Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.0% → 99.5%

Time: 1.2min

Alternatives: 25

Speedup: 4.7×

• 46.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 70.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

   3. Simplified 99.7%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around inf 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around inf 0.0%

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

   5. Taylor expanded in x1 around inf 98.7%

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

4. Final simplification 99.4%

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

Alternative 2: 99.3% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

      1. fma-def 99.4%

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

      2. div-sub 99.4%

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

      3. fma-def 99.4%

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

      4. count-2 99.4%

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

   3. Applied egg-rr 99.4%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around inf 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around inf 0.0%

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

   5. Taylor expanded in x1 around inf 98.7%

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

4. Final simplification 99.2%

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

Alternative 3: 99.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around inf 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around inf 0.0%

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

   5. Taylor expanded in x1 around inf 98.7%

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

4. Final simplification 99.2%

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

Alternative 4: 93.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1100000000 \lor \neg \left(x1 \leq 24\right):\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right) + 3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -1100000000.0) (not (<= x1 24.0)))
   (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) 9.0))
   (-
    x1
    (+
     (- (* 4.0 (* x2 (* x1 (- 3.0 (* 2.0 x2))))) x1)
     (* 3.0 (/ (- x1 (- (* x1 (* x1 3.0)) (* 2.0 x2))) (+ (* x1 x1) 1.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -1100000000.0) || !(x1 <= 24.0)) {
		tmp = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + 9.0);
	} else {
		tmp = x1 - (((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / ((x1 * x1) + 1.0))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-1100000000.0d0)) .or. (.not. (x1 <= 24.0d0))) then
        tmp = x1 + ((x1 + (6.0d0 * (x1 ** 4.0d0))) + 9.0d0)
    else
        tmp = x1 - (((4.0d0 * (x2 * (x1 * (3.0d0 - (2.0d0 * x2))))) - x1) + (3.0d0 * ((x1 - ((x1 * (x1 * 3.0d0)) - (2.0d0 * x2))) / ((x1 * x1) + 1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -1100000000.0) || !(x1 <= 24.0)) {
		tmp = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + 9.0);
	} else {
		tmp = x1 - (((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / ((x1 * x1) + 1.0))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -1100000000.0) or not (x1 <= 24.0):
		tmp = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + 9.0)
	else:
		tmp = x1 - (((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / ((x1 * x1) + 1.0))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -1100000000.0) || !(x1 <= 24.0))
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + 9.0));
	else
		tmp = Float64(x1 - Float64(Float64(Float64(4.0 * Float64(x2 * Float64(x1 * Float64(3.0 - Float64(2.0 * x2))))) - x1) + Float64(3.0 * Float64(Float64(x1 - Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2))) / Float64(Float64(x1 * x1) + 1.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -1100000000.0) || ~((x1 <= 24.0)))
		tmp = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + 9.0);
	else
		tmp = x1 - (((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / ((x1 * x1) + 1.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -1100000000.0], N[Not[LessEqual[x1, 24.0]], $MachinePrecision]], N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision], N[(x1 - N[(N[(N[(4.0 * N[(x2 * N[(x1 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] + N[(3.0 * N[(N[(x1 - N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.1e9 or 24 < x1

   1. Initial program 36.6%

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

   2. Taylor expanded in x1 around inf 34.1%

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

   3. Taylor expanded in x1 around inf 34.1%

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

   4. Taylor expanded in x1 around inf 34.1%

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

   5. Taylor expanded in x1 around inf 92.5%

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

   if -1.1e9 < x1 < 24

   1. Initial program 98.7%

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

   2. Taylor expanded in x1 around 0 98.4%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1100000000 \lor \neg \left(x1 \leq 24\right):\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right) + 3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\\ \end{array} \]

Alternative 5: 96.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := t_0 + 2 \cdot x2\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{x1 - t_1}{t_2}\\ \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+105} \lor \neg \left(x1 \leq 4 \cdot 10^{+75}\right):\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_2} - \left(\left(\left(t_0 \cdot t_3 + t_2 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{t_1 - x1}{t_2}\right) \cdot \left(3 + t_3\right) - \left(x1 \cdot x1\right) \cdot 6\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ t_0 (* 2.0 x2)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (/ (- x1 t_1) t_2)))
   (if (or (<= x1 -9.5e+105) (not (<= x1 4e+75)))
     (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) 9.0))
     (+
      x1
      (-
       (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_2))
       (-
        (-
         (+
          (* t_0 t_3)
          (*
           t_2
           (-
            (* (* (* x1 2.0) (/ (- t_1 x1) t_2)) (+ 3.0 t_3))
            (* (* x1 x1) 6.0))))
         (* x1 (* x1 x1)))
        x1))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = t_0 + (2.0 * x2);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = (x1 - t_1) / t_2;
	double tmp;
	if ((x1 <= -9.5e+105) || !(x1 <= 4e+75)) {
		tmp = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + 9.0);
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) - ((((t_0 * t_3) + (t_2 * ((((x1 * 2.0) * ((t_1 - x1) / t_2)) * (3.0 + t_3)) - ((x1 * x1) * 6.0)))) - (x1 * (x1 * x1))) - x1));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = t_0 + (2.0d0 * x2)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = (x1 - t_1) / t_2
    if ((x1 <= (-9.5d+105)) .or. (.not. (x1 <= 4d+75))) then
        tmp = x1 + ((x1 + (6.0d0 * (x1 ** 4.0d0))) + 9.0d0)
    else
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_2)) - ((((t_0 * t_3) + (t_2 * ((((x1 * 2.0d0) * ((t_1 - x1) / t_2)) * (3.0d0 + t_3)) - ((x1 * x1) * 6.0d0)))) - (x1 * (x1 * x1))) - x1))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = t_0 + (2.0 * x2);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = (x1 - t_1) / t_2;
	double tmp;
	if ((x1 <= -9.5e+105) || !(x1 <= 4e+75)) {
		tmp = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + 9.0);
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) - ((((t_0 * t_3) + (t_2 * ((((x1 * 2.0) * ((t_1 - x1) / t_2)) * (3.0 + t_3)) - ((x1 * x1) * 6.0)))) - (x1 * (x1 * x1))) - x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = t_0 + (2.0 * x2)
	t_2 = (x1 * x1) + 1.0
	t_3 = (x1 - t_1) / t_2
	tmp = 0
	if (x1 <= -9.5e+105) or not (x1 <= 4e+75):
		tmp = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + 9.0)
	else:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) - ((((t_0 * t_3) + (t_2 * ((((x1 * 2.0) * ((t_1 - x1) / t_2)) * (3.0 + t_3)) - ((x1 * x1) * 6.0)))) - (x1 * (x1 * x1))) - x1))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(t_0 + Float64(2.0 * x2))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(x1 - t_1) / t_2)
	tmp = 0.0
	if ((x1 <= -9.5e+105) || !(x1 <= 4e+75))
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + 9.0));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_2)) - Float64(Float64(Float64(Float64(t_0 * t_3) + Float64(t_2 * Float64(Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(t_1 - x1) / t_2)) * Float64(3.0 + t_3)) - Float64(Float64(x1 * x1) * 6.0)))) - Float64(x1 * Float64(x1 * x1))) - x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = t_0 + (2.0 * x2);
	t_2 = (x1 * x1) + 1.0;
	t_3 = (x1 - t_1) / t_2;
	tmp = 0.0;
	if ((x1 <= -9.5e+105) || ~((x1 <= 4e+75)))
		tmp = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + 9.0);
	else
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) - ((((t_0 * t_3) + (t_2 * ((((x1 * 2.0) * ((t_1 - x1) / t_2)) * (3.0 + t_3)) - ((x1 * x1) * 6.0)))) - (x1 * (x1 * x1))) - 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[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 - t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[Or[LessEqual[x1, -9.5e+105], N[Not[LessEqual[x1, 4e+75]], $MachinePrecision]], N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(t$95$0 * t$95$3), $MachinePrecision] + N[(t$95$2 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(t$95$1 - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] * N[(3.0 + t$95$3), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -9.4999999999999995e105 or 3.99999999999999971e75 < x1

   1. Initial program 11.5%

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

   2. Taylor expanded in x1 around inf 11.5%

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

   3. Taylor expanded in x1 around inf 11.5%

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

   4. Taylor expanded in x1 around inf 11.5%

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

   5. Taylor expanded in x1 around inf 100.0%

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

   if -9.4999999999999995e105 < x1 < 3.99999999999999971e75

   1. Initial program 98.8%

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

   2. Taylor expanded in x1 around inf 97.0%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+105} \lor \neg \left(x1 \leq 4 \cdot 10^{+75}\right):\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot 6\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \end{array} \]

Alternative 6: 91.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{x1} - 3\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot \left(x1 \cdot x1\right)\\ t_3 := x1 + \left(\left(x1 + \left(6 + x2 \cdot -4\right)\right) - 3 \cdot \left(x1 - 3 \cdot \left(x1 \cdot x1\right)\right)\right)\\ t_4 := t_1 + 2 \cdot x2\\ t_5 := x1 \cdot x1 + 1\\ t_6 := \frac{t_4 - x1}{t_5}\\ t_7 := \left(x1 \cdot 2\right) \cdot t_0\\ \mathbf{if}\;x1 \leq -6 \cdot 10^{+108}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x1 \leq -7400000:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(t_2 + \left(t_5 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t_6 \cdot 4 - 6\right) + \frac{1}{x1} \cdot t_7\right) + t_1 \cdot \left(3 + \frac{-1}{x1}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 75:\\ \;\;\;\;x1 - \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right) + 3 \cdot \frac{x1 - \left(t_1 - 2 \cdot x2\right)}{t_5}\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(9 - \frac{3}{x1}\right) - \left(\left(\left(t_1 \cdot t_0 + t_5 \cdot \left(\left(t_6 - 3\right) \cdot t_7 + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - t_4}{t_5}\right)\right)\right) - t_2\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (/ 1.0 x1) 3.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (* x1 (* x1 x1)))
        (t_3
         (+
          x1
          (- (+ x1 (+ 6.0 (* x2 -4.0))) (* 3.0 (- x1 (* 3.0 (* x1 x1)))))))
        (t_4 (+ t_1 (* 2.0 x2)))
        (t_5 (+ (* x1 x1) 1.0))
        (t_6 (/ (- t_4 x1) t_5))
        (t_7 (* (* x1 2.0) t_0)))
   (if (<= x1 -6e+108)
     t_3
     (if (<= x1 -7400000.0)
       (+
        x1
        (+
         9.0
         (+
          x1
          (+
           t_2
           (+
            (* t_5 (+ (* (* x1 x1) (- (* t_6 4.0) 6.0)) (* (/ 1.0 x1) t_7)))
            (* t_1 (+ 3.0 (/ -1.0 x1))))))))
       (if (<= x1 75.0)
         (-
          x1
          (+
           (- (* 4.0 (* x2 (* x1 (- 3.0 (* 2.0 x2))))) x1)
           (* 3.0 (/ (- x1 (- t_1 (* 2.0 x2))) t_5))))
         (if (<= x1 5e+153)
           (+
            x1
            (-
             (- 9.0 (/ 3.0 x1))
             (-
              (-
               (+
                (* t_1 t_0)
                (*
                 t_5
                 (+
                  (* (- t_6 3.0) t_7)
                  (* (* x1 x1) (+ 6.0 (* 4.0 (/ (- x1 t_4) t_5)))))))
               t_2)
              x1)))
           t_3))))))

C

double code(double x1, double x2) {
	double t_0 = (1.0 / x1) - 3.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))));
	double t_4 = t_1 + (2.0 * x2);
	double t_5 = (x1 * x1) + 1.0;
	double t_6 = (t_4 - x1) / t_5;
	double t_7 = (x1 * 2.0) * t_0;
	double tmp;
	if (x1 <= -6e+108) {
		tmp = t_3;
	} else if (x1 <= -7400000.0) {
		tmp = x1 + (9.0 + (x1 + (t_2 + ((t_5 * (((x1 * x1) * ((t_6 * 4.0) - 6.0)) + ((1.0 / x1) * t_7))) + (t_1 * (3.0 + (-1.0 / x1)))))));
	} else if (x1 <= 75.0) {
		tmp = x1 - (((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 - (t_1 - (2.0 * x2))) / t_5)));
	} else if (x1 <= 5e+153) {
		tmp = x1 + ((9.0 - (3.0 / x1)) - ((((t_1 * t_0) + (t_5 * (((t_6 - 3.0) * t_7) + ((x1 * x1) * (6.0 + (4.0 * ((x1 - t_4) / t_5))))))) - t_2) - x1));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = (1.0d0 / x1) - 3.0d0
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = x1 * (x1 * x1)
    t_3 = x1 + ((x1 + (6.0d0 + (x2 * (-4.0d0)))) - (3.0d0 * (x1 - (3.0d0 * (x1 * x1)))))
    t_4 = t_1 + (2.0d0 * x2)
    t_5 = (x1 * x1) + 1.0d0
    t_6 = (t_4 - x1) / t_5
    t_7 = (x1 * 2.0d0) * t_0
    if (x1 <= (-6d+108)) then
        tmp = t_3
    else if (x1 <= (-7400000.0d0)) then
        tmp = x1 + (9.0d0 + (x1 + (t_2 + ((t_5 * (((x1 * x1) * ((t_6 * 4.0d0) - 6.0d0)) + ((1.0d0 / x1) * t_7))) + (t_1 * (3.0d0 + ((-1.0d0) / x1)))))))
    else if (x1 <= 75.0d0) then
        tmp = x1 - (((4.0d0 * (x2 * (x1 * (3.0d0 - (2.0d0 * x2))))) - x1) + (3.0d0 * ((x1 - (t_1 - (2.0d0 * x2))) / t_5)))
    else if (x1 <= 5d+153) then
        tmp = x1 + ((9.0d0 - (3.0d0 / x1)) - ((((t_1 * t_0) + (t_5 * (((t_6 - 3.0d0) * t_7) + ((x1 * x1) * (6.0d0 + (4.0d0 * ((x1 - t_4) / t_5))))))) - t_2) - x1))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (1.0 / x1) - 3.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))));
	double t_4 = t_1 + (2.0 * x2);
	double t_5 = (x1 * x1) + 1.0;
	double t_6 = (t_4 - x1) / t_5;
	double t_7 = (x1 * 2.0) * t_0;
	double tmp;
	if (x1 <= -6e+108) {
		tmp = t_3;
	} else if (x1 <= -7400000.0) {
		tmp = x1 + (9.0 + (x1 + (t_2 + ((t_5 * (((x1 * x1) * ((t_6 * 4.0) - 6.0)) + ((1.0 / x1) * t_7))) + (t_1 * (3.0 + (-1.0 / x1)))))));
	} else if (x1 <= 75.0) {
		tmp = x1 - (((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 - (t_1 - (2.0 * x2))) / t_5)));
	} else if (x1 <= 5e+153) {
		tmp = x1 + ((9.0 - (3.0 / x1)) - ((((t_1 * t_0) + (t_5 * (((t_6 - 3.0) * t_7) + ((x1 * x1) * (6.0 + (4.0 * ((x1 - t_4) / t_5))))))) - t_2) - x1));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (1.0 / x1) - 3.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = x1 * (x1 * x1)
	t_3 = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))))
	t_4 = t_1 + (2.0 * x2)
	t_5 = (x1 * x1) + 1.0
	t_6 = (t_4 - x1) / t_5
	t_7 = (x1 * 2.0) * t_0
	tmp = 0
	if x1 <= -6e+108:
		tmp = t_3
	elif x1 <= -7400000.0:
		tmp = x1 + (9.0 + (x1 + (t_2 + ((t_5 * (((x1 * x1) * ((t_6 * 4.0) - 6.0)) + ((1.0 / x1) * t_7))) + (t_1 * (3.0 + (-1.0 / x1)))))))
	elif x1 <= 75.0:
		tmp = x1 - (((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 - (t_1 - (2.0 * x2))) / t_5)))
	elif x1 <= 5e+153:
		tmp = x1 + ((9.0 - (3.0 / x1)) - ((((t_1 * t_0) + (t_5 * (((t_6 - 3.0) * t_7) + ((x1 * x1) * (6.0 + (4.0 * ((x1 - t_4) / t_5))))))) - t_2) - x1))
	else:
		tmp = t_3
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(1.0 / x1) - 3.0)
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(x1 * Float64(x1 * x1))
	t_3 = Float64(x1 + Float64(Float64(x1 + Float64(6.0 + Float64(x2 * -4.0))) - Float64(3.0 * Float64(x1 - Float64(3.0 * Float64(x1 * x1))))))
	t_4 = Float64(t_1 + Float64(2.0 * x2))
	t_5 = Float64(Float64(x1 * x1) + 1.0)
	t_6 = Float64(Float64(t_4 - x1) / t_5)
	t_7 = Float64(Float64(x1 * 2.0) * t_0)
	tmp = 0.0
	if (x1 <= -6e+108)
		tmp = t_3;
	elseif (x1 <= -7400000.0)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_2 + Float64(Float64(t_5 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_6 * 4.0) - 6.0)) + Float64(Float64(1.0 / x1) * t_7))) + Float64(t_1 * Float64(3.0 + Float64(-1.0 / x1))))))));
	elseif (x1 <= 75.0)
		tmp = Float64(x1 - Float64(Float64(Float64(4.0 * Float64(x2 * Float64(x1 * Float64(3.0 - Float64(2.0 * x2))))) - x1) + Float64(3.0 * Float64(Float64(x1 - Float64(t_1 - Float64(2.0 * x2))) / t_5))));
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + Float64(Float64(9.0 - Float64(3.0 / x1)) - Float64(Float64(Float64(Float64(t_1 * t_0) + Float64(t_5 * Float64(Float64(Float64(t_6 - 3.0) * t_7) + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * Float64(Float64(x1 - t_4) / t_5))))))) - t_2) - x1)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (1.0 / x1) - 3.0;
	t_1 = x1 * (x1 * 3.0);
	t_2 = x1 * (x1 * x1);
	t_3 = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))));
	t_4 = t_1 + (2.0 * x2);
	t_5 = (x1 * x1) + 1.0;
	t_6 = (t_4 - x1) / t_5;
	t_7 = (x1 * 2.0) * t_0;
	tmp = 0.0;
	if (x1 <= -6e+108)
		tmp = t_3;
	elseif (x1 <= -7400000.0)
		tmp = x1 + (9.0 + (x1 + (t_2 + ((t_5 * (((x1 * x1) * ((t_6 * 4.0) - 6.0)) + ((1.0 / x1) * t_7))) + (t_1 * (3.0 + (-1.0 / x1)))))));
	elseif (x1 <= 75.0)
		tmp = x1 - (((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 - (t_1 - (2.0 * x2))) / t_5)));
	elseif (x1 <= 5e+153)
		tmp = x1 + ((9.0 - (3.0 / x1)) - ((((t_1 * t_0) + (t_5 * (((t_6 - 3.0) * t_7) + ((x1 * x1) * (6.0 + (4.0 * ((x1 - t_4) / t_5))))))) - t_2) - x1));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(1.0 / x1), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(N[(x1 + N[(6.0 + N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * N[(x1 - N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$6 = N[(N[(t$95$4 - x1), $MachinePrecision] / t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x1 * 2.0), $MachinePrecision] * t$95$0), $MachinePrecision]}, If[LessEqual[x1, -6e+108], t$95$3, If[LessEqual[x1, -7400000.0], N[(x1 + N[(9.0 + N[(x1 + N[(t$95$2 + N[(N[(t$95$5 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$6 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 / x1), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(3.0 + N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 75.0], N[(x1 - N[(N[(N[(4.0 * N[(x2 * N[(x1 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] + N[(3.0 * N[(N[(x1 - N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], N[(x1 + N[(N[(9.0 - N[(3.0 / x1), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(t$95$1 * t$95$0), $MachinePrecision] + N[(t$95$5 * N[(N[(N[(t$95$6 - 3.0), $MachinePrecision] * t$95$7), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * N[(N[(x1 - t$95$4), $MachinePrecision] / t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.99999999999999968e108 or 5.00000000000000018e153 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around inf 0.0%

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

   3. Taylor expanded in x1 around 0 0.1%

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

      1. sub-neg 0.1%

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

      2. metadata-eval 0.1%

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

      3. distribute-lft-in 0.1%

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

      4. *-commutative 0.1%

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

      5. associate-*l* 0.1%

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

      6. metadata-eval 0.1%

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

      7. metadata-eval 0.1%

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

      8. distribute-rgt-in 0.1%

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

      9. +-commutative 0.1%

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

      10. distribute-lft-in 0.1%

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

      11. metadata-eval 0.1%

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

      12. associate-*r* 0.1%

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

      13. metadata-eval 0.1%

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

   5. Simplified 0.1%

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

   6. Taylor expanded in x1 around 0 61.9%

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

      1. +-commutative 61.9%

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

      2. +-commutative 61.9%

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

      3. associate-+l+ 61.9%

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

      4. metadata-eval 61.9%

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

      5. distribute-lft-neg-in 61.9%

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

      6. mul-1-neg 61.9%

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

      7. distribute-neg-in 61.9%

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

      8. fma-udef 61.9%

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

      9. unsub-neg 61.9%

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

      10. *-commutative 61.9%

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

      11. unpow2 61.9%

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

      12. associate-*l* 61.9%

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

      13. cancel-sign-sub-inv 61.9%

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

      14. metadata-eval 61.9%

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

      15. +-commutative 61.9%

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

      16. count-2 61.9%

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

   8. Simplified 61.9%

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

   9. Taylor expanded in x2 around 0 86.9%

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

       1. *-commutative 86.9%

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

       2. unpow2 86.9%

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

   11. Simplified 86.9%

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

   if -5.99999999999999968e108 < x1 < -7.4e6

   1. Initial program 99.4%

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

   2. Taylor expanded in x1 around inf 99.4%

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

   3. Taylor expanded in x1 around inf 99.4%

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

   4. Taylor expanded in x1 around inf 99.4%

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

   5. Taylor expanded in x1 around inf 99.4%

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

   if -7.4e6 < x1 < 75

   1. Initial program 98.7%

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

   2. Taylor expanded in x1 around 0 98.4%

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

   if 75 < x1 < 5.00000000000000018e153

   1. Initial program 99.2%

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

   2. Taylor expanded in x1 around inf 87.8%

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

   3. Taylor expanded in x1 around inf 87.8%

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

   4. Taylor expanded in x1 around inf 87.8%

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

      1. associate-*r/ 87.8%

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

      2. metadata-eval 87.8%

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

   6. Simplified 87.8%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6 \cdot 10^{+108}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(6 + x2 \cdot -4\right)\right) - 3 \cdot \left(x1 - 3 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -7400000:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \frac{1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 + \frac{-1}{x1}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 75:\\ \;\;\;\;x1 - \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right) + 3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(9 - \frac{3}{x1}\right) - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(\frac{1}{x1} - 3\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(6 + x2 \cdot -4\right)\right) - 3 \cdot \left(x1 - 3 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \end{array} \]

Alternative 7: 91.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := x1 + \left(\left(x1 + \left(6 + x2 \cdot -4\right)\right) - 3 \cdot \left(x1 - 3 \cdot \left(x1 \cdot x1\right)\right)\right)\\ t_3 := t_0 + 2 \cdot x2\\ t_4 := x1 \cdot x1 + 1\\ t_5 := \frac{t_3 - x1}{t_4}\\ t_6 := \left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\\ \mathbf{if}\;x1 \leq -2.6 \cdot 10^{+108}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x1 \leq -600000:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(t_1 + \left(t_4 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t_5 \cdot 4 - 6\right) + \frac{1}{x1} \cdot t_6\right) + t_0 \cdot \left(3 + \frac{-1}{x1}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 145:\\ \;\;\;\;x1 - \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right) + 3 \cdot \frac{x1 - \left(t_0 - 2 \cdot x2\right)}{t_4}\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - \left(\left(t_4 \cdot \left(\left(t_5 - 3\right) \cdot t_6 + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - t_3}{t_4}\right)\right) - x1 \cdot \left(-3 + x1 \cdot 9\right)\right) - t_1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (* x1 (* x1 x1)))
        (t_2
         (+
          x1
          (- (+ x1 (+ 6.0 (* x2 -4.0))) (* 3.0 (- x1 (* 3.0 (* x1 x1)))))))
        (t_3 (+ t_0 (* 2.0 x2)))
        (t_4 (+ (* x1 x1) 1.0))
        (t_5 (/ (- t_3 x1) t_4))
        (t_6 (* (* x1 2.0) (- (/ 1.0 x1) 3.0))))
   (if (<= x1 -2.6e+108)
     t_2
     (if (<= x1 -600000.0)
       (+
        x1
        (+
         9.0
         (+
          x1
          (+
           t_1
           (+
            (* t_4 (+ (* (* x1 x1) (- (* t_5 4.0) 6.0)) (* (/ 1.0 x1) t_6)))
            (* t_0 (+ 3.0 (/ -1.0 x1))))))))
       (if (<= x1 145.0)
         (-
          x1
          (+
           (- (* 4.0 (* x2 (* x1 (- 3.0 (* 2.0 x2))))) x1)
           (* 3.0 (/ (- x1 (- t_0 (* 2.0 x2))) t_4))))
         (if (<= x1 5e+153)
           (+
            x1
            (+
             9.0
             (-
              x1
              (-
               (-
                (*
                 t_4
                 (+
                  (* (- t_5 3.0) t_6)
                  (* (* x1 x1) (+ 6.0 (* 4.0 (/ (- x1 t_3) t_4))))))
                (* x1 (+ -3.0 (* x1 9.0))))
               t_1))))
           t_2))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * (x1 * x1);
	double t_2 = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))));
	double t_3 = t_0 + (2.0 * x2);
	double t_4 = (x1 * x1) + 1.0;
	double t_5 = (t_3 - x1) / t_4;
	double t_6 = (x1 * 2.0) * ((1.0 / x1) - 3.0);
	double tmp;
	if (x1 <= -2.6e+108) {
		tmp = t_2;
	} else if (x1 <= -600000.0) {
		tmp = x1 + (9.0 + (x1 + (t_1 + ((t_4 * (((x1 * x1) * ((t_5 * 4.0) - 6.0)) + ((1.0 / x1) * t_6))) + (t_0 * (3.0 + (-1.0 / x1)))))));
	} else if (x1 <= 145.0) {
		tmp = x1 - (((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_4)));
	} else if (x1 <= 5e+153) {
		tmp = x1 + (9.0 + (x1 - (((t_4 * (((t_5 - 3.0) * t_6) + ((x1 * x1) * (6.0 + (4.0 * ((x1 - t_3) / t_4)))))) - (x1 * (-3.0 + (x1 * 9.0)))) - t_1)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = x1 * (x1 * x1)
    t_2 = x1 + ((x1 + (6.0d0 + (x2 * (-4.0d0)))) - (3.0d0 * (x1 - (3.0d0 * (x1 * x1)))))
    t_3 = t_0 + (2.0d0 * x2)
    t_4 = (x1 * x1) + 1.0d0
    t_5 = (t_3 - x1) / t_4
    t_6 = (x1 * 2.0d0) * ((1.0d0 / x1) - 3.0d0)
    if (x1 <= (-2.6d+108)) then
        tmp = t_2
    else if (x1 <= (-600000.0d0)) then
        tmp = x1 + (9.0d0 + (x1 + (t_1 + ((t_4 * (((x1 * x1) * ((t_5 * 4.0d0) - 6.0d0)) + ((1.0d0 / x1) * t_6))) + (t_0 * (3.0d0 + ((-1.0d0) / x1)))))))
    else if (x1 <= 145.0d0) then
        tmp = x1 - (((4.0d0 * (x2 * (x1 * (3.0d0 - (2.0d0 * x2))))) - x1) + (3.0d0 * ((x1 - (t_0 - (2.0d0 * x2))) / t_4)))
    else if (x1 <= 5d+153) then
        tmp = x1 + (9.0d0 + (x1 - (((t_4 * (((t_5 - 3.0d0) * t_6) + ((x1 * x1) * (6.0d0 + (4.0d0 * ((x1 - t_3) / t_4)))))) - (x1 * ((-3.0d0) + (x1 * 9.0d0)))) - t_1)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * (x1 * x1);
	double t_2 = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))));
	double t_3 = t_0 + (2.0 * x2);
	double t_4 = (x1 * x1) + 1.0;
	double t_5 = (t_3 - x1) / t_4;
	double t_6 = (x1 * 2.0) * ((1.0 / x1) - 3.0);
	double tmp;
	if (x1 <= -2.6e+108) {
		tmp = t_2;
	} else if (x1 <= -600000.0) {
		tmp = x1 + (9.0 + (x1 + (t_1 + ((t_4 * (((x1 * x1) * ((t_5 * 4.0) - 6.0)) + ((1.0 / x1) * t_6))) + (t_0 * (3.0 + (-1.0 / x1)))))));
	} else if (x1 <= 145.0) {
		tmp = x1 - (((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_4)));
	} else if (x1 <= 5e+153) {
		tmp = x1 + (9.0 + (x1 - (((t_4 * (((t_5 - 3.0) * t_6) + ((x1 * x1) * (6.0 + (4.0 * ((x1 - t_3) / t_4)))))) - (x1 * (-3.0 + (x1 * 9.0)))) - t_1)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = x1 * (x1 * x1)
	t_2 = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))))
	t_3 = t_0 + (2.0 * x2)
	t_4 = (x1 * x1) + 1.0
	t_5 = (t_3 - x1) / t_4
	t_6 = (x1 * 2.0) * ((1.0 / x1) - 3.0)
	tmp = 0
	if x1 <= -2.6e+108:
		tmp = t_2
	elif x1 <= -600000.0:
		tmp = x1 + (9.0 + (x1 + (t_1 + ((t_4 * (((x1 * x1) * ((t_5 * 4.0) - 6.0)) + ((1.0 / x1) * t_6))) + (t_0 * (3.0 + (-1.0 / x1)))))))
	elif x1 <= 145.0:
		tmp = x1 - (((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_4)))
	elif x1 <= 5e+153:
		tmp = x1 + (9.0 + (x1 - (((t_4 * (((t_5 - 3.0) * t_6) + ((x1 * x1) * (6.0 + (4.0 * ((x1 - t_3) / t_4)))))) - (x1 * (-3.0 + (x1 * 9.0)))) - t_1)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(x1 * Float64(x1 * x1))
	t_2 = Float64(x1 + Float64(Float64(x1 + Float64(6.0 + Float64(x2 * -4.0))) - Float64(3.0 * Float64(x1 - Float64(3.0 * Float64(x1 * x1))))))
	t_3 = Float64(t_0 + Float64(2.0 * x2))
	t_4 = Float64(Float64(x1 * x1) + 1.0)
	t_5 = Float64(Float64(t_3 - x1) / t_4)
	t_6 = Float64(Float64(x1 * 2.0) * Float64(Float64(1.0 / x1) - 3.0))
	tmp = 0.0
	if (x1 <= -2.6e+108)
		tmp = t_2;
	elseif (x1 <= -600000.0)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_1 + Float64(Float64(t_4 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_5 * 4.0) - 6.0)) + Float64(Float64(1.0 / x1) * t_6))) + Float64(t_0 * Float64(3.0 + Float64(-1.0 / x1))))))));
	elseif (x1 <= 145.0)
		tmp = Float64(x1 - Float64(Float64(Float64(4.0 * Float64(x2 * Float64(x1 * Float64(3.0 - Float64(2.0 * x2))))) - x1) + Float64(3.0 * Float64(Float64(x1 - Float64(t_0 - Float64(2.0 * x2))) / t_4))));
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 - Float64(Float64(Float64(t_4 * Float64(Float64(Float64(t_5 - 3.0) * t_6) + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * Float64(Float64(x1 - t_3) / t_4)))))) - Float64(x1 * Float64(-3.0 + Float64(x1 * 9.0)))) - t_1))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = x1 * (x1 * x1);
	t_2 = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))));
	t_3 = t_0 + (2.0 * x2);
	t_4 = (x1 * x1) + 1.0;
	t_5 = (t_3 - x1) / t_4;
	t_6 = (x1 * 2.0) * ((1.0 / x1) - 3.0);
	tmp = 0.0;
	if (x1 <= -2.6e+108)
		tmp = t_2;
	elseif (x1 <= -600000.0)
		tmp = x1 + (9.0 + (x1 + (t_1 + ((t_4 * (((x1 * x1) * ((t_5 * 4.0) - 6.0)) + ((1.0 / x1) * t_6))) + (t_0 * (3.0 + (-1.0 / x1)))))));
	elseif (x1 <= 145.0)
		tmp = x1 - (((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_4)));
	elseif (x1 <= 5e+153)
		tmp = x1 + (9.0 + (x1 - (((t_4 * (((t_5 - 3.0) * t_6) + ((x1 * x1) * (6.0 + (4.0 * ((x1 - t_3) / t_4)))))) - (x1 * (-3.0 + (x1 * 9.0)))) - t_1)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(N[(x1 + N[(6.0 + N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * N[(x1 - N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$3 - x1), $MachinePrecision] / t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(1.0 / x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.6e+108], t$95$2, If[LessEqual[x1, -600000.0], N[(x1 + N[(9.0 + N[(x1 + N[(t$95$1 + N[(N[(t$95$4 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$5 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 / x1), $MachinePrecision] * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(3.0 + N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 145.0], N[(x1 - N[(N[(N[(4.0 * N[(x2 * N[(x1 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] + N[(3.0 * N[(N[(x1 - N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], N[(x1 + N[(9.0 + N[(x1 - N[(N[(N[(t$95$4 * N[(N[(N[(t$95$5 - 3.0), $MachinePrecision] * t$95$6), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * N[(N[(x1 - t$95$3), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(-3.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.6000000000000002e108 or 5.00000000000000018e153 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around inf 0.0%

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

   3. Taylor expanded in x1 around 0 0.1%

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

      1. sub-neg 0.1%

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

      2. metadata-eval 0.1%

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

      3. distribute-lft-in 0.1%

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

      4. *-commutative 0.1%

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

      5. associate-*l* 0.1%

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

      6. metadata-eval 0.1%

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

      7. metadata-eval 0.1%

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

      8. distribute-rgt-in 0.1%

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

      9. +-commutative 0.1%

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

      10. distribute-lft-in 0.1%

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

      11. metadata-eval 0.1%

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

      12. associate-*r* 0.1%

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

      13. metadata-eval 0.1%

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

   5. Simplified 0.1%

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

   6. Taylor expanded in x1 around 0 61.9%

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

      1. +-commutative 61.9%

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

      2. +-commutative 61.9%

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

      3. associate-+l+ 61.9%

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

      4. metadata-eval 61.9%

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

      5. distribute-lft-neg-in 61.9%

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

      6. mul-1-neg 61.9%

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

      7. distribute-neg-in 61.9%

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

      8. fma-udef 61.9%

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

      9. unsub-neg 61.9%

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

      10. *-commutative 61.9%

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

      11. unpow2 61.9%

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

      12. associate-*l* 61.9%

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

      13. cancel-sign-sub-inv 61.9%

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

      14. metadata-eval 61.9%

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

      15. +-commutative 61.9%

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

      16. count-2 61.9%

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

   8. Simplified 61.9%

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

   9. Taylor expanded in x2 around 0 86.9%

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

       1. *-commutative 86.9%

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

       2. unpow2 86.9%

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

   11. Simplified 86.9%

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

   if -2.6000000000000002e108 < x1 < -6e5

   1. Initial program 99.4%

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

   2. Taylor expanded in x1 around inf 99.4%

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

   3. Taylor expanded in x1 around inf 99.4%

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

   4. Taylor expanded in x1 around inf 99.4%

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

   5. Taylor expanded in x1 around inf 99.4%

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

   if -6e5 < x1 < 145

   1. Initial program 98.7%

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

   2. Taylor expanded in x1 around 0 98.4%

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

   if 145 < x1 < 5.00000000000000018e153

   1. Initial program 99.2%

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

   2. Taylor expanded in x1 around inf 87.8%

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

   3. Taylor expanded in x1 around inf 87.8%

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

   4. Taylor expanded in x1 around inf 87.8%

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

   5. Taylor expanded in x1 around 0 87.8%

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

      1. +-commutative 87.8%

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

      2. *-commutative 87.8%

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

      3. *-commutative 87.8%

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

      4. unpow2 87.8%

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

      5. associate-*l* 87.8%

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

      6. distribute-lft-out 87.8%

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

   7. Simplified 87.8%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.6 \cdot 10^{+108}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(6 + x2 \cdot -4\right)\right) - 3 \cdot \left(x1 - 3 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -600000:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \frac{1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 + \frac{-1}{x1}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 145:\\ \;\;\;\;x1 - \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right) + 3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right) - x1 \cdot \left(-3 + x1 \cdot 9\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(6 + x2 \cdot -4\right)\right) - 3 \cdot \left(x1 - 3 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \end{array} \]

Alternative 8: 91.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := x1 + \left(\left(x1 + \left(6 + x2 \cdot -4\right)\right) - 3 \cdot \left(x1 - 3 \cdot \left(x1 \cdot x1\right)\right)\right)\\ t_3 := t_0 + 2 \cdot x2\\ t_4 := x1 \cdot x1 + 1\\ t_5 := \frac{t_3 - x1}{t_4}\\ t_6 := \left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\\ \mathbf{if}\;x1 \leq -5.4 \cdot 10^{+108}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x1 \leq -600000:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(t_1 + \left(t_4 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t_5 \cdot 4 - 6\right) + \frac{1}{x1} \cdot t_6\right) + t_0 \cdot \left(3 + \frac{-1}{x1}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 195:\\ \;\;\;\;x1 - \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right) + 3 \cdot \frac{x1 - \left(t_0 - 2 \cdot x2\right)}{t_4}\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 - \left(\left(\left(t_4 \cdot \left(\left(t_5 - 3\right) \cdot t_6 + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - t_3}{t_4}\right)\right) - \left(x1 \cdot x1\right) \cdot 9\right) - t_1\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (* x1 (* x1 x1)))
        (t_2
         (+
          x1
          (- (+ x1 (+ 6.0 (* x2 -4.0))) (* 3.0 (- x1 (* 3.0 (* x1 x1)))))))
        (t_3 (+ t_0 (* 2.0 x2)))
        (t_4 (+ (* x1 x1) 1.0))
        (t_5 (/ (- t_3 x1) t_4))
        (t_6 (* (* x1 2.0) (- (/ 1.0 x1) 3.0))))
   (if (<= x1 -5.4e+108)
     t_2
     (if (<= x1 -600000.0)
       (+
        x1
        (+
         9.0
         (+
          x1
          (+
           t_1
           (+
            (* t_4 (+ (* (* x1 x1) (- (* t_5 4.0) 6.0)) (* (/ 1.0 x1) t_6)))
            (* t_0 (+ 3.0 (/ -1.0 x1))))))))
       (if (<= x1 195.0)
         (-
          x1
          (+
           (- (* 4.0 (* x2 (* x1 (- 3.0 (* 2.0 x2))))) x1)
           (* 3.0 (/ (- x1 (- t_0 (* 2.0 x2))) t_4))))
         (if (<= x1 5e+153)
           (+
            x1
            (-
             9.0
             (-
              (-
               (-
                (*
                 t_4
                 (+
                  (* (- t_5 3.0) t_6)
                  (* (* x1 x1) (+ 6.0 (* 4.0 (/ (- x1 t_3) t_4))))))
                (* (* x1 x1) 9.0))
               t_1)
              x1)))
           t_2))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * (x1 * x1);
	double t_2 = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))));
	double t_3 = t_0 + (2.0 * x2);
	double t_4 = (x1 * x1) + 1.0;
	double t_5 = (t_3 - x1) / t_4;
	double t_6 = (x1 * 2.0) * ((1.0 / x1) - 3.0);
	double tmp;
	if (x1 <= -5.4e+108) {
		tmp = t_2;
	} else if (x1 <= -600000.0) {
		tmp = x1 + (9.0 + (x1 + (t_1 + ((t_4 * (((x1 * x1) * ((t_5 * 4.0) - 6.0)) + ((1.0 / x1) * t_6))) + (t_0 * (3.0 + (-1.0 / x1)))))));
	} else if (x1 <= 195.0) {
		tmp = x1 - (((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_4)));
	} else if (x1 <= 5e+153) {
		tmp = x1 + (9.0 - ((((t_4 * (((t_5 - 3.0) * t_6) + ((x1 * x1) * (6.0 + (4.0 * ((x1 - t_3) / t_4)))))) - ((x1 * x1) * 9.0)) - t_1) - x1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = x1 * (x1 * x1)
    t_2 = x1 + ((x1 + (6.0d0 + (x2 * (-4.0d0)))) - (3.0d0 * (x1 - (3.0d0 * (x1 * x1)))))
    t_3 = t_0 + (2.0d0 * x2)
    t_4 = (x1 * x1) + 1.0d0
    t_5 = (t_3 - x1) / t_4
    t_6 = (x1 * 2.0d0) * ((1.0d0 / x1) - 3.0d0)
    if (x1 <= (-5.4d+108)) then
        tmp = t_2
    else if (x1 <= (-600000.0d0)) then
        tmp = x1 + (9.0d0 + (x1 + (t_1 + ((t_4 * (((x1 * x1) * ((t_5 * 4.0d0) - 6.0d0)) + ((1.0d0 / x1) * t_6))) + (t_0 * (3.0d0 + ((-1.0d0) / x1)))))))
    else if (x1 <= 195.0d0) then
        tmp = x1 - (((4.0d0 * (x2 * (x1 * (3.0d0 - (2.0d0 * x2))))) - x1) + (3.0d0 * ((x1 - (t_0 - (2.0d0 * x2))) / t_4)))
    else if (x1 <= 5d+153) then
        tmp = x1 + (9.0d0 - ((((t_4 * (((t_5 - 3.0d0) * t_6) + ((x1 * x1) * (6.0d0 + (4.0d0 * ((x1 - t_3) / t_4)))))) - ((x1 * x1) * 9.0d0)) - t_1) - x1))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * (x1 * x1);
	double t_2 = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))));
	double t_3 = t_0 + (2.0 * x2);
	double t_4 = (x1 * x1) + 1.0;
	double t_5 = (t_3 - x1) / t_4;
	double t_6 = (x1 * 2.0) * ((1.0 / x1) - 3.0);
	double tmp;
	if (x1 <= -5.4e+108) {
		tmp = t_2;
	} else if (x1 <= -600000.0) {
		tmp = x1 + (9.0 + (x1 + (t_1 + ((t_4 * (((x1 * x1) * ((t_5 * 4.0) - 6.0)) + ((1.0 / x1) * t_6))) + (t_0 * (3.0 + (-1.0 / x1)))))));
	} else if (x1 <= 195.0) {
		tmp = x1 - (((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_4)));
	} else if (x1 <= 5e+153) {
		tmp = x1 + (9.0 - ((((t_4 * (((t_5 - 3.0) * t_6) + ((x1 * x1) * (6.0 + (4.0 * ((x1 - t_3) / t_4)))))) - ((x1 * x1) * 9.0)) - t_1) - x1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = x1 * (x1 * x1)
	t_2 = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))))
	t_3 = t_0 + (2.0 * x2)
	t_4 = (x1 * x1) + 1.0
	t_5 = (t_3 - x1) / t_4
	t_6 = (x1 * 2.0) * ((1.0 / x1) - 3.0)
	tmp = 0
	if x1 <= -5.4e+108:
		tmp = t_2
	elif x1 <= -600000.0:
		tmp = x1 + (9.0 + (x1 + (t_1 + ((t_4 * (((x1 * x1) * ((t_5 * 4.0) - 6.0)) + ((1.0 / x1) * t_6))) + (t_0 * (3.0 + (-1.0 / x1)))))))
	elif x1 <= 195.0:
		tmp = x1 - (((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_4)))
	elif x1 <= 5e+153:
		tmp = x1 + (9.0 - ((((t_4 * (((t_5 - 3.0) * t_6) + ((x1 * x1) * (6.0 + (4.0 * ((x1 - t_3) / t_4)))))) - ((x1 * x1) * 9.0)) - t_1) - x1))
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(x1 * Float64(x1 * x1))
	t_2 = Float64(x1 + Float64(Float64(x1 + Float64(6.0 + Float64(x2 * -4.0))) - Float64(3.0 * Float64(x1 - Float64(3.0 * Float64(x1 * x1))))))
	t_3 = Float64(t_0 + Float64(2.0 * x2))
	t_4 = Float64(Float64(x1 * x1) + 1.0)
	t_5 = Float64(Float64(t_3 - x1) / t_4)
	t_6 = Float64(Float64(x1 * 2.0) * Float64(Float64(1.0 / x1) - 3.0))
	tmp = 0.0
	if (x1 <= -5.4e+108)
		tmp = t_2;
	elseif (x1 <= -600000.0)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_1 + Float64(Float64(t_4 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_5 * 4.0) - 6.0)) + Float64(Float64(1.0 / x1) * t_6))) + Float64(t_0 * Float64(3.0 + Float64(-1.0 / x1))))))));
	elseif (x1 <= 195.0)
		tmp = Float64(x1 - Float64(Float64(Float64(4.0 * Float64(x2 * Float64(x1 * Float64(3.0 - Float64(2.0 * x2))))) - x1) + Float64(3.0 * Float64(Float64(x1 - Float64(t_0 - Float64(2.0 * x2))) / t_4))));
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + Float64(9.0 - Float64(Float64(Float64(Float64(t_4 * Float64(Float64(Float64(t_5 - 3.0) * t_6) + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * Float64(Float64(x1 - t_3) / t_4)))))) - Float64(Float64(x1 * x1) * 9.0)) - t_1) - x1)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = x1 * (x1 * x1);
	t_2 = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))));
	t_3 = t_0 + (2.0 * x2);
	t_4 = (x1 * x1) + 1.0;
	t_5 = (t_3 - x1) / t_4;
	t_6 = (x1 * 2.0) * ((1.0 / x1) - 3.0);
	tmp = 0.0;
	if (x1 <= -5.4e+108)
		tmp = t_2;
	elseif (x1 <= -600000.0)
		tmp = x1 + (9.0 + (x1 + (t_1 + ((t_4 * (((x1 * x1) * ((t_5 * 4.0) - 6.0)) + ((1.0 / x1) * t_6))) + (t_0 * (3.0 + (-1.0 / x1)))))));
	elseif (x1 <= 195.0)
		tmp = x1 - (((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_4)));
	elseif (x1 <= 5e+153)
		tmp = x1 + (9.0 - ((((t_4 * (((t_5 - 3.0) * t_6) + ((x1 * x1) * (6.0 + (4.0 * ((x1 - t_3) / t_4)))))) - ((x1 * x1) * 9.0)) - t_1) - x1));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(N[(x1 + N[(6.0 + N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * N[(x1 - N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$3 - x1), $MachinePrecision] / t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(1.0 / x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.4e+108], t$95$2, If[LessEqual[x1, -600000.0], N[(x1 + N[(9.0 + N[(x1 + N[(t$95$1 + N[(N[(t$95$4 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$5 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 / x1), $MachinePrecision] * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(3.0 + N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 195.0], N[(x1 - N[(N[(N[(4.0 * N[(x2 * N[(x1 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] + N[(3.0 * N[(N[(x1 - N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], N[(x1 + N[(9.0 - N[(N[(N[(N[(t$95$4 * N[(N[(N[(t$95$5 - 3.0), $MachinePrecision] * t$95$6), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * N[(N[(x1 - t$95$3), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.4e108 or 5.00000000000000018e153 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around inf 0.0%

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

   3. Taylor expanded in x1 around 0 0.1%

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

      1. sub-neg 0.1%

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

      2. metadata-eval 0.1%

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

      3. distribute-lft-in 0.1%

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

      4. *-commutative 0.1%

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

      5. associate-*l* 0.1%

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

      6. metadata-eval 0.1%

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

      7. metadata-eval 0.1%

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

      8. distribute-rgt-in 0.1%

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

      9. +-commutative 0.1%

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

      10. distribute-lft-in 0.1%

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

      11. metadata-eval 0.1%

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

      12. associate-*r* 0.1%

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

      13. metadata-eval 0.1%

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

   5. Simplified 0.1%

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

   6. Taylor expanded in x1 around 0 61.9%

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

      1. +-commutative 61.9%

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

      2. +-commutative 61.9%

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

      3. associate-+l+ 61.9%

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

      4. metadata-eval 61.9%

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

      5. distribute-lft-neg-in 61.9%

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

      6. mul-1-neg 61.9%

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

      7. distribute-neg-in 61.9%

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

      8. fma-udef 61.9%

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

      9. unsub-neg 61.9%

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

      10. *-commutative 61.9%

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

      11. unpow2 61.9%

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

      12. associate-*l* 61.9%

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

      13. cancel-sign-sub-inv 61.9%

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

      14. metadata-eval 61.9%

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

      15. +-commutative 61.9%

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

      16. count-2 61.9%

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

   8. Simplified 61.9%

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

   9. Taylor expanded in x2 around 0 86.9%

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

       1. *-commutative 86.9%

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

       2. unpow2 86.9%

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

   11. Simplified 86.9%

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

   if -5.4e108 < x1 < -6e5

   1. Initial program 99.4%

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

   2. Taylor expanded in x1 around inf 99.4%

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

   3. Taylor expanded in x1 around inf 99.4%

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

   4. Taylor expanded in x1 around inf 99.4%

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

   5. Taylor expanded in x1 around inf 99.4%

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

   if -6e5 < x1 < 195

   1. Initial program 98.7%

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

   2. Taylor expanded in x1 around 0 98.4%

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

   if 195 < x1 < 5.00000000000000018e153

   1. Initial program 99.2%

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

   2. Taylor expanded in x1 around inf 87.8%

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

   3. Taylor expanded in x1 around inf 87.8%

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

   4. Taylor expanded in x1 around inf 87.8%

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

   5. Taylor expanded in x1 around inf 87.3%

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

      1. *-commutative 87.3%

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

      2. unpow2 87.3%

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

   7. Simplified 87.3%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.4 \cdot 10^{+108}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(6 + x2 \cdot -4\right)\right) - 3 \cdot \left(x1 - 3 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -600000:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \frac{1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 + \frac{-1}{x1}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 195:\\ \;\;\;\;x1 - \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right) + 3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 - \left(\left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right) - \left(x1 \cdot x1\right) \cdot 9\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(6 + x2 \cdot -4\right)\right) - 3 \cdot \left(x1 - 3 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \end{array} \]

Alternative 9: 91.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 + \left(\left(x1 + \left(6 + x2 \cdot -4\right)\right) - 3 \cdot \left(x1 - 3 \cdot \left(x1 \cdot x1\right)\right)\right)\\ t_3 := x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_1} \cdot 4 - 6\right) + \frac{1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right)\right) + t_0 \cdot \left(3 + \frac{-1}{x1}\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -1.1 \cdot 10^{+107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x1 \leq -600000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x1 \leq 50:\\ \;\;\;\;x1 - \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right) + 3 \cdot \frac{x1 - \left(t_0 - 2 \cdot x2\right)}{t_1}\right)\\ \mathbf{elif}\;x1 \leq 1.5 \cdot 10^{+154}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2
         (+
          x1
          (- (+ x1 (+ 6.0 (* x2 -4.0))) (* 3.0 (- x1 (* 3.0 (* x1 x1)))))))
        (t_3
         (+
          x1
          (+
           9.0
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (*
               t_1
               (+
                (* (* x1 x1) (- (* (/ (- (+ t_0 (* 2.0 x2)) x1) t_1) 4.0) 6.0))
                (* (/ 1.0 x1) (* (* x1 2.0) (- (/ 1.0 x1) 3.0)))))
              (* t_0 (+ 3.0 (/ -1.0 x1))))))))))
   (if (<= x1 -1.1e+107)
     t_2
     (if (<= x1 -600000.0)
       t_3
       (if (<= x1 50.0)
         (-
          x1
          (+
           (- (* 4.0 (* x2 (* x1 (- 3.0 (* 2.0 x2))))) x1)
           (* 3.0 (/ (- x1 (- t_0 (* 2.0 x2))) t_1))))
         (if (<= x1 1.5e+154) t_3 t_2))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))));
	double t_3 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((x1 * x1) * (((((t_0 + (2.0 * x2)) - x1) / t_1) * 4.0) - 6.0)) + ((1.0 / x1) * ((x1 * 2.0) * ((1.0 / x1) - 3.0))))) + (t_0 * (3.0 + (-1.0 / x1)))))));
	double tmp;
	if (x1 <= -1.1e+107) {
		tmp = t_2;
	} else if (x1 <= -600000.0) {
		tmp = t_3;
	} else if (x1 <= 50.0) {
		tmp = x1 - (((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_1)));
	} else if (x1 <= 1.5e+154) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = x1 + ((x1 + (6.0d0 + (x2 * (-4.0d0)))) - (3.0d0 * (x1 - (3.0d0 * (x1 * x1)))))
    t_3 = x1 + (9.0d0 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((x1 * x1) * (((((t_0 + (2.0d0 * x2)) - x1) / t_1) * 4.0d0) - 6.0d0)) + ((1.0d0 / x1) * ((x1 * 2.0d0) * ((1.0d0 / x1) - 3.0d0))))) + (t_0 * (3.0d0 + ((-1.0d0) / x1)))))))
    if (x1 <= (-1.1d+107)) then
        tmp = t_2
    else if (x1 <= (-600000.0d0)) then
        tmp = t_3
    else if (x1 <= 50.0d0) then
        tmp = x1 - (((4.0d0 * (x2 * (x1 * (3.0d0 - (2.0d0 * x2))))) - x1) + (3.0d0 * ((x1 - (t_0 - (2.0d0 * x2))) / t_1)))
    else if (x1 <= 1.5d+154) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))));
	double t_3 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((x1 * x1) * (((((t_0 + (2.0 * x2)) - x1) / t_1) * 4.0) - 6.0)) + ((1.0 / x1) * ((x1 * 2.0) * ((1.0 / x1) - 3.0))))) + (t_0 * (3.0 + (-1.0 / x1)))))));
	double tmp;
	if (x1 <= -1.1e+107) {
		tmp = t_2;
	} else if (x1 <= -600000.0) {
		tmp = t_3;
	} else if (x1 <= 50.0) {
		tmp = x1 - (((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_1)));
	} else if (x1 <= 1.5e+154) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))))
	t_3 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((x1 * x1) * (((((t_0 + (2.0 * x2)) - x1) / t_1) * 4.0) - 6.0)) + ((1.0 / x1) * ((x1 * 2.0) * ((1.0 / x1) - 3.0))))) + (t_0 * (3.0 + (-1.0 / x1)))))))
	tmp = 0
	if x1 <= -1.1e+107:
		tmp = t_2
	elif x1 <= -600000.0:
		tmp = t_3
	elif x1 <= 50.0:
		tmp = x1 - (((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_1)))
	elif x1 <= 1.5e+154:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(x1 + Float64(Float64(x1 + Float64(6.0 + Float64(x2 * -4.0))) - Float64(3.0 * Float64(x1 - Float64(3.0 * Float64(x1 * x1))))))
	t_3 = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1) * 4.0) - 6.0)) + Float64(Float64(1.0 / x1) * Float64(Float64(x1 * 2.0) * Float64(Float64(1.0 / x1) - 3.0))))) + Float64(t_0 * Float64(3.0 + Float64(-1.0 / x1))))))))
	tmp = 0.0
	if (x1 <= -1.1e+107)
		tmp = t_2;
	elseif (x1 <= -600000.0)
		tmp = t_3;
	elseif (x1 <= 50.0)
		tmp = Float64(x1 - Float64(Float64(Float64(4.0 * Float64(x2 * Float64(x1 * Float64(3.0 - Float64(2.0 * x2))))) - x1) + Float64(3.0 * Float64(Float64(x1 - Float64(t_0 - Float64(2.0 * x2))) / t_1))));
	elseif (x1 <= 1.5e+154)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))));
	t_3 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((x1 * x1) * (((((t_0 + (2.0 * x2)) - x1) / t_1) * 4.0) - 6.0)) + ((1.0 / x1) * ((x1 * 2.0) * ((1.0 / x1) - 3.0))))) + (t_0 * (3.0 + (-1.0 / x1)))))));
	tmp = 0.0;
	if (x1 <= -1.1e+107)
		tmp = t_2;
	elseif (x1 <= -600000.0)
		tmp = t_3;
	elseif (x1 <= 50.0)
		tmp = x1 - (((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_1)));
	elseif (x1 <= 1.5e+154)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(N[(x1 + N[(6.0 + N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * N[(x1 - N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(9.0 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision] * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 / x1), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(1.0 / x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(3.0 + N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.1e+107], t$95$2, If[LessEqual[x1, -600000.0], t$95$3, If[LessEqual[x1, 50.0], N[(x1 - N[(N[(N[(4.0 * N[(x2 * N[(x1 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] + N[(3.0 * N[(N[(x1 - N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.5e+154], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.1e107 or 1.50000000000000013e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around inf 0.0%

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

   3. Taylor expanded in x1 around 0 0.1%

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

      1. sub-neg 0.1%

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

      2. metadata-eval 0.1%

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

      3. distribute-lft-in 0.1%

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

      4. *-commutative 0.1%

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

      5. associate-*l* 0.1%

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

      6. metadata-eval 0.1%

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

      7. metadata-eval 0.1%

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

      8. distribute-rgt-in 0.1%

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

      9. +-commutative 0.1%

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

      10. distribute-lft-in 0.1%

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

      11. metadata-eval 0.1%

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

      12. associate-*r* 0.1%

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

      13. metadata-eval 0.1%

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

   5. Simplified 0.1%

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

   6. Taylor expanded in x1 around 0 61.9%

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

      1. +-commutative 61.9%

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

      2. +-commutative 61.9%

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

      3. associate-+l+ 61.9%

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

      4. metadata-eval 61.9%

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

      5. distribute-lft-neg-in 61.9%

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

      6. mul-1-neg 61.9%

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

      7. distribute-neg-in 61.9%

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

      8. fma-udef 61.9%

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

      9. unsub-neg 61.9%

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

      10. *-commutative 61.9%

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

      11. unpow2 61.9%

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

      12. associate-*l* 61.9%

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

      13. cancel-sign-sub-inv 61.9%

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

      14. metadata-eval 61.9%

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

      15. +-commutative 61.9%

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

      16. count-2 61.9%

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

   8. Simplified 61.9%

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

   9. Taylor expanded in x2 around 0 86.9%

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

       1. *-commutative 86.9%

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

       2. unpow2 86.9%

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

   11. Simplified 86.9%

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

   if -1.1e107 < x1 < -6e5 or 50 < x1 < 1.50000000000000013e154

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around inf 92.4%

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

   3. Taylor expanded in x1 around inf 92.5%

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

   4. Taylor expanded in x1 around inf 92.5%

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

   5. Taylor expanded in x1 around inf 92.1%

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

   if -6e5 < x1 < 50

   1. Initial program 98.7%

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

   2. Taylor expanded in x1 around 0 98.4%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.1 \cdot 10^{+107}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(6 + x2 \cdot -4\right)\right) - 3 \cdot \left(x1 - 3 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -600000:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \frac{1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 + \frac{-1}{x1}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 50:\\ \;\;\;\;x1 - \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right) + 3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 1.5 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \frac{1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 + \frac{-1}{x1}\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(6 + x2 \cdot -4\right)\right) - 3 \cdot \left(x1 - 3 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \end{array} \]

Alternative 10: 89.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 + \left(\left(x1 + \left(6 + x2 \cdot -4\right)\right) - 3 \cdot \left(x1 - 3 \cdot \left(x1 \cdot x1\right)\right)\right)\\ t_3 := x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_1 \cdot \left(3 + \frac{-1}{x1}\right) - \left(\left(x1 \cdot x1\right) \cdot 6 - \left(\frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_0} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right)\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x1 \leq -8200000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x1 \leq 520:\\ \;\;\;\;x1 - \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right) + 3 \cdot \frac{x1 - \left(t_1 - 2 \cdot x2\right)}{t_0}\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2
         (+
          x1
          (- (+ x1 (+ 6.0 (* x2 -4.0))) (* 3.0 (- x1 (* 3.0 (* x1 x1)))))))
        (t_3
         (+
          x1
          (+
           9.0
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (-
              (* t_1 (+ 3.0 (/ -1.0 x1)))
              (*
               (-
                (* (* x1 x1) 6.0)
                (*
                 (- (/ (- (+ t_1 (* 2.0 x2)) x1) t_0) 3.0)
                 (* (* x1 2.0) (- (/ 1.0 x1) 3.0))))
               (- -1.0 (* x1 x1))))))))))
   (if (<= x1 -5.5e+102)
     t_2
     (if (<= x1 -8200000.0)
       t_3
       (if (<= x1 520.0)
         (-
          x1
          (+
           (- (* 4.0 (* x2 (* x1 (- 3.0 (* 2.0 x2))))) x1)
           (* 3.0 (/ (- x1 (- t_1 (* 2.0 x2))) t_0))))
         (if (<= x1 5e+153) t_3 t_2))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))));
	double t_3 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (3.0 + (-1.0 / x1))) - ((((x1 * x1) * 6.0) - (((((t_1 + (2.0 * x2)) - x1) / t_0) - 3.0) * ((x1 * 2.0) * ((1.0 / x1) - 3.0)))) * (-1.0 - (x1 * x1)))))));
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = t_2;
	} else if (x1 <= -8200000.0) {
		tmp = t_3;
	} else if (x1 <= 520.0) {
		tmp = x1 - (((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 - (t_1 - (2.0 * x2))) / t_0)));
	} else if (x1 <= 5e+153) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = x1 + ((x1 + (6.0d0 + (x2 * (-4.0d0)))) - (3.0d0 * (x1 - (3.0d0 * (x1 * x1)))))
    t_3 = x1 + (9.0d0 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (3.0d0 + ((-1.0d0) / x1))) - ((((x1 * x1) * 6.0d0) - (((((t_1 + (2.0d0 * x2)) - x1) / t_0) - 3.0d0) * ((x1 * 2.0d0) * ((1.0d0 / x1) - 3.0d0)))) * ((-1.0d0) - (x1 * x1)))))))
    if (x1 <= (-5.5d+102)) then
        tmp = t_2
    else if (x1 <= (-8200000.0d0)) then
        tmp = t_3
    else if (x1 <= 520.0d0) then
        tmp = x1 - (((4.0d0 * (x2 * (x1 * (3.0d0 - (2.0d0 * x2))))) - x1) + (3.0d0 * ((x1 - (t_1 - (2.0d0 * x2))) / t_0)))
    else if (x1 <= 5d+153) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))));
	double t_3 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (3.0 + (-1.0 / x1))) - ((((x1 * x1) * 6.0) - (((((t_1 + (2.0 * x2)) - x1) / t_0) - 3.0) * ((x1 * 2.0) * ((1.0 / x1) - 3.0)))) * (-1.0 - (x1 * x1)))))));
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = t_2;
	} else if (x1 <= -8200000.0) {
		tmp = t_3;
	} else if (x1 <= 520.0) {
		tmp = x1 - (((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 - (t_1 - (2.0 * x2))) / t_0)));
	} else if (x1 <= 5e+153) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))))
	t_3 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (3.0 + (-1.0 / x1))) - ((((x1 * x1) * 6.0) - (((((t_1 + (2.0 * x2)) - x1) / t_0) - 3.0) * ((x1 * 2.0) * ((1.0 / x1) - 3.0)))) * (-1.0 - (x1 * x1)))))))
	tmp = 0
	if x1 <= -5.5e+102:
		tmp = t_2
	elif x1 <= -8200000.0:
		tmp = t_3
	elif x1 <= 520.0:
		tmp = x1 - (((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 - (t_1 - (2.0 * x2))) / t_0)))
	elif x1 <= 5e+153:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(x1 + Float64(Float64(x1 + Float64(6.0 + Float64(x2 * -4.0))) - Float64(3.0 * Float64(x1 - Float64(3.0 * Float64(x1 * x1))))))
	t_3 = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * Float64(3.0 + Float64(-1.0 / x1))) - Float64(Float64(Float64(Float64(x1 * x1) * 6.0) - Float64(Float64(Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_0) - 3.0) * Float64(Float64(x1 * 2.0) * Float64(Float64(1.0 / x1) - 3.0)))) * Float64(-1.0 - Float64(x1 * x1))))))))
	tmp = 0.0
	if (x1 <= -5.5e+102)
		tmp = t_2;
	elseif (x1 <= -8200000.0)
		tmp = t_3;
	elseif (x1 <= 520.0)
		tmp = Float64(x1 - Float64(Float64(Float64(4.0 * Float64(x2 * Float64(x1 * Float64(3.0 - Float64(2.0 * x2))))) - x1) + Float64(3.0 * Float64(Float64(x1 - Float64(t_1 - Float64(2.0 * x2))) / t_0))));
	elseif (x1 <= 5e+153)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * 3.0);
	t_2 = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))));
	t_3 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (3.0 + (-1.0 / x1))) - ((((x1 * x1) * 6.0) - (((((t_1 + (2.0 * x2)) - x1) / t_0) - 3.0) * ((x1 * 2.0) * ((1.0 / x1) - 3.0)))) * (-1.0 - (x1 * x1)))))));
	tmp = 0.0;
	if (x1 <= -5.5e+102)
		tmp = t_2;
	elseif (x1 <= -8200000.0)
		tmp = t_3;
	elseif (x1 <= 520.0)
		tmp = x1 - (((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 - (t_1 - (2.0 * x2))) / t_0)));
	elseif (x1 <= 5e+153)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(N[(x1 + N[(6.0 + N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * N[(x1 - N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(9.0 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * N[(3.0 + N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision] - N[(N[(N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision] - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(1.0 / x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.5e+102], t$95$2, If[LessEqual[x1, -8200000.0], t$95$3, If[LessEqual[x1, 520.0], N[(x1 - N[(N[(N[(4.0 * N[(x2 * N[(x1 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] + N[(3.0 * N[(N[(x1 - N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.49999999999999981e102 or 5.00000000000000018e153 < x1

   1. Initial program 1.3%

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

   2. Taylor expanded in x1 around inf 1.3%

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

   3. Taylor expanded in x1 around 0 0.1%

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

      1. sub-neg 0.1%

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

      2. metadata-eval 0.1%

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

      3. distribute-lft-in 0.1%

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

      4. *-commutative 0.1%

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

      5. associate-*l* 0.1%

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

      6. metadata-eval 0.1%

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

      7. metadata-eval 0.1%

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

      8. distribute-rgt-in 0.1%

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

      9. +-commutative 0.1%

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

      10. distribute-lft-in 0.1%

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

      11. metadata-eval 0.1%

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

      12. associate-*r* 0.1%

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

      13. metadata-eval 0.1%

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

   5. Simplified 0.1%

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

   6. Taylor expanded in x1 around 0 62.3%

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

      1. +-commutative 62.3%

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

      2. +-commutative 62.3%

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

      3. associate-+l+ 62.3%

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

      4. metadata-eval 62.3%

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

      5. distribute-lft-neg-in 62.3%

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

      6. mul-1-neg 62.3%

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

      7. distribute-neg-in 62.3%

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

      8. fma-udef 62.3%

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

      9. unsub-neg 62.3%

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

      10. *-commutative 62.3%

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

      11. unpow2 62.3%

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

      12. associate-*l* 62.3%

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

      13. cancel-sign-sub-inv 62.3%

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

      14. metadata-eval 62.3%

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

      15. +-commutative 62.3%

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

      16. count-2 62.3%

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

   8. Simplified 62.3%

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

   9. Taylor expanded in x2 around 0 85.8%

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

       1. *-commutative 85.8%

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

       2. unpow2 85.8%

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

   11. Simplified 85.8%

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

   if -5.49999999999999981e102 < x1 < -8.2e6 or 520 < x1 < 5.00000000000000018e153

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around inf 92.3%

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

   3. Taylor expanded in x1 around inf 92.3%

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

   4. Taylor expanded in x1 around inf 92.3%

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

   5. Taylor expanded in x1 around inf 80.9%

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

   if -8.2e6 < x1 < 520

   1. Initial program 98.7%

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

   2. Taylor expanded in x1 around 0 98.4%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(6 + x2 \cdot -4\right)\right) - 3 \cdot \left(x1 - 3 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -8200000:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 + \frac{-1}{x1}\right) - \left(\left(x1 \cdot x1\right) \cdot 6 - \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right)\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 520:\\ \;\;\;\;x1 - \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right) + 3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 + \frac{-1}{x1}\right) - \left(\left(x1 \cdot x1\right) \cdot 6 - \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right)\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(6 + x2 \cdot -4\right)\right) - 3 \cdot \left(x1 - 3 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \end{array} \]

Alternative 11: 80.0% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.6 \cdot 10^{+108} \lor \neg \left(x1 \leq 1.5 \cdot 10^{+154}\right):\\ \;\;\;\;x1 + \left(\left(x1 + \left(6 + x2 \cdot -4\right)\right) - 3 \cdot \left(x1 - 3 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right) + 3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -2.6e+108) (not (<= x1 1.5e+154)))
   (+ x1 (- (+ x1 (+ 6.0 (* x2 -4.0))) (* 3.0 (- x1 (* 3.0 (* x1 x1))))))
   (-
    x1
    (+
     (- (* 4.0 (* x2 (* x1 (- 3.0 (* 2.0 x2))))) x1)
     (* 3.0 (/ (- x1 (- (* x1 (* x1 3.0)) (* 2.0 x2))) (+ (* x1 x1) 1.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -2.6e+108) || !(x1 <= 1.5e+154)) {
		tmp = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))));
	} else {
		tmp = x1 - (((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / ((x1 * x1) + 1.0))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-2.6d+108)) .or. (.not. (x1 <= 1.5d+154))) then
        tmp = x1 + ((x1 + (6.0d0 + (x2 * (-4.0d0)))) - (3.0d0 * (x1 - (3.0d0 * (x1 * x1)))))
    else
        tmp = x1 - (((4.0d0 * (x2 * (x1 * (3.0d0 - (2.0d0 * x2))))) - x1) + (3.0d0 * ((x1 - ((x1 * (x1 * 3.0d0)) - (2.0d0 * x2))) / ((x1 * x1) + 1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -2.6e+108) || !(x1 <= 1.5e+154)) {
		tmp = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))));
	} else {
		tmp = x1 - (((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / ((x1 * x1) + 1.0))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -2.6e+108) or not (x1 <= 1.5e+154):
		tmp = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))))
	else:
		tmp = x1 - (((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / ((x1 * x1) + 1.0))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -2.6e+108) || !(x1 <= 1.5e+154))
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(6.0 + Float64(x2 * -4.0))) - Float64(3.0 * Float64(x1 - Float64(3.0 * Float64(x1 * x1))))));
	else
		tmp = Float64(x1 - Float64(Float64(Float64(4.0 * Float64(x2 * Float64(x1 * Float64(3.0 - Float64(2.0 * x2))))) - x1) + Float64(3.0 * Float64(Float64(x1 - Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2))) / Float64(Float64(x1 * x1) + 1.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -2.6e+108) || ~((x1 <= 1.5e+154)))
		tmp = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))));
	else
		tmp = x1 - (((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / ((x1 * x1) + 1.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -2.6e+108], N[Not[LessEqual[x1, 1.5e+154]], $MachinePrecision]], N[(x1 + N[(N[(x1 + N[(6.0 + N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * N[(x1 - N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 - N[(N[(N[(4.0 * N[(x2 * N[(x1 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] + N[(3.0 * N[(N[(x1 - N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -2.6000000000000002e108 or 1.50000000000000013e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around inf 0.0%

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

   3. Taylor expanded in x1 around 0 0.1%

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

      1. sub-neg 0.1%

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

      2. metadata-eval 0.1%

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

      3. distribute-lft-in 0.1%

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

      4. *-commutative 0.1%

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

      5. associate-*l* 0.1%

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

      6. metadata-eval 0.1%

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

      7. metadata-eval 0.1%

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

      8. distribute-rgt-in 0.1%

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

      9. +-commutative 0.1%

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

      10. distribute-lft-in 0.1%

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

      11. metadata-eval 0.1%

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

      12. associate-*r* 0.1%

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

      13. metadata-eval 0.1%

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

   5. Simplified 0.1%

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

   6. Taylor expanded in x1 around 0 61.9%

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

      1. +-commutative 61.9%

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

      2. +-commutative 61.9%

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

      3. associate-+l+ 61.9%

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

      4. metadata-eval 61.9%

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

      5. distribute-lft-neg-in 61.9%

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

      6. mul-1-neg 61.9%

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

      7. distribute-neg-in 61.9%

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

      8. fma-udef 61.9%

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

      9. unsub-neg 61.9%

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

      10. *-commutative 61.9%

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

      11. unpow2 61.9%

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

      12. associate-*l* 61.9%

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

      13. cancel-sign-sub-inv 61.9%

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

      14. metadata-eval 61.9%

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

      15. +-commutative 61.9%

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

      16. count-2 61.9%

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

   8. Simplified 61.9%

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

   9. Taylor expanded in x2 around 0 86.9%

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

       1. *-commutative 86.9%

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

       2. unpow2 86.9%

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

   11. Simplified 86.9%

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

   if -2.6000000000000002e108 < x1 < 1.50000000000000013e154

   1. Initial program 98.8%

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

   2. Taylor expanded in x1 around 0 80.5%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.6 \cdot 10^{+108} \lor \neg \left(x1 \leq 1.5 \cdot 10^{+154}\right):\\ \;\;\;\;x1 + \left(\left(x1 + \left(6 + x2 \cdot -4\right)\right) - 3 \cdot \left(x1 - 3 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right) + 3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\\ \end{array} \]

Alternative 12: 69.8% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + x2 \cdot -6\right)\\ \mathbf{if}\;x1 \leq -2.25 \cdot 10^{+77}:\\ \;\;\;\;x1 - x2 \cdot \left(\left(x1 \cdot x1\right) \cdot -6 + 10\right)\\ \mathbf{elif}\;x1 \leq -1.06 \cdot 10^{-163}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{-178}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (+
          x1
          (+ (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0)) (* x2 -6.0)))))
   (if (<= x1 -2.25e+77)
     (- x1 (* x2 (+ (* (* x1 x1) -6.0) 10.0)))
     (if (<= x1 -1.06e-163)
       t_0
       (if (<= x1 5e-178)
         (- (* x2 -6.0) x1)
         (if (<= x1 1.4e+154) t_0 (/ (* x1 x1) (- x1 (* x2 -6.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0));
	double tmp;
	if (x1 <= -2.25e+77) {
		tmp = x1 - (x2 * (((x1 * x1) * -6.0) + 10.0));
	} else if (x1 <= -1.06e-163) {
		tmp = t_0;
	} else if (x1 <= 5e-178) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 1.4e+154) {
		tmp = t_0;
	} else {
		tmp = (x1 * x1) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + ((x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)) + (x2 * (-6.0d0)))
    if (x1 <= (-2.25d+77)) then
        tmp = x1 - (x2 * (((x1 * x1) * (-6.0d0)) + 10.0d0))
    else if (x1 <= (-1.06d-163)) then
        tmp = t_0
    else if (x1 <= 5d-178) then
        tmp = (x2 * (-6.0d0)) - x1
    else if (x1 <= 1.4d+154) then
        tmp = t_0
    else
        tmp = (x1 * x1) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0));
	double tmp;
	if (x1 <= -2.25e+77) {
		tmp = x1 - (x2 * (((x1 * x1) * -6.0) + 10.0));
	} else if (x1 <= -1.06e-163) {
		tmp = t_0;
	} else if (x1 <= 5e-178) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 1.4e+154) {
		tmp = t_0;
	} else {
		tmp = (x1 * x1) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0))
	tmp = 0
	if x1 <= -2.25e+77:
		tmp = x1 - (x2 * (((x1 * x1) * -6.0) + 10.0))
	elif x1 <= -1.06e-163:
		tmp = t_0
	elif x1 <= 5e-178:
		tmp = (x2 * -6.0) - x1
	elif x1 <= 1.4e+154:
		tmp = t_0
	else:
		tmp = (x1 * x1) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0)) + Float64(x2 * -6.0)))
	tmp = 0.0
	if (x1 <= -2.25e+77)
		tmp = Float64(x1 - Float64(x2 * Float64(Float64(Float64(x1 * x1) * -6.0) + 10.0)));
	elseif (x1 <= -1.06e-163)
		tmp = t_0;
	elseif (x1 <= 5e-178)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	elseif (x1 <= 1.4e+154)
		tmp = t_0;
	else
		tmp = Float64(Float64(x1 * x1) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0));
	tmp = 0.0;
	if (x1 <= -2.25e+77)
		tmp = x1 - (x2 * (((x1 * x1) * -6.0) + 10.0));
	elseif (x1 <= -1.06e-163)
		tmp = t_0;
	elseif (x1 <= 5e-178)
		tmp = (x2 * -6.0) - x1;
	elseif (x1 <= 1.4e+154)
		tmp = t_0;
	else
		tmp = (x1 * x1) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.25e+77], N[(x1 - N[(x2 * N[(N[(N[(x1 * x1), $MachinePrecision] * -6.0), $MachinePrecision] + 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.06e-163], t$95$0, If[LessEqual[x1, 5e-178], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 1.4e+154], t$95$0, N[(N[(x1 * x1), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.25000000000000012e77

   1. Initial program 14.8%

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

   2. Taylor expanded in x1 around inf 14.8%

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

   3. Taylor expanded in x1 around 0 0.3%

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

      1. sub-neg 0.3%

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

      2. metadata-eval 0.3%

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

      3. distribute-lft-in 0.3%

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

      4. *-commutative 0.3%

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

      5. associate-*l* 0.3%

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

      6. metadata-eval 0.3%

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

      7. metadata-eval 0.3%

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

      8. distribute-rgt-in 0.3%

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

      9. +-commutative 0.3%

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

      10. distribute-lft-in 0.3%

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

      11. metadata-eval 0.3%

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

      12. associate-*r* 0.3%

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

      13. metadata-eval 0.3%

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

   5. Simplified 0.3%

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

   6. Taylor expanded in x1 around 0 51.4%

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

      1. +-commutative 51.4%

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

      2. +-commutative 51.4%

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

      3. associate-+l+ 51.4%

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

      4. metadata-eval 51.4%

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

      5. distribute-lft-neg-in 51.4%

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

      6. mul-1-neg 51.4%

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

      7. distribute-neg-in 51.4%

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

      8. fma-udef 51.4%

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

      9. unsub-neg 51.4%

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

      10. *-commutative 51.4%

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

      11. unpow2 51.4%

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

      12. associate-*l* 51.4%

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

      13. cancel-sign-sub-inv 51.4%

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

      14. metadata-eval 51.4%

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

      15. +-commutative 51.4%

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

      16. count-2 51.4%

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

   8. Simplified 51.4%

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

   9. Taylor expanded in x2 around -inf 37.5%

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

       1. mul-1-neg 37.5%

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

       2. *-commutative 37.5%

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

       3. distribute-rgt-neg-in 37.5%

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

       4. distribute-rgt-in 37.5%

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

       5. metadata-eval 37.5%

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

       6. associate-+l+ 37.5%

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

       7. *-commutative 37.5%

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

       8. associate-*l* 37.5%

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

       9. metadata-eval 37.5%

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

       10. unpow2 37.5%

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

       11. metadata-eval 37.5%

           \[\leadsto x1 + \left(\left(x1 \cdot x1\right) \cdot -6 + \color{blue}{10}\right) \cdot \left(-x2\right) \]

   11. Simplified 37.5%

       \[\leadsto x1 + \color{blue}{\left(\left(x1 \cdot x1\right) \cdot -6 + 10\right) \cdot \left(-x2\right)} \]

   if -2.25000000000000012e77 < x1 < -1.06000000000000006e-163 or 4.99999999999999976e-178 < x1 < 1.4e154

   1. Initial program 98.3%

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

   2. Taylor expanded in x1 around 0 70.2%

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

   3. Taylor expanded in x1 around 0 66.6%

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

   if -1.06000000000000006e-163 < x1 < 4.99999999999999976e-178

   1. Initial program 99.6%

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

   2. Taylor expanded in x2 around inf 77.1%

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

      1. associate-/l* 77.1%

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

      2. unpow2 77.1%

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

      3. +-commutative 77.1%

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

      4. unpow2 77.1%

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

      5. fma-udef 77.1%

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

   4. Simplified 77.1%

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

   5. Taylor expanded in x1 around 0 75.8%

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

      1. fma-def 76.0%

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

      2. fma-neg 76.0%

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

      3. unpow2 76.0%

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

      4. metadata-eval 76.0%

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

   7. Simplified 76.0%

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

   8. Taylor expanded in x2 around 0 84.6%

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

      1. associate-+r+ 84.6%

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

      2. +-commutative 84.6%

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

      3. associate-+l+ 84.6%

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

      4. distribute-rgt1-in 84.6%

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

      5. metadata-eval 84.6%

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

      6. mul-1-neg 84.6%

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

      7. sub-neg 84.6%

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

      8. *-commutative 84.6%

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

   10. Simplified 84.6%

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

   if 1.4e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 6.1%

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

      1. *-commutative 6.1%

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

   5. Simplified 6.1%

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

      1. flip-+ 77.4%

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

   7. Applied egg-rr 77.4%

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

      1. swap-sqr 77.4%

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

      2. metadata-eval 77.4%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot \color{blue}{36}}{x1 - x2 \cdot -6} \]

   9. Simplified 77.4%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}} \]

   10. Taylor expanded in x1 around inf 93.5%

       \[\leadsto \frac{\color{blue}{{x1}^{2}}}{x1 - x2 \cdot -6} \]
   11. Step-by-step derivation

       1. unpow2 93.5%

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

   12. Simplified 93.5%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.25 \cdot 10^{+77}:\\ \;\;\;\;x1 - x2 \cdot \left(\left(x1 \cdot x1\right) \cdot -6 + 10\right)\\ \mathbf{elif}\;x1 \leq -1.06 \cdot 10^{-163}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{-178}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 13: 75.8% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(\left(x1 + \left(6 + x2 \cdot -4\right)\right) - 3 \cdot \left(x1 - 3 \cdot \left(x1 \cdot x1\right)\right)\right)\\ t_1 := x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + x2 \cdot -6\right)\\ \mathbf{if}\;x1 \leq -2.4 \cdot 10^{+107}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq -5.5 \cdot 10^{-167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{-178}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 4.4 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (+
          x1
          (- (+ x1 (+ 6.0 (* x2 -4.0))) (* 3.0 (- x1 (* 3.0 (* x1 x1)))))))
        (t_1
         (+
          x1
          (+ (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0)) (* x2 -6.0)))))
   (if (<= x1 -2.4e+107)
     t_0
     (if (<= x1 -5.5e-167)
       t_1
       (if (<= x1 5e-178) (- (* x2 -6.0) x1) (if (<= x1 4.4e+153) t_1 t_0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))));
	double t_1 = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0));
	double tmp;
	if (x1 <= -2.4e+107) {
		tmp = t_0;
	} else if (x1 <= -5.5e-167) {
		tmp = t_1;
	} else if (x1 <= 5e-178) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 4.4e+153) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x1 + ((x1 + (6.0d0 + (x2 * (-4.0d0)))) - (3.0d0 * (x1 - (3.0d0 * (x1 * x1)))))
    t_1 = x1 + ((x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)) + (x2 * (-6.0d0)))
    if (x1 <= (-2.4d+107)) then
        tmp = t_0
    else if (x1 <= (-5.5d-167)) then
        tmp = t_1
    else if (x1 <= 5d-178) then
        tmp = (x2 * (-6.0d0)) - x1
    else if (x1 <= 4.4d+153) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))));
	double t_1 = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0));
	double tmp;
	if (x1 <= -2.4e+107) {
		tmp = t_0;
	} else if (x1 <= -5.5e-167) {
		tmp = t_1;
	} else if (x1 <= 5e-178) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 4.4e+153) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))))
	t_1 = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0))
	tmp = 0
	if x1 <= -2.4e+107:
		tmp = t_0
	elif x1 <= -5.5e-167:
		tmp = t_1
	elif x1 <= 5e-178:
		tmp = (x2 * -6.0) - x1
	elif x1 <= 4.4e+153:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x1 + Float64(6.0 + Float64(x2 * -4.0))) - Float64(3.0 * Float64(x1 - Float64(3.0 * Float64(x1 * x1))))))
	t_1 = Float64(x1 + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0)) + Float64(x2 * -6.0)))
	tmp = 0.0
	if (x1 <= -2.4e+107)
		tmp = t_0;
	elseif (x1 <= -5.5e-167)
		tmp = t_1;
	elseif (x1 <= 5e-178)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	elseif (x1 <= 4.4e+153)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))));
	t_1 = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0));
	tmp = 0.0;
	if (x1 <= -2.4e+107)
		tmp = t_0;
	elseif (x1 <= -5.5e-167)
		tmp = t_1;
	elseif (x1 <= 5e-178)
		tmp = (x2 * -6.0) - x1;
	elseif (x1 <= 4.4e+153)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x1 + N[(6.0 + N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * N[(x1 - N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.4e+107], t$95$0, If[LessEqual[x1, -5.5e-167], t$95$1, If[LessEqual[x1, 5e-178], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 4.4e+153], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.4000000000000001e107 or 4.3999999999999999e153 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around inf 0.0%

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

   3. Taylor expanded in x1 around 0 0.1%

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

      1. sub-neg 0.1%

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

      2. metadata-eval 0.1%

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

      3. distribute-lft-in 0.1%

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

      4. *-commutative 0.1%

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

      5. associate-*l* 0.1%

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

      6. metadata-eval 0.1%

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

      7. metadata-eval 0.1%

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

      8. distribute-rgt-in 0.1%

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

      9. +-commutative 0.1%

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

      10. distribute-lft-in 0.1%

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

      11. metadata-eval 0.1%

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

      12. associate-*r* 0.1%

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

      13. metadata-eval 0.1%

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

   5. Simplified 0.1%

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

   6. Taylor expanded in x1 around 0 61.9%

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

      1. +-commutative 61.9%

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

      2. +-commutative 61.9%

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

      3. associate-+l+ 61.9%

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

      4. metadata-eval 61.9%

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

      5. distribute-lft-neg-in 61.9%

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

      6. mul-1-neg 61.9%

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

      7. distribute-neg-in 61.9%

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

      8. fma-udef 61.9%

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

      9. unsub-neg 61.9%

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

      10. *-commutative 61.9%

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

      11. unpow2 61.9%

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

      12. associate-*l* 61.9%

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

      13. cancel-sign-sub-inv 61.9%

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

      14. metadata-eval 61.9%

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

      15. +-commutative 61.9%

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

      16. count-2 61.9%

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

   8. Simplified 61.9%

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

   9. Taylor expanded in x2 around 0 86.9%

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

       1. *-commutative 86.9%

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

       2. unpow2 86.9%

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

   11. Simplified 86.9%

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

   if -2.4000000000000001e107 < x1 < -5.5000000000000003e-167 or 4.99999999999999976e-178 < x1 < 4.3999999999999999e153

   1. Initial program 98.4%

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

   2. Taylor expanded in x1 around 0 68.7%

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

   3. Taylor expanded in x1 around 0 65.5%

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

   if -5.5000000000000003e-167 < x1 < 4.99999999999999976e-178

   1. Initial program 99.6%

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

   2. Taylor expanded in x2 around inf 77.1%

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

      1. associate-/l* 77.1%

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

      2. unpow2 77.1%

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

      3. +-commutative 77.1%

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

      4. unpow2 77.1%

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

      5. fma-udef 77.1%

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

   4. Simplified 77.1%

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

   5. Taylor expanded in x1 around 0 75.8%

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

      1. fma-def 76.0%

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

      2. fma-neg 76.0%

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

      3. unpow2 76.0%

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

      4. metadata-eval 76.0%

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

   7. Simplified 76.0%

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

   8. Taylor expanded in x2 around 0 84.6%

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

      1. associate-+r+ 84.6%

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

      2. +-commutative 84.6%

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

      3. associate-+l+ 84.6%

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

      4. distribute-rgt1-in 84.6%

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

      5. metadata-eval 84.6%

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

      6. mul-1-neg 84.6%

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

      7. sub-neg 84.6%

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

      8. *-commutative 84.6%

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

   10. Simplified 84.6%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.4 \cdot 10^{+107}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(6 + x2 \cdot -4\right)\right) - 3 \cdot \left(x1 - 3 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.5 \cdot 10^{-167}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{-178}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(6 + x2 \cdot -4\right)\right) - 3 \cdot \left(x1 - 3 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \end{array} \]

Alternative 14: 75.9% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(\left(x1 + \left(6 + x2 \cdot -4\right)\right) - 3 \cdot \left(x1 - 3 \cdot \left(x1 \cdot x1\right)\right)\right)\\ t_1 := x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + x2 \cdot -6\right)\\ \mathbf{if}\;x1 \leq -4.6 \cdot 10^{+108}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq -6.6 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{-177}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) - \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (+
          x1
          (- (+ x1 (+ 6.0 (* x2 -4.0))) (* 3.0 (- x1 (* 3.0 (* x1 x1)))))))
        (t_1
         (+
          x1
          (+ (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0)) (* x2 -6.0)))))
   (if (<= x1 -4.6e+108)
     t_0
     (if (<= x1 -6.6e-239)
       t_1
       (if (<= x1 6e-177)
         (+
          x1
          (-
           (* 3.0 (* x2 -2.0))
           (- (* 4.0 (* x2 (* x1 (- 3.0 (* 2.0 x2))))) x1)))
         (if (<= x1 4.5e+153) t_1 t_0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))));
	double t_1 = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0));
	double tmp;
	if (x1 <= -4.6e+108) {
		tmp = t_0;
	} else if (x1 <= -6.6e-239) {
		tmp = t_1;
	} else if (x1 <= 6e-177) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1));
	} else if (x1 <= 4.5e+153) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x1 + ((x1 + (6.0d0 + (x2 * (-4.0d0)))) - (3.0d0 * (x1 - (3.0d0 * (x1 * x1)))))
    t_1 = x1 + ((x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)) + (x2 * (-6.0d0)))
    if (x1 <= (-4.6d+108)) then
        tmp = t_0
    else if (x1 <= (-6.6d-239)) then
        tmp = t_1
    else if (x1 <= 6d-177) then
        tmp = x1 + ((3.0d0 * (x2 * (-2.0d0))) - ((4.0d0 * (x2 * (x1 * (3.0d0 - (2.0d0 * x2))))) - x1))
    else if (x1 <= 4.5d+153) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))));
	double t_1 = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0));
	double tmp;
	if (x1 <= -4.6e+108) {
		tmp = t_0;
	} else if (x1 <= -6.6e-239) {
		tmp = t_1;
	} else if (x1 <= 6e-177) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1));
	} else if (x1 <= 4.5e+153) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))))
	t_1 = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0))
	tmp = 0
	if x1 <= -4.6e+108:
		tmp = t_0
	elif x1 <= -6.6e-239:
		tmp = t_1
	elif x1 <= 6e-177:
		tmp = x1 + ((3.0 * (x2 * -2.0)) - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1))
	elif x1 <= 4.5e+153:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x1 + Float64(6.0 + Float64(x2 * -4.0))) - Float64(3.0 * Float64(x1 - Float64(3.0 * Float64(x1 * x1))))))
	t_1 = Float64(x1 + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0)) + Float64(x2 * -6.0)))
	tmp = 0.0
	if (x1 <= -4.6e+108)
		tmp = t_0;
	elseif (x1 <= -6.6e-239)
		tmp = t_1;
	elseif (x1 <= 6e-177)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(x2 * -2.0)) - Float64(Float64(4.0 * Float64(x2 * Float64(x1 * Float64(3.0 - Float64(2.0 * x2))))) - x1)));
	elseif (x1 <= 4.5e+153)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))));
	t_1 = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0));
	tmp = 0.0;
	if (x1 <= -4.6e+108)
		tmp = t_0;
	elseif (x1 <= -6.6e-239)
		tmp = t_1;
	elseif (x1 <= 6e-177)
		tmp = x1 + ((3.0 * (x2 * -2.0)) - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1));
	elseif (x1 <= 4.5e+153)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x1 + N[(6.0 + N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * N[(x1 - N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.6e+108], t$95$0, If[LessEqual[x1, -6.6e-239], t$95$1, If[LessEqual[x1, 6e-177], N[(x1 + N[(N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * N[(x2 * N[(x1 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.5e+153], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4.5999999999999998e108 or 4.5000000000000001e153 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around inf 0.0%

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

   3. Taylor expanded in x1 around 0 0.1%

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

      1. sub-neg 0.1%

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

      2. metadata-eval 0.1%

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

      3. distribute-lft-in 0.1%

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

      4. *-commutative 0.1%

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

      5. associate-*l* 0.1%

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

      6. metadata-eval 0.1%

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

      7. metadata-eval 0.1%

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

      8. distribute-rgt-in 0.1%

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

      9. +-commutative 0.1%

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

      10. distribute-lft-in 0.1%

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

      11. metadata-eval 0.1%

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

      12. associate-*r* 0.1%

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

      13. metadata-eval 0.1%

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

   5. Simplified 0.1%

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

   6. Taylor expanded in x1 around 0 61.9%

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

      1. +-commutative 61.9%

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

      2. +-commutative 61.9%

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

      3. associate-+l+ 61.9%

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

      4. metadata-eval 61.9%

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

      5. distribute-lft-neg-in 61.9%

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

      6. mul-1-neg 61.9%

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

      7. distribute-neg-in 61.9%

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

      8. fma-udef 61.9%

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

      9. unsub-neg 61.9%

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

      10. *-commutative 61.9%

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

      11. unpow2 61.9%

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

      12. associate-*l* 61.9%

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

      13. cancel-sign-sub-inv 61.9%

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

      14. metadata-eval 61.9%

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

      15. +-commutative 61.9%

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

      16. count-2 61.9%

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

   8. Simplified 61.9%

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

   9. Taylor expanded in x2 around 0 86.9%

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

       1. *-commutative 86.9%

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

       2. unpow2 86.9%

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

   11. Simplified 86.9%

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

   if -4.5999999999999998e108 < x1 < -6.5999999999999999e-239 or 6.00000000000000015e-177 < x1 < 4.5000000000000001e153

   1. Initial program 98.6%

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

   2. Taylor expanded in x1 around 0 74.4%

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

   3. Taylor expanded in x1 around 0 68.3%

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

   if -6.5999999999999999e-239 < x1 < 6.00000000000000015e-177

   1. Initial program 99.6%

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

   2. Taylor expanded in x1 around 0 99.6%

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

   3. Taylor expanded in x1 around 0 97.8%

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

      1. *-commutative 97.8%

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

   5. Simplified 97.8%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.6 \cdot 10^{+108}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(6 + x2 \cdot -4\right)\right) - 3 \cdot \left(x1 - 3 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -6.6 \cdot 10^{-239}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{-177}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) - \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(6 + x2 \cdot -4\right)\right) - 3 \cdot \left(x1 - 3 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \end{array} \]

Alternative 15: 79.6% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.15 \cdot 10^{+108} \lor \neg \left(x1 \leq 4.5 \cdot 10^{+153}\right):\\ \;\;\;\;x1 + \left(\left(x1 + \left(6 + x2 \cdot -4\right)\right) - 3 \cdot \left(x1 - 3 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -1.15e+108) (not (<= x1 4.5e+153)))
   (+ x1 (- (+ x1 (+ 6.0 (* x2 -4.0))) (* 3.0 (- x1 (* 3.0 (* x1 x1))))))
   (+
    x1
    (+
     (+ x1 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0)))))
     (* 3.0 (- (* x2 -2.0) x1))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -1.15e+108) || !(x1 <= 4.5e+153)) {
		tmp = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))));
	} else {
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))) + (3.0 * ((x2 * -2.0) - x1)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-1.15d+108)) .or. (.not. (x1 <= 4.5d+153))) then
        tmp = x1 + ((x1 + (6.0d0 + (x2 * (-4.0d0)))) - (3.0d0 * (x1 - (3.0d0 * (x1 * x1)))))
    else
        tmp = x1 + ((x1 + (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0))))) + (3.0d0 * ((x2 * (-2.0d0)) - x1)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -1.15e+108) || !(x1 <= 4.5e+153)) {
		tmp = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))));
	} else {
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))) + (3.0 * ((x2 * -2.0) - x1)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -1.15e+108) or not (x1 <= 4.5e+153):
		tmp = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))))
	else:
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))) + (3.0 * ((x2 * -2.0) - x1)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -1.15e+108) || !(x1 <= 4.5e+153))
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(6.0 + Float64(x2 * -4.0))) - Float64(3.0 * Float64(x1 - Float64(3.0 * Float64(x1 * x1))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0))))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -1.15e+108) || ~((x1 <= 4.5e+153)))
		tmp = x1 + ((x1 + (6.0 + (x2 * -4.0))) - (3.0 * (x1 - (3.0 * (x1 * x1)))));
	else
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))) + (3.0 * ((x2 * -2.0) - x1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -1.15e+108], N[Not[LessEqual[x1, 4.5e+153]], $MachinePrecision]], N[(x1 + N[(N[(x1 + N[(6.0 + N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * N[(x1 - N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.1499999999999999e108 or 4.5000000000000001e153 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around inf 0.0%

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

   3. Taylor expanded in x1 around 0 0.1%

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

      1. sub-neg 0.1%

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

      2. metadata-eval 0.1%

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

      3. distribute-lft-in 0.1%

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

      4. *-commutative 0.1%

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

      5. associate-*l* 0.1%

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

      6. metadata-eval 0.1%

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

      7. metadata-eval 0.1%

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

      8. distribute-rgt-in 0.1%

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

      9. +-commutative 0.1%

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

      10. distribute-lft-in 0.1%

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

      11. metadata-eval 0.1%

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

      12. associate-*r* 0.1%

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

      13. metadata-eval 0.1%

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

   5. Simplified 0.1%

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

   6. Taylor expanded in x1 around 0 61.9%

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

      1. +-commutative 61.9%

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

      2. +-commutative 61.9%

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

      3. associate-+l+ 61.9%

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

      4. metadata-eval 61.9%

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

      5. distribute-lft-neg-in 61.9%

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

      6. mul-1-neg 61.9%

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

      7. distribute-neg-in 61.9%

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

      8. fma-udef 61.9%

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

      9. unsub-neg 61.9%

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

      10. *-commutative 61.9%

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

      11. unpow2 61.9%

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

      12. associate-*l* 61.9%

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

      13. cancel-sign-sub-inv 61.9%

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

      14. metadata-eval 61.9%

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

      15. +-commutative 61.9%

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

      16. count-2 61.9%

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

   8. Simplified 61.9%

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

   9. Taylor expanded in x2 around 0 86.9%

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

       1. *-commutative 86.9%

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

       2. unpow2 86.9%

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

   11. Simplified 86.9%

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

   if -1.1499999999999999e108 < x1 < 4.5000000000000001e153

   1. Initial program 98.8%

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

   2. Taylor expanded in x1 around 0 80.5%

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

   3. Taylor expanded in x1 around 0 79.8%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.15 \cdot 10^{+108} \lor \neg \left(x1 \leq 4.5 \cdot 10^{+153}\right):\\ \;\;\;\;x1 + \left(\left(x1 + \left(6 + x2 \cdot -4\right)\right) - 3 \cdot \left(x1 - 3 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \end{array} \]

Alternative 16: 60.9% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.05 \cdot 10^{+77}:\\ \;\;\;\;x1 - x2 \cdot \left(\left(x1 \cdot x1\right) \cdot -6 + 10\right)\\ \mathbf{elif}\;x1 \leq 1.85 \cdot 10^{-9}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -2.05e+77)
   (- x1 (* x2 (+ (* (* x1 x1) -6.0) 10.0)))
   (if (<= x1 1.85e-9)
     (- (* x2 -6.0) x1)
     (if (<= x1 1.4e+154)
       (+ x1 (* x1 (+ 1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))))
       (/ (* x1 x1) (- x1 (* x2 -6.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.05e+77) {
		tmp = x1 - (x2 * (((x1 * x1) * -6.0) + 10.0));
	} else if (x1 <= 1.85e-9) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 1.4e+154) {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	} else {
		tmp = (x1 * x1) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-2.05d+77)) then
        tmp = x1 - (x2 * (((x1 * x1) * (-6.0d0)) + 10.0d0))
    else if (x1 <= 1.85d-9) then
        tmp = (x2 * (-6.0d0)) - x1
    else if (x1 <= 1.4d+154) then
        tmp = x1 + (x1 * (1.0d0 + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0)))))
    else
        tmp = (x1 * x1) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.05e+77) {
		tmp = x1 - (x2 * (((x1 * x1) * -6.0) + 10.0));
	} else if (x1 <= 1.85e-9) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 1.4e+154) {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	} else {
		tmp = (x1 * x1) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -2.05e+77:
		tmp = x1 - (x2 * (((x1 * x1) * -6.0) + 10.0))
	elif x1 <= 1.85e-9:
		tmp = (x2 * -6.0) - x1
	elif x1 <= 1.4e+154:
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))))
	else:
		tmp = (x1 * x1) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -2.05e+77)
		tmp = Float64(x1 - Float64(x2 * Float64(Float64(Float64(x1 * x1) * -6.0) + 10.0)));
	elseif (x1 <= 1.85e-9)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	elseif (x1 <= 1.4e+154)
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))));
	else
		tmp = Float64(Float64(x1 * x1) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -2.05e+77)
		tmp = x1 - (x2 * (((x1 * x1) * -6.0) + 10.0));
	elseif (x1 <= 1.85e-9)
		tmp = (x2 * -6.0) - x1;
	elseif (x1 <= 1.4e+154)
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	else
		tmp = (x1 * x1) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -2.05e+77], N[(x1 - N[(x2 * N[(N[(N[(x1 * x1), $MachinePrecision] * -6.0), $MachinePrecision] + 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.85e-9], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 1.4e+154], N[(x1 + N[(x1 * N[(1.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x1 * x1), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.05e77

   1. Initial program 14.8%

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

   2. Taylor expanded in x1 around inf 14.8%

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

   3. Taylor expanded in x1 around 0 0.3%

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

      1. sub-neg 0.3%

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

      2. metadata-eval 0.3%

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

      3. distribute-lft-in 0.3%

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

      4. *-commutative 0.3%

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

      5. associate-*l* 0.3%

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

      6. metadata-eval 0.3%

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

      7. metadata-eval 0.3%

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

      8. distribute-rgt-in 0.3%

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

      9. +-commutative 0.3%

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

      10. distribute-lft-in 0.3%

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

      11. metadata-eval 0.3%

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

      12. associate-*r* 0.3%

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

      13. metadata-eval 0.3%

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

   5. Simplified 0.3%

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

   6. Taylor expanded in x1 around 0 51.4%

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

      1. +-commutative 51.4%

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

      2. +-commutative 51.4%

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

      3. associate-+l+ 51.4%

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

      4. metadata-eval 51.4%

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

      5. distribute-lft-neg-in 51.4%

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

      6. mul-1-neg 51.4%

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

      7. distribute-neg-in 51.4%

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

      8. fma-udef 51.4%

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

      9. unsub-neg 51.4%

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

      10. *-commutative 51.4%

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

      11. unpow2 51.4%

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

      12. associate-*l* 51.4%

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

      13. cancel-sign-sub-inv 51.4%

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

      14. metadata-eval 51.4%

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

      15. +-commutative 51.4%

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

      16. count-2 51.4%

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

   8. Simplified 51.4%

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

   9. Taylor expanded in x2 around -inf 37.5%

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

       1. mul-1-neg 37.5%

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

       2. *-commutative 37.5%

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

       3. distribute-rgt-neg-in 37.5%

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

       4. distribute-rgt-in 37.5%

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

       5. metadata-eval 37.5%

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

       6. associate-+l+ 37.5%

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

       7. *-commutative 37.5%

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

       8. associate-*l* 37.5%

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

       9. metadata-eval 37.5%

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

       10. unpow2 37.5%

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

       11. metadata-eval 37.5%

           \[\leadsto x1 + \left(\left(x1 \cdot x1\right) \cdot -6 + \color{blue}{10}\right) \cdot \left(-x2\right) \]

   11. Simplified 37.5%

       \[\leadsto x1 + \color{blue}{\left(\left(x1 \cdot x1\right) \cdot -6 + 10\right) \cdot \left(-x2\right)} \]

   if -2.05e77 < x1 < 1.85e-9

   1. Initial program 98.7%

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

   2. Taylor expanded in x2 around inf 80.0%

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

      1. associate-/l* 79.9%

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

      2. unpow2 79.9%

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

      3. +-commutative 79.9%

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

      4. unpow2 79.9%

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

      5. fma-udef 79.9%

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

   4. Simplified 79.9%

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

   5. Taylor expanded in x1 around 0 78.6%

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

      1. fma-def 78.7%

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

      2. fma-neg 78.7%

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

      3. unpow2 78.7%

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

      4. metadata-eval 78.7%

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

   7. Simplified 78.7%

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

   8. Taylor expanded in x2 around 0 68.1%

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

      1. associate-+r+ 68.1%

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

      2. +-commutative 68.1%

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

      3. associate-+l+ 68.1%

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

      4. distribute-rgt1-in 68.1%

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

      5. metadata-eval 68.1%

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

      6. mul-1-neg 68.1%

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

      7. sub-neg 68.1%

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

      8. *-commutative 68.1%

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

   10. Simplified 68.1%

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

   if 1.85e-9 < x1 < 1.4e154

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 30.5%

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

   3. Taylor expanded in x1 around inf 30.5%

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

   if 1.4e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 6.1%

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

      1. *-commutative 6.1%

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

   5. Simplified 6.1%

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

      1. flip-+ 77.4%

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

   7. Applied egg-rr 77.4%

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

      1. swap-sqr 77.4%

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

      2. metadata-eval 77.4%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot \color{blue}{36}}{x1 - x2 \cdot -6} \]

   9. Simplified 77.4%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}} \]

   10. Taylor expanded in x1 around inf 93.5%

       \[\leadsto \frac{\color{blue}{{x1}^{2}}}{x1 - x2 \cdot -6} \]
   11. Step-by-step derivation

       1. unpow2 93.5%

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

   12. Simplified 93.5%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.05 \cdot 10^{+77}:\\ \;\;\;\;x1 - x2 \cdot \left(\left(x1 \cdot x1\right) \cdot -6 + 10\right)\\ \mathbf{elif}\;x1 \leq 1.85 \cdot 10^{-9}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 17: 57.4% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x1 \cdot \left(x2 \cdot x2\right)\right) \cdot 8\\ t_1 := x1 - x2 \cdot -6\\ \mathbf{if}\;x1 \leq -2.15 \cdot 10^{+106}:\\ \;\;\;\;\frac{\left(x2 \cdot x2\right) \cdot -36}{t_1}\\ \mathbf{elif}\;x1 \leq -8.5 \cdot 10^{-17}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 1.02 \cdot 10^{-8}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* (* x1 (* x2 x2)) 8.0))) (t_1 (- x1 (* x2 -6.0))))
   (if (<= x1 -2.15e+106)
     (/ (* (* x2 x2) -36.0) t_1)
     (if (<= x1 -8.5e-17)
       t_0
       (if (<= x1 1.02e-8)
         (- (* x2 -6.0) x1)
         (if (<= x1 1.4e+154) t_0 (/ (* x1 x1) t_1)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x1 * (x2 * x2)) * 8.0);
	double t_1 = x1 - (x2 * -6.0);
	double tmp;
	if (x1 <= -2.15e+106) {
		tmp = ((x2 * x2) * -36.0) / t_1;
	} else if (x1 <= -8.5e-17) {
		tmp = t_0;
	} else if (x1 <= 1.02e-8) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 1.4e+154) {
		tmp = t_0;
	} else {
		tmp = (x1 * x1) / t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x1 + ((x1 * (x2 * x2)) * 8.0d0)
    t_1 = x1 - (x2 * (-6.0d0))
    if (x1 <= (-2.15d+106)) then
        tmp = ((x2 * x2) * (-36.0d0)) / t_1
    else if (x1 <= (-8.5d-17)) then
        tmp = t_0
    else if (x1 <= 1.02d-8) then
        tmp = (x2 * (-6.0d0)) - x1
    else if (x1 <= 1.4d+154) then
        tmp = t_0
    else
        tmp = (x1 * x1) / t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x1 * (x2 * x2)) * 8.0);
	double t_1 = x1 - (x2 * -6.0);
	double tmp;
	if (x1 <= -2.15e+106) {
		tmp = ((x2 * x2) * -36.0) / t_1;
	} else if (x1 <= -8.5e-17) {
		tmp = t_0;
	} else if (x1 <= 1.02e-8) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 1.4e+154) {
		tmp = t_0;
	} else {
		tmp = (x1 * x1) / t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x1 * (x2 * x2)) * 8.0)
	t_1 = x1 - (x2 * -6.0)
	tmp = 0
	if x1 <= -2.15e+106:
		tmp = ((x2 * x2) * -36.0) / t_1
	elif x1 <= -8.5e-17:
		tmp = t_0
	elif x1 <= 1.02e-8:
		tmp = (x2 * -6.0) - x1
	elif x1 <= 1.4e+154:
		tmp = t_0
	else:
		tmp = (x1 * x1) / t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x1 * Float64(x2 * x2)) * 8.0))
	t_1 = Float64(x1 - Float64(x2 * -6.0))
	tmp = 0.0
	if (x1 <= -2.15e+106)
		tmp = Float64(Float64(Float64(x2 * x2) * -36.0) / t_1);
	elseif (x1 <= -8.5e-17)
		tmp = t_0;
	elseif (x1 <= 1.02e-8)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	elseif (x1 <= 1.4e+154)
		tmp = t_0;
	else
		tmp = Float64(Float64(x1 * x1) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x1 * (x2 * x2)) * 8.0);
	t_1 = x1 - (x2 * -6.0);
	tmp = 0.0;
	if (x1 <= -2.15e+106)
		tmp = ((x2 * x2) * -36.0) / t_1;
	elseif (x1 <= -8.5e-17)
		tmp = t_0;
	elseif (x1 <= 1.02e-8)
		tmp = (x2 * -6.0) - x1;
	elseif (x1 <= 1.4e+154)
		tmp = t_0;
	else
		tmp = (x1 * x1) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x1 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.15e+106], N[(N[(N[(x2 * x2), $MachinePrecision] * -36.0), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[x1, -8.5e-17], t$95$0, If[LessEqual[x1, 1.02e-8], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 1.4e+154], t$95$0, N[(N[(x1 * x1), $MachinePrecision] / t$95$1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.15e106

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.1%

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

   3. Taylor expanded in x1 around 0 0.7%

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

      1. *-commutative 0.7%

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

   5. Simplified 0.7%

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

      1. flip-+ 2.2%

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

   7. Applied egg-rr 2.2%

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

      1. swap-sqr 2.2%

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

      2. metadata-eval 2.2%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot \color{blue}{36}}{x1 - x2 \cdot -6} \]

   9. Simplified 2.2%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}} \]

   10. Taylor expanded in x1 around 0 23.2%

       \[\leadsto \frac{\color{blue}{-36 \cdot {x2}^{2}}}{x1 - x2 \cdot -6} \]
   11. Step-by-step derivation

       1. unpow2 23.2%

          \[\leadsto \frac{-36 \cdot \color{blue}{\left(x2 \cdot x2\right)}}{x1 - x2 \cdot -6} \]

   12. Simplified 23.2%

       \[\leadsto \frac{\color{blue}{-36 \cdot \left(x2 \cdot x2\right)}}{x1 - x2 \cdot -6} \]

   if -2.15e106 < x1 < -8.5e-17 or 1.02000000000000003e-8 < x1 < 1.4e154

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 31.5%

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

   3. Taylor expanded in x2 around inf 31.5%

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

      1. *-commutative 31.5%

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

      2. *-commutative 31.5%

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

      3. unpow2 31.5%

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

   5. Simplified 31.5%

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

   if -8.5e-17 < x1 < 1.02000000000000003e-8

   1. Initial program 98.7%

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

   2. Taylor expanded in x2 around inf 85.5%

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

      1. associate-/l* 85.5%

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

      2. unpow2 85.5%

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

      3. +-commutative 85.5%

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

      4. unpow2 85.5%

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

      5. fma-udef 85.5%

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

   4. Simplified 85.5%

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

   5. Taylor expanded in x1 around 0 84.3%

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

      1. fma-def 84.5%

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

      2. fma-neg 84.5%

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

      3. unpow2 84.5%

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

      4. metadata-eval 84.5%

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

   7. Simplified 84.5%

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

   8. Taylor expanded in x2 around 0 75.0%

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

      1. associate-+r+ 75.0%

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

      2. +-commutative 75.0%

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

      3. associate-+l+ 75.0%

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

      4. distribute-rgt1-in 75.0%

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

      5. metadata-eval 75.0%

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

      6. mul-1-neg 75.0%

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

      7. sub-neg 75.0%

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

      8. *-commutative 75.0%

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

   10. Simplified 75.0%

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

   if 1.4e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 6.1%

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

      1. *-commutative 6.1%

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

   5. Simplified 6.1%

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

      1. flip-+ 77.4%

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

   7. Applied egg-rr 77.4%

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

      1. swap-sqr 77.4%

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

      2. metadata-eval 77.4%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot \color{blue}{36}}{x1 - x2 \cdot -6} \]

   9. Simplified 77.4%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}} \]

   10. Taylor expanded in x1 around inf 93.5%

       \[\leadsto \frac{\color{blue}{{x1}^{2}}}{x1 - x2 \cdot -6} \]
   11. Step-by-step derivation

       1. unpow2 93.5%

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

   12. Simplified 93.5%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.15 \cdot 10^{+106}:\\ \;\;\;\;\frac{\left(x2 \cdot x2\right) \cdot -36}{x1 - x2 \cdot -6}\\ \mathbf{elif}\;x1 \leq -8.5 \cdot 10^{-17}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x2 \cdot x2\right)\right) \cdot 8\\ \mathbf{elif}\;x1 \leq 1.02 \cdot 10^{-8}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x2 \cdot x2\right)\right) \cdot 8\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 18: 60.9% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.05 \cdot 10^{+77}:\\ \;\;\;\;x1 - x2 \cdot \left(\left(x1 \cdot x1\right) \cdot -6 + 10\right)\\ \mathbf{elif}\;x1 \leq 1.15 \cdot 10^{-9}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x2 \cdot x2\right)\right) \cdot 8\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -2.05e+77)
   (- x1 (* x2 (+ (* (* x1 x1) -6.0) 10.0)))
   (if (<= x1 1.15e-9)
     (- (* x2 -6.0) x1)
     (if (<= x1 1.4e+154)
       (+ x1 (* (* x1 (* x2 x2)) 8.0))
       (/ (* x1 x1) (- x1 (* x2 -6.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.05e+77) {
		tmp = x1 - (x2 * (((x1 * x1) * -6.0) + 10.0));
	} else if (x1 <= 1.15e-9) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 1.4e+154) {
		tmp = x1 + ((x1 * (x2 * x2)) * 8.0);
	} else {
		tmp = (x1 * x1) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-2.05d+77)) then
        tmp = x1 - (x2 * (((x1 * x1) * (-6.0d0)) + 10.0d0))
    else if (x1 <= 1.15d-9) then
        tmp = (x2 * (-6.0d0)) - x1
    else if (x1 <= 1.4d+154) then
        tmp = x1 + ((x1 * (x2 * x2)) * 8.0d0)
    else
        tmp = (x1 * x1) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.05e+77) {
		tmp = x1 - (x2 * (((x1 * x1) * -6.0) + 10.0));
	} else if (x1 <= 1.15e-9) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 1.4e+154) {
		tmp = x1 + ((x1 * (x2 * x2)) * 8.0);
	} else {
		tmp = (x1 * x1) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -2.05e+77:
		tmp = x1 - (x2 * (((x1 * x1) * -6.0) + 10.0))
	elif x1 <= 1.15e-9:
		tmp = (x2 * -6.0) - x1
	elif x1 <= 1.4e+154:
		tmp = x1 + ((x1 * (x2 * x2)) * 8.0)
	else:
		tmp = (x1 * x1) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -2.05e+77)
		tmp = Float64(x1 - Float64(x2 * Float64(Float64(Float64(x1 * x1) * -6.0) + 10.0)));
	elseif (x1 <= 1.15e-9)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	elseif (x1 <= 1.4e+154)
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(x2 * x2)) * 8.0));
	else
		tmp = Float64(Float64(x1 * x1) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -2.05e+77)
		tmp = x1 - (x2 * (((x1 * x1) * -6.0) + 10.0));
	elseif (x1 <= 1.15e-9)
		tmp = (x2 * -6.0) - x1;
	elseif (x1 <= 1.4e+154)
		tmp = x1 + ((x1 * (x2 * x2)) * 8.0);
	else
		tmp = (x1 * x1) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -2.05e+77], N[(x1 - N[(x2 * N[(N[(N[(x1 * x1), $MachinePrecision] * -6.0), $MachinePrecision] + 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.15e-9], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 1.4e+154], N[(x1 + N[(N[(x1 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision], N[(N[(x1 * x1), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.05e77

   1. Initial program 14.8%

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

   2. Taylor expanded in x1 around inf 14.8%

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

   3. Taylor expanded in x1 around 0 0.3%

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

      1. sub-neg 0.3%

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

      2. metadata-eval 0.3%

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

      3. distribute-lft-in 0.3%

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

      4. *-commutative 0.3%

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

      5. associate-*l* 0.3%

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

      6. metadata-eval 0.3%

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

      7. metadata-eval 0.3%

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

      8. distribute-rgt-in 0.3%

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

      9. +-commutative 0.3%

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

      10. distribute-lft-in 0.3%

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

      11. metadata-eval 0.3%

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

      12. associate-*r* 0.3%

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

      13. metadata-eval 0.3%

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

   5. Simplified 0.3%

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

   6. Taylor expanded in x1 around 0 51.4%

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

      1. +-commutative 51.4%

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

      2. +-commutative 51.4%

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

      3. associate-+l+ 51.4%

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

      4. metadata-eval 51.4%

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

      5. distribute-lft-neg-in 51.4%

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

      6. mul-1-neg 51.4%

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

      7. distribute-neg-in 51.4%

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

      8. fma-udef 51.4%

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

      9. unsub-neg 51.4%

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

      10. *-commutative 51.4%

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

      11. unpow2 51.4%

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

      12. associate-*l* 51.4%

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

      13. cancel-sign-sub-inv 51.4%

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

      14. metadata-eval 51.4%

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

      15. +-commutative 51.4%

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

      16. count-2 51.4%

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

   8. Simplified 51.4%

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

   9. Taylor expanded in x2 around -inf 37.5%

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

       1. mul-1-neg 37.5%

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

       2. *-commutative 37.5%

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

       3. distribute-rgt-neg-in 37.5%

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

       4. distribute-rgt-in 37.5%

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

       5. metadata-eval 37.5%

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

       6. associate-+l+ 37.5%

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

       7. *-commutative 37.5%

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

       8. associate-*l* 37.5%

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

       9. metadata-eval 37.5%

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

       10. unpow2 37.5%

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

       11. metadata-eval 37.5%

           \[\leadsto x1 + \left(\left(x1 \cdot x1\right) \cdot -6 + \color{blue}{10}\right) \cdot \left(-x2\right) \]

   11. Simplified 37.5%

       \[\leadsto x1 + \color{blue}{\left(\left(x1 \cdot x1\right) \cdot -6 + 10\right) \cdot \left(-x2\right)} \]

   if -2.05e77 < x1 < 1.15e-9

   1. Initial program 98.7%

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

   2. Taylor expanded in x2 around inf 80.0%

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

      1. associate-/l* 79.9%

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

      2. unpow2 79.9%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{\color{blue}{x2 \cdot x2}}{\frac{1 + {x1}^{2}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      3. +-commutative 79.9%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{{x1}^{2} + 1}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      4. unpow2 79.9%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{x1 \cdot x1} + 1}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      5. fma-udef 79.9%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Simplified 79.9%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Taylor expanded in x1 around 0 78.6%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)} \]
   6. Step-by-step derivation

      1. fma-def 78.7%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)} \]

      2. fma-neg 78.7%

         \[\leadsto x1 + \mathsf{fma}\left(-6, x2, x1 \cdot \color{blue}{\mathsf{fma}\left(8, {x2}^{2}, -2\right)}\right) \]

      3. unpow2 78.7%

         \[\leadsto x1 + \mathsf{fma}\left(-6, x2, x1 \cdot \mathsf{fma}\left(8, \color{blue}{x2 \cdot x2}, -2\right)\right) \]

      4. metadata-eval 78.7%

         \[\leadsto x1 + \mathsf{fma}\left(-6, x2, x1 \cdot \mathsf{fma}\left(8, x2 \cdot x2, \color{blue}{-2}\right)\right) \]

   7. Simplified 78.7%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \mathsf{fma}\left(8, x2 \cdot x2, -2\right)\right)} \]

   8. Taylor expanded in x2 around 0 68.1%

      \[\leadsto \color{blue}{x1 + \left(-6 \cdot x2 + -2 \cdot x1\right)} \]
   9. Step-by-step derivation

      1. associate-+r+ 68.1%

         \[\leadsto \color{blue}{\left(x1 + -6 \cdot x2\right) + -2 \cdot x1} \]

      2. +-commutative 68.1%

         \[\leadsto \color{blue}{\left(-6 \cdot x2 + x1\right)} + -2 \cdot x1 \]

      3. associate-+l+ 68.1%

         \[\leadsto \color{blue}{-6 \cdot x2 + \left(x1 + -2 \cdot x1\right)} \]

      4. distribute-rgt1-in 68.1%

         \[\leadsto -6 \cdot x2 + \color{blue}{\left(-2 + 1\right) \cdot x1} \]

      5. metadata-eval 68.1%

         \[\leadsto -6 \cdot x2 + \color{blue}{-1} \cdot x1 \]

      6. mul-1-neg 68.1%

         \[\leadsto -6 \cdot x2 + \color{blue}{\left(-x1\right)} \]

      7. sub-neg 68.1%

         \[\leadsto \color{blue}{-6 \cdot x2 - x1} \]

      8. *-commutative 68.1%

         \[\leadsto \color{blue}{x2 \cdot -6} - x1 \]

   10. Simplified 68.1%

       \[\leadsto \color{blue}{x2 \cdot -6 - x1} \]

   if 1.15e-9 < x1 < 1.4e154

   1. Initial program 99.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 30.5%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x2 around inf 30.5%

      \[\leadsto x1 + \color{blue}{8 \cdot \left({x2}^{2} \cdot x1\right)} \]
   4. Step-by-step derivation

      1. *-commutative 30.5%

         \[\leadsto x1 + \color{blue}{\left({x2}^{2} \cdot x1\right) \cdot 8} \]

      2. *-commutative 30.5%

         \[\leadsto x1 + \color{blue}{\left(x1 \cdot {x2}^{2}\right)} \cdot 8 \]

      3. unpow2 30.5%

         \[\leadsto x1 + \left(x1 \cdot \color{blue}{\left(x2 \cdot x2\right)}\right) \cdot 8 \]

   5. Simplified 30.5%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(x2 \cdot x2\right)\right) \cdot 8} \]

   if 1.4e154 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 6.1%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 6.1%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 6.1%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
   6. Step-by-step derivation

      1. flip-+ 77.4%

         \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]

   7. Applied egg-rr 77.4%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]
   8. Step-by-step derivation

      1. swap-sqr 77.4%

         \[\leadsto \frac{x1 \cdot x1 - \color{blue}{\left(x2 \cdot x2\right) \cdot \left(-6 \cdot -6\right)}}{x1 - x2 \cdot -6} \]

      2. metadata-eval 77.4%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot \color{blue}{36}}{x1 - x2 \cdot -6} \]

   9. Simplified 77.4%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}} \]

   10. Taylor expanded in x1 around inf 93.5%

       \[\leadsto \frac{\color{blue}{{x1}^{2}}}{x1 - x2 \cdot -6} \]
   11. Step-by-step derivation

       1. unpow2 93.5%

          \[\leadsto \frac{\color{blue}{x1 \cdot x1}}{x1 - x2 \cdot -6} \]

   12. Simplified 93.5%

       \[\leadsto \frac{\color{blue}{x1 \cdot x1}}{x1 - x2 \cdot -6} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.05 \cdot 10^{+77}:\\ \;\;\;\;x1 - x2 \cdot \left(\left(x1 \cdot x1\right) \cdot -6 + 10\right)\\ \mathbf{elif}\;x1 \leq 1.15 \cdot 10^{-9}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x2 \cdot x2\right)\right) \cdot 8\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 19: 48.9% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -4.8 \cdot 10^{+126} \lor \neg \left(x2 \leq 4.2 \cdot 10^{+41}\right):\\ \;\;\;\;x1 + \left(x1 \cdot \left(x2 \cdot x2\right)\right) \cdot 8\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -4.8e+126) (not (<= x2 4.2e+41)))
   (+ x1 (* (* x1 (* x2 x2)) 8.0))
   (- (* x2 -6.0) x1)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -4.8e+126) || !(x2 <= 4.2e+41)) {
		tmp = x1 + ((x1 * (x2 * x2)) * 8.0);
	} else {
		tmp = (x2 * -6.0) - x1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-4.8d+126)) .or. (.not. (x2 <= 4.2d+41))) then
        tmp = x1 + ((x1 * (x2 * x2)) * 8.0d0)
    else
        tmp = (x2 * (-6.0d0)) - x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -4.8e+126) || !(x2 <= 4.2e+41)) {
		tmp = x1 + ((x1 * (x2 * x2)) * 8.0);
	} else {
		tmp = (x2 * -6.0) - x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -4.8e+126) or not (x2 <= 4.2e+41):
		tmp = x1 + ((x1 * (x2 * x2)) * 8.0)
	else:
		tmp = (x2 * -6.0) - x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -4.8e+126) || !(x2 <= 4.2e+41))
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(x2 * x2)) * 8.0));
	else
		tmp = Float64(Float64(x2 * -6.0) - x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -4.8e+126) || ~((x2 <= 4.2e+41)))
		tmp = x1 + ((x1 * (x2 * x2)) * 8.0);
	else
		tmp = (x2 * -6.0) - x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -4.8e+126], N[Not[LessEqual[x2, 4.2e+41]], $MachinePrecision]], N[(x1 + N[(N[(x1 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -4.80000000000000024e126 or 4.1999999999999999e41 < x2

   1. Initial program 68.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 64.6%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x2 around inf 52.5%

      \[\leadsto x1 + \color{blue}{8 \cdot \left({x2}^{2} \cdot x1\right)} \]
   4. Step-by-step derivation

      1. *-commutative 52.5%

         \[\leadsto x1 + \color{blue}{\left({x2}^{2} \cdot x1\right) \cdot 8} \]

      2. *-commutative 52.5%

         \[\leadsto x1 + \color{blue}{\left(x1 \cdot {x2}^{2}\right)} \cdot 8 \]

      3. unpow2 52.5%

         \[\leadsto x1 + \left(x1 \cdot \color{blue}{\left(x2 \cdot x2\right)}\right) \cdot 8 \]

   5. Simplified 52.5%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(x2 \cdot x2\right)\right) \cdot 8} \]

   if -4.80000000000000024e126 < x2 < 4.1999999999999999e41

   1. Initial program 69.6%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x2 around inf 51.6%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{{x2}^{2} \cdot x1}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   3. Step-by-step derivation

      1. associate-/l* 51.6%

         \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\frac{{x2}^{2}}{\frac{1 + {x1}^{2}}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. unpow2 51.6%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{\color{blue}{x2 \cdot x2}}{\frac{1 + {x1}^{2}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      3. +-commutative 51.6%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{{x1}^{2} + 1}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      4. unpow2 51.6%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{x1 \cdot x1} + 1}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      5. fma-udef 51.6%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Simplified 51.6%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Taylor expanded in x1 around 0 52.7%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)} \]
   6. Step-by-step derivation

      1. fma-def 52.8%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)} \]

      2. fma-neg 52.8%

         \[\leadsto x1 + \mathsf{fma}\left(-6, x2, x1 \cdot \color{blue}{\mathsf{fma}\left(8, {x2}^{2}, -2\right)}\right) \]

      3. unpow2 52.8%

         \[\leadsto x1 + \mathsf{fma}\left(-6, x2, x1 \cdot \mathsf{fma}\left(8, \color{blue}{x2 \cdot x2}, -2\right)\right) \]

      4. metadata-eval 52.8%

         \[\leadsto x1 + \mathsf{fma}\left(-6, x2, x1 \cdot \mathsf{fma}\left(8, x2 \cdot x2, \color{blue}{-2}\right)\right) \]

   7. Simplified 52.8%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \mathsf{fma}\left(8, x2 \cdot x2, -2\right)\right)} \]

   8. Taylor expanded in x2 around 0 51.3%

      \[\leadsto \color{blue}{x1 + \left(-6 \cdot x2 + -2 \cdot x1\right)} \]
   9. Step-by-step derivation

      1. associate-+r+ 51.3%

         \[\leadsto \color{blue}{\left(x1 + -6 \cdot x2\right) + -2 \cdot x1} \]

      2. +-commutative 51.3%

         \[\leadsto \color{blue}{\left(-6 \cdot x2 + x1\right)} + -2 \cdot x1 \]

      3. associate-+l+ 51.3%

         \[\leadsto \color{blue}{-6 \cdot x2 + \left(x1 + -2 \cdot x1\right)} \]

      4. distribute-rgt1-in 51.3%

         \[\leadsto -6 \cdot x2 + \color{blue}{\left(-2 + 1\right) \cdot x1} \]

      5. metadata-eval 51.3%

         \[\leadsto -6 \cdot x2 + \color{blue}{-1} \cdot x1 \]

      6. mul-1-neg 51.3%

         \[\leadsto -6 \cdot x2 + \color{blue}{\left(-x1\right)} \]

      7. sub-neg 51.3%

         \[\leadsto \color{blue}{-6 \cdot x2 - x1} \]

      8. *-commutative 51.3%

         \[\leadsto \color{blue}{x2 \cdot -6} - x1 \]

   10. Simplified 51.3%

       \[\leadsto \color{blue}{x2 \cdot -6 - x1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -4.8 \cdot 10^{+126} \lor \neg \left(x2 \leq 4.2 \cdot 10^{+41}\right):\\ \;\;\;\;x1 + \left(x1 \cdot \left(x2 \cdot x2\right)\right) \cdot 8\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \]

Alternative 20: 54.0% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq 4.8 \cdot 10^{-10}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x2 \cdot x2\right)\right) \cdot 8\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 4.8e-10)
   (- (* x2 -6.0) x1)
   (if (<= x1 1.4e+154)
     (+ x1 (* (* x1 (* x2 x2)) 8.0))
     (/ (* x1 x1) (- x1 (* x2 -6.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= 4.8e-10) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 1.4e+154) {
		tmp = x1 + ((x1 * (x2 * x2)) * 8.0);
	} else {
		tmp = (x1 * x1) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= 4.8d-10) then
        tmp = (x2 * (-6.0d0)) - x1
    else if (x1 <= 1.4d+154) then
        tmp = x1 + ((x1 * (x2 * x2)) * 8.0d0)
    else
        tmp = (x1 * x1) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= 4.8e-10) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 1.4e+154) {
		tmp = x1 + ((x1 * (x2 * x2)) * 8.0);
	} else {
		tmp = (x1 * x1) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= 4.8e-10:
		tmp = (x2 * -6.0) - x1
	elif x1 <= 1.4e+154:
		tmp = x1 + ((x1 * (x2 * x2)) * 8.0)
	else:
		tmp = (x1 * x1) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= 4.8e-10)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	elseif (x1 <= 1.4e+154)
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(x2 * x2)) * 8.0));
	else
		tmp = Float64(Float64(x1 * x1) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= 4.8e-10)
		tmp = (x2 * -6.0) - x1;
	elseif (x1 <= 1.4e+154)
		tmp = x1 + ((x1 * (x2 * x2)) * 8.0);
	else
		tmp = (x1 * x1) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, 4.8e-10], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 1.4e+154], N[(x1 + N[(N[(x1 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision], N[(N[(x1 * x1), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < 4.8e-10

   1. Initial program 75.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x2 around inf 60.1%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{{x2}^{2} \cdot x1}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   3. Step-by-step derivation

      1. associate-/l* 60.1%

         \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\frac{{x2}^{2}}{\frac{1 + {x1}^{2}}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. unpow2 60.1%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{\color{blue}{x2 \cdot x2}}{\frac{1 + {x1}^{2}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      3. +-commutative 60.1%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{{x1}^{2} + 1}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      4. unpow2 60.1%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{x1 \cdot x1} + 1}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      5. fma-udef 60.1%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Simplified 60.1%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Taylor expanded in x1 around 0 59.8%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)} \]
   6. Step-by-step derivation

      1. fma-def 59.9%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)} \]

      2. fma-neg 59.9%

         \[\leadsto x1 + \mathsf{fma}\left(-6, x2, x1 \cdot \color{blue}{\mathsf{fma}\left(8, {x2}^{2}, -2\right)}\right) \]

      3. unpow2 59.9%

         \[\leadsto x1 + \mathsf{fma}\left(-6, x2, x1 \cdot \mathsf{fma}\left(8, \color{blue}{x2 \cdot x2}, -2\right)\right) \]

      4. metadata-eval 59.9%

         \[\leadsto x1 + \mathsf{fma}\left(-6, x2, x1 \cdot \mathsf{fma}\left(8, x2 \cdot x2, \color{blue}{-2}\right)\right) \]

   7. Simplified 59.9%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \mathsf{fma}\left(8, x2 \cdot x2, -2\right)\right)} \]

   8. Taylor expanded in x2 around 0 51.0%

      \[\leadsto \color{blue}{x1 + \left(-6 \cdot x2 + -2 \cdot x1\right)} \]
   9. Step-by-step derivation

      1. associate-+r+ 51.0%

         \[\leadsto \color{blue}{\left(x1 + -6 \cdot x2\right) + -2 \cdot x1} \]

      2. +-commutative 51.0%

         \[\leadsto \color{blue}{\left(-6 \cdot x2 + x1\right)} + -2 \cdot x1 \]

      3. associate-+l+ 51.0%

         \[\leadsto \color{blue}{-6 \cdot x2 + \left(x1 + -2 \cdot x1\right)} \]

      4. distribute-rgt1-in 51.0%

         \[\leadsto -6 \cdot x2 + \color{blue}{\left(-2 + 1\right) \cdot x1} \]

      5. metadata-eval 51.0%

         \[\leadsto -6 \cdot x2 + \color{blue}{-1} \cdot x1 \]

      6. mul-1-neg 51.0%

         \[\leadsto -6 \cdot x2 + \color{blue}{\left(-x1\right)} \]

      7. sub-neg 51.0%

         \[\leadsto \color{blue}{-6 \cdot x2 - x1} \]

      8. *-commutative 51.0%

         \[\leadsto \color{blue}{x2 \cdot -6} - x1 \]

   10. Simplified 51.0%

       \[\leadsto \color{blue}{x2 \cdot -6 - x1} \]

   if 4.8e-10 < x1 < 1.4e154

   1. Initial program 99.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 30.5%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x2 around inf 30.5%

      \[\leadsto x1 + \color{blue}{8 \cdot \left({x2}^{2} \cdot x1\right)} \]
   4. Step-by-step derivation

      1. *-commutative 30.5%

         \[\leadsto x1 + \color{blue}{\left({x2}^{2} \cdot x1\right) \cdot 8} \]

      2. *-commutative 30.5%

         \[\leadsto x1 + \color{blue}{\left(x1 \cdot {x2}^{2}\right)} \cdot 8 \]

      3. unpow2 30.5%

         \[\leadsto x1 + \left(x1 \cdot \color{blue}{\left(x2 \cdot x2\right)}\right) \cdot 8 \]

   5. Simplified 30.5%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(x2 \cdot x2\right)\right) \cdot 8} \]

   if 1.4e154 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 6.1%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 6.1%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 6.1%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
   6. Step-by-step derivation

      1. flip-+ 77.4%

         \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]

   7. Applied egg-rr 77.4%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]
   8. Step-by-step derivation

      1. swap-sqr 77.4%

         \[\leadsto \frac{x1 \cdot x1 - \color{blue}{\left(x2 \cdot x2\right) \cdot \left(-6 \cdot -6\right)}}{x1 - x2 \cdot -6} \]

      2. metadata-eval 77.4%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot \color{blue}{36}}{x1 - x2 \cdot -6} \]

   9. Simplified 77.4%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}} \]

   10. Taylor expanded in x1 around inf 93.5%

       \[\leadsto \frac{\color{blue}{{x1}^{2}}}{x1 - x2 \cdot -6} \]
   11. Step-by-step derivation

       1. unpow2 93.5%

          \[\leadsto \frac{\color{blue}{x1 \cdot x1}}{x1 - x2 \cdot -6} \]

   12. Simplified 93.5%

       \[\leadsto \frac{\color{blue}{x1 \cdot x1}}{x1 - x2 \cdot -6} \]
3. Recombined 3 regimes into one program.

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq 4.8 \cdot 10^{-10}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x2 \cdot x2\right)\right) \cdot 8\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 21: 30.8% accurate, 13.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -1.05 \cdot 10^{-254}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 1.45 \cdot 10^{-173}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 -1.05e-254)
   (* x2 -6.0)
   (if (<= x2 1.45e-173) (- x1) (+ x1 (* x2 -6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= -1.05e-254) {
		tmp = x2 * -6.0;
	} else if (x2 <= 1.45e-173) {
		tmp = -x1;
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x2 <= (-1.05d-254)) then
        tmp = x2 * (-6.0d0)
    else if (x2 <= 1.45d-173) then
        tmp = -x1
    else
        tmp = x1 + (x2 * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x2 <= -1.05e-254) {
		tmp = x2 * -6.0;
	} else if (x2 <= 1.45e-173) {
		tmp = -x1;
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= -1.05e-254:
		tmp = x2 * -6.0
	elif x2 <= 1.45e-173:
		tmp = -x1
	else:
		tmp = x1 + (x2 * -6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= -1.05e-254)
		tmp = Float64(x2 * -6.0);
	elseif (x2 <= 1.45e-173)
		tmp = Float64(-x1);
	else
		tmp = Float64(x1 + Float64(x2 * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= -1.05e-254)
		tmp = x2 * -6.0;
	elseif (x2 <= 1.45e-173)
		tmp = -x1;
	else
		tmp = x1 + (x2 * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, -1.05e-254], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x2, 1.45e-173], (-x1), N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -1.04999999999999998e-254

   1. Initial program 70.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 55.2%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 27.4%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 27.4%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 27.4%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   6. Taylor expanded in x1 around 0 27.9%

      \[\leadsto \color{blue}{-6 \cdot x2} \]
   7. Step-by-step derivation

      1. *-commutative 27.9%

         \[\leadsto \color{blue}{x2 \cdot -6} \]

   8. Simplified 27.9%

      \[\leadsto \color{blue}{x2 \cdot -6} \]

   if -1.04999999999999998e-254 < x2 < 1.4499999999999999e-173

   1. Initial program 61.9%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x2 around inf 48.7%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{{x2}^{2} \cdot x1}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   3. Step-by-step derivation

      1. associate-/l* 48.7%

         \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\frac{{x2}^{2}}{\frac{1 + {x1}^{2}}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. unpow2 48.7%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{\color{blue}{x2 \cdot x2}}{\frac{1 + {x1}^{2}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      3. +-commutative 48.7%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{{x1}^{2} + 1}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      4. unpow2 48.7%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{x1 \cdot x1} + 1}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      5. fma-udef 48.7%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Simplified 48.7%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Taylor expanded in x1 around 0 50.1%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)} \]
   6. Step-by-step derivation

      1. fma-def 50.1%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)} \]

      2. fma-neg 50.1%

         \[\leadsto x1 + \mathsf{fma}\left(-6, x2, x1 \cdot \color{blue}{\mathsf{fma}\left(8, {x2}^{2}, -2\right)}\right) \]

      3. unpow2 50.1%

         \[\leadsto x1 + \mathsf{fma}\left(-6, x2, x1 \cdot \mathsf{fma}\left(8, \color{blue}{x2 \cdot x2}, -2\right)\right) \]

      4. metadata-eval 50.1%

         \[\leadsto x1 + \mathsf{fma}\left(-6, x2, x1 \cdot \mathsf{fma}\left(8, x2 \cdot x2, \color{blue}{-2}\right)\right) \]

   7. Simplified 50.1%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \mathsf{fma}\left(8, x2 \cdot x2, -2\right)\right)} \]

   8. Taylor expanded in x2 around 0 49.6%

      \[\leadsto \color{blue}{x1 + -2 \cdot x1} \]
   9. Step-by-step derivation

      1. distribute-rgt1-in 49.6%

         \[\leadsto \color{blue}{\left(-2 + 1\right) \cdot x1} \]

      2. metadata-eval 49.6%

         \[\leadsto \color{blue}{-1} \cdot x1 \]

      3. mul-1-neg 49.6%

         \[\leadsto \color{blue}{-x1} \]

   10. Simplified 49.6%

       \[\leadsto \color{blue}{-x1} \]

   if 1.4499999999999999e-173 < x2

   1. Initial program 69.6%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 60.6%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 34.6%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 34.6%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 34.6%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
3. Recombined 3 regimes into one program.

4. Final simplification 33.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.05 \cdot 10^{-254}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 1.45 \cdot 10^{-173}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \]

Alternative 22: 30.6% accurate, 17.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -1.05 \cdot 10^{-254}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 4 \cdot 10^{-172}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 -1.05e-254) (* x2 -6.0) (if (<= x2 4e-172) (- x1) (* x2 -6.0))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= -1.05e-254) {
		tmp = x2 * -6.0;
	} else if (x2 <= 4e-172) {
		tmp = -x1;
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x2 <= (-1.05d-254)) then
        tmp = x2 * (-6.0d0)
    else if (x2 <= 4d-172) then
        tmp = -x1
    else
        tmp = x2 * (-6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x2 <= -1.05e-254) {
		tmp = x2 * -6.0;
	} else if (x2 <= 4e-172) {
		tmp = -x1;
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= -1.05e-254:
		tmp = x2 * -6.0
	elif x2 <= 4e-172:
		tmp = -x1
	else:
		tmp = x2 * -6.0
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= -1.05e-254)
		tmp = Float64(x2 * -6.0);
	elseif (x2 <= 4e-172)
		tmp = Float64(-x1);
	else
		tmp = Float64(x2 * -6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= -1.05e-254)
		tmp = x2 * -6.0;
	elseif (x2 <= 4e-172)
		tmp = -x1;
	else
		tmp = x2 * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, -1.05e-254], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x2, 4e-172], (-x1), N[(x2 * -6.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x2 < -1.04999999999999998e-254 or 4.0000000000000002e-172 < x2

   1. Initial program 70.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 57.5%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 30.4%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 30.4%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 30.4%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   6. Taylor expanded in x1 around 0 30.4%

      \[\leadsto \color{blue}{-6 \cdot x2} \]
   7. Step-by-step derivation

      1. *-commutative 30.4%

         \[\leadsto \color{blue}{x2 \cdot -6} \]

   8. Simplified 30.4%

      \[\leadsto \color{blue}{x2 \cdot -6} \]

   if -1.04999999999999998e-254 < x2 < 4.0000000000000002e-172

   1. Initial program 61.9%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x2 around inf 48.7%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{{x2}^{2} \cdot x1}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   3. Step-by-step derivation

      1. associate-/l* 48.7%

         \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\frac{{x2}^{2}}{\frac{1 + {x1}^{2}}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. unpow2 48.7%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{\color{blue}{x2 \cdot x2}}{\frac{1 + {x1}^{2}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      3. +-commutative 48.7%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{{x1}^{2} + 1}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      4. unpow2 48.7%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{x1 \cdot x1} + 1}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      5. fma-udef 48.7%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Simplified 48.7%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Taylor expanded in x1 around 0 50.1%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)} \]
   6. Step-by-step derivation

      1. fma-def 50.1%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)} \]

      2. fma-neg 50.1%

         \[\leadsto x1 + \mathsf{fma}\left(-6, x2, x1 \cdot \color{blue}{\mathsf{fma}\left(8, {x2}^{2}, -2\right)}\right) \]

      3. unpow2 50.1%

         \[\leadsto x1 + \mathsf{fma}\left(-6, x2, x1 \cdot \mathsf{fma}\left(8, \color{blue}{x2 \cdot x2}, -2\right)\right) \]

      4. metadata-eval 50.1%

         \[\leadsto x1 + \mathsf{fma}\left(-6, x2, x1 \cdot \mathsf{fma}\left(8, x2 \cdot x2, \color{blue}{-2}\right)\right) \]

   7. Simplified 50.1%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \mathsf{fma}\left(8, x2 \cdot x2, -2\right)\right)} \]

   8. Taylor expanded in x2 around 0 49.6%

      \[\leadsto \color{blue}{x1 + -2 \cdot x1} \]
   9. Step-by-step derivation

      1. distribute-rgt1-in 49.6%

         \[\leadsto \color{blue}{\left(-2 + 1\right) \cdot x1} \]

      2. metadata-eval 49.6%

         \[\leadsto \color{blue}{-1} \cdot x1 \]

      3. mul-1-neg 49.6%

         \[\leadsto \color{blue}{-x1} \]

   10. Simplified 49.6%

       \[\leadsto \color{blue}{-x1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.05 \cdot 10^{-254}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 4 \cdot 10^{-172}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]

Alternative 23: 38.9% 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 69.1%

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

2. Taylor expanded in x2 around inf 49.8%

   \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{{x2}^{2} \cdot x1}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Step-by-step derivation

   1. associate-/l* 49.4%

      \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\frac{{x2}^{2}}{\frac{1 + {x1}^{2}}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. unpow2 49.4%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{\color{blue}{x2 \cdot x2}}{\frac{1 + {x1}^{2}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. +-commutative 49.4%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{{x1}^{2} + 1}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. unpow2 49.4%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{x1 \cdot x1} + 1}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. fma-udef 49.4%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

4. Simplified 49.4%

   \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

5. Taylor expanded in x1 around 0 54.2%

   \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)} \]
6. Step-by-step derivation

   1. fma-def 54.3%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)} \]

   2. fma-neg 54.3%

      \[\leadsto x1 + \mathsf{fma}\left(-6, x2, x1 \cdot \color{blue}{\mathsf{fma}\left(8, {x2}^{2}, -2\right)}\right) \]

   3. unpow2 54.3%

      \[\leadsto x1 + \mathsf{fma}\left(-6, x2, x1 \cdot \mathsf{fma}\left(8, \color{blue}{x2 \cdot x2}, -2\right)\right) \]

   4. metadata-eval 54.3%

      \[\leadsto x1 + \mathsf{fma}\left(-6, x2, x1 \cdot \mathsf{fma}\left(8, x2 \cdot x2, \color{blue}{-2}\right)\right) \]

7. Simplified 54.3%

   \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \mathsf{fma}\left(8, x2 \cdot x2, -2\right)\right)} \]

8. Taylor expanded in x2 around 0 39.5%

   \[\leadsto \color{blue}{x1 + \left(-6 \cdot x2 + -2 \cdot x1\right)} \]
9. Step-by-step derivation

   1. associate-+r+ 39.5%

      \[\leadsto \color{blue}{\left(x1 + -6 \cdot x2\right) + -2 \cdot x1} \]

   2. +-commutative 39.5%

      \[\leadsto \color{blue}{\left(-6 \cdot x2 + x1\right)} + -2 \cdot x1 \]

   3. associate-+l+ 39.5%

      \[\leadsto \color{blue}{-6 \cdot x2 + \left(x1 + -2 \cdot x1\right)} \]

   4. distribute-rgt1-in 39.5%

      \[\leadsto -6 \cdot x2 + \color{blue}{\left(-2 + 1\right) \cdot x1} \]

   5. metadata-eval 39.5%

      \[\leadsto -6 \cdot x2 + \color{blue}{-1} \cdot x1 \]

   6. mul-1-neg 39.5%

      \[\leadsto -6 \cdot x2 + \color{blue}{\left(-x1\right)} \]

   7. sub-neg 39.5%

      \[\leadsto \color{blue}{-6 \cdot x2 - x1} \]

   8. *-commutative 39.5%

      \[\leadsto \color{blue}{x2 \cdot -6} - x1 \]

10. Simplified 39.5%

    \[\leadsto \color{blue}{x2 \cdot -6 - x1} \]

11. Final simplification 39.5%

    \[\leadsto x2 \cdot -6 - x1 \]

Alternative 24: 14.5% accurate, 63.5× speedup

Math

\[\begin{array}{l} \\ -x1 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (- x1))

C

double code(double x1, double x2) {
	return -x1;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = -x1
end function

Java

public static double code(double x1, double x2) {
	return -x1;
}

Python

def code(x1, x2):
	return -x1

Julia

function code(x1, x2)
	return Float64(-x1)
end

MATLAB

function tmp = code(x1, x2)
	tmp = -x1;
end

Wolfram

code[x1_, x2_] := (-x1)

Derivation

1. Initial program 69.1%

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

2. Taylor expanded in x2 around inf 49.8%

   \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{{x2}^{2} \cdot x1}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Step-by-step derivation

   1. associate-/l* 49.4%

      \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\frac{{x2}^{2}}{\frac{1 + {x1}^{2}}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. unpow2 49.4%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{\color{blue}{x2 \cdot x2}}{\frac{1 + {x1}^{2}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. +-commutative 49.4%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{{x1}^{2} + 1}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. unpow2 49.4%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{x1 \cdot x1} + 1}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. fma-udef 49.4%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

4. Simplified 49.4%

   \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

5. Taylor expanded in x1 around 0 54.2%

   \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)} \]
6. Step-by-step derivation

   1. fma-def 54.3%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \left(8 \cdot {x2}^{2} - 2\right)\right)} \]

   2. fma-neg 54.3%

      \[\leadsto x1 + \mathsf{fma}\left(-6, x2, x1 \cdot \color{blue}{\mathsf{fma}\left(8, {x2}^{2}, -2\right)}\right) \]

   3. unpow2 54.3%

      \[\leadsto x1 + \mathsf{fma}\left(-6, x2, x1 \cdot \mathsf{fma}\left(8, \color{blue}{x2 \cdot x2}, -2\right)\right) \]

   4. metadata-eval 54.3%

      \[\leadsto x1 + \mathsf{fma}\left(-6, x2, x1 \cdot \mathsf{fma}\left(8, x2 \cdot x2, \color{blue}{-2}\right)\right) \]

7. Simplified 54.3%

   \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \mathsf{fma}\left(8, x2 \cdot x2, -2\right)\right)} \]

8. Taylor expanded in x2 around 0 13.7%

   \[\leadsto \color{blue}{x1 + -2 \cdot x1} \]
9. Step-by-step derivation

   1. distribute-rgt1-in 13.7%

      \[\leadsto \color{blue}{\left(-2 + 1\right) \cdot x1} \]

   2. metadata-eval 13.7%

      \[\leadsto \color{blue}{-1} \cdot x1 \]

   3. mul-1-neg 13.7%

      \[\leadsto \color{blue}{-x1} \]

10. Simplified 13.7%

    \[\leadsto \color{blue}{-x1} \]

11. Final simplification 13.7%

    \[\leadsto -x1 \]

Alternative 25: 3.2% 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 69.1%

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

2. Taylor expanded in x1 around 0 56.3%

   \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

3. Taylor expanded in x1 around 0 26.7%

   \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
4. Step-by-step derivation

   1. *-commutative 26.7%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

5. Simplified 26.7%

   \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

6. Taylor expanded in x1 around inf 3.2%

   \[\leadsto \color{blue}{x1} \]

7. Final simplification 3.2%

   \[\leadsto x1 \]

Reproduce

herbie shell --seed 2023279 
(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))))))