) + 1.0;
	t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	tmp = 0.0;
	if ((x1 + ((x1 + (((t_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + (t_0 * t_3)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)))) <= Inf)
		tmp = ((x1 * -3.0) + (x2 * -6.0)) + (((x1 * 2.0) + (t_2 * (((x1 * x1) * -6.0) + ((x1 * ((-6.0 - (t_1 / ((-1.0 - (x1 * x1)) / 2.0))) + (x1 * 4.0))) / (t_2 / t_1))))) + (x1 * (x1 * (x1 + 9.0))));
	else
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 + ((((15.0 - (18.0 + (x2 * -8.0))) / 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[(2.0 * x2), $MachinePrecision] - N[(x1 * N[(1.0 - N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$2 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(x1 * -3.0), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] + N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * -6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(-6.0 - N[(t$95$1 / N[(N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * N[(x1 + 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(6.0 + N[(N[(N[(N[(15.0 - N[(18.0 + N[(x2 * -8.0), $MachinePrecision]), $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 99.5%

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

   3. Simplified 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), -6\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{+.f64}\left(-6, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), 2\right)\right)\right), \mathsf{*.f64}\left(x1, 4\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right)\right)\right)\right), \mathsf{*.f64}\left(2, x1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right) \]
   8. Step-by-step derivation

   9. Simplified 97.5%

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

   10. Taylor expanded in x1 around 0

       \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(-6 \cdot x2 + -3 \cdot x1\right)}, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), -6\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{+.f64}\left(-6, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), 2\right)\right)\right), \mathsf{*.f64}\left(x1, 4\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right)\right)\right)\right), \mathsf{*.f64}\left(2, x1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, 9\right)\right)\right)\right)\right) \]
   11. Step-by-step derivation

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(-6 \cdot x2\right), \left(-3 \cdot x1\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), -6\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{+.f64}\left(-6, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), 2\right)\right)\right), \mathsf{*.f64}\left(x1, 4\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right)\right)\right)\right), \mathsf{*.f64}\left(2, x1\right)\right)}, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, 9\right)\right)\right)\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(-3 \cdot x1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), -6\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{+.f64}\left(-6, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), 2\right)\right)\right), \mathsf{*.f64}\left(x1, 4\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right)\right)\right)\right)}, \mathsf{*.f64}\left(2, x1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, 9\right)\right)\right)\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(x1 \cdot -3\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), -6\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{+.f64}\left(-6, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), 2\right)\right)\right), \mathsf{*.f64}\left(x1, 4\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right)\right)\right)\right), \color{blue}{\mathsf{*.f64}\left(2, x1\right)}\right), \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, 9\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 99.5%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, -3\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), -6\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{+.f64}\left(-6, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), 2\right)\right)\right), \mathsf{*.f64}\left(x1, 4\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right)\right)\right)\right), \color{blue}{\mathsf{*.f64}\left(2, x1\right)}\right), \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, 9\right)\right)\right)\right)\right) \]

   12. Simplified 99.5%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   6. Applied egg-rr 0.0%

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

   7. Taylor expanded in x1 around -inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)} \]
   8. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \left(\mathsf{neg}\left(\frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right)\right)\right) \]

      10. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - \color{blue}{\frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}}\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \color{blue}{\left(\frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}\right), \color{blue}{x1}\right)\right)\right) \]

   9. Simplified 100.0%

      \[\leadsto \color{blue}{\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \frac{3 - \frac{15 - \left(18 + x2 \cdot -8\right)}{x1}}{x1}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \leq \infty:\\ \;\;\;\;\left(x1 \cdot -3 + x2 \cdot -6\right) + \left(\left(x1 \cdot 2 + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot -6 + \frac{x1 \cdot \left(\left(-6 - \frac{2 \cdot x2 - x1 \cdot \left(1 - x1 \cdot 3\right)}{\frac{-1 - x1 \cdot x1}{2}}\right) + x1 \cdot 4\right)}{\frac{x1 \cdot x1 + 1}{2 \cdot x2 - x1 \cdot \left(1 - x1 \cdot 3\right)}}\right)\right) + x1 \cdot \left(x1 \cdot \left(x1 + 9\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 + \frac{\frac{15 - \left(18 + x2 \cdot -8\right)}{x1} - 3}{x1}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 + \frac{\frac{15 - \left(18 + x2 \cdot -8\right)}{x1} - 3}{x1}\right)\\ t_2 := x1 \cdot \left(1 - x1 \cdot 3\right)\\ \mathbf{if}\;x1 \leq -2.7 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq 3000000000000:\\ \;\;\;\;\frac{3 \cdot \left(x2 \cdot -2 - t\_2\right)}{t\_0} + \left(t\_0 \cdot \frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{t\_0 \cdot t\_0} + x1 \cdot \left(2 + x1 \cdot \left(x1 - \left(2 \cdot x2 - t\_2\right) \cdot \frac{3}{-1 - x1 \cdot x1}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1
         (*
          (* (* x1 x1) (* x1 x1))
          (+ 6.0 (/ (- (/ (- 15.0 (+ 18.0 (* x2 -8.0))) x1) 3.0) x1))))
        (t_2 (* x1 (- 1.0 (* x1 3.0)))))
   (if (<= x1 -2.7e+19)
     t_1
     (if (<= x1 3000000000000.0)
       (+
        (/ (* 3.0 (- (* x2 -2.0) t_2)) t_0)
        (+
         (* t_0 (/ (* 8.0 (* x1 (* x2 x2))) (* t_0 t_0)))
         (*
          x1
          (+
           2.0
           (* x1 (- x1 (* (- (* 2.0 x2) t_2) (/ 3.0 (- -1.0 (* x1 x1))))))))))
       t_1))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = ((x1 * x1) * (x1 * x1)) * (6.0 + ((((15.0 - (18.0 + (x2 * -8.0))) / x1) - 3.0) / x1));
	double t_2 = x1 * (1.0 - (x1 * 3.0));
	double tmp;
	if (x1 <= -2.7e+19) {
		tmp = t_1;
	} else if (x1 <= 3000000000000.0) {
		tmp = ((3.0 * ((x2 * -2.0) - t_2)) / t_0) + ((t_0 * ((8.0 * (x1 * (x2 * x2))) / (t_0 * t_0))) + (x1 * (2.0 + (x1 * (x1 - (((2.0 * x2) - t_2) * (3.0 / (-1.0 - (x1 * x1)))))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = ((x1 * x1) * (x1 * x1)) * (6.0d0 + ((((15.0d0 - (18.0d0 + (x2 * (-8.0d0)))) / x1) - 3.0d0) / x1))
    t_2 = x1 * (1.0d0 - (x1 * 3.0d0))
    if (x1 <= (-2.7d+19)) then
        tmp = t_1
    else if (x1 <= 3000000000000.0d0) then
        tmp = ((3.0d0 * ((x2 * (-2.0d0)) - t_2)) / t_0) + ((t_0 * ((8.0d0 * (x1 * (x2 * x2))) / (t_0 * t_0))) + (x1 * (2.0d0 + (x1 * (x1 - (((2.0d0 * x2) - t_2) * (3.0d0 / ((-1.0d0) - (x1 * x1)))))))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = ((x1 * x1) * (x1 * x1)) * (6.0 + ((((15.0 - (18.0 + (x2 * -8.0))) / x1) - 3.0) / x1));
	double t_2 = x1 * (1.0 - (x1 * 3.0));
	double tmp;
	if (x1 <= -2.7e+19) {
		tmp = t_1;
	} else if (x1 <= 3000000000000.0) {
		tmp = ((3.0 * ((x2 * -2.0) - t_2)) / t_0) + ((t_0 * ((8.0 * (x1 * (x2 * x2))) / (t_0 * t_0))) + (x1 * (2.0 + (x1 * (x1 - (((2.0 * x2) - t_2) * (3.0 / (-1.0 - (x1 * x1)))))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = ((x1 * x1) * (x1 * x1)) * (6.0 + ((((15.0 - (18.0 + (x2 * -8.0))) / x1) - 3.0) / x1))
	t_2 = x1 * (1.0 - (x1 * 3.0))
	tmp = 0
	if x1 <= -2.7e+19:
		tmp = t_1
	elif x1 <= 3000000000000.0:
		tmp = ((3.0 * ((x2 * -2.0) - t_2)) / t_0) + ((t_0 * ((8.0 * (x1 * (x2 * x2))) / (t_0 * t_0))) + (x1 * (2.0 + (x1 * (x1 - (((2.0 * x2) - t_2) * (3.0 / (-1.0 - (x1 * x1)))))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(Float64(Float64(x1 * x1) * Float64(x1 * x1)) * Float64(6.0 + Float64(Float64(Float64(Float64(15.0 - Float64(18.0 + Float64(x2 * -8.0))) / x1) - 3.0) / x1)))
	t_2 = Float64(x1 * Float64(1.0 - Float64(x1 * 3.0)))
	tmp = 0.0
	if (x1 <= -2.7e+19)
		tmp = t_1;
	elseif (x1 <= 3000000000000.0)
		tmp = Float64(Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - t_2)) / t_0) + Float64(Float64(t_0 * Float64(Float64(8.0 * Float64(x1 * Float64(x2 * x2))) / Float64(t_0 * t_0))) + Float64(x1 * Float64(2.0 + Float64(x1 * Float64(x1 - Float64(Float64(Float64(2.0 * x2) - t_2) * Float64(3.0 / Float64(-1.0 - Float64(x1 * x1))))))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = ((x1 * x1) * (x1 * x1)) * (6.0 + ((((15.0 - (18.0 + (x2 * -8.0))) / x1) - 3.0) / x1));
	t_2 = x1 * (1.0 - (x1 * 3.0));
	tmp = 0.0;
	if (x1 <= -2.7e+19)
		tmp = t_1;
	elseif (x1 <= 3000000000000.0)
		tmp = ((3.0 * ((x2 * -2.0) - t_2)) / t_0) + ((t_0 * ((8.0 * (x1 * (x2 * x2))) / (t_0 * t_0))) + (x1 * (2.0 + (x1 * (x1 - (((2.0 * x2) - t_2) * (3.0 / (-1.0 - (x1 * x1)))))))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(6.0 + N[(N[(N[(N[(15.0 - N[(18.0 + N[(x2 * -8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision] - 3.0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(1.0 - N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.7e+19], t$95$1, If[LessEqual[x1, 3000000000000.0], N[(N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision] + N[(N[(t$95$0 * N[(N[(8.0 * N[(x1 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t$95$0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(2.0 + N[(x1 * N[(x1 - N[(N[(N[(2.0 * x2), $MachinePrecision] - t$95$2), $MachinePrecision] * N[(3.0 / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -2.7e19 or 3e12 < x1

   1. Initial program 35.6%

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

   3. Simplified 35.6%

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

   6. Applied egg-rr 35.6%

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

   7. Taylor expanded in x1 around -inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)} \]
   8. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \left(\mathsf{neg}\left(\frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right)\right)\right) \]

      10. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - \color{blue}{\frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}}\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \color{blue}{\left(\frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}\right), \color{blue}{x1}\right)\right)\right) \]

   9. Simplified 97.0%

      \[\leadsto \color{blue}{\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \frac{3 - \frac{15 - \left(18 + x2 \cdot -8\right)}{x1}}{x1}\right)} \]

   if -2.7e19 < x1 < 3e12

   1. Initial program 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x2 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \color{blue}{\left(8 \cdot \frac{x1 \cdot {x2}^{2}}{{\left(1 + {x1}^{2}\right)}^{2}}\right)}\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \left(\frac{8 \cdot \left(x1 \cdot {x2}^{2}\right)}{{\left(1 + {x1}^{2}\right)}^{2}}\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{/.f64}\left(\left(8 \cdot \left(x1 \cdot {x2}^{2}\right)\right), \left({\left(1 + {x1}^{2}\right)}^{2}\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(8, \left(x1 \cdot {x2}^{2}\right)\right), \left({\left(1 + {x1}^{2}\right)}^{2}\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \left({x2}^{2}\right)\right)\right), \left({\left(1 + {x1}^{2}\right)}^{2}\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \left(x2 \cdot x2\right)\right)\right), \left({\left(1 + {x1}^{2}\right)}^{2}\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, x2\right)\right)\right), \left({\left(1 + {x1}^{2}\right)}^{2}\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, x2\right)\right)\right), \left(\left(1 + {x1}^{2}\right) \cdot \left(1 + {x1}^{2}\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, x2\right)\right)\right), \mathsf{*.f64}\left(\left(1 + {x1}^{2}\right), \left(1 + {x1}^{2}\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, x2\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(1, \left({x1}^{2}\right)\right), \left(1 + {x1}^{2}\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, x2\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(1, \left(x1 \cdot x1\right)\right), \left(1 + {x1}^{2}\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, x2\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x1, x1\right)\right), \left(1 + {x1}^{2}\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, x2\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(1, \left({x1}^{2}\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      13. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, x2\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(1, \left(x1 \cdot x1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 88.4%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, x2\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x1, x1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 88.4%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.7 \cdot 10^{+19}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 + \frac{\frac{15 - \left(18 + x2 \cdot -8\right)}{x1} - 3}{x1}\right)\\ \mathbf{elif}\;x1 \leq 3000000000000:\\ \;\;\;\;\frac{3 \cdot \left(x2 \cdot -2 - x1 \cdot \left(1 - x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot x1 + 1\right)} + x1 \cdot \left(2 + x1 \cdot \left(x1 - \left(2 \cdot x2 - x1 \cdot \left(1 - x1 \cdot 3\right)\right) \cdot \frac{3}{-1 - x1 \cdot x1}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 + \frac{\frac{15 - \left(18 + x2 \cdot -8\right)}{x1} - 3}{x1}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 + \frac{\frac{15 - \left(18 + x2 \cdot -8\right)}{x1} - 3}{x1}\right)\\ \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 580:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(\left(2 \cdot x2\right) \cdot \left(-6 + x2 \cdot 4\right) + \left(-1 + x1 \cdot \left(-6 + \left(\left(6 + x2 \cdot -4\right) + \left(3 \cdot \left(3 + 2 \cdot x2\right) + x2 \cdot 10\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (*
          (* (* x1 x1) (* x1 x1))
          (+ 6.0 (/ (- (/ (- 15.0 (+ 18.0 (* x2 -8.0))) x1) 3.0) x1)))))
   (if (<= x1 -1.5e+19)
     t_0
     (if (<= x1 580.0)
       (+
        (* x2 -6.0)
        (*
         x1
         (+
          (* (* 2.0 x2) (+ -6.0 (* x2 4.0)))
          (+
           -1.0
           (*
            x1
            (+
             -6.0
             (+
              (+ 6.0 (* x2 -4.0))
              (+ (* 3.0 (+ 3.0 (* 2.0 x2))) (* x2 10.0)))))))))
       t_0))))

C

double code(double x1, double x2) {
	double t_0 = ((x1 * x1) * (x1 * x1)) * (6.0 + ((((15.0 - (18.0 + (x2 * -8.0))) / x1) - 3.0) / x1));
	double tmp;
	if (x1 <= -1.5e+19) {
		tmp = t_0;
	} else if (x1 <= 580.0) {
		tmp = (x2 * -6.0) + (x1 * (((2.0 * x2) * (-6.0 + (x2 * 4.0))) + (-1.0 + (x1 * (-6.0 + ((6.0 + (x2 * -4.0)) + ((3.0 * (3.0 + (2.0 * x2))) + (x2 * 10.0))))))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((x1 * x1) * (x1 * x1)) * (6.0d0 + ((((15.0d0 - (18.0d0 + (x2 * (-8.0d0)))) / x1) - 3.0d0) / x1))
    if (x1 <= (-1.5d+19)) then
        tmp = t_0
    else if (x1 <= 580.0d0) then
        tmp = (x2 * (-6.0d0)) + (x1 * (((2.0d0 * x2) * ((-6.0d0) + (x2 * 4.0d0))) + ((-1.0d0) + (x1 * ((-6.0d0) + ((6.0d0 + (x2 * (-4.0d0))) + ((3.0d0 * (3.0d0 + (2.0d0 * x2))) + (x2 * 10.0d0))))))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = ((x1 * x1) * (x1 * x1)) * (6.0 + ((((15.0 - (18.0 + (x2 * -8.0))) / x1) - 3.0) / x1));
	double tmp;
	if (x1 <= -1.5e+19) {
		tmp = t_0;
	} else if (x1 <= 580.0) {
		tmp = (x2 * -6.0) + (x1 * (((2.0 * x2) * (-6.0 + (x2 * 4.0))) + (-1.0 + (x1 * (-6.0 + ((6.0 + (x2 * -4.0)) + ((3.0 * (3.0 + (2.0 * x2))) + (x2 * 10.0))))))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = ((x1 * x1) * (x1 * x1)) * (6.0 + ((((15.0 - (18.0 + (x2 * -8.0))) / x1) - 3.0) / x1))
	tmp = 0
	if x1 <= -1.5e+19:
		tmp = t_0
	elif x1 <= 580.0:
		tmp = (x2 * -6.0) + (x1 * (((2.0 * x2) * (-6.0 + (x2 * 4.0))) + (-1.0 + (x1 * (-6.0 + ((6.0 + (x2 * -4.0)) + ((3.0 * (3.0 + (2.0 * x2))) + (x2 * 10.0))))))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(Float64(x1 * x1) * Float64(x1 * x1)) * Float64(6.0 + Float64(Float64(Float64(Float64(15.0 - Float64(18.0 + Float64(x2 * -8.0))) / x1) - 3.0) / x1)))
	tmp = 0.0
	if (x1 <= -1.5e+19)
		tmp = t_0;
	elseif (x1 <= 580.0)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(2.0 * x2) * Float64(-6.0 + Float64(x2 * 4.0))) + Float64(-1.0 + Float64(x1 * Float64(-6.0 + Float64(Float64(6.0 + Float64(x2 * -4.0)) + Float64(Float64(3.0 * Float64(3.0 + Float64(2.0 * x2))) + Float64(x2 * 10.0)))))))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = ((x1 * x1) * (x1 * x1)) * (6.0 + ((((15.0 - (18.0 + (x2 * -8.0))) / x1) - 3.0) / x1));
	tmp = 0.0;
	if (x1 <= -1.5e+19)
		tmp = t_0;
	elseif (x1 <= 580.0)
		tmp = (x2 * -6.0) + (x1 * (((2.0 * x2) * (-6.0 + (x2 * 4.0))) + (-1.0 + (x1 * (-6.0 + ((6.0 + (x2 * -4.0)) + ((3.0 * (3.0 + (2.0 * x2))) + (x2 * 10.0))))))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(6.0 + N[(N[(N[(N[(15.0 - N[(18.0 + N[(x2 * -8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision] - 3.0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.5e+19], t$95$0, If[LessEqual[x1, 580.0], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(2.0 * x2), $MachinePrecision] * N[(-6.0 + N[(x2 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1.0 + N[(x1 * N[(-6.0 + N[(N[(6.0 + N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * N[(3.0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.5e19 or 580 < x1

   1. Initial program 35.6%

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

   3. Simplified 35.6%

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

   6. Applied egg-rr 35.6%

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

   7. Taylor expanded in x1 around -inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)} \]
   8. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \left(\mathsf{neg}\left(\frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right)\right)\right) \]

      10. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - \color{blue}{\frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}}\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \color{blue}{\left(\frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}\right), \color{blue}{x1}\right)\right)\right) \]

   9. Simplified 97.0%

      \[\leadsto \color{blue}{\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \frac{3 - \frac{15 - \left(18 + x2 \cdot -8\right)}{x1}}{x1}\right)} \]

   if -1.5e19 < x1 < 580

   1. Initial program 99.5%

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

   3. Simplified 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in x1 around 0

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

   9. Simplified 86.9%

      \[\leadsto \color{blue}{x2 \cdot -6 + x1 \cdot \left(\left(2 \cdot x2\right) \cdot \left(x2 \cdot 4 + -6\right) + \left(x1 \cdot \left(\left(\left(x2 \cdot -4 + 6\right) + \left(3 \cdot \left(3 + 2 \cdot x2\right) + x2 \cdot 10\right)\right) + -6\right) + -1\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 + \frac{\frac{15 - \left(18 + x2 \cdot -8\right)}{x1} - 3}{x1}\right)\\ \mathbf{elif}\;x1 \leq 580:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(\left(2 \cdot x2\right) \cdot \left(-6 + x2 \cdot 4\right) + \left(-1 + x1 \cdot \left(-6 + \left(\left(6 + x2 \cdot -4\right) + \left(3 \cdot \left(3 + 2 \cdot x2\right) + x2 \cdot 10\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 + \frac{\frac{15 - \left(18 + x2 \cdot -8\right)}{x1} - 3}{x1}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.9% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 + \frac{\frac{15 - \left(18 + x2 \cdot -8\right)}{x1} - 3}{x1}\right)\\ \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 15000:\\ \;\;\;\;\frac{3 \cdot \left(x2 \cdot -2 - x1 \cdot \left(1 - x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} + x1 \cdot \left(2 + \left(2 \cdot x2\right) \cdot \left(-6 + x2 \cdot 4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (*
          (* (* x1 x1) (* x1 x1))
          (+ 6.0 (/ (- (/ (- 15.0 (+ 18.0 (* x2 -8.0))) x1) 3.0) x1)))))
   (if (<= x1 -1.5e+19)
     t_0
     (if (<= x1 15000.0)
       (+
        (/ (* 3.0 (- (* x2 -2.0) (* x1 (- 1.0 (* x1 3.0))))) (+ (* x1 x1) 1.0))
        (* x1 (+ 2.0 (* (* 2.0 x2) (+ -6.0 (* x2 4.0))))))
       t_0))))

C

double code(double x1, double x2) {
	double t_0 = ((x1 * x1) * (x1 * x1)) * (6.0 + ((((15.0 - (18.0 + (x2 * -8.0))) / x1) - 3.0) / x1));
	double tmp;
	if (x1 <= -1.5e+19) {
		tmp = t_0;
	} else if (x1 <= 15000.0) {
		tmp = ((3.0 * ((x2 * -2.0) - (x1 * (1.0 - (x1 * 3.0))))) / ((x1 * x1) + 1.0)) + (x1 * (2.0 + ((2.0 * x2) * (-6.0 + (x2 * 4.0)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((x1 * x1) * (x1 * x1)) * (6.0d0 + ((((15.0d0 - (18.0d0 + (x2 * (-8.0d0)))) / x1) - 3.0d0) / x1))
    if (x1 <= (-1.5d+19)) then
        tmp = t_0
    else if (x1 <= 15000.0d0) then
        tmp = ((3.0d0 * ((x2 * (-2.0d0)) - (x1 * (1.0d0 - (x1 * 3.0d0))))) / ((x1 * x1) + 1.0d0)) + (x1 * (2.0d0 + ((2.0d0 * x2) * ((-6.0d0) + (x2 * 4.0d0)))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = ((x1 * x1) * (x1 * x1)) * (6.0 + ((((15.0 - (18.0 + (x2 * -8.0))) / x1) - 3.0) / x1));
	double tmp;
	if (x1 <= -1.5e+19) {
		tmp = t_0;
	} else if (x1 <= 15000.0) {
		tmp = ((3.0 * ((x2 * -2.0) - (x1 * (1.0 - (x1 * 3.0))))) / ((x1 * x1) + 1.0)) + (x1 * (2.0 + ((2.0 * x2) * (-6.0 + (x2 * 4.0)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = ((x1 * x1) * (x1 * x1)) * (6.0 + ((((15.0 - (18.0 + (x2 * -8.0))) / x1) - 3.0) / x1))
	tmp = 0
	if x1 <= -1.5e+19:
		tmp = t_0
	elif x1 <= 15000.0:
		tmp = ((3.0 * ((x2 * -2.0) - (x1 * (1.0 - (x1 * 3.0))))) / ((x1 * x1) + 1.0)) + (x1 * (2.0 + ((2.0 * x2) * (-6.0 + (x2 * 4.0)))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(Float64(x1 * x1) * Float64(x1 * x1)) * Float64(6.0 + Float64(Float64(Float64(Float64(15.0 - Float64(18.0 + Float64(x2 * -8.0))) / x1) - 3.0) / x1)))
	tmp = 0.0
	if (x1 <= -1.5e+19)
		tmp = t_0;
	elseif (x1 <= 15000.0)
		tmp = Float64(Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - Float64(x1 * Float64(1.0 - Float64(x1 * 3.0))))) / Float64(Float64(x1 * x1) + 1.0)) + Float64(x1 * Float64(2.0 + Float64(Float64(2.0 * x2) * Float64(-6.0 + Float64(x2 * 4.0))))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = ((x1 * x1) * (x1 * x1)) * (6.0 + ((((15.0 - (18.0 + (x2 * -8.0))) / x1) - 3.0) / x1));
	tmp = 0.0;
	if (x1 <= -1.5e+19)
		tmp = t_0;
	elseif (x1 <= 15000.0)
		tmp = ((3.0 * ((x2 * -2.0) - (x1 * (1.0 - (x1 * 3.0))))) / ((x1 * x1) + 1.0)) + (x1 * (2.0 + ((2.0 * x2) * (-6.0 + (x2 * 4.0)))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(6.0 + N[(N[(N[(N[(15.0 - N[(18.0 + N[(x2 * -8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision] - 3.0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.5e+19], t$95$0, If[LessEqual[x1, 15000.0], N[(N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - N[(x1 * N[(1.0 - N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(2.0 + N[(N[(2.0 * x2), $MachinePrecision] * N[(-6.0 + N[(x2 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.5e19 or 15000 < x1

   1. Initial program 35.6%

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

   3. Simplified 35.6%

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

   6. Applied egg-rr 35.6%

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

   7. Taylor expanded in x1 around -inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)} \]
   8. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \left(\mathsf{neg}\left(\frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right)\right)\right) \]

      10. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - \color{blue}{\frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}}\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \color{blue}{\left(\frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}\right), \color{blue}{x1}\right)\right)\right) \]

   9. Simplified 97.0%

      \[\leadsto \color{blue}{\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \frac{3 - \frac{15 - \left(18 + x2 \cdot -8\right)}{x1}}{x1}\right)} \]

   if -1.5e19 < x1 < 15000

   1. Initial program 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \color{blue}{\left(x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \color{blue}{\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \left(\left(2 \cdot x2\right) \cdot \color{blue}{\left(4 \cdot x2 - 6\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(\left(2 \cdot x2\right), \color{blue}{\left(4 \cdot x2 - 6\right)}\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(\left(x2 \cdot 2\right), \left(\color{blue}{4 \cdot x2} - 6\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \left(\color{blue}{4 \cdot x2} - 6\right)\right)\right)\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \left(4 \cdot x2 + -6\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\left(4 \cdot x2\right), \color{blue}{-6}\right)\right)\right)\right)\right) \]

      10. *-lowering-*.f64 86.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right)\right)\right) \]

   7. Simplified 86.7%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 + \frac{\frac{15 - \left(18 + x2 \cdot -8\right)}{x1} - 3}{x1}\right)\\ \mathbf{elif}\;x1 \leq 15000:\\ \;\;\;\;\frac{3 \cdot \left(x2 \cdot -2 - x1 \cdot \left(1 - x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} + x1 \cdot \left(2 + \left(2 \cdot x2\right) \cdot \left(-6 + x2 \cdot 4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 + \frac{\frac{15 - \left(18 + x2 \cdot -8\right)}{x1} - 3}{x1}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.8% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 + \frac{\frac{15 - \left(18 + x2 \cdot -8\right)}{x1} - 3}{x1}\right)\\ \mathbf{if}\;x1 \leq -1.55 \cdot 10^{+19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 95:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(2 \cdot x2\right) \cdot \left(-6 + x2 \cdot 4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (*
          (* (* x1 x1) (* x1 x1))
          (+ 6.0 (/ (- (/ (- 15.0 (+ 18.0 (* x2 -8.0))) x1) 3.0) x1)))))
   (if (<= x1 -1.55e+19)
     t_0
     (if (<= x1 95.0)
       (+ (* x2 -6.0) (* x1 (+ -1.0 (* (* 2.0 x2) (+ -6.0 (* x2 4.0))))))
       t_0))))

C

double code(double x1, double x2) {
	double t_0 = ((x1 * x1) * (x1 * x1)) * (6.0 + ((((15.0 - (18.0 + (x2 * -8.0))) / x1) - 3.0) / x1));
	double tmp;
	if (x1 <= -1.55e+19) {
		tmp = t_0;
	} else if (x1 <= 95.0) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((2.0 * x2) * (-6.0 + (x2 * 4.0)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((x1 * x1) * (x1 * x1)) * (6.0d0 + ((((15.0d0 - (18.0d0 + (x2 * (-8.0d0)))) / x1) - 3.0d0) / x1))
    if (x1 <= (-1.55d+19)) then
        tmp = t_0
    else if (x1 <= 95.0d0) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + ((2.0d0 * x2) * ((-6.0d0) + (x2 * 4.0d0)))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = ((x1 * x1) * (x1 * x1)) * (6.0 + ((((15.0 - (18.0 + (x2 * -8.0))) / x1) - 3.0) / x1));
	double tmp;
	if (x1 <= -1.55e+19) {
		tmp = t_0;
	} else if (x1 <= 95.0) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((2.0 * x2) * (-6.0 + (x2 * 4.0)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = ((x1 * x1) * (x1 * x1)) * (6.0 + ((((15.0 - (18.0 + (x2 * -8.0))) / x1) - 3.0) / x1))
	tmp = 0
	if x1 <= -1.55e+19:
		tmp = t_0
	elif x1 <= 95.0:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((2.0 * x2) * (-6.0 + (x2 * 4.0)))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(Float64(x1 * x1) * Float64(x1 * x1)) * Float64(6.0 + Float64(Float64(Float64(Float64(15.0 - Float64(18.0 + Float64(x2 * -8.0))) / x1) - 3.0) / x1)))
	tmp = 0.0
	if (x1 <= -1.55e+19)
		tmp = t_0;
	elseif (x1 <= 95.0)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(Float64(2.0 * x2) * Float64(-6.0 + Float64(x2 * 4.0))))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = ((x1 * x1) * (x1 * x1)) * (6.0 + ((((15.0 - (18.0 + (x2 * -8.0))) / x1) - 3.0) / x1));
	tmp = 0.0;
	if (x1 <= -1.55e+19)
		tmp = t_0;
	elseif (x1 <= 95.0)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((2.0 * x2) * (-6.0 + (x2 * 4.0)))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(6.0 + N[(N[(N[(N[(15.0 - N[(18.0 + N[(x2 * -8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision] - 3.0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.55e+19], t$95$0, If[LessEqual[x1, 95.0], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(N[(2.0 * x2), $MachinePrecision] * N[(-6.0 + N[(x2 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.55e19 or 95 < x1

   1. Initial program 35.6%

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

   3. Simplified 35.6%

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

   6. Applied egg-rr 35.6%

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

   7. Taylor expanded in x1 around -inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)} \]
   8. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \left(\mathsf{neg}\left(\frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)\right)\right)\right) \]

      10. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - \color{blue}{\frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}}\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \color{blue}{\left(\frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}}{x1}\right)}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(3 + -1 \cdot \frac{15 + -1 \cdot \left(18 + -8 \cdot x2\right)}{x1}\right), \color{blue}{x1}\right)\right)\right) \]

   9. Simplified 97.0%

      \[\leadsto \color{blue}{\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \frac{3 - \frac{15 - \left(18 + x2 \cdot -8\right)}{x1}}{x1}\right)} \]

   if -1.55e19 < x1 < 95

   1. Initial program 99.5%

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

   3. Simplified 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in x1 around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) - 1\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x2 \cdot -6\right), \left(\color{blue}{x1} \cdot \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) - 1\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \left(\color{blue}{x1} \cdot \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) - 1\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) - 1\right)}\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + -1\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \color{blue}{-1}\right)\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(\left(2 \cdot x2\right) \cdot \left(4 \cdot x2 - 6\right)\right), -1\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(2 \cdot x2\right), \left(4 \cdot x2 - 6\right)\right), -1\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, x2\right), \left(4 \cdot x2 - 6\right)\right), -1\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, x2\right), \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right), -1\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, x2\right), \left(4 \cdot x2 + -6\right)\right), -1\right)\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right), -1\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right), -1\right)\right)\right) \]

      15. *-lowering-*.f64 85.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), -1\right)\right)\right) \]

   9. Simplified 85.9%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.55 \cdot 10^{+19}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 + \frac{\frac{15 - \left(18 + x2 \cdot -8\right)}{x1} - 3}{x1}\right)\\ \mathbf{elif}\;x1 \leq 95:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(2 \cdot x2\right) \cdot \left(-6 + x2 \cdot 4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 + \frac{\frac{15 - \left(18 + x2 \cdot -8\right)}{x1} - 3}{x1}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.0% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;x1 + 6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -7.6 \cdot 10^{-141}:\\ \;\;\;\;\left(x2 \cdot x2\right) \cdot \left(\frac{x1 \cdot 8}{x1 \cdot x1 + 1} - \frac{6}{x2}\right)\\ \mathbf{elif}\;x1 \leq 2.1:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(x1 \cdot 3\right) \cdot \left(3 + 2 \cdot x2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 + \frac{-3}{x1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.5e+19)
   (+ x1 (* 6.0 (* x1 (* x1 (* x1 x1)))))
   (if (<= x1 -7.6e-141)
     (* (* x2 x2) (- (/ (* x1 8.0) (+ (* x1 x1) 1.0)) (/ 6.0 x2)))
     (if (<= x1 2.1)
       (+ (* x2 -6.0) (* x1 (+ -1.0 (* (* x1 3.0) (+ 3.0 (* 2.0 x2))))))
       (* (* (* x1 x1) (* x1 x1)) (+ 6.0 (/ -3.0 x1)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.5e+19) {
		tmp = x1 + (6.0 * (x1 * (x1 * (x1 * x1))));
	} else if (x1 <= -7.6e-141) {
		tmp = (x2 * x2) * (((x1 * 8.0) / ((x1 * x1) + 1.0)) - (6.0 / x2));
	} else if (x1 <= 2.1) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x1 * 3.0) * (3.0 + (2.0 * x2)))));
	} else {
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 + (-3.0 / x1));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-1.5d+19)) then
        tmp = x1 + (6.0d0 * (x1 * (x1 * (x1 * x1))))
    else if (x1 <= (-7.6d-141)) then
        tmp = (x2 * x2) * (((x1 * 8.0d0) / ((x1 * x1) + 1.0d0)) - (6.0d0 / x2))
    else if (x1 <= 2.1d0) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + ((x1 * 3.0d0) * (3.0d0 + (2.0d0 * x2)))))
    else
        tmp = ((x1 * x1) * (x1 * x1)) * (6.0d0 + ((-3.0d0) / x1))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.5e+19) {
		tmp = x1 + (6.0 * (x1 * (x1 * (x1 * x1))));
	} else if (x1 <= -7.6e-141) {
		tmp = (x2 * x2) * (((x1 * 8.0) / ((x1 * x1) + 1.0)) - (6.0 / x2));
	} else if (x1 <= 2.1) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x1 * 3.0) * (3.0 + (2.0 * x2)))));
	} else {
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 + (-3.0 / x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.5e+19:
		tmp = x1 + (6.0 * (x1 * (x1 * (x1 * x1))))
	elif x1 <= -7.6e-141:
		tmp = (x2 * x2) * (((x1 * 8.0) / ((x1 * x1) + 1.0)) - (6.0 / x2))
	elif x1 <= 2.1:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x1 * 3.0) * (3.0 + (2.0 * x2)))))
	else:
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 + (-3.0 / x1))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.5e+19)
		tmp = Float64(x1 + Float64(6.0 * Float64(x1 * Float64(x1 * Float64(x1 * x1)))));
	elseif (x1 <= -7.6e-141)
		tmp = Float64(Float64(x2 * x2) * Float64(Float64(Float64(x1 * 8.0) / Float64(Float64(x1 * x1) + 1.0)) - Float64(6.0 / x2)));
	elseif (x1 <= 2.1)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(Float64(x1 * 3.0) * Float64(3.0 + Float64(2.0 * x2))))));
	else
		tmp = Float64(Float64(Float64(x1 * x1) * Float64(x1 * x1)) * Float64(6.0 + Float64(-3.0 / x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -1.5e+19)
		tmp = x1 + (6.0 * (x1 * (x1 * (x1 * x1))));
	elseif (x1 <= -7.6e-141)
		tmp = (x2 * x2) * (((x1 * 8.0) / ((x1 * x1) + 1.0)) - (6.0 / x2));
	elseif (x1 <= 2.1)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x1 * 3.0) * (3.0 + (2.0 * x2)))));
	else
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 + (-3.0 / x1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.5e+19], N[(x1 + N[(6.0 * N[(x1 * N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -7.6e-141], N[(N[(x2 * x2), $MachinePrecision] * N[(N[(N[(x1 * 8.0), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - N[(6.0 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.1], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(N[(x1 * 3.0), $MachinePrecision] * N[(3.0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(6.0 + N[(-3.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.5e19

   1. Initial program 28.4%

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

   3. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(x1, \color{blue}{\left(6 \cdot {x1}^{4}\right)}\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(6, \color{blue}{\left({x1}^{4}\right)}\right)\right) \]

      2. pow-lowering-pow.f64 93.0%

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(6, \mathsf{pow.f64}\left(x1, \color{blue}{4}\right)\right)\right) \]

   5. Simplified 93.0%

      \[\leadsto x1 + \color{blue}{6 \cdot {x1}^{4}} \]
   6. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(6 \cdot {x1}^{\left(2 + \color{blue}{2}\right)}\right)\right) \]

      2. pow-prod-up N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(6 \cdot \left({x1}^{2} \cdot \color{blue}{{x1}^{2}}\right)\right)\right) \]

      3. pow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(6 \cdot \left(\left(x1 \cdot x1\right) \cdot {\color{blue}{x1}}^{2}\right)\right)\right) \]

      4. pow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(6 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \color{blue}{x1}\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \color{blue}{6}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right), \color{blue}{6}\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right), 6\right)\right) \]

      8. cube-mult N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\left(x1 \cdot {x1}^{3}\right), 6\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left({x1}^{3}\right)\right), 6\right)\right) \]

      10. cube-mult N/A

          \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right), 6\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \left(x1 \cdot x1\right)\right)\right), 6\right)\right) \]

      12. *-lowering-*.f64 93.0%

          \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right)\right), 6\right)\right) \]

   7. Applied egg-rr 93.0%

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

   if -1.5e19 < x1 < -7.59999999999999973e-141

   1. Initial program 99.4%

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

   3. Simplified 99.3%

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

   6. Applied egg-rr 99.3%

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

   7. Taylor expanded in x2 around -inf

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

   9. Simplified 69.8%

      \[\leadsto \color{blue}{\left(x2 \cdot x2\right) \cdot \left(\frac{8 \cdot x1}{1 + x1 \cdot x1} - \frac{\frac{\left(x1 \cdot x1\right) \cdot -6}{1 + x1 \cdot x1} + \left(x1 \cdot \left(\frac{-4 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{1 + x1 \cdot x1} + \left(-2 \cdot \left(\frac{2 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{1 + x1 \cdot x1} + x1 \cdot 4\right) + 12\right)\right) + \frac{6}{1 + x1 \cdot x1}\right)}{x2}\right)} \]

   10. Taylor expanded in x1 around 0

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(8, x1\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x1, x1\right)\right)\right), \mathsf{/.f64}\left(\color{blue}{6}, x2\right)\right)\right) \]
   11. Step-by-step derivation

   12. Simplified 69.8%

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

   if -7.59999999999999973e-141 < x1 < 2.10000000000000009

   1. Initial program 99.5%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \color{blue}{\left(6 \cdot {x1}^{2}\right)}\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \left(x1 \cdot x1\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. *-lowering-*.f64 78.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, x1\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 78.9%

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

   8. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \color{blue}{\left(2 \cdot x1\right)}\right) \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \left(x1 \cdot \color{blue}{2}\right)\right) \]

      2. *-lowering-*.f64 79.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \color{blue}{2}\right)\right) \]

   10. Simplified 79.3%

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

   11. Taylor expanded in x1 around 0

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

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\color{blue}{x1} \cdot \left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right) \]

       4. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

       5. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) + -1\right)\right)\right) \]

       6. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right), \color{blue}{-1}\right)\right)\right) \]

       7. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(\left(3 \cdot x1\right) \cdot \left(3 - -2 \cdot x2\right)\right), -1\right)\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(3 \cdot x1\right), \left(3 - -2 \cdot x2\right)\right), -1\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(3, x1\right), \left(3 - -2 \cdot x2\right)\right), -1\right)\right)\right) \]

       10. cancel-sign-sub-inv N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(3, x1\right), \left(3 + \left(\mathsf{neg}\left(-2\right)\right) \cdot x2\right)\right), -1\right)\right)\right) \]

       11. metadata-eval N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(3, x1\right), \left(3 + 2 \cdot x2\right)\right), -1\right)\right)\right) \]

       12. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(3, x1\right), \mathsf{+.f64}\left(3, \left(2 \cdot x2\right)\right)\right), -1\right)\right)\right) \]

       13. *-commutative N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(3, x1\right), \mathsf{+.f64}\left(3, \left(x2 \cdot 2\right)\right)\right), -1\right)\right)\right) \]

       14. *-lowering-*.f64 79.5%

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(3, x1\right), \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x2, 2\right)\right)\right), -1\right)\right)\right) \]

   13. Simplified 79.5%

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

   if 2.10000000000000009 < x1

   1. Initial program 44.3%

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

   3. Simplified 44.3%

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

   6. Applied egg-rr 44.2%

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

   7. Taylor expanded in x1 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 - 3 \cdot \frac{1}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3 \cdot 1}{x1}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3}{x1}\right)\right)\right)\right) \]

      13. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{\mathsf{neg}\left(3\right)}{\color{blue}{x1}}\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{-3}{x1}\right)\right)\right) \]

      15. /-lowering-/.f64 90.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \mathsf{/.f64}\left(-3, \color{blue}{x1}\right)\right)\right) \]

   9. Simplified 90.9%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;x1 + 6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -7.6 \cdot 10^{-141}:\\ \;\;\;\;\left(x2 \cdot x2\right) \cdot \left(\frac{x1 \cdot 8}{x1 \cdot x1 + 1} - \frac{6}{x2}\right)\\ \mathbf{elif}\;x1 \leq 2.1:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(x1 \cdot 3\right) \cdot \left(3 + 2 \cdot x2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 + \frac{-3}{x1}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.7% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.55 \cdot 10^{+22}:\\ \;\;\;\;x1 + 6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2.8 \cdot 10^{-147}:\\ \;\;\;\;\left(x2 \cdot x2\right) \cdot \left(\frac{x1 \cdot 8}{x1 \cdot x1 + 1} - \frac{6}{x2}\right)\\ \mathbf{elif}\;x1 \leq 6.5:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 + \frac{-3}{x1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.55e+22)
   (+ x1 (* 6.0 (* x1 (* x1 (* x1 x1)))))
   (if (<= x1 -2.8e-147)
     (* (* x2 x2) (- (/ (* x1 8.0) (+ (* x1 x1) 1.0)) (/ 6.0 x2)))
     (if (<= x1 6.5)
       (- (* x2 -6.0) x1)
       (* (* (* x1 x1) (* x1 x1)) (+ 6.0 (/ -3.0 x1)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.55e+22) {
		tmp = x1 + (6.0 * (x1 * (x1 * (x1 * x1))));
	} else if (x1 <= -2.8e-147) {
		tmp = (x2 * x2) * (((x1 * 8.0) / ((x1 * x1) + 1.0)) - (6.0 / x2));
	} else if (x1 <= 6.5) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 + (-3.0 / x1));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-1.55d+22)) then
        tmp = x1 + (6.0d0 * (x1 * (x1 * (x1 * x1))))
    else if (x1 <= (-2.8d-147)) then
        tmp = (x2 * x2) * (((x1 * 8.0d0) / ((x1 * x1) + 1.0d0)) - (6.0d0 / x2))
    else if (x1 <= 6.5d0) then
        tmp = (x2 * (-6.0d0)) - x1
    else
        tmp = ((x1 * x1) * (x1 * x1)) * (6.0d0 + ((-3.0d0) / x1))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.55e+22) {
		tmp = x1 + (6.0 * (x1 * (x1 * (x1 * x1))));
	} else if (x1 <= -2.8e-147) {
		tmp = (x2 * x2) * (((x1 * 8.0) / ((x1 * x1) + 1.0)) - (6.0 / x2));
	} else if (x1 <= 6.5) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 + (-3.0 / x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.55e+22:
		tmp = x1 + (6.0 * (x1 * (x1 * (x1 * x1))))
	elif x1 <= -2.8e-147:
		tmp = (x2 * x2) * (((x1 * 8.0) / ((x1 * x1) + 1.0)) - (6.0 / x2))
	elif x1 <= 6.5:
		tmp = (x2 * -6.0) - x1
	else:
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 + (-3.0 / x1))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.55e+22)
		tmp = Float64(x1 + Float64(6.0 * Float64(x1 * Float64(x1 * Float64(x1 * x1)))));
	elseif (x1 <= -2.8e-147)
		tmp = Float64(Float64(x2 * x2) * Float64(Float64(Float64(x1 * 8.0) / Float64(Float64(x1 * x1) + 1.0)) - Float64(6.0 / x2)));
	elseif (x1 <= 6.5)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	else
		tmp = Float64(Float64(Float64(x1 * x1) * Float64(x1 * x1)) * Float64(6.0 + Float64(-3.0 / x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -1.55e+22)
		tmp = x1 + (6.0 * (x1 * (x1 * (x1 * x1))));
	elseif (x1 <= -2.8e-147)
		tmp = (x2 * x2) * (((x1 * 8.0) / ((x1 * x1) + 1.0)) - (6.0 / x2));
	elseif (x1 <= 6.5)
		tmp = (x2 * -6.0) - x1;
	else
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 + (-3.0 / x1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.55e+22], N[(x1 + N[(6.0 * N[(x1 * N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.8e-147], N[(N[(x2 * x2), $MachinePrecision] * N[(N[(N[(x1 * 8.0), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - N[(6.0 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6.5], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(6.0 + N[(-3.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.5500000000000001e22

   1. Initial program 28.4%

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

   3. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(x1, \color{blue}{\left(6 \cdot {x1}^{4}\right)}\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(6, \color{blue}{\left({x1}^{4}\right)}\right)\right) \]

      2. pow-lowering-pow.f64 93.0%

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(6, \mathsf{pow.f64}\left(x1, \color{blue}{4}\right)\right)\right) \]

   5. Simplified 93.0%

      \[\leadsto x1 + \color{blue}{6 \cdot {x1}^{4}} \]
   6. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(6 \cdot {x1}^{\left(2 + \color{blue}{2}\right)}\right)\right) \]

      2. pow-prod-up N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(6 \cdot \left({x1}^{2} \cdot \color{blue}{{x1}^{2}}\right)\right)\right) \]

      3. pow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(6 \cdot \left(\left(x1 \cdot x1\right) \cdot {\color{blue}{x1}}^{2}\right)\right)\right) \]

      4. pow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(6 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \color{blue}{x1}\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \color{blue}{6}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right), \color{blue}{6}\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right), 6\right)\right) \]

      8. cube-mult N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\left(x1 \cdot {x1}^{3}\right), 6\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left({x1}^{3}\right)\right), 6\right)\right) \]

      10. cube-mult N/A

          \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right), 6\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \left(x1 \cdot x1\right)\right)\right), 6\right)\right) \]

      12. *-lowering-*.f64 93.0%

          \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right)\right), 6\right)\right) \]

   7. Applied egg-rr 93.0%

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

   if -1.5500000000000001e22 < x1 < -2.8e-147

   1. Initial program 99.4%

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

   3. Simplified 99.3%

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

   6. Applied egg-rr 99.3%

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

   7. Taylor expanded in x2 around -inf

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

   9. Simplified 69.8%

      \[\leadsto \color{blue}{\left(x2 \cdot x2\right) \cdot \left(\frac{8 \cdot x1}{1 + x1 \cdot x1} - \frac{\frac{\left(x1 \cdot x1\right) \cdot -6}{1 + x1 \cdot x1} + \left(x1 \cdot \left(\frac{-4 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{1 + x1 \cdot x1} + \left(-2 \cdot \left(\frac{2 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{1 + x1 \cdot x1} + x1 \cdot 4\right) + 12\right)\right) + \frac{6}{1 + x1 \cdot x1}\right)}{x2}\right)} \]

   10. Taylor expanded in x1 around 0

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(8, x1\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x1, x1\right)\right)\right), \mathsf{/.f64}\left(\color{blue}{6}, x2\right)\right)\right) \]
   11. Step-by-step derivation

   12. Simplified 69.8%

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

   if -2.8e-147 < x1 < 6.5

   1. Initial program 99.5%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \color{blue}{\left(6 \cdot {x1}^{2}\right)}\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \left(x1 \cdot x1\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. *-lowering-*.f64 78.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, x1\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 78.2%

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

   8. Taylor expanded in x1 around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(-6 \cdot x2\right), \color{blue}{x1}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x2 \cdot -6\right), x1\right) \]

      5. *-lowering-*.f64 78.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x2, -6\right), x1\right) \]

   10. Simplified 78.4%

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

   if 6.5 < x1

   1. Initial program 43.2%

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

   3. Simplified 43.2%

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

   6. Applied egg-rr 43.2%

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

   7. Taylor expanded in x1 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 - 3 \cdot \frac{1}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3 \cdot 1}{x1}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3}{x1}\right)\right)\right)\right) \]

      13. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{\mathsf{neg}\left(3\right)}{\color{blue}{x1}}\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{-3}{x1}\right)\right)\right) \]

      15. /-lowering-/.f64 92.5%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \mathsf{/.f64}\left(-3, \color{blue}{x1}\right)\right)\right) \]

   9. Simplified 92.5%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.55 \cdot 10^{+22}:\\ \;\;\;\;x1 + 6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2.8 \cdot 10^{-147}:\\ \;\;\;\;\left(x2 \cdot x2\right) \cdot \left(\frac{x1 \cdot 8}{x1 \cdot x1 + 1} - \frac{6}{x2}\right)\\ \mathbf{elif}\;x1 \leq 6.5:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 + \frac{-3}{x1}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.1% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;x1 + 6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5 \cdot 10^{-145}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-3 + 8 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq 6.5:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 + \frac{-3}{x1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.5e+19)
   (+ x1 (* 6.0 (* x1 (* x1 (* x1 x1)))))
   (if (<= x1 -5e-145)
     (+ (* x2 -6.0) (* x1 (+ -3.0 (* 8.0 (* x2 x2)))))
     (if (<= x1 6.5)
       (- (* x2 -6.0) x1)
       (* (* (* x1 x1) (* x1 x1)) (+ 6.0 (/ -3.0 x1)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.5e+19) {
		tmp = x1 + (6.0 * (x1 * (x1 * (x1 * x1))));
	} else if (x1 <= -5e-145) {
		tmp = (x2 * -6.0) + (x1 * (-3.0 + (8.0 * (x2 * x2))));
	} else if (x1 <= 6.5) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 + (-3.0 / x1));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-1.5d+19)) then
        tmp = x1 + (6.0d0 * (x1 * (x1 * (x1 * x1))))
    else if (x1 <= (-5d-145)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-3.0d0) + (8.0d0 * (x2 * x2))))
    else if (x1 <= 6.5d0) then
        tmp = (x2 * (-6.0d0)) - x1
    else
        tmp = ((x1 * x1) * (x1 * x1)) * (6.0d0 + ((-3.0d0) / x1))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.5e+19) {
		tmp = x1 + (6.0 * (x1 * (x1 * (x1 * x1))));
	} else if (x1 <= -5e-145) {
		tmp = (x2 * -6.0) + (x1 * (-3.0 + (8.0 * (x2 * x2))));
	} else if (x1 <= 6.5) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 + (-3.0 / x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.5e+19:
		tmp = x1 + (6.0 * (x1 * (x1 * (x1 * x1))))
	elif x1 <= -5e-145:
		tmp = (x2 * -6.0) + (x1 * (-3.0 + (8.0 * (x2 * x2))))
	elif x1 <= 6.5:
		tmp = (x2 * -6.0) - x1
	else:
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 + (-3.0 / x1))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.5e+19)
		tmp = Float64(x1 + Float64(6.0 * Float64(x1 * Float64(x1 * Float64(x1 * x1)))));
	elseif (x1 <= -5e-145)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-3.0 + Float64(8.0 * Float64(x2 * x2)))));
	elseif (x1 <= 6.5)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	else
		tmp = Float64(Float64(Float64(x1 * x1) * Float64(x1 * x1)) * Float64(6.0 + Float64(-3.0 / x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -1.5e+19)
		tmp = x1 + (6.0 * (x1 * (x1 * (x1 * x1))));
	elseif (x1 <= -5e-145)
		tmp = (x2 * -6.0) + (x1 * (-3.0 + (8.0 * (x2 * x2))));
	elseif (x1 <= 6.5)
		tmp = (x2 * -6.0) - x1;
	else
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 + (-3.0 / x1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.5e+19], N[(x1 + N[(6.0 * N[(x1 * N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5e-145], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-3.0 + N[(8.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6.5], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(6.0 + N[(-3.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.5e19

   1. Initial program 28.4%

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

   3. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(x1, \color{blue}{\left(6 \cdot {x1}^{4}\right)}\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(6, \color{blue}{\left({x1}^{4}\right)}\right)\right) \]

      2. pow-lowering-pow.f64 93.0%

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(6, \mathsf{pow.f64}\left(x1, \color{blue}{4}\right)\right)\right) \]

   5. Simplified 93.0%

      \[\leadsto x1 + \color{blue}{6 \cdot {x1}^{4}} \]
   6. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(6 \cdot {x1}^{\left(2 + \color{blue}{2}\right)}\right)\right) \]

      2. pow-prod-up N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(6 \cdot \left({x1}^{2} \cdot \color{blue}{{x1}^{2}}\right)\right)\right) \]

      3. pow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(6 \cdot \left(\left(x1 \cdot x1\right) \cdot {\color{blue}{x1}}^{2}\right)\right)\right) \]

      4. pow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(6 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \color{blue}{x1}\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \color{blue}{6}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right), \color{blue}{6}\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right), 6\right)\right) \]

      8. cube-mult N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\left(x1 \cdot {x1}^{3}\right), 6\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left({x1}^{3}\right)\right), 6\right)\right) \]

      10. cube-mult N/A

          \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right), 6\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \left(x1 \cdot x1\right)\right)\right), 6\right)\right) \]

      12. *-lowering-*.f64 93.0%

          \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right)\right), 6\right)\right) \]

   7. Applied egg-rr 93.0%

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

   if -1.5e19 < x1 < -4.9999999999999998e-145

   1. Initial program 99.4%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \color{blue}{\left(x1 \cdot \left(2 + \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(\left(-1 \cdot \left(4 \cdot x2 - 6\right) + \left(4 \cdot x2 + \left(6 \cdot x2 + x1 \cdot \left(\left(3 \cdot \left(4 \cdot x2 - 6\right) + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + x1 \cdot \left(-2 \cdot \left(3 - 2 \cdot x2\right) + \left(3 \cdot \left(3 - 2 \cdot x2\right) + 4 \cdot x2\right)\right)\right)\right) - 4\right)\right)\right)\right) - 6\right)\right)\right)\right)}\right) \]

   7. Simplified 68.8%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \color{blue}{x1 \cdot \left(\left(2 + \left(x2 \cdot 2\right) \cdot \left(4 \cdot x2 + -6\right)\right) + x1 \cdot \left(\left(\left(x2 \cdot 10 + x1 \cdot \left(\left(\left(\left(3 \cdot \left(4 \cdot x2\right) + -18\right) + 4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right) + x1 \cdot \left(\left(-6 + -2 \cdot \left(x2 \cdot -2\right)\right) + \left(3 \cdot \left(3 + x2 \cdot -2\right) + 4 \cdot x2\right)\right)\right) + -4\right)\right) - \left(4 \cdot x2 + -6\right)\right) + -6\right)\right)} \]

   8. Taylor expanded in x2 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \color{blue}{\left({x2}^{2} \cdot \left(8 + -8 \cdot {x1}^{2}\right)\right)}\right)\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(\left({x2}^{2}\right), \color{blue}{\left(8 + -8 \cdot {x1}^{2}\right)}\right)\right)\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(\left(x2 \cdot x2\right), \left(\color{blue}{8} + -8 \cdot {x1}^{2}\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \left(\color{blue}{8} + -8 \cdot {x1}^{2}\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(8, \color{blue}{\left(-8 \cdot {x1}^{2}\right)}\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(8, \left({x1}^{2} \cdot \color{blue}{-8}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(8, \mathsf{*.f64}\left(\left({x1}^{2}\right), \color{blue}{-8}\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(8, \mathsf{*.f64}\left(\left(x1 \cdot x1\right), -8\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 64.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(8, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), -8\right)\right)\right)\right)\right) \]

   10. Simplified 64.3%

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

   11. Taylor expanded in x1 around 0

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

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(8 \cdot {x2}^{2} - 3\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(x2 \cdot -6\right), \left(\color{blue}{x1} \cdot \left(8 \cdot {x2}^{2} - 3\right)\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \left(\color{blue}{x1} \cdot \left(8 \cdot {x2}^{2} - 3\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(8 \cdot {x2}^{2} - 3\right)}\right)\right) \]

       5. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \left(8 \cdot {x2}^{2} + \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right)\right) \]

       6. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \left(8 \cdot {x2}^{2} + -3\right)\right)\right) \]

       7. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(8 \cdot {x2}^{2}\right), \color{blue}{-3}\right)\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(8, \left({x2}^{2}\right)\right), -3\right)\right)\right) \]

       9. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(8, \left(x2 \cdot x2\right)\right), -3\right)\right)\right) \]

       10. *-lowering-*.f64 69.0%

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x2, x2\right)\right), -3\right)\right)\right) \]

   13. Simplified 69.0%

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

   if -4.9999999999999998e-145 < x1 < 6.5

   1. Initial program 99.5%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \color{blue}{\left(6 \cdot {x1}^{2}\right)}\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \left(x1 \cdot x1\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. *-lowering-*.f64 78.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, x1\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 78.2%

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

   8. Taylor expanded in x1 around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(-6 \cdot x2\right), \color{blue}{x1}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x2 \cdot -6\right), x1\right) \]

      5. *-lowering-*.f64 78.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x2, -6\right), x1\right) \]

   10. Simplified 78.4%

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

   if 6.5 < x1

   1. Initial program 43.2%

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

   3. Simplified 43.2%

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

   6. Applied egg-rr 43.2%

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

   7. Taylor expanded in x1 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 - 3 \cdot \frac{1}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3 \cdot 1}{x1}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3}{x1}\right)\right)\right)\right) \]

      13. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{\mathsf{neg}\left(3\right)}{\color{blue}{x1}}\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{-3}{x1}\right)\right)\right) \]

      15. /-lowering-/.f64 92.5%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \mathsf{/.f64}\left(-3, \color{blue}{x1}\right)\right)\right) \]

   9. Simplified 92.5%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;x1 + 6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5 \cdot 10^{-145}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-3 + 8 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq 6.5:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 + \frac{-3}{x1}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 87.8% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;x1 + 6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1950:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(2 \cdot x2\right) \cdot \left(-6 + x2 \cdot 4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 + \frac{-3}{x1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.5e+19)
   (+ x1 (* 6.0 (* x1 (* x1 (* x1 x1)))))
   (if (<= x1 1950.0)
     (+ (* x2 -6.0) (* x1 (+ -1.0 (* (* 2.0 x2) (+ -6.0 (* x2 4.0))))))
     (* (* (* x1 x1) (* x1 x1)) (+ 6.0 (/ -3.0 x1))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.5e+19) {
		tmp = x1 + (6.0 * (x1 * (x1 * (x1 * x1))));
	} else if (x1 <= 1950.0) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((2.0 * x2) * (-6.0 + (x2 * 4.0)))));
	} else {
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 + (-3.0 / x1));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-1.5d+19)) then
        tmp = x1 + (6.0d0 * (x1 * (x1 * (x1 * x1))))
    else if (x1 <= 1950.0d0) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + ((2.0d0 * x2) * ((-6.0d0) + (x2 * 4.0d0)))))
    else
        tmp = ((x1 * x1) * (x1 * x1)) * (6.0d0 + ((-3.0d0) / x1))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.5e+19) {
		tmp = x1 + (6.0 * (x1 * (x1 * (x1 * x1))));
	} else if (x1 <= 1950.0) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((2.0 * x2) * (-6.0 + (x2 * 4.0)))));
	} else {
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 + (-3.0 / x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.5e+19:
		tmp = x1 + (6.0 * (x1 * (x1 * (x1 * x1))))
	elif x1 <= 1950.0:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((2.0 * x2) * (-6.0 + (x2 * 4.0)))))
	else:
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 + (-3.0 / x1))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.5e+19)
		tmp = Float64(x1 + Float64(6.0 * Float64(x1 * Float64(x1 * Float64(x1 * x1)))));
	elseif (x1 <= 1950.0)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(Float64(2.0 * x2) * Float64(-6.0 + Float64(x2 * 4.0))))));
	else
		tmp = Float64(Float64(Float64(x1 * x1) * Float64(x1 * x1)) * Float64(6.0 + Float64(-3.0 / x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -1.5e+19)
		tmp = x1 + (6.0 * (x1 * (x1 * (x1 * x1))));
	elseif (x1 <= 1950.0)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((2.0 * x2) * (-6.0 + (x2 * 4.0)))));
	else
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 + (-3.0 / x1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.5e+19], N[(x1 + N[(6.0 * N[(x1 * N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1950.0], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(N[(2.0 * x2), $MachinePrecision] * N[(-6.0 + N[(x2 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(6.0 + N[(-3.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.5e19

   1. Initial program 28.4%

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

   3. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(x1, \color{blue}{\left(6 \cdot {x1}^{4}\right)}\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(6, \color{blue}{\left({x1}^{4}\right)}\right)\right) \]

      2. pow-lowering-pow.f64 93.0%

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(6, \mathsf{pow.f64}\left(x1, \color{blue}{4}\right)\right)\right) \]

   5. Simplified 93.0%

      \[\leadsto x1 + \color{blue}{6 \cdot {x1}^{4}} \]
   6. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(6 \cdot {x1}^{\left(2 + \color{blue}{2}\right)}\right)\right) \]

      2. pow-prod-up N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(6 \cdot \left({x1}^{2} \cdot \color{blue}{{x1}^{2}}\right)\right)\right) \]

      3. pow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(6 \cdot \left(\left(x1 \cdot x1\right) \cdot {\color{blue}{x1}}^{2}\right)\right)\right) \]

      4. pow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(6 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \color{blue}{x1}\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \color{blue}{6}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right), \color{blue}{6}\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right), 6\right)\right) \]

      8. cube-mult N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\left(x1 \cdot {x1}^{3}\right), 6\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left({x1}^{3}\right)\right), 6\right)\right) \]

      10. cube-mult N/A

          \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right), 6\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \left(x1 \cdot x1\right)\right)\right), 6\right)\right) \]

      12. *-lowering-*.f64 93.0%

          \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right)\right), 6\right)\right) \]

   7. Applied egg-rr 93.0%

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

   if -1.5e19 < x1 < 1950

   1. Initial program 99.5%

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

   3. Simplified 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in x1 around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) - 1\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x2 \cdot -6\right), \left(\color{blue}{x1} \cdot \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) - 1\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \left(\color{blue}{x1} \cdot \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) - 1\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) - 1\right)}\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + -1\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \color{blue}{-1}\right)\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(\left(2 \cdot x2\right) \cdot \left(4 \cdot x2 - 6\right)\right), -1\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(2 \cdot x2\right), \left(4 \cdot x2 - 6\right)\right), -1\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, x2\right), \left(4 \cdot x2 - 6\right)\right), -1\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, x2\right), \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right), -1\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, x2\right), \left(4 \cdot x2 + -6\right)\right), -1\right)\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right), -1\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right), -1\right)\right)\right) \]

      15. *-lowering-*.f64 85.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -6\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), -1\right)\right)\right) \]

   9. Simplified 85.9%

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

   if 1950 < x1

   1. Initial program 43.2%

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

   3. Simplified 43.2%

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

   6. Applied egg-rr 43.2%

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

   7. Taylor expanded in x1 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 - 3 \cdot \frac{1}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3 \cdot 1}{x1}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3}{x1}\right)\right)\right)\right) \]

      13. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{\mathsf{neg}\left(3\right)}{\color{blue}{x1}}\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{-3}{x1}\right)\right)\right) \]

      15. /-lowering-/.f64 92.5%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \mathsf{/.f64}\left(-3, \color{blue}{x1}\right)\right)\right) \]

   9. Simplified 92.5%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;x1 + 6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1950:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(2 \cdot x2\right) \cdot \left(-6 + x2 \cdot 4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 + \frac{-3}{x1}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 80.7% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;x1 + 6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6.5:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 + \frac{-3}{x1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.5e+19)
   (+ x1 (* 6.0 (* x1 (* x1 (* x1 x1)))))
   (if (<= x1 6.5)
     (- (* x2 -6.0) x1)
     (* (* (* x1 x1) (* x1 x1)) (+ 6.0 (/ -3.0 x1))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.5e+19) {
		tmp = x1 + (6.0 * (x1 * (x1 * (x1 * x1))));
	} else if (x1 <= 6.5) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 + (-3.0 / x1));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-1.5d+19)) then
        tmp = x1 + (6.0d0 * (x1 * (x1 * (x1 * x1))))
    else if (x1 <= 6.5d0) then
        tmp = (x2 * (-6.0d0)) - x1
    else
        tmp = ((x1 * x1) * (x1 * x1)) * (6.0d0 + ((-3.0d0) / x1))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.5e+19) {
		tmp = x1 + (6.0 * (x1 * (x1 * (x1 * x1))));
	} else if (x1 <= 6.5) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 + (-3.0 / x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.5e+19:
		tmp = x1 + (6.0 * (x1 * (x1 * (x1 * x1))))
	elif x1 <= 6.5:
		tmp = (x2 * -6.0) - x1
	else:
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 + (-3.0 / x1))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.5e+19)
		tmp = Float64(x1 + Float64(6.0 * Float64(x1 * Float64(x1 * Float64(x1 * x1)))));
	elseif (x1 <= 6.5)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	else
		tmp = Float64(Float64(Float64(x1 * x1) * Float64(x1 * x1)) * Float64(6.0 + Float64(-3.0 / x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -1.5e+19)
		tmp = x1 + (6.0 * (x1 * (x1 * (x1 * x1))));
	elseif (x1 <= 6.5)
		tmp = (x2 * -6.0) - x1;
	else
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 + (-3.0 / x1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.5e+19], N[(x1 + N[(6.0 * N[(x1 * N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6.5], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(6.0 + N[(-3.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.5e19

   1. Initial program 28.4%

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

   3. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(x1, \color{blue}{\left(6 \cdot {x1}^{4}\right)}\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(6, \color{blue}{\left({x1}^{4}\right)}\right)\right) \]

      2. pow-lowering-pow.f64 93.0%

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(6, \mathsf{pow.f64}\left(x1, \color{blue}{4}\right)\right)\right) \]

   5. Simplified 93.0%

      \[\leadsto x1 + \color{blue}{6 \cdot {x1}^{4}} \]
   6. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(6 \cdot {x1}^{\left(2 + \color{blue}{2}\right)}\right)\right) \]

      2. pow-prod-up N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(6 \cdot \left({x1}^{2} \cdot \color{blue}{{x1}^{2}}\right)\right)\right) \]

      3. pow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(6 \cdot \left(\left(x1 \cdot x1\right) \cdot {\color{blue}{x1}}^{2}\right)\right)\right) \]

      4. pow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(6 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \color{blue}{x1}\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \color{blue}{6}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right), \color{blue}{6}\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right), 6\right)\right) \]

      8. cube-mult N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\left(x1 \cdot {x1}^{3}\right), 6\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left({x1}^{3}\right)\right), 6\right)\right) \]

      10. cube-mult N/A

          \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right), 6\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \left(x1 \cdot x1\right)\right)\right), 6\right)\right) \]

      12. *-lowering-*.f64 93.0%

          \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right)\right), 6\right)\right) \]

   7. Applied egg-rr 93.0%

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

   if -1.5e19 < x1 < 6.5

   1. Initial program 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \color{blue}{\left(6 \cdot {x1}^{2}\right)}\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \left(x1 \cdot x1\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. *-lowering-*.f64 70.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, x1\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 70.7%

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

   8. Taylor expanded in x1 around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(-6 \cdot x2\right), \color{blue}{x1}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x2 \cdot -6\right), x1\right) \]

      5. *-lowering-*.f64 71.0%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x2, -6\right), x1\right) \]

   10. Simplified 71.0%

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

   if 6.5 < x1

   1. Initial program 43.2%

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

   3. Simplified 43.2%

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

   6. Applied egg-rr 43.2%

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

   7. Taylor expanded in x1 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 - 3 \cdot \frac{1}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3 \cdot 1}{x1}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3}{x1}\right)\right)\right)\right) \]

      13. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{\mathsf{neg}\left(3\right)}{\color{blue}{x1}}\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{-3}{x1}\right)\right)\right) \]

      15. /-lowering-/.f64 92.5%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \mathsf{/.f64}\left(-3, \color{blue}{x1}\right)\right)\right) \]

   9. Simplified 92.5%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;x1 + 6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6.5:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 + \frac{-3}{x1}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 64.0% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+102}:\\ \;\;\;\;-3 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\\ \mathbf{elif}\;x1 \leq -0.00022:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 2.55 \cdot 10^{-14}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 8.0 (* x1 (* x2 x2)))))
   (if (<= x1 -1e+102)
     (* -3.0 (* x1 (* x1 x1)))
     (if (<= x1 -0.00022) t_0 (if (<= x1 2.55e-14) (- (* x2 -6.0) x1) t_0)))))

C

double code(double x1, double x2) {
	double t_0 = 8.0 * (x1 * (x2 * x2));
	double tmp;
	if (x1 <= -1e+102) {
		tmp = -3.0 * (x1 * (x1 * x1));
	} else if (x1 <= -0.00022) {
		tmp = t_0;
	} else if (x1 <= 2.55e-14) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 8.0d0 * (x1 * (x2 * x2))
    if (x1 <= (-1d+102)) then
        tmp = (-3.0d0) * (x1 * (x1 * x1))
    else if (x1 <= (-0.00022d0)) then
        tmp = t_0
    else if (x1 <= 2.55d-14) then
        tmp = (x2 * (-6.0d0)) - x1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 8.0 * (x1 * (x2 * x2));
	double tmp;
	if (x1 <= -1e+102) {
		tmp = -3.0 * (x1 * (x1 * x1));
	} else if (x1 <= -0.00022) {
		tmp = t_0;
	} else if (x1 <= 2.55e-14) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 8.0 * (x1 * (x2 * x2))
	tmp = 0
	if x1 <= -1e+102:
		tmp = -3.0 * (x1 * (x1 * x1))
	elif x1 <= -0.00022:
		tmp = t_0
	elif x1 <= 2.55e-14:
		tmp = (x2 * -6.0) - x1
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(8.0 * Float64(x1 * Float64(x2 * x2)))
	tmp = 0.0
	if (x1 <= -1e+102)
		tmp = Float64(-3.0 * Float64(x1 * Float64(x1 * x1)));
	elseif (x1 <= -0.00022)
		tmp = t_0;
	elseif (x1 <= 2.55e-14)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 8.0 * (x1 * (x2 * x2));
	tmp = 0.0;
	if (x1 <= -1e+102)
		tmp = -3.0 * (x1 * (x1 * x1));
	elseif (x1 <= -0.00022)
		tmp = t_0;
	elseif (x1 <= 2.55e-14)
		tmp = (x2 * -6.0) - x1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(8.0 * N[(x1 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1e+102], N[(-3.0 * N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -0.00022], t$95$0, If[LessEqual[x1, 2.55e-14], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -9.99999999999999977e101

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   6. Applied egg-rr 0.0%

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

   7. Taylor expanded in x1 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 - 3 \cdot \frac{1}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3 \cdot 1}{x1}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3}{x1}\right)\right)\right)\right) \]

      13. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{\mathsf{neg}\left(3\right)}{\color{blue}{x1}}\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{-3}{x1}\right)\right)\right) \]

      15. /-lowering-/.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \mathsf{/.f64}\left(-3, \color{blue}{x1}\right)\right)\right) \]

   9. Simplified 100.0%

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

   10. Taylor expanded in x1 around 0

       \[\leadsto \color{blue}{-3 \cdot {x1}^{3}} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto {x1}^{3} \cdot \color{blue}{-3} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({x1}^{3}\right), \color{blue}{-3}\right) \]

       3. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(\left(x1 \cdot \left(x1 \cdot x1\right)\right), -3\right) \]

       4. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(x1 \cdot {x1}^{2}\right), -3\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left({x1}^{2}\right)\right), -3\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left(x1 \cdot x1\right)\right), -3\right) \]

       7. *-lowering-*.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), -3\right) \]

   12. Simplified 100.0%

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

   if -9.99999999999999977e101 < x1 < -2.20000000000000008e-4 or 2.5499999999999999e-14 < x1

   1. Initial program 61.7%

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

   3. Simplified 61.7%

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

   5. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \color{blue}{\left(x1 \cdot \left(4 \cdot x2 - 6\right)\right)}\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \left(4 \cdot x2 - 6\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 15.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 15.1%

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

   8. Taylor expanded in x2 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(8, \color{blue}{\left(x1 \cdot {x2}^{2}\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \color{blue}{\left({x2}^{2}\right)}\right)\right) \]

      3. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \left(x2 \cdot \color{blue}{x2}\right)\right)\right) \]

      4. *-lowering-*.f64 31.5%

         \[\leadsto \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, \color{blue}{x2}\right)\right)\right) \]

   10. Simplified 31.5%

       \[\leadsto \color{blue}{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)} \]

   if -2.20000000000000008e-4 < x1 < 2.5499999999999999e-14

   1. Initial program 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \color{blue}{\left(6 \cdot {x1}^{2}\right)}\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \left(x1 \cdot x1\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. *-lowering-*.f64 75.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, x1\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 75.4%

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

   8. Taylor expanded in x1 around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(-6 \cdot x2\right), \color{blue}{x1}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x2 \cdot -6\right), x1\right) \]

      5. *-lowering-*.f64 75.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x2, -6\right), x1\right) \]

   10. Simplified 75.5%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+102}:\\ \;\;\;\;-3 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\\ \mathbf{elif}\;x1 \leq -0.00022:\\ \;\;\;\;8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq 2.55 \cdot 10^{-14}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 80.5% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;x1 + 6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6.5:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.5e+19)
   (+ x1 (* 6.0 (* x1 (* x1 (* x1 x1)))))
   (if (<= x1 6.5) (- (* x2 -6.0) x1) (+ x1 (* x1 (* x1 (* (* x1 x1) 6.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.5e+19) {
		tmp = x1 + (6.0 * (x1 * (x1 * (x1 * x1))));
	} else if (x1 <= 6.5) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = x1 + (x1 * (x1 * ((x1 * x1) * 6.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-1.5d+19)) then
        tmp = x1 + (6.0d0 * (x1 * (x1 * (x1 * x1))))
    else if (x1 <= 6.5d0) then
        tmp = (x2 * (-6.0d0)) - x1
    else
        tmp = x1 + (x1 * (x1 * ((x1 * x1) * 6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.5e+19) {
		tmp = x1 + (6.0 * (x1 * (x1 * (x1 * x1))));
	} else if (x1 <= 6.5) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = x1 + (x1 * (x1 * ((x1 * x1) * 6.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.5e+19:
		tmp = x1 + (6.0 * (x1 * (x1 * (x1 * x1))))
	elif x1 <= 6.5:
		tmp = (x2 * -6.0) - x1
	else:
		tmp = x1 + (x1 * (x1 * ((x1 * x1) * 6.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.5e+19)
		tmp = Float64(x1 + Float64(6.0 * Float64(x1 * Float64(x1 * Float64(x1 * x1)))));
	elseif (x1 <= 6.5)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	else
		tmp = Float64(x1 + Float64(x1 * Float64(x1 * Float64(Float64(x1 * x1) * 6.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -1.5e+19)
		tmp = x1 + (6.0 * (x1 * (x1 * (x1 * x1))));
	elseif (x1 <= 6.5)
		tmp = (x2 * -6.0) - x1;
	else
		tmp = x1 + (x1 * (x1 * ((x1 * x1) * 6.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.5e+19], N[(x1 + N[(6.0 * N[(x1 * N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6.5], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], N[(x1 + N[(x1 * N[(x1 * N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.5e19

   1. Initial program 28.4%

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

   3. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(x1, \color{blue}{\left(6 \cdot {x1}^{4}\right)}\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(6, \color{blue}{\left({x1}^{4}\right)}\right)\right) \]

      2. pow-lowering-pow.f64 93.0%

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(6, \mathsf{pow.f64}\left(x1, \color{blue}{4}\right)\right)\right) \]

   5. Simplified 93.0%

      \[\leadsto x1 + \color{blue}{6 \cdot {x1}^{4}} \]
   6. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(6 \cdot {x1}^{\left(2 + \color{blue}{2}\right)}\right)\right) \]

      2. pow-prod-up N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(6 \cdot \left({x1}^{2} \cdot \color{blue}{{x1}^{2}}\right)\right)\right) \]

      3. pow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(6 \cdot \left(\left(x1 \cdot x1\right) \cdot {\color{blue}{x1}}^{2}\right)\right)\right) \]

      4. pow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(6 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \color{blue}{x1}\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \color{blue}{6}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right), \color{blue}{6}\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right), 6\right)\right) \]

      8. cube-mult N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\left(x1 \cdot {x1}^{3}\right), 6\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left({x1}^{3}\right)\right), 6\right)\right) \]

      10. cube-mult N/A

          \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right), 6\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \left(x1 \cdot x1\right)\right)\right), 6\right)\right) \]

      12. *-lowering-*.f64 93.0%

          \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right)\right), 6\right)\right) \]

   7. Applied egg-rr 93.0%

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

   if -1.5e19 < x1 < 6.5

   1. Initial program 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \color{blue}{\left(6 \cdot {x1}^{2}\right)}\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \left(x1 \cdot x1\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. *-lowering-*.f64 70.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, x1\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 70.7%

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

   8. Taylor expanded in x1 around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(-6 \cdot x2\right), \color{blue}{x1}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x2 \cdot -6\right), x1\right) \]

      5. *-lowering-*.f64 71.0%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x2, -6\right), x1\right) \]

   10. Simplified 71.0%

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

   if 6.5 < x1

   1. Initial program 43.2%

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

   3. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(x1, \color{blue}{\left(6 \cdot {x1}^{4}\right)}\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(6, \color{blue}{\left({x1}^{4}\right)}\right)\right) \]

      2. pow-lowering-pow.f64 92.5%

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(6, \mathsf{pow.f64}\left(x1, \color{blue}{4}\right)\right)\right) \]

   5. Simplified 92.5%

      \[\leadsto x1 + \color{blue}{6 \cdot {x1}^{4}} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto 6 \cdot {x1}^{4} + \color{blue}{x1} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(6 \cdot {x1}^{4}\right), \color{blue}{x1}\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(6 \cdot {x1}^{\left(2 + 2\right)}\right), x1\right) \]

      4. pow-prod-up N/A

         \[\leadsto \mathsf{+.f64}\left(\left(6 \cdot \left({x1}^{2} \cdot {x1}^{2}\right)\right), x1\right) \]

      5. pow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(6 \cdot \left(\left(x1 \cdot x1\right) \cdot {x1}^{2}\right)\right), x1\right) \]

      6. pow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(6 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right)\right), x1\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot 6\right), x1\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right), x1\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(x1 \cdot x1\right) \cdot \left(6 \cdot \left(x1 \cdot x1\right)\right)\right), x1\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left(6 \cdot \left(x1 \cdot x1\right)\right)\right), x1\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(6 \cdot \left(x1 \cdot x1\right)\right)\right), x1\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(\left(x1 \cdot x1\right) \cdot 6\right)\right), x1\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(\left(x1 \cdot x1\right), 6\right)\right), x1\right) \]

      14. *-lowering-*.f64 92.4%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 6\right)\right), x1\right) \]

   7. Applied egg-rr 92.4%

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

      1. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x1 \cdot \left(x1 \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\right), x1\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(x1 \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right) \cdot x1\right), x1\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right), x1\right), x1\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot \left(6 \cdot \left(x1 \cdot x1\right)\right)\right), x1\right), x1\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot \left(\left(\mathsf{neg}\left(-6\right)\right) \cdot \left(x1 \cdot x1\right)\right)\right), x1\right), x1\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot \left(\mathsf{neg}\left(-6 \cdot \left(x1 \cdot x1\right)\right)\right)\right), x1\right), x1\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot \left(\mathsf{neg}\left(\left(x1 \cdot x1\right) \cdot -6\right)\right)\right), x1\right), x1\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left(\mathsf{neg}\left(\left(x1 \cdot x1\right) \cdot -6\right)\right)\right), x1\right), x1\right) \]

      9. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left(\left(x1 \cdot x1\right) \cdot \left(\mathsf{neg}\left(-6\right)\right)\right)\right), x1\right), x1\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left(\left(x1 \cdot x1\right) \cdot 6\right)\right), x1\right), x1\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(\left(x1 \cdot x1\right), 6\right)\right), x1\right), x1\right) \]

      12. *-lowering-*.f64 92.4%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 6\right)\right), x1\right), x1\right) \]

   9. Applied egg-rr 92.4%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;x1 + 6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6.5:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 80.7% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;x1 + 6 \cdot \left(x1 \cdot t\_0\right)\\ \mathbf{elif}\;x1 \leq 6.5:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \left(-3 + x1 \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1))))
   (if (<= x1 -1.5e+19)
     (+ x1 (* 6.0 (* x1 t_0)))
     (if (<= x1 6.5) (- (* x2 -6.0) x1) (* t_0 (+ -3.0 (* x1 6.0)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -1.5e+19) {
		tmp = x1 + (6.0 * (x1 * t_0));
	} else if (x1 <= 6.5) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = t_0 * (-3.0 + (x1 * 6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 * (x1 * x1)
    if (x1 <= (-1.5d+19)) then
        tmp = x1 + (6.0d0 * (x1 * t_0))
    else if (x1 <= 6.5d0) then
        tmp = (x2 * (-6.0d0)) - x1
    else
        tmp = t_0 * ((-3.0d0) + (x1 * 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -1.5e+19) {
		tmp = x1 + (6.0 * (x1 * t_0));
	} else if (x1 <= 6.5) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = t_0 * (-3.0 + (x1 * 6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	tmp = 0
	if x1 <= -1.5e+19:
		tmp = x1 + (6.0 * (x1 * t_0))
	elif x1 <= 6.5:
		tmp = (x2 * -6.0) - x1
	else:
		tmp = t_0 * (-3.0 + (x1 * 6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	tmp = 0.0
	if (x1 <= -1.5e+19)
		tmp = Float64(x1 + Float64(6.0 * Float64(x1 * t_0)));
	elseif (x1 <= 6.5)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	else
		tmp = Float64(t_0 * Float64(-3.0 + Float64(x1 * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	tmp = 0.0;
	if (x1 <= -1.5e+19)
		tmp = x1 + (6.0 * (x1 * t_0));
	elseif (x1 <= 6.5)
		tmp = (x2 * -6.0) - x1;
	else
		tmp = t_0 * (-3.0 + (x1 * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.5e+19], N[(x1 + N[(6.0 * N[(x1 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6.5], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], N[(t$95$0 * N[(-3.0 + N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.5e19

   1. Initial program 28.4%

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

   3. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(x1, \color{blue}{\left(6 \cdot {x1}^{4}\right)}\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(6, \color{blue}{\left({x1}^{4}\right)}\right)\right) \]

      2. pow-lowering-pow.f64 93.0%

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(6, \mathsf{pow.f64}\left(x1, \color{blue}{4}\right)\right)\right) \]

   5. Simplified 93.0%

      \[\leadsto x1 + \color{blue}{6 \cdot {x1}^{4}} \]
   6. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(6 \cdot {x1}^{\left(2 + \color{blue}{2}\right)}\right)\right) \]

      2. pow-prod-up N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(6 \cdot \left({x1}^{2} \cdot \color{blue}{{x1}^{2}}\right)\right)\right) \]

      3. pow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(6 \cdot \left(\left(x1 \cdot x1\right) \cdot {\color{blue}{x1}}^{2}\right)\right)\right) \]

      4. pow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(6 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \color{blue}{x1}\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \left(\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \color{blue}{6}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right), \color{blue}{6}\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right), 6\right)\right) \]

      8. cube-mult N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\left(x1 \cdot {x1}^{3}\right), 6\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left({x1}^{3}\right)\right), 6\right)\right) \]

      10. cube-mult N/A

          \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right), 6\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \left(x1 \cdot x1\right)\right)\right), 6\right)\right) \]

      12. *-lowering-*.f64 93.0%

          \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right)\right), 6\right)\right) \]

   7. Applied egg-rr 93.0%

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

   if -1.5e19 < x1 < 6.5

   1. Initial program 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \color{blue}{\left(6 \cdot {x1}^{2}\right)}\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \left(x1 \cdot x1\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. *-lowering-*.f64 70.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, x1\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 70.7%

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

   8. Taylor expanded in x1 around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(-6 \cdot x2\right), \color{blue}{x1}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x2 \cdot -6\right), x1\right) \]

      5. *-lowering-*.f64 71.0%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x2, -6\right), x1\right) \]

   10. Simplified 71.0%

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

   if 6.5 < x1

   1. Initial program 43.2%

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

   3. Simplified 43.2%

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

   6. Applied egg-rr 43.2%

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

   7. Taylor expanded in x1 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 - 3 \cdot \frac{1}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3 \cdot 1}{x1}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3}{x1}\right)\right)\right)\right) \]

      13. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{\mathsf{neg}\left(3\right)}{\color{blue}{x1}}\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{-3}{x1}\right)\right)\right) \]

      15. /-lowering-/.f64 92.5%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \mathsf{/.f64}\left(-3, \color{blue}{x1}\right)\right)\right) \]

   9. Simplified 92.5%

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

   10. Taylor expanded in x1 around 0

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({x1}^{3}\right), \color{blue}{\left(6 \cdot x1 - 3\right)}\right) \]

       2. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(\left(x1 \cdot \left(x1 \cdot x1\right)\right), \left(\color{blue}{6 \cdot x1} - 3\right)\right) \]

       3. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(x1 \cdot {x1}^{2}\right), \left(6 \cdot \color{blue}{x1} - 3\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left({x1}^{2}\right)\right), \left(\color{blue}{6 \cdot x1} - 3\right)\right) \]

       5. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left(x1 \cdot x1\right)\right), \left(6 \cdot \color{blue}{x1} - 3\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 \cdot \color{blue}{x1} - 3\right)\right) \]

       7. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

       8. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 \cdot x1 + -3\right)\right) \]

       9. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\left(6 \cdot x1\right), \color{blue}{-3}\right)\right) \]

       10. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot 6\right), -3\right)\right) \]

       11. *-lowering-*.f64 92.4%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 6\right), -3\right)\right) \]

   12. Simplified 92.4%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;x1 + 6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6.5:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;\left(x1 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(-3 + x1 \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 80.7% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x1 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(-3 + x1 \cdot 6\right)\\ \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 6.5:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* x1 (* x1 x1)) (+ -3.0 (* x1 6.0)))))
   (if (<= x1 -1.5e+19) t_0 (if (<= x1 6.5) (- (* x2 -6.0) x1) t_0))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * (x1 * x1)) * (-3.0 + (x1 * 6.0));
	double tmp;
	if (x1 <= -1.5e+19) {
		tmp = t_0;
	} else if (x1 <= 6.5) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x1 * (x1 * x1)) * ((-3.0d0) + (x1 * 6.0d0))
    if (x1 <= (-1.5d+19)) then
        tmp = t_0
    else if (x1 <= 6.5d0) then
        tmp = (x2 * (-6.0d0)) - x1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * (x1 * x1)) * (-3.0 + (x1 * 6.0));
	double tmp;
	if (x1 <= -1.5e+19) {
		tmp = t_0;
	} else if (x1 <= 6.5) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * (x1 * x1)) * (-3.0 + (x1 * 6.0))
	tmp = 0
	if x1 <= -1.5e+19:
		tmp = t_0
	elif x1 <= 6.5:
		tmp = (x2 * -6.0) - x1
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * Float64(x1 * x1)) * Float64(-3.0 + Float64(x1 * 6.0)))
	tmp = 0.0
	if (x1 <= -1.5e+19)
		tmp = t_0;
	elseif (x1 <= 6.5)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * (x1 * x1)) * (-3.0 + (x1 * 6.0));
	tmp = 0.0;
	if (x1 <= -1.5e+19)
		tmp = t_0;
	elseif (x1 <= 6.5)
		tmp = (x2 * -6.0) - x1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(-3.0 + N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.5e+19], t$95$0, If[LessEqual[x1, 6.5], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.5e19 or 6.5 < x1

   1. Initial program 35.6%

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

   3. Simplified 35.6%

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

   6. Applied egg-rr 35.6%

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

   7. Taylor expanded in x1 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 - 3 \cdot \frac{1}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3 \cdot 1}{x1}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3}{x1}\right)\right)\right)\right) \]

      13. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{\mathsf{neg}\left(3\right)}{\color{blue}{x1}}\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{-3}{x1}\right)\right)\right) \]

      15. /-lowering-/.f64 92.7%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \mathsf{/.f64}\left(-3, \color{blue}{x1}\right)\right)\right) \]

   9. Simplified 92.7%

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

   10. Taylor expanded in x1 around 0

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({x1}^{3}\right), \color{blue}{\left(6 \cdot x1 - 3\right)}\right) \]

       2. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(\left(x1 \cdot \left(x1 \cdot x1\right)\right), \left(\color{blue}{6 \cdot x1} - 3\right)\right) \]

       3. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(x1 \cdot {x1}^{2}\right), \left(6 \cdot \color{blue}{x1} - 3\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left({x1}^{2}\right)\right), \left(\color{blue}{6 \cdot x1} - 3\right)\right) \]

       5. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left(x1 \cdot x1\right)\right), \left(6 \cdot \color{blue}{x1} - 3\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 \cdot \color{blue}{x1} - 3\right)\right) \]

       7. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

       8. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 \cdot x1 + -3\right)\right) \]

       9. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\left(6 \cdot x1\right), \color{blue}{-3}\right)\right) \]

       10. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot 6\right), -3\right)\right) \]

       11. *-lowering-*.f64 92.7%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 6\right), -3\right)\right) \]

   12. Simplified 92.7%

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

   if -1.5e19 < x1 < 6.5

   1. Initial program 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \color{blue}{\left(6 \cdot {x1}^{2}\right)}\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \left(x1 \cdot x1\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. *-lowering-*.f64 70.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, x1\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 70.7%

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

   8. Taylor expanded in x1 around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(-6 \cdot x2\right), \color{blue}{x1}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x2 \cdot -6\right), x1\right) \]

      5. *-lowering-*.f64 71.0%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x2, -6\right), x1\right) \]

   10. Simplified 71.0%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;\left(x1 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(-3 + x1 \cdot 6\right)\\ \mathbf{elif}\;x1 \leq 6.5:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;\left(x1 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(-3 + x1 \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 80.5% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(6 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right) + 1\right)\\ \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 6.5:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ (* 6.0 (* x1 (* x1 x1))) 1.0))))
   (if (<= x1 -1.5e+19) t_0 (if (<= x1 6.5) (- (* x2 -6.0) x1) t_0))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((6.0 * (x1 * (x1 * x1))) + 1.0);
	double tmp;
	if (x1 <= -1.5e+19) {
		tmp = t_0;
	} else if (x1 <= 6.5) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 * ((6.0d0 * (x1 * (x1 * x1))) + 1.0d0)
    if (x1 <= (-1.5d+19)) then
        tmp = t_0
    else if (x1 <= 6.5d0) then
        tmp = (x2 * (-6.0d0)) - x1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * ((6.0 * (x1 * (x1 * x1))) + 1.0);
	double tmp;
	if (x1 <= -1.5e+19) {
		tmp = t_0;
	} else if (x1 <= 6.5) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((6.0 * (x1 * (x1 * x1))) + 1.0)
	tmp = 0
	if x1 <= -1.5e+19:
		tmp = t_0
	elif x1 <= 6.5:
		tmp = (x2 * -6.0) - x1
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(6.0 * Float64(x1 * Float64(x1 * x1))) + 1.0))
	tmp = 0.0
	if (x1 <= -1.5e+19)
		tmp = t_0;
	elseif (x1 <= 6.5)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((6.0 * (x1 * (x1 * x1))) + 1.0);
	tmp = 0.0;
	if (x1 <= -1.5e+19)
		tmp = t_0;
	elseif (x1 <= 6.5)
		tmp = (x2 * -6.0) - x1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(N[(6.0 * N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.5e+19], t$95$0, If[LessEqual[x1, 6.5], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.5e19 or 6.5 < x1

   1. Initial program 35.6%

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

   3. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(x1, \color{blue}{\left(6 \cdot {x1}^{4}\right)}\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(6, \color{blue}{\left({x1}^{4}\right)}\right)\right) \]

      2. pow-lowering-pow.f64 92.7%

         \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(6, \mathsf{pow.f64}\left(x1, \color{blue}{4}\right)\right)\right) \]

   5. Simplified 92.7%

      \[\leadsto x1 + \color{blue}{6 \cdot {x1}^{4}} \]

   6. Taylor expanded in x1 around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(1 + 6 \cdot {x1}^{3}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(1, \color{blue}{\left(6 \cdot {x1}^{3}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(6, \color{blue}{\left({x1}^{3}\right)}\right)\right)\right) \]

      4. cube-mult N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(6, \left(x1 \cdot \color{blue}{\left(x1 \cdot x1\right)}\right)\right)\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(6, \left(x1 \cdot {x1}^{\color{blue}{2}}\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \color{blue}{\left({x1}^{2}\right)}\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \left(x1 \cdot \color{blue}{x1}\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 92.7%

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \color{blue}{x1}\right)\right)\right)\right)\right) \]

   8. Simplified 92.7%

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

   if -1.5e19 < x1 < 6.5

   1. Initial program 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \color{blue}{\left(6 \cdot {x1}^{2}\right)}\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \left(x1 \cdot x1\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. *-lowering-*.f64 70.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, x1\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 70.7%

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

   8. Taylor expanded in x1 around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(-6 \cdot x2\right), \color{blue}{x1}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x2 \cdot -6\right), x1\right) \]

      5. *-lowering-*.f64 71.0%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x2, -6\right), x1\right) \]

   10. Simplified 71.0%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;x1 \cdot \left(6 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right) + 1\right)\\ \mathbf{elif}\;x1 \leq 6.5:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(6 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 80.5% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right)\\ \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 6.5:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 6.0 (* (* x1 x1) (* x1 x1)))))
   (if (<= x1 -1.5e+19) t_0 (if (<= x1 6.5) (- (* x2 -6.0) x1) t_0))))

C

double code(double x1, double x2) {
	double t_0 = 6.0 * ((x1 * x1) * (x1 * x1));
	double tmp;
	if (x1 <= -1.5e+19) {
		tmp = t_0;
	} else if (x1 <= 6.5) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 6.0d0 * ((x1 * x1) * (x1 * x1))
    if (x1 <= (-1.5d+19)) then
        tmp = t_0
    else if (x1 <= 6.5d0) then
        tmp = (x2 * (-6.0d0)) - x1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 6.0 * ((x1 * x1) * (x1 * x1));
	double tmp;
	if (x1 <= -1.5e+19) {
		tmp = t_0;
	} else if (x1 <= 6.5) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 6.0 * ((x1 * x1) * (x1 * x1))
	tmp = 0
	if x1 <= -1.5e+19:
		tmp = t_0
	elif x1 <= 6.5:
		tmp = (x2 * -6.0) - x1
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(6.0 * Float64(Float64(x1 * x1) * Float64(x1 * x1)))
	tmp = 0.0
	if (x1 <= -1.5e+19)
		tmp = t_0;
	elseif (x1 <= 6.5)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 6.0 * ((x1 * x1) * (x1 * x1));
	tmp = 0.0;
	if (x1 <= -1.5e+19)
		tmp = t_0;
	elseif (x1 <= 6.5)
		tmp = (x2 * -6.0) - x1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(6.0 * N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.5e+19], t$95$0, If[LessEqual[x1, 6.5], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.5e19 or 6.5 < x1

   1. Initial program 35.6%

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

   3. Simplified 35.6%

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

   6. Applied egg-rr 35.6%

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

   7. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{6 \cdot {x1}^{4}} \]
   8. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left({x1}^{4}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(6, \left({x1}^{\left(2 \cdot \color{blue}{2}\right)}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(6, \left({x1}^{2} \cdot \color{blue}{{x1}^{2}}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(\left({x1}^{2}\right), \color{blue}{\left({x1}^{2}\right)}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({\color{blue}{x1}}^{2}\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({\color{blue}{x1}}^{2}\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot \color{blue}{x1}\right)\right)\right) \]

      8. *-lowering-*.f64 92.6%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \color{blue}{x1}\right)\right)\right) \]

   9. Simplified 92.6%

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

   if -1.5e19 < x1 < 6.5

   1. Initial program 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \color{blue}{\left(6 \cdot {x1}^{2}\right)}\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \left(x1 \cdot x1\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. *-lowering-*.f64 70.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, x1\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 70.7%

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

   8. Taylor expanded in x1 around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(-6 \cdot x2\right), \color{blue}{x1}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x2 \cdot -6\right), x1\right) \]

      5. *-lowering-*.f64 71.0%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x2, -6\right), x1\right) \]

   10. Simplified 71.0%

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

Alternative 17: 54.4% accurate, 7.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -3.05 \cdot 10^{+35}:\\ \;\;\;\;8 \cdot \left(x2 \cdot \left(x1 \cdot x1\right)\right)\\ \mathbf{elif}\;x1 \leq 5.2 \cdot 10^{-14}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -3.05e+35)
   (* 8.0 (* x2 (* x1 x1)))
   (if (<= x1 5.2e-14) (- (* x2 -6.0) x1) (* 8.0 (* x1 (* x2 x2))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3.05e+35) {
		tmp = 8.0 * (x2 * (x1 * x1));
	} else if (x1 <= 5.2e-14) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = 8.0 * (x1 * (x2 * x2));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-3.05d+35)) then
        tmp = 8.0d0 * (x2 * (x1 * x1))
    else if (x1 <= 5.2d-14) then
        tmp = (x2 * (-6.0d0)) - x1
    else
        tmp = 8.0d0 * (x1 * (x2 * x2))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3.05e+35) {
		tmp = 8.0 * (x2 * (x1 * x1));
	} else if (x1 <= 5.2e-14) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = 8.0 * (x1 * (x2 * x2));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -3.05e+35:
		tmp = 8.0 * (x2 * (x1 * x1))
	elif x1 <= 5.2e-14:
		tmp = (x2 * -6.0) - x1
	else:
		tmp = 8.0 * (x1 * (x2 * x2))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -3.05e+35)
		tmp = Float64(8.0 * Float64(x2 * Float64(x1 * x1)));
	elseif (x1 <= 5.2e-14)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	else
		tmp = Float64(8.0 * Float64(x1 * Float64(x2 * x2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -3.05e+35)
		tmp = 8.0 * (x2 * (x1 * x1));
	elseif (x1 <= 5.2e-14)
		tmp = (x2 * -6.0) - x1;
	else
		tmp = 8.0 * (x1 * (x2 * x2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -3.05e+35], N[(8.0 * N[(x2 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.2e-14], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], N[(8.0 * N[(x1 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.04999999999999989e35

   1. Initial program 25.8%

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

   3. Simplified 25.8%

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

   6. Applied egg-rr 25.7%

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

   7. Taylor expanded in x2 around -inf

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

   9. Simplified 13.2%

      \[\leadsto \color{blue}{\left(x2 \cdot x2\right) \cdot \left(\frac{8 \cdot x1}{1 + x1 \cdot x1} - \frac{\frac{\left(x1 \cdot x1\right) \cdot -6}{1 + x1 \cdot x1} + \left(x1 \cdot \left(\frac{-4 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{1 + x1 \cdot x1} + \left(-2 \cdot \left(\frac{2 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{1 + x1 \cdot x1} + x1 \cdot 4\right) + 12\right)\right) + \frac{6}{1 + x1 \cdot x1}\right)}{x2}\right)} \]

   10. Taylor expanded in x1 around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(8, \color{blue}{\left({x1}^{2} \cdot x2\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(8, \left(x2 \cdot \color{blue}{{x1}^{2}}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x2, \color{blue}{\left({x1}^{2}\right)}\right)\right) \]

       4. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x2, \left(x1 \cdot \color{blue}{x1}\right)\right)\right) \]

       5. *-lowering-*.f64 28.1%

          \[\leadsto \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x2, \mathsf{*.f64}\left(x1, \color{blue}{x1}\right)\right)\right) \]

   12. Simplified 28.1%

       \[\leadsto \color{blue}{8 \cdot \left(x2 \cdot \left(x1 \cdot x1\right)\right)} \]

   if -3.04999999999999989e35 < x1 < 5.19999999999999993e-14

   1. Initial program 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \color{blue}{\left(6 \cdot {x1}^{2}\right)}\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \left(x1 \cdot x1\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. *-lowering-*.f64 73.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, x1\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 73.6%

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

   8. Taylor expanded in x1 around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(-6 \cdot x2\right), \color{blue}{x1}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x2 \cdot -6\right), x1\right) \]

      5. *-lowering-*.f64 72.6%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x2, -6\right), x1\right) \]

   10. Simplified 72.6%

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

   if 5.19999999999999993e-14 < x1

   1. Initial program 48.9%

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

   3. Simplified 48.9%

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

   5. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \color{blue}{\left(x1 \cdot \left(4 \cdot x2 - 6\right)\right)}\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \left(4 \cdot x2 - 6\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 9.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 9.2%

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

   8. Taylor expanded in x2 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(8, \color{blue}{\left(x1 \cdot {x2}^{2}\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \color{blue}{\left({x2}^{2}\right)}\right)\right) \]

      3. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \left(x2 \cdot \color{blue}{x2}\right)\right)\right) \]

      4. *-lowering-*.f64 32.7%

         \[\leadsto \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, \color{blue}{x2}\right)\right)\right) \]

   10. Simplified 32.7%

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

Alternative 18: 49.0% accurate, 7.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{if}\;x2 \leq -8.5 \cdot 10^{+79}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x2 \leq 1.55 \cdot 10^{+90}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 8.0 (* x1 (* x2 x2)))))
   (if (<= x2 -8.5e+79) t_0 (if (<= x2 1.55e+90) (- (* x2 -6.0) x1) t_0))))

C

double code(double x1, double x2) {
	double t_0 = 8.0 * (x1 * (x2 * x2));
	double tmp;
	if (x2 <= -8.5e+79) {
		tmp = t_0;
	} else if (x2 <= 1.55e+90) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 8.0d0 * (x1 * (x2 * x2))
    if (x2 <= (-8.5d+79)) then
        tmp = t_0
    else if (x2 <= 1.55d+90) then
        tmp = (x2 * (-6.0d0)) - x1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 8.0 * (x1 * (x2 * x2));
	double tmp;
	if (x2 <= -8.5e+79) {
		tmp = t_0;
	} else if (x2 <= 1.55e+90) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 8.0 * (x1 * (x2 * x2))
	tmp = 0
	if x2 <= -8.5e+79:
		tmp = t_0
	elif x2 <= 1.55e+90:
		tmp = (x2 * -6.0) - x1
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(8.0 * Float64(x1 * Float64(x2 * x2)))
	tmp = 0.0
	if (x2 <= -8.5e+79)
		tmp = t_0;
	elseif (x2 <= 1.55e+90)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 8.0 * (x1 * (x2 * x2));
	tmp = 0.0;
	if (x2 <= -8.5e+79)
		tmp = t_0;
	elseif (x2 <= 1.55e+90)
		tmp = (x2 * -6.0) - x1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(8.0 * N[(x1 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x2, -8.5e+79], t$95$0, If[LessEqual[x2, 1.55e+90], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x2 < -8.4999999999999998e79 or 1.54999999999999994e90 < x2

   1. Initial program 74.0%

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

   3. Simplified 74.0%

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

   5. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \color{blue}{\left(x1 \cdot \left(4 \cdot x2 - 6\right)\right)}\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \left(4 \cdot x2 - 6\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 64.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 64.2%

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

   8. Taylor expanded in x2 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(8, \color{blue}{\left(x1 \cdot {x2}^{2}\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \color{blue}{\left({x2}^{2}\right)}\right)\right) \]

      3. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \left(x2 \cdot \color{blue}{x2}\right)\right)\right) \]

      4. *-lowering-*.f64 51.9%

         \[\leadsto \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, \color{blue}{x2}\right)\right)\right) \]

   10. Simplified 51.9%

       \[\leadsto \color{blue}{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)} \]

   if -8.4999999999999998e79 < x2 < 1.54999999999999994e90

   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 71.4%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \color{blue}{\left(6 \cdot {x1}^{2}\right)}\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \left(x1 \cdot x1\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. *-lowering-*.f64 67.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, x1\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 67.7%

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

   8. Taylor expanded in x1 around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(-6 \cdot x2\right), \color{blue}{x1}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x2 \cdot -6\right), x1\right) \]

      5. *-lowering-*.f64 53.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x2, -6\right), x1\right) \]

   10. Simplified 53.1%

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

Alternative 19: 37.9% accurate, 25.4× speedup

Math

\[\begin{array}{l} \\ x2 \cdot -6 - x1 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 72.3%

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

3. Simplified 72.3%

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

5. Taylor expanded in x1 around inf

   \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \color{blue}{\left(6 \cdot {x1}^{2}\right)}\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]
6. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   2. unpow2 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \left(x1 \cdot x1\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   3. *-lowering-*.f64 53.1%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, x1\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

7. Simplified 53.1%

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

8. Taylor expanded in x1 around 0

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

   1. mul-1-neg N/A

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

   2. unsub-neg N/A

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

   3. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(-6 \cdot x2\right), \color{blue}{x1}\right) \]

   4. *-commutative N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(x2 \cdot -6\right), x1\right) \]

   5. *-lowering-*.f64 42.2%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x2, -6\right), x1\right) \]

10. Simplified 42.2%

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

Alternative 20: 25.8% accurate, 25.4× speedup

Math

\[\begin{array}{l} \\ x1 + x2 \cdot -6 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 72.3%

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

3. Taylor expanded in x1 around 0

   \[\leadsto \mathsf{+.f64}\left(x1, \color{blue}{\left(-6 \cdot x2\right)}\right) \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x1, \left(x2 \cdot \color{blue}{-6}\right)\right) \]

   2. *-lowering-*.f64 30.9%

      \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(x2, \color{blue}{-6}\right)\right) \]

5. Simplified 30.9%

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

Alternative 21: 25.6% accurate, 42.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 72.3%

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

3. Simplified 72.3%

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

6. Applied egg-rr 72.3%

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

7. Taylor expanded in x1 around 0

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

   1. *-commutative N/A

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

   2. *-lowering-*.f64 30.9%

      \[\leadsto \mathsf{*.f64}\left(x2, \color{blue}{-6}\right) \]

9. Simplified 30.9%

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

Alternative 22: 3.3% accurate, 42.3× speedup

Math

\[\begin{array}{l} \\ x1 \cdot 2 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (* x1 2.0))

C

double code(double x1, double x2) {
	return x1 * 2.0;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x1 * 2.0d0
end function

Java

public static double code(double x1, double x2) {
	return x1 * 2.0;
}

Python

def code(x1, x2):
	return x1 * 2.0

Julia

function code(x1, x2)
	return Float64(x1 * 2.0)
end

MATLAB

function tmp = code(x1, x2)
	tmp = x1 * 2.0;
end

Wolfram

code[x1_, x2_] := N[(x1 * 2.0), $MachinePrecision]

Derivation

1. Initial program 72.3%

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

3. Simplified 72.3%

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

5. Taylor expanded in x1 around inf

   \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \color{blue}{\left(6 \cdot {x1}^{2}\right)}\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]
6. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   2. unpow2 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \left(x1 \cdot x1\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   3. *-lowering-*.f64 53.1%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, x1\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

7. Simplified 53.1%

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

8. Taylor expanded in x1 around 0

   \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \color{blue}{\left(2 \cdot x1\right)}\right) \]
9. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \left(x1 \cdot \color{blue}{2}\right)\right) \]

   2. *-lowering-*.f64 41.7%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \color{blue}{2}\right)\right) \]

10. Simplified 41.7%

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

11. Taylor expanded in x1 around inf

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

    1. *-commutative N/A

       \[\leadsto x1 \cdot \color{blue}{2} \]

    2. *-lowering-*.f64 3.2%

       \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{2}\right) \]

13. Simplified 3.2%

    \[\leadsto \color{blue}{x1 \cdot 2} \]
14. Add Preprocessing

Alternative 23: 3.3% accurate, 127.0× speedup

Math

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

FPCore

(FPCore (x1 x2) :precision binary64 x1)

C

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

Fortran

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

Java

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

Python

def code(x1, x2):
	return x1

Julia

function code(x1, x2)
	return x1
end

MATLAB

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

Wolfram

code[x1_, x2_] := x1

Derivation

1. Initial program 72.3%

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

3. Taylor expanded in x1 around 0

   \[\leadsto \mathsf{+.f64}\left(x1, \color{blue}{\left(-6 \cdot x2\right)}\right) \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x1, \left(x2 \cdot \color{blue}{-6}\right)\right) \]

   2. *-lowering-*.f64 30.9%

      \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(x2, \color{blue}{-6}\right)\right) \]

5. Simplified 30.9%

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

6. Taylor expanded in x1 around inf

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

8. Simplified 3.1%

   \[\leadsto \color{blue}{x1} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024161 
(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))))))