Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.7% → 99.4%

Time: 2.2min

Alternatives: 24

Speedup: 1.7×

• 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: 70.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   3. Applied egg-rr 91.1%

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

   5. Simplified 99.4%

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

   if +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 10.8%

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

      1. *-commutative 10.8%

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

   4. Simplified 10.8%

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

   5. Taylor expanded in x1 around inf 97.3%

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

4. Final simplification 98.8%

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

Alternative 2: 99.4% 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 10.8%

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

      1. *-commutative 10.8%

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

   4. Simplified 10.8%

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

   5. Taylor expanded in x1 around inf 97.3%

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

4. Final simplification 98.8%

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

Alternative 3: 95.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -9 \cdot 10^{+52} \lor \neg \left(x1 \leq 1.3 \cdot 10^{+67}\right):\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_0 \cdot t_2 + t_1 \cdot \left(\left(t_2 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(2 \cdot x2 + 3 \cdot \left(x1 \cdot x1\right)\right) - x1}{t_1} - 6\right)\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (if (or (<= x1 -9e+52) (not (<= x1 1.3e+67)))
     (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) 9.0))
     (+
      x1
      (+
       (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (* t_0 t_2)
          (*
           t_1
           (+
            (* (- t_2 3.0) (* (* x1 2.0) (- (* 2.0 x2) x1)))
            (*
             (* x1 x1)
             (-
              (* 4.0 (/ (- (+ (* 2.0 x2) (* 3.0 (* x1 x1))) x1) t_1))
              6.0))))))))))))

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 tmp;
	if ((x1 <= -9e+52) || !(x1 <= 1.3e+67)) {
		tmp = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + 9.0);
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((t_2 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - x1))) + ((x1 * x1) * ((4.0 * ((((2.0 * x2) + (3.0 * (x1 * x1))) - x1) / t_1)) - 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    if ((x1 <= (-9d+52)) .or. (.not. (x1 <= 1.3d+67))) then
        tmp = x1 + ((x1 + (6.0d0 * (x1 ** 4.0d0))) + 9.0d0)
    else
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((t_2 - 3.0d0) * ((x1 * 2.0d0) * ((2.0d0 * x2) - x1))) + ((x1 * x1) * ((4.0d0 * ((((2.0d0 * x2) + (3.0d0 * (x1 * x1))) - x1) / t_1)) - 6.0d0))))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -9e+52) || !(x1 <= 1.3e+67)) {
		tmp = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + 9.0);
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((t_2 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - x1))) + ((x1 * x1) * ((4.0 * ((((2.0 * x2) + (3.0 * (x1 * x1))) - x1) / t_1)) - 6.0))))))));
	}
	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
	tmp = 0
	if (x1 <= -9e+52) or not (x1 <= 1.3e+67):
		tmp = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + 9.0)
	else:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((t_2 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - x1))) + ((x1 * x1) * ((4.0 * ((((2.0 * x2) + (3.0 * (x1 * x1))) - x1) / t_1)) - 6.0))))))))
	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)
	tmp = 0.0
	if ((x1 <= -9e+52) || !(x1 <= 1.3e+67))
		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_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * t_2) + Float64(t_1 * Float64(Float64(Float64(t_2 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(Float64(2.0 * x2) - x1))) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(Float64(Float64(Float64(2.0 * x2) + Float64(3.0 * Float64(x1 * x1))) - x1) / t_1)) - 6.0)))))))));
	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;
	tmp = 0.0;
	if ((x1 <= -9e+52) || ~((x1 <= 1.3e+67)))
		tmp = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + 9.0);
	else
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((t_2 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - x1))) + ((x1 * x1) * ((4.0 * ((((2.0 * x2) + (3.0 * (x1 * x1))) - x1) / t_1)) - 6.0))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[x1, -9e+52], N[Not[LessEqual[x1, 1.3e+67]], $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$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * t$95$2), $MachinePrecision] + N[(t$95$1 * N[(N[(N[(t$95$2 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(N[(N[(N[(2.0 * x2), $MachinePrecision] + N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -8.9999999999999999e52 or 1.3e67 < x1

   1. Initial program 34.1%

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

   2. Taylor expanded in x1 around inf 39.7%

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

      1. *-commutative 39.7%

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

   4. Simplified 39.7%

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

   5. Taylor expanded in x1 around inf 97.4%

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

   if -8.9999999999999999e52 < x1 < 1.3e67

   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 94.9%

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

   3. Taylor expanded in x1 around 0 94.9%

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

      1. unpow2 94.9%

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

   5. Simplified 94.9%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9 \cdot 10^{+52} \lor \neg \left(x1 \leq 1.3 \cdot 10^{+67}\right):\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(2 \cdot x2 + 3 \cdot \left(x1 \cdot x1\right)\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 4: 95.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -4 \cdot 10^{+101} \lor \neg \left(x1 \leq 2.6 \cdot 10^{+67}\right):\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_0 \cdot t_2 + t_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t_2 \cdot 4 - 6\right) + \left(t_2 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right)\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (if (or (<= x1 -4e+101) (not (<= x1 2.6e+67)))
     (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) 9.0))
     (+
      x1
      (+
       (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (* t_0 t_2)
          (*
           t_1
           (+
            (* (* x1 x1) (- (* t_2 4.0) 6.0))
            (* (- t_2 3.0) (* (* x1 2.0) (- (* 2.0 x2) x1)))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -4e+101) || !(x1 <= 2.6e+67)) {
		tmp = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + 9.0);
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((x1 * x1) * ((t_2 * 4.0) - 6.0)) + ((t_2 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - x1)))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    if ((x1 <= (-4d+101)) .or. (.not. (x1 <= 2.6d+67))) then
        tmp = x1 + ((x1 + (6.0d0 * (x1 ** 4.0d0))) + 9.0d0)
    else
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((x1 * x1) * ((t_2 * 4.0d0) - 6.0d0)) + ((t_2 - 3.0d0) * ((x1 * 2.0d0) * ((2.0d0 * x2) - x1)))))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -4e+101) || !(x1 <= 2.6e+67)) {
		tmp = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + 9.0);
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((x1 * x1) * ((t_2 * 4.0) - 6.0)) + ((t_2 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - x1)))))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1
	tmp = 0
	if (x1 <= -4e+101) or not (x1 <= 2.6e+67):
		tmp = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + 9.0)
	else:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((x1 * x1) * ((t_2 * 4.0) - 6.0)) + ((t_2 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - x1)))))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if ((x1 <= -4e+101) || !(x1 <= 2.6e+67))
		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_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * t_2) + Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)) + Float64(Float64(t_2 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(Float64(2.0 * x2) - x1))))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	tmp = 0.0;
	if ((x1 <= -4e+101) || ~((x1 <= 2.6e+67)))
		tmp = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + 9.0);
	else
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((x1 * x1) * ((t_2 * 4.0) - 6.0)) + ((t_2 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - x1)))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[x1, -4e+101], N[Not[LessEqual[x1, 2.6e+67]], $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$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * t$95$2), $MachinePrecision] + N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -3.9999999999999999e101 or 2.6e67 < x1

   1. Initial program 27.7%

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

   2. Taylor expanded in x1 around inf 33.7%

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

      1. *-commutative 33.7%

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

   4. Simplified 33.7%

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

   5. Taylor expanded in x1 around inf 97.1%

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

   if -3.9999999999999999e101 < x1 < 2.6e67

   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 95.2%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+101} \lor \neg \left(x1 \leq 2.6 \cdot 10^{+67}\right):\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right)\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 5: 96.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_2}\\ t_4 := x1 + \left(\left(x1 + \left(\left(t_2 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_3\right) \cdot \left(t_3 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t_3 \cdot 4 - 6\right)\right) + t_0 \cdot t_3\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 9\right)\\ \mathbf{if}\;x1 \leq -1.22 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq -0.0011:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x1 \leq 1.1 \cdot 10^{-27}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_2} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2\right) + x1 \cdot -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{+69}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) 9.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (/ (- (+ t_0 (* 2.0 x2)) x1) t_2))
        (t_4
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               t_2
               (+
                (* (* (* x1 2.0) t_3) (- t_3 3.0))
                (* (* x1 x1) (- (* t_3 4.0) 6.0))))
              (* t_0 t_3))
             (* x1 (* x1 x1))))
           9.0))))
   (if (<= x1 -1.22e+53)
     t_1
     (if (<= x1 -0.0011)
       t_4
       (if (<= x1 1.1e-27)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_2))
           (+ x1 (* 4.0 (* x2 (+ (* x1 (* 2.0 x2)) (* x1 -3.0)))))))
         (if (<= x1 4.2e+69) t_4 t_1))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + 9.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	double t_4 = x1 + ((x1 + (((t_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + (t_0 * t_3)) + (x1 * (x1 * x1)))) + 9.0);
	double tmp;
	if (x1 <= -1.22e+53) {
		tmp = t_1;
	} else if (x1 <= -0.0011) {
		tmp = t_4;
	} else if (x1 <= 1.1e-27) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) + (x1 + (4.0 * (x2 * ((x1 * (2.0 * x2)) + (x1 * -3.0))))));
	} else if (x1 <= 4.2e+69) {
		tmp = t_4;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = x1 + ((x1 + (6.0d0 * (x1 ** 4.0d0))) + 9.0d0)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = ((t_0 + (2.0d0 * x2)) - x1) / t_2
    t_4 = x1 + ((x1 + (((t_2 * ((((x1 * 2.0d0) * t_3) * (t_3 - 3.0d0)) + ((x1 * x1) * ((t_3 * 4.0d0) - 6.0d0)))) + (t_0 * t_3)) + (x1 * (x1 * x1)))) + 9.0d0)
    if (x1 <= (-1.22d+53)) then
        tmp = t_1
    else if (x1 <= (-0.0011d0)) then
        tmp = t_4
    else if (x1 <= 1.1d-27) then
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_2)) + (x1 + (4.0d0 * (x2 * ((x1 * (2.0d0 * x2)) + (x1 * (-3.0d0)))))))
    else if (x1 <= 4.2d+69) then
        tmp = t_4
    else
        tmp = t_1
    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 + (6.0 * Math.pow(x1, 4.0))) + 9.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	double t_4 = x1 + ((x1 + (((t_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + (t_0 * t_3)) + (x1 * (x1 * x1)))) + 9.0);
	double tmp;
	if (x1 <= -1.22e+53) {
		tmp = t_1;
	} else if (x1 <= -0.0011) {
		tmp = t_4;
	} else if (x1 <= 1.1e-27) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) + (x1 + (4.0 * (x2 * ((x1 * (2.0 * x2)) + (x1 * -3.0))))));
	} else if (x1 <= 4.2e+69) {
		tmp = t_4;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + 9.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2
	t_4 = x1 + ((x1 + (((t_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + (t_0 * t_3)) + (x1 * (x1 * x1)))) + 9.0)
	tmp = 0
	if x1 <= -1.22e+53:
		tmp = t_1
	elif x1 <= -0.0011:
		tmp = t_4
	elif x1 <= 1.1e-27:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) + (x1 + (4.0 * (x2 * ((x1 * (2.0 * x2)) + (x1 * -3.0))))))
	elif x1 <= 4.2e+69:
		tmp = t_4
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + 9.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_2)
	t_4 = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_2 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(t_3 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0)))) + Float64(t_0 * t_3)) + Float64(x1 * Float64(x1 * x1)))) + 9.0))
	tmp = 0.0
	if (x1 <= -1.22e+53)
		tmp = t_1;
	elseif (x1 <= -0.0011)
		tmp = t_4;
	elseif (x1 <= 1.1e-27)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_2)) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(Float64(x1 * Float64(2.0 * x2)) + Float64(x1 * -3.0)))))));
	elseif (x1 <= 4.2e+69)
		tmp = t_4;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + 9.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	t_4 = x1 + ((x1 + (((t_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + (t_0 * t_3)) + (x1 * (x1 * x1)))) + 9.0);
	tmp = 0.0;
	if (x1 <= -1.22e+53)
		tmp = t_1;
	elseif (x1 <= -0.0011)
		tmp = t_4;
	elseif (x1 <= 1.1e-27)
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) + (x1 + (4.0 * (x2 * ((x1 * (2.0 * x2)) + (x1 * -3.0))))));
	elseif (x1 <= 4.2e+69)
		tmp = t_4;
	else
		tmp = t_1;
	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[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$2 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.22e+53], t$95$1, If[LessEqual[x1, -0.0011], t$95$4, If[LessEqual[x1, 1.1e-27], 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[(x1 + N[(4.0 * N[(x2 * N[(N[(x1 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.2e+69], t$95$4, t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.21999999999999999e53 or 4.2000000000000003e69 < x1

   1. Initial program 32.9%

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

   2. Taylor expanded in x1 around inf 39.4%

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

      1. *-commutative 39.4%

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

   4. Simplified 39.4%

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

   5. Taylor expanded in x1 around inf 98.1%

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

   if -1.21999999999999999e53 < x1 < -0.00110000000000000007 or 1.09999999999999993e-27 < x1 < 4.2000000000000003e69

   1. Initial program 96.2%

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

   2. Taylor expanded in x1 around inf 96.3%

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

   if -0.00110000000000000007 < x1 < 1.09999999999999993e-27

   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 87.7%

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

      1. associate-*r* 99.3%

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

      2. sub-neg 99.3%

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

      3. metadata-eval 99.3%

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

      4. distribute-rgt-in 99.3%

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

      5. *-commutative 99.3%

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

   4. Applied egg-rr 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-*r* 99.3%

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

      3. associate-*r* 99.3%

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

      4. distribute-rgt-out 99.3%

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

      5. *-commutative 99.3%

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

      6. *-commutative 99.3%

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

   6. Applied egg-rr 99.3%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.22 \cdot 10^{+53}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{elif}\;x1 \leq -0.0011:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 9\right)\\ \mathbf{elif}\;x1 \leq 1.1 \cdot 10^{-27}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2\right) + x1 \cdot -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{+69}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \end{array} \]

Alternative 6: 93.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_2}\\ t_4 := 3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_2}\\ \mathbf{if}\;x1 \leq -2.6 \cdot 10^{+34}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 58000000000:\\ \;\;\;\;x1 + \left(t_4 + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2\right) + x1 \cdot -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{+69}:\\ \;\;\;\;x1 + \left(t_4 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_1 \cdot t_3 + t_2 \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(t_3 \cdot 4 - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) 9.0)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (/ (- (+ t_1 (* 2.0 x2)) x1) t_2))
        (t_4 (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2))))
   (if (<= x1 -2.6e+34)
     t_0
     (if (<= x1 58000000000.0)
       (+ x1 (+ t_4 (+ x1 (* 4.0 (* x2 (+ (* x1 (* 2.0 x2)) (* x1 -3.0)))))))
       (if (<= x1 4.2e+69)
         (+
          x1
          (+
           t_4
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* t_1 t_3)
              (* t_2 (+ (* x1 2.0) (* (* x1 x1) (- (* t_3 4.0) 6.0)))))))))
         t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + 9.0);
	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 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double tmp;
	if (x1 <= -2.6e+34) {
		tmp = t_0;
	} else if (x1 <= 58000000000.0) {
		tmp = x1 + (t_4 + (x1 + (4.0 * (x2 * ((x1 * (2.0 * x2)) + (x1 * -3.0))))));
	} else if (x1 <= 4.2e+69) {
		tmp = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_3) + (t_2 * ((x1 * 2.0) + ((x1 * x1) * ((t_3 * 4.0) - 6.0))))))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = x1 + ((x1 + (6.0d0 * (x1 ** 4.0d0))) + 9.0d0)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = ((t_1 + (2.0d0 * x2)) - x1) / t_2
    t_4 = 3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_2)
    if (x1 <= (-2.6d+34)) then
        tmp = t_0
    else if (x1 <= 58000000000.0d0) then
        tmp = x1 + (t_4 + (x1 + (4.0d0 * (x2 * ((x1 * (2.0d0 * x2)) + (x1 * (-3.0d0)))))))
    else if (x1 <= 4.2d+69) then
        tmp = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_3) + (t_2 * ((x1 * 2.0d0) + ((x1 * x1) * ((t_3 * 4.0d0) - 6.0d0))))))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + 9.0);
	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 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double tmp;
	if (x1 <= -2.6e+34) {
		tmp = t_0;
	} else if (x1 <= 58000000000.0) {
		tmp = x1 + (t_4 + (x1 + (4.0 * (x2 * ((x1 * (2.0 * x2)) + (x1 * -3.0))))));
	} else if (x1 <= 4.2e+69) {
		tmp = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_3) + (t_2 * ((x1 * 2.0) + ((x1 * x1) * ((t_3 * 4.0) - 6.0))))))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + 9.0)
	t_1 = x1 * (x1 * 3.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2
	t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)
	tmp = 0
	if x1 <= -2.6e+34:
		tmp = t_0
	elif x1 <= 58000000000.0:
		tmp = x1 + (t_4 + (x1 + (4.0 * (x2 * ((x1 * (2.0 * x2)) + (x1 * -3.0))))))
	elif x1 <= 4.2e+69:
		tmp = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_3) + (t_2 * ((x1 * 2.0) + ((x1 * x1) * ((t_3 * 4.0) - 6.0))))))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + 9.0))
	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(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2))
	tmp = 0.0
	if (x1 <= -2.6e+34)
		tmp = t_0;
	elseif (x1 <= 58000000000.0)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(Float64(x1 * Float64(2.0 * x2)) + Float64(x1 * -3.0)))))));
	elseif (x1 <= 4.2e+69)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * t_3) + Float64(t_2 * Float64(Float64(x1 * 2.0) + Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0)))))))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + 9.0);
	t_1 = x1 * (x1 * 3.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	tmp = 0.0;
	if (x1 <= -2.6e+34)
		tmp = t_0;
	elseif (x1 <= 58000000000.0)
		tmp = x1 + (t_4 + (x1 + (4.0 * (x2 * ((x1 * (2.0 * x2)) + (x1 * -3.0))))));
	elseif (x1 <= 4.2e+69)
		tmp = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_3) + (t_2 * ((x1 * 2.0) + ((x1 * x1) * ((t_3 * 4.0) - 6.0))))))));
	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[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9.0), $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[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.6e+34], t$95$0, If[LessEqual[x1, 58000000000.0], N[(x1 + N[(t$95$4 + N[(x1 + N[(4.0 * N[(x2 * N[(N[(x1 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.2e+69], N[(x1 + N[(t$95$4 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * t$95$3), $MachinePrecision] + N[(t$95$2 * N[(N[(x1 * 2.0), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.59999999999999997e34 or 4.2000000000000003e69 < x1

   1. Initial program 36.4%

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

   2. Taylor expanded in x1 around inf 40.6%

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

      1. *-commutative 40.6%

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

   4. Simplified 40.6%

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

   5. Taylor expanded in x1 around inf 96.3%

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

   if -2.59999999999999997e34 < x1 < 5.8e10

   1. Initial program 98.5%

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

   2. Taylor expanded in x1 around 0 84.4%

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

      1. associate-*r* 94.8%

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

      2. sub-neg 94.8%

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

      3. metadata-eval 94.8%

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

      4. distribute-rgt-in 94.8%

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

      5. *-commutative 94.8%

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

   4. Applied egg-rr 94.8%

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

      1. *-commutative 94.8%

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

      2. associate-*r* 94.8%

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

      3. associate-*r* 94.8%

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

      4. distribute-rgt-out 94.8%

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

      5. *-commutative 94.8%

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

      6. *-commutative 94.8%

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

   6. Applied egg-rr 94.8%

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

   if 5.8e10 < x1 < 4.2000000000000003e69

   1. Initial program 99.1%

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

   2. Taylor expanded in x1 around 0 78.4%

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

   3. Taylor expanded in x1 around inf 88.7%

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

      1. *-commutative 88.7%

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

   5. Simplified 88.7%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.6 \cdot 10^{+34}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{elif}\;x1 \leq 58000000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2\right) + x1 \cdot -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{+69}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \end{array} \]

Alternative 7: 78.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_0}\\ t_3 := 3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_0}\\ t_4 := t_1 \cdot t_2\\ t_5 := x1 + x2 \cdot 6\\ t_6 := x1 \cdot \left(x1 \cdot x1\right)\\ t_7 := \left(x1 \cdot x1\right) \cdot \left(t_2 \cdot 4 - 6\right)\\ \mathbf{if}\;x1 \leq -6 \cdot 10^{+124}:\\ \;\;\;\;\frac{x1}{\frac{t_5}{x1}} - \frac{36}{\frac{t_5}{x2 \cdot x2}}\\ \mathbf{elif}\;x1 \leq -0.47:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(t_6 + \left(t_4 + t_0 \cdot \left(t_7 + \left(t_2 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 30500000:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2\right) + x1 \cdot -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + \left(t_6 + \left(t_4 + t_0 \cdot \left(x1 \cdot 2 + t_7\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{36 \cdot \left(x2 \cdot x2\right) - x1 \cdot x1}{x2 \cdot -6 - x1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (/ (- (+ t_1 (* 2.0 x2)) x1) t_0))
        (t_3 (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_0)))
        (t_4 (* t_1 t_2))
        (t_5 (+ x1 (* x2 6.0)))
        (t_6 (* x1 (* x1 x1)))
        (t_7 (* (* x1 x1) (- (* t_2 4.0) 6.0))))
   (if (<= x1 -6e+124)
     (- (/ x1 (/ t_5 x1)) (/ 36.0 (/ t_5 (* x2 x2))))
     (if (<= x1 -0.47)
       (+
        x1
        (+
         9.0
         (+
          x1
          (+
           t_6
           (+
            t_4
            (*
             t_0
             (+ t_7 (* (- t_2 3.0) (* (* x1 2.0) (- (* 2.0 x2) x1))))))))))
       (if (<= x1 30500000.0)
         (+ x1 (+ t_3 (+ x1 (* 4.0 (* x2 (+ (* x1 (* 2.0 x2)) (* x1 -3.0)))))))
         (if (<= x1 1.35e+154)
           (+ x1 (+ t_3 (+ x1 (+ t_6 (+ t_4 (* t_0 (+ (* x1 2.0) t_7)))))))
           (/ (- (* 36.0 (* x2 x2)) (* x1 x1)) (- (* x2 -6.0) x1))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0;
	double t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0);
	double t_4 = t_1 * t_2;
	double t_5 = x1 + (x2 * 6.0);
	double t_6 = x1 * (x1 * x1);
	double t_7 = (x1 * x1) * ((t_2 * 4.0) - 6.0);
	double tmp;
	if (x1 <= -6e+124) {
		tmp = (x1 / (t_5 / x1)) - (36.0 / (t_5 / (x2 * x2)));
	} else if (x1 <= -0.47) {
		tmp = x1 + (9.0 + (x1 + (t_6 + (t_4 + (t_0 * (t_7 + ((t_2 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - x1)))))))));
	} else if (x1 <= 30500000.0) {
		tmp = x1 + (t_3 + (x1 + (4.0 * (x2 * ((x1 * (2.0 * x2)) + (x1 * -3.0))))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + (t_3 + (x1 + (t_6 + (t_4 + (t_0 * ((x1 * 2.0) + t_7))))));
	} else {
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = ((t_1 + (2.0d0 * x2)) - x1) / t_0
    t_3 = 3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_0)
    t_4 = t_1 * t_2
    t_5 = x1 + (x2 * 6.0d0)
    t_6 = x1 * (x1 * x1)
    t_7 = (x1 * x1) * ((t_2 * 4.0d0) - 6.0d0)
    if (x1 <= (-6d+124)) then
        tmp = (x1 / (t_5 / x1)) - (36.0d0 / (t_5 / (x2 * x2)))
    else if (x1 <= (-0.47d0)) then
        tmp = x1 + (9.0d0 + (x1 + (t_6 + (t_4 + (t_0 * (t_7 + ((t_2 - 3.0d0) * ((x1 * 2.0d0) * ((2.0d0 * x2) - x1)))))))))
    else if (x1 <= 30500000.0d0) then
        tmp = x1 + (t_3 + (x1 + (4.0d0 * (x2 * ((x1 * (2.0d0 * x2)) + (x1 * (-3.0d0)))))))
    else if (x1 <= 1.35d+154) then
        tmp = x1 + (t_3 + (x1 + (t_6 + (t_4 + (t_0 * ((x1 * 2.0d0) + t_7))))))
    else
        tmp = ((36.0d0 * (x2 * x2)) - (x1 * x1)) / ((x2 * (-6.0d0)) - x1)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0;
	double t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0);
	double t_4 = t_1 * t_2;
	double t_5 = x1 + (x2 * 6.0);
	double t_6 = x1 * (x1 * x1);
	double t_7 = (x1 * x1) * ((t_2 * 4.0) - 6.0);
	double tmp;
	if (x1 <= -6e+124) {
		tmp = (x1 / (t_5 / x1)) - (36.0 / (t_5 / (x2 * x2)));
	} else if (x1 <= -0.47) {
		tmp = x1 + (9.0 + (x1 + (t_6 + (t_4 + (t_0 * (t_7 + ((t_2 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - x1)))))))));
	} else if (x1 <= 30500000.0) {
		tmp = x1 + (t_3 + (x1 + (4.0 * (x2 * ((x1 * (2.0 * x2)) + (x1 * -3.0))))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + (t_3 + (x1 + (t_6 + (t_4 + (t_0 * ((x1 * 2.0) + t_7))))));
	} else {
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0
	t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)
	t_4 = t_1 * t_2
	t_5 = x1 + (x2 * 6.0)
	t_6 = x1 * (x1 * x1)
	t_7 = (x1 * x1) * ((t_2 * 4.0) - 6.0)
	tmp = 0
	if x1 <= -6e+124:
		tmp = (x1 / (t_5 / x1)) - (36.0 / (t_5 / (x2 * x2)))
	elif x1 <= -0.47:
		tmp = x1 + (9.0 + (x1 + (t_6 + (t_4 + (t_0 * (t_7 + ((t_2 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - x1)))))))))
	elif x1 <= 30500000.0:
		tmp = x1 + (t_3 + (x1 + (4.0 * (x2 * ((x1 * (2.0 * x2)) + (x1 * -3.0))))))
	elif x1 <= 1.35e+154:
		tmp = x1 + (t_3 + (x1 + (t_6 + (t_4 + (t_0 * ((x1 * 2.0) + t_7))))))
	else:
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_0)
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_0))
	t_4 = Float64(t_1 * t_2)
	t_5 = Float64(x1 + Float64(x2 * 6.0))
	t_6 = Float64(x1 * Float64(x1 * x1))
	t_7 = Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0))
	tmp = 0.0
	if (x1 <= -6e+124)
		tmp = Float64(Float64(x1 / Float64(t_5 / x1)) - Float64(36.0 / Float64(t_5 / Float64(x2 * x2))));
	elseif (x1 <= -0.47)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_6 + Float64(t_4 + Float64(t_0 * Float64(t_7 + Float64(Float64(t_2 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(Float64(2.0 * x2) - x1))))))))));
	elseif (x1 <= 30500000.0)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(Float64(x1 * Float64(2.0 * x2)) + Float64(x1 * -3.0)))))));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(t_6 + Float64(t_4 + Float64(t_0 * Float64(Float64(x1 * 2.0) + t_7)))))));
	else
		tmp = Float64(Float64(Float64(36.0 * Float64(x2 * x2)) - Float64(x1 * x1)) / Float64(Float64(x2 * -6.0) - x1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * 3.0);
	t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0;
	t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0);
	t_4 = t_1 * t_2;
	t_5 = x1 + (x2 * 6.0);
	t_6 = x1 * (x1 * x1);
	t_7 = (x1 * x1) * ((t_2 * 4.0) - 6.0);
	tmp = 0.0;
	if (x1 <= -6e+124)
		tmp = (x1 / (t_5 / x1)) - (36.0 / (t_5 / (x2 * x2)));
	elseif (x1 <= -0.47)
		tmp = x1 + (9.0 + (x1 + (t_6 + (t_4 + (t_0 * (t_7 + ((t_2 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - x1)))))))));
	elseif (x1 <= 30500000.0)
		tmp = x1 + (t_3 + (x1 + (4.0 * (x2 * ((x1 * (2.0 * x2)) + (x1 * -3.0))))));
	elseif (x1 <= 1.35e+154)
		tmp = x1 + (t_3 + (x1 + (t_6 + (t_4 + (t_0 * ((x1 * 2.0) + t_7))))));
	else
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$1 * t$95$2), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -6e+124], N[(N[(x1 / N[(t$95$5 / x1), $MachinePrecision]), $MachinePrecision] - N[(36.0 / N[(t$95$5 / N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -0.47], N[(x1 + N[(9.0 + N[(x1 + N[(t$95$6 + N[(t$95$4 + N[(t$95$0 * N[(t$95$7 + N[(N[(t$95$2 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 30500000.0], N[(x1 + N[(t$95$3 + N[(x1 + N[(4.0 * N[(x2 * N[(N[(x1 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(t$95$3 + N[(x1 + N[(t$95$6 + N[(t$95$4 + N[(t$95$0 * N[(N[(x1 * 2.0), $MachinePrecision] + t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(36.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision] - N[(x1 * x1), $MachinePrecision]), $MachinePrecision] / N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -5.9999999999999999e124

   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%

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

   3. Taylor expanded in x1 around 0 1.1%

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

      1. *-commutative 1.1%

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

   5. Simplified 1.1%

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

      1. flip-+ 7.0%

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

      2. div-sub 7.0%

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

      3. *-commutative 7.0%

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

      4. cancel-sign-sub-inv 7.0%

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

      5. metadata-eval 7.0%

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

      6. *-commutative 7.0%

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

      7. *-commutative 7.0%

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

      8. swap-sqr 7.0%

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

      9. metadata-eval 7.0%

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

      10. *-commutative 7.0%

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

      11. cancel-sign-sub-inv 7.0%

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

      12. metadata-eval 7.0%

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

   7. Applied egg-rr 7.0%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1}{x1 + 6 \cdot x2} - \frac{36 \cdot \left(x2 \cdot x2\right)}{x1 + 6 \cdot x2}} \]
   8. Step-by-step derivation

      1. associate-/l* 28.0%

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

      2. unpow2 28.0%

         \[\leadsto \frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \frac{36 \cdot \color{blue}{{x2}^{2}}}{x1 + 6 \cdot x2} \]

      3. associate-/l* 28.0%

         \[\leadsto \frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \color{blue}{\frac{36}{\frac{x1 + 6 \cdot x2}{{x2}^{2}}}} \]

      4. unpow2 28.0%

         \[\leadsto \frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \frac{36}{\frac{x1 + 6 \cdot x2}{\color{blue}{x2 \cdot x2}}} \]

   9. Simplified 28.0%

      \[\leadsto \color{blue}{\frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \frac{36}{\frac{x1 + 6 \cdot x2}{x2 \cdot x2}}} \]

   if -5.9999999999999999e124 < x1 < -0.46999999999999997

   1. Initial program 92.0%

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

   2. Taylor expanded in x1 around 0 79.7%

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

   3. Taylor expanded in x1 around inf 79.7%

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

   if -0.46999999999999997 < x1 < 3.05e7

   1. Initial program 98.5%

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

   2. Taylor expanded in x1 around 0 87.3%

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

      1. associate-*r* 98.5%

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

      2. sub-neg 98.5%

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

      3. metadata-eval 98.5%

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

      4. distribute-rgt-in 98.5%

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

      5. *-commutative 98.5%

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

   4. Applied egg-rr 98.5%

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

      1. *-commutative 98.5%

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

      2. associate-*r* 98.5%

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

      3. associate-*r* 98.5%

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

      4. distribute-rgt-out 98.5%

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

      5. *-commutative 98.5%

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

      6. *-commutative 98.5%

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

   6. Applied egg-rr 98.5%

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

   if 3.05e7 < x1 < 1.35000000000000003e154

   1. Initial program 97.1%

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

   2. Taylor expanded in x1 around 0 84.9%

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

   3. Taylor expanded in x1 around inf 93.5%

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

      1. *-commutative 93.5%

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

   5. Simplified 93.5%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 6.8%

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

      1. *-commutative 6.8%

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

   5. Simplified 6.8%

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

      1. +-commutative 6.8%

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

      2. flip-+ 74.1%

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

      3. *-commutative 74.1%

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

      4. *-commutative 74.1%

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

      5. swap-sqr 74.1%

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

      6. metadata-eval 74.1%

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

   7. Applied egg-rr 74.1%

      \[\leadsto \color{blue}{\frac{36 \cdot \left(x2 \cdot x2\right) - x1 \cdot x1}{x2 \cdot -6 - x1}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6 \cdot 10^{+124}:\\ \;\;\;\;\frac{x1}{\frac{x1 + x2 \cdot 6}{x1}} - \frac{36}{\frac{x1 + x2 \cdot 6}{x2 \cdot x2}}\\ \mathbf{elif}\;x1 \leq -0.47:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 30500000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2\right) + x1 \cdot -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{36 \cdot \left(x2 \cdot x2\right) - x1 \cdot x1}{x2 \cdot -6 - x1}\\ \end{array} \]

Alternative 8: 78.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + x2 \cdot 6\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := 3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_2}\\ t_4 := \frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_2}\\ t_5 := x1 + \left(t_3 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_1 \cdot t_4 + t_2 \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(t_4 \cdot 4 - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -1.22 \cdot 10^{+125}:\\ \;\;\;\;\frac{x1}{\frac{t_0}{x1}} - \frac{36}{\frac{t_0}{x2 \cdot x2}}\\ \mathbf{elif}\;x1 \leq -22000000000000:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x1 \leq 1450000000:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2\right) + x1 \cdot -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;\frac{36 \cdot \left(x2 \cdot x2\right) - x1 \cdot x1}{x2 \cdot -6 - x1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* x2 6.0)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2)))
        (t_4 (/ (- (+ t_1 (* 2.0 x2)) x1) t_2))
        (t_5
         (+
          x1
          (+
           t_3
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* t_1 t_4)
              (* t_2 (+ (* x1 2.0) (* (* x1 x1) (- (* t_4 4.0) 6.0)))))))))))
   (if (<= x1 -1.22e+125)
     (- (/ x1 (/ t_0 x1)) (/ 36.0 (/ t_0 (* x2 x2))))
     (if (<= x1 -22000000000000.0)
       t_5
       (if (<= x1 1450000000.0)
         (+ x1 (+ t_3 (+ x1 (* 4.0 (* x2 (+ (* x1 (* 2.0 x2)) (* x1 -3.0)))))))
         (if (<= x1 1.35e+154)
           t_5
           (/ (- (* 36.0 (* x2 x2)) (* x1 x1)) (- (* x2 -6.0) x1))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x2 * 6.0);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double t_4 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	double t_5 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_4) + (t_2 * ((x1 * 2.0) + ((x1 * x1) * ((t_4 * 4.0) - 6.0))))))));
	double tmp;
	if (x1 <= -1.22e+125) {
		tmp = (x1 / (t_0 / x1)) - (36.0 / (t_0 / (x2 * x2)));
	} else if (x1 <= -22000000000000.0) {
		tmp = t_5;
	} else if (x1 <= 1450000000.0) {
		tmp = x1 + (t_3 + (x1 + (4.0 * (x2 * ((x1 * (2.0 * x2)) + (x1 * -3.0))))));
	} else if (x1 <= 1.35e+154) {
		tmp = t_5;
	} else {
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = x1 + (x2 * 6.0d0)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = 3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_2)
    t_4 = ((t_1 + (2.0d0 * x2)) - x1) / t_2
    t_5 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_4) + (t_2 * ((x1 * 2.0d0) + ((x1 * x1) * ((t_4 * 4.0d0) - 6.0d0))))))))
    if (x1 <= (-1.22d+125)) then
        tmp = (x1 / (t_0 / x1)) - (36.0d0 / (t_0 / (x2 * x2)))
    else if (x1 <= (-22000000000000.0d0)) then
        tmp = t_5
    else if (x1 <= 1450000000.0d0) then
        tmp = x1 + (t_3 + (x1 + (4.0d0 * (x2 * ((x1 * (2.0d0 * x2)) + (x1 * (-3.0d0)))))))
    else if (x1 <= 1.35d+154) then
        tmp = t_5
    else
        tmp = ((36.0d0 * (x2 * x2)) - (x1 * x1)) / ((x2 * (-6.0d0)) - x1)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x2 * 6.0);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double t_4 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	double t_5 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_4) + (t_2 * ((x1 * 2.0) + ((x1 * x1) * ((t_4 * 4.0) - 6.0))))))));
	double tmp;
	if (x1 <= -1.22e+125) {
		tmp = (x1 / (t_0 / x1)) - (36.0 / (t_0 / (x2 * x2)));
	} else if (x1 <= -22000000000000.0) {
		tmp = t_5;
	} else if (x1 <= 1450000000.0) {
		tmp = x1 + (t_3 + (x1 + (4.0 * (x2 * ((x1 * (2.0 * x2)) + (x1 * -3.0))))));
	} else if (x1 <= 1.35e+154) {
		tmp = t_5;
	} else {
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x2 * 6.0)
	t_1 = x1 * (x1 * 3.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)
	t_4 = ((t_1 + (2.0 * x2)) - x1) / t_2
	t_5 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_4) + (t_2 * ((x1 * 2.0) + ((x1 * x1) * ((t_4 * 4.0) - 6.0))))))))
	tmp = 0
	if x1 <= -1.22e+125:
		tmp = (x1 / (t_0 / x1)) - (36.0 / (t_0 / (x2 * x2)))
	elif x1 <= -22000000000000.0:
		tmp = t_5
	elif x1 <= 1450000000.0:
		tmp = x1 + (t_3 + (x1 + (4.0 * (x2 * ((x1 * (2.0 * x2)) + (x1 * -3.0))))))
	elif x1 <= 1.35e+154:
		tmp = t_5
	else:
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x2 * 6.0))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2))
	t_4 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_2)
	t_5 = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * t_4) + Float64(t_2 * Float64(Float64(x1 * 2.0) + Float64(Float64(x1 * x1) * Float64(Float64(t_4 * 4.0) - 6.0)))))))))
	tmp = 0.0
	if (x1 <= -1.22e+125)
		tmp = Float64(Float64(x1 / Float64(t_0 / x1)) - Float64(36.0 / Float64(t_0 / Float64(x2 * x2))));
	elseif (x1 <= -22000000000000.0)
		tmp = t_5;
	elseif (x1 <= 1450000000.0)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(Float64(x1 * Float64(2.0 * x2)) + Float64(x1 * -3.0)))))));
	elseif (x1 <= 1.35e+154)
		tmp = t_5;
	else
		tmp = Float64(Float64(Float64(36.0 * Float64(x2 * x2)) - Float64(x1 * x1)) / Float64(Float64(x2 * -6.0) - x1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x2 * 6.0);
	t_1 = x1 * (x1 * 3.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	t_4 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	t_5 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_4) + (t_2 * ((x1 * 2.0) + ((x1 * x1) * ((t_4 * 4.0) - 6.0))))))));
	tmp = 0.0;
	if (x1 <= -1.22e+125)
		tmp = (x1 / (t_0 / x1)) - (36.0 / (t_0 / (x2 * x2)));
	elseif (x1 <= -22000000000000.0)
		tmp = t_5;
	elseif (x1 <= 1450000000.0)
		tmp = x1 + (t_3 + (x1 + (4.0 * (x2 * ((x1 * (2.0 * x2)) + (x1 * -3.0))))));
	elseif (x1 <= 1.35e+154)
		tmp = t_5;
	else
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x2 * 6.0), $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[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(t$95$3 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * t$95$4), $MachinePrecision] + N[(t$95$2 * N[(N[(x1 * 2.0), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$4 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.22e+125], N[(N[(x1 / N[(t$95$0 / x1), $MachinePrecision]), $MachinePrecision] - N[(36.0 / N[(t$95$0 / N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -22000000000000.0], t$95$5, If[LessEqual[x1, 1450000000.0], N[(x1 + N[(t$95$3 + N[(x1 + N[(4.0 * N[(x2 * N[(N[(x1 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], t$95$5, N[(N[(N[(36.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision] - N[(x1 * x1), $MachinePrecision]), $MachinePrecision] / N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.22e125

   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%

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

   3. Taylor expanded in x1 around 0 1.1%

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

      1. *-commutative 1.1%

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

   5. Simplified 1.1%

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

      1. flip-+ 7.0%

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

      2. div-sub 7.0%

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

      3. *-commutative 7.0%

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

      4. cancel-sign-sub-inv 7.0%

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

      5. metadata-eval 7.0%

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

      6. *-commutative 7.0%

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

      7. *-commutative 7.0%

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

      8. swap-sqr 7.0%

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

      9. metadata-eval 7.0%

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

      10. *-commutative 7.0%

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

      11. cancel-sign-sub-inv 7.0%

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

      12. metadata-eval 7.0%

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

   7. Applied egg-rr 7.0%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1}{x1 + 6 \cdot x2} - \frac{36 \cdot \left(x2 \cdot x2\right)}{x1 + 6 \cdot x2}} \]
   8. Step-by-step derivation

      1. associate-/l* 28.0%

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

      2. unpow2 28.0%

         \[\leadsto \frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \frac{36 \cdot \color{blue}{{x2}^{2}}}{x1 + 6 \cdot x2} \]

      3. associate-/l* 28.0%

         \[\leadsto \frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \color{blue}{\frac{36}{\frac{x1 + 6 \cdot x2}{{x2}^{2}}}} \]

      4. unpow2 28.0%

         \[\leadsto \frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \frac{36}{\frac{x1 + 6 \cdot x2}{\color{blue}{x2 \cdot x2}}} \]

   9. Simplified 28.0%

      \[\leadsto \color{blue}{\frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \frac{36}{\frac{x1 + 6 \cdot x2}{x2 \cdot x2}}} \]

   if -1.22e125 < x1 < -2.2e13 or 1.45e9 < x1 < 1.35000000000000003e154

   1. Initial program 94.8%

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

   2. Taylor expanded in x1 around 0 85.6%

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

   3. Taylor expanded in x1 around inf 89.3%

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

      1. *-commutative 89.3%

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

   5. Simplified 89.3%

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

   if -2.2e13 < x1 < 1.45e9

   1. Initial program 98.5%

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

   2. Taylor expanded in x1 around 0 85.5%

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

      1. associate-*r* 96.2%

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

      2. sub-neg 96.2%

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

      3. metadata-eval 96.2%

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

      4. distribute-rgt-in 96.2%

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

      5. *-commutative 96.2%

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

   4. Applied egg-rr 96.2%

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

      1. *-commutative 96.2%

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

      2. associate-*r* 96.2%

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

      3. associate-*r* 96.2%

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

      4. distribute-rgt-out 96.2%

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

      5. *-commutative 96.2%

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

      6. *-commutative 96.2%

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

   6. Applied egg-rr 96.2%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 6.8%

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

      1. *-commutative 6.8%

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

   5. Simplified 6.8%

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

      1. +-commutative 6.8%

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

      2. flip-+ 74.1%

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

      3. *-commutative 74.1%

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

      4. *-commutative 74.1%

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

      5. swap-sqr 74.1%

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

      6. metadata-eval 74.1%

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

   7. Applied egg-rr 74.1%

      \[\leadsto \color{blue}{\frac{36 \cdot \left(x2 \cdot x2\right) - x1 \cdot x1}{x2 \cdot -6 - x1}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.22 \cdot 10^{+125}:\\ \;\;\;\;\frac{x1}{\frac{x1 + x2 \cdot 6}{x1}} - \frac{36}{\frac{x1 + x2 \cdot 6}{x2 \cdot x2}}\\ \mathbf{elif}\;x1 \leq -22000000000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1450000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2\right) + x1 \cdot -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{36 \cdot \left(x2 \cdot x2\right) - x1 \cdot x1}{x2 \cdot -6 - x1}\\ \end{array} \]

Alternative 9: 76.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 + x2 \cdot 6\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \frac{\left(t_2 + 2 \cdot x2\right) - x1}{t_0}\\ t_4 := x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_2 \cdot t_3 + t_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t_3 \cdot 4 - 6\right) + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -9.8 \cdot 10^{+124}:\\ \;\;\;\;\frac{x1}{\frac{t_1}{x1}} - \frac{36}{\frac{t_1}{x2 \cdot x2}}\\ \mathbf{elif}\;x1 \leq -4.4 \cdot 10^{-27}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x1 \leq 4.8 \cdot 10^{+21}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_2 - 2 \cdot x2\right) - x1}{t_0} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2\right) + x1 \cdot -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;\frac{36 \cdot \left(x2 \cdot x2\right) - x1 \cdot x1}{x2 \cdot -6 - x1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (+ x1 (* x2 6.0)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (/ (- (+ t_2 (* 2.0 x2)) x1) t_0))
        (t_4
         (+
          x1
          (+
           9.0
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* t_2 t_3)
              (*
               t_0
               (+
                (* (* x1 x1) (- (* t_3 4.0) 6.0))
                (* 4.0 (* x1 (* x2 (- (* 2.0 x2) 3.0)))))))))))))
   (if (<= x1 -9.8e+124)
     (- (/ x1 (/ t_1 x1)) (/ 36.0 (/ t_1 (* x2 x2))))
     (if (<= x1 -4.4e-27)
       t_4
       (if (<= x1 4.8e+21)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_0))
           (+ x1 (* 4.0 (* x2 (+ (* x1 (* 2.0 x2)) (* x1 -3.0)))))))
         (if (<= x1 1.35e+154)
           t_4
           (/ (- (* 36.0 (* x2 x2)) (* x1 x1)) (- (* x2 -6.0) x1))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 + (x2 * 6.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = ((t_2 + (2.0 * x2)) - x1) / t_0;
	double t_4 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_3) + (t_0 * (((x1 * x1) * ((t_3 * 4.0) - 6.0)) + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))))))));
	double tmp;
	if (x1 <= -9.8e+124) {
		tmp = (x1 / (t_1 / x1)) - (36.0 / (t_1 / (x2 * x2)));
	} else if (x1 <= -4.4e-27) {
		tmp = t_4;
	} else if (x1 <= 4.8e+21) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * ((x1 * (2.0 * x2)) + (x1 * -3.0))))));
	} else if (x1 <= 1.35e+154) {
		tmp = t_4;
	} else {
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 + (x2 * 6.0d0)
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = ((t_2 + (2.0d0 * x2)) - x1) / t_0
    t_4 = x1 + (9.0d0 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_3) + (t_0 * (((x1 * x1) * ((t_3 * 4.0d0) - 6.0d0)) + (4.0d0 * (x1 * (x2 * ((2.0d0 * x2) - 3.0d0))))))))))
    if (x1 <= (-9.8d+124)) then
        tmp = (x1 / (t_1 / x1)) - (36.0d0 / (t_1 / (x2 * x2)))
    else if (x1 <= (-4.4d-27)) then
        tmp = t_4
    else if (x1 <= 4.8d+21) then
        tmp = x1 + ((3.0d0 * (((t_2 - (2.0d0 * x2)) - x1) / t_0)) + (x1 + (4.0d0 * (x2 * ((x1 * (2.0d0 * x2)) + (x1 * (-3.0d0)))))))
    else if (x1 <= 1.35d+154) then
        tmp = t_4
    else
        tmp = ((36.0d0 * (x2 * x2)) - (x1 * x1)) / ((x2 * (-6.0d0)) - x1)
    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 + (x2 * 6.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = ((t_2 + (2.0 * x2)) - x1) / t_0;
	double t_4 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_3) + (t_0 * (((x1 * x1) * ((t_3 * 4.0) - 6.0)) + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))))))));
	double tmp;
	if (x1 <= -9.8e+124) {
		tmp = (x1 / (t_1 / x1)) - (36.0 / (t_1 / (x2 * x2)));
	} else if (x1 <= -4.4e-27) {
		tmp = t_4;
	} else if (x1 <= 4.8e+21) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * ((x1 * (2.0 * x2)) + (x1 * -3.0))))));
	} else if (x1 <= 1.35e+154) {
		tmp = t_4;
	} else {
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 + (x2 * 6.0)
	t_2 = x1 * (x1 * 3.0)
	t_3 = ((t_2 + (2.0 * x2)) - x1) / t_0
	t_4 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_3) + (t_0 * (((x1 * x1) * ((t_3 * 4.0) - 6.0)) + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))))))))
	tmp = 0
	if x1 <= -9.8e+124:
		tmp = (x1 / (t_1 / x1)) - (36.0 / (t_1 / (x2 * x2)))
	elif x1 <= -4.4e-27:
		tmp = t_4
	elif x1 <= 4.8e+21:
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * ((x1 * (2.0 * x2)) + (x1 * -3.0))))))
	elif x1 <= 1.35e+154:
		tmp = t_4
	else:
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 + Float64(x2 * 6.0))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(Float64(t_2 + Float64(2.0 * x2)) - x1) / t_0)
	t_4 = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_2 * t_3) + Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0)) + Float64(4.0 * Float64(x1 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))))))))))
	tmp = 0.0
	if (x1 <= -9.8e+124)
		tmp = Float64(Float64(x1 / Float64(t_1 / x1)) - Float64(36.0 / Float64(t_1 / Float64(x2 * x2))));
	elseif (x1 <= -4.4e-27)
		tmp = t_4;
	elseif (x1 <= 4.8e+21)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(Float64(x1 * Float64(2.0 * x2)) + Float64(x1 * -3.0)))))));
	elseif (x1 <= 1.35e+154)
		tmp = t_4;
	else
		tmp = Float64(Float64(Float64(36.0 * Float64(x2 * x2)) - Float64(x1 * x1)) / Float64(Float64(x2 * -6.0) - x1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 + (x2 * 6.0);
	t_2 = x1 * (x1 * 3.0);
	t_3 = ((t_2 + (2.0 * x2)) - x1) / t_0;
	t_4 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_3) + (t_0 * (((x1 * x1) * ((t_3 * 4.0) - 6.0)) + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))))))));
	tmp = 0.0;
	if (x1 <= -9.8e+124)
		tmp = (x1 / (t_1 / x1)) - (36.0 / (t_1 / (x2 * x2)));
	elseif (x1 <= -4.4e-27)
		tmp = t_4;
	elseif (x1 <= 4.8e+21)
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * ((x1 * (2.0 * x2)) + (x1 * -3.0))))));
	elseif (x1 <= 1.35e+154)
		tmp = t_4;
	else
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1);
	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[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(9.0 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * t$95$3), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x1 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -9.8e+124], N[(N[(x1 / N[(t$95$1 / x1), $MachinePrecision]), $MachinePrecision] - N[(36.0 / N[(t$95$1 / N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -4.4e-27], t$95$4, If[LessEqual[x1, 4.8e+21], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x2 * N[(N[(x1 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], t$95$4, N[(N[(N[(36.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision] - N[(x1 * x1), $MachinePrecision]), $MachinePrecision] / N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -9.80000000000000069e124

   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%

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

   3. Taylor expanded in x1 around 0 1.1%

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

      1. *-commutative 1.1%

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

   5. Simplified 1.1%

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

      1. flip-+ 7.0%

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

      2. div-sub 7.0%

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

      3. *-commutative 7.0%

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

      4. cancel-sign-sub-inv 7.0%

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

      5. metadata-eval 7.0%

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

      6. *-commutative 7.0%

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

      7. *-commutative 7.0%

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

      8. swap-sqr 7.0%

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

      9. metadata-eval 7.0%

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

      10. *-commutative 7.0%

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

      11. cancel-sign-sub-inv 7.0%

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

      12. metadata-eval 7.0%

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

   7. Applied egg-rr 7.0%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1}{x1 + 6 \cdot x2} - \frac{36 \cdot \left(x2 \cdot x2\right)}{x1 + 6 \cdot x2}} \]
   8. Step-by-step derivation

      1. associate-/l* 28.0%

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

      2. unpow2 28.0%

         \[\leadsto \frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \frac{36 \cdot \color{blue}{{x2}^{2}}}{x1 + 6 \cdot x2} \]

      3. associate-/l* 28.0%

         \[\leadsto \frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \color{blue}{\frac{36}{\frac{x1 + 6 \cdot x2}{{x2}^{2}}}} \]

      4. unpow2 28.0%

         \[\leadsto \frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \frac{36}{\frac{x1 + 6 \cdot x2}{\color{blue}{x2 \cdot x2}}} \]

   9. Simplified 28.0%

      \[\leadsto \color{blue}{\frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \frac{36}{\frac{x1 + 6 \cdot x2}{x2 \cdot x2}}} \]

   if -9.80000000000000069e124 < x1 < -4.39999999999999974e-27 or 4.8e21 < x1 < 1.35000000000000003e154

   1. Initial program 95.1%

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

   2. Taylor expanded in x1 around 0 84.3%

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

   3. Taylor expanded in x1 around 0 81.8%

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

   4. Taylor expanded in x1 around inf 81.8%

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

   if -4.39999999999999974e-27 < x1 < 4.8e21

   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 86.5%

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

      1. associate-*r* 97.7%

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

      2. sub-neg 97.7%

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

      3. metadata-eval 97.7%

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

      4. distribute-rgt-in 97.7%

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

      5. *-commutative 97.7%

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

   4. Applied egg-rr 97.7%

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

      1. *-commutative 97.7%

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

      2. associate-*r* 97.7%

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

      3. associate-*r* 97.7%

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

      4. distribute-rgt-out 97.7%

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

      5. *-commutative 97.7%

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

      6. *-commutative 97.7%

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

   6. Applied egg-rr 97.7%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 6.8%

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

      1. *-commutative 6.8%

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

   5. Simplified 6.8%

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

      1. +-commutative 6.8%

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

      2. flip-+ 74.1%

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

      3. *-commutative 74.1%

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

      4. *-commutative 74.1%

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

      5. swap-sqr 74.1%

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

      6. metadata-eval 74.1%

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

   7. Applied egg-rr 74.1%

      \[\leadsto \color{blue}{\frac{36 \cdot \left(x2 \cdot x2\right) - x1 \cdot x1}{x2 \cdot -6 - x1}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9.8 \cdot 10^{+124}:\\ \;\;\;\;\frac{x1}{\frac{x1 + x2 \cdot 6}{x1}} - \frac{36}{\frac{x1 + x2 \cdot 6}{x2 \cdot x2}}\\ \mathbf{elif}\;x1 \leq -4.4 \cdot 10^{-27}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.8 \cdot 10^{+21}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2\right) + x1 \cdot -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{36 \cdot \left(x2 \cdot x2\right) - x1 \cdot x1}{x2 \cdot -6 - x1}\\ \end{array} \]

Alternative 10: 76.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + x2 \cdot 6\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := 3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_2}\\ t_4 := x1 + \left(t_3 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_1 \cdot \frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_2} + t_2 \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;\frac{x1}{\frac{t_0}{x1}} - \frac{36}{\frac{t_0}{x2 \cdot x2}}\\ \mathbf{elif}\;x1 \leq -5.2 \cdot 10^{+16}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x1 \leq 16200000000:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2\right) + x1 \cdot -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;\frac{36 \cdot \left(x2 \cdot x2\right) - x1 \cdot x1}{x2 \cdot -6 - x1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* x2 6.0)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2)))
        (t_4
         (+
          x1
          (+
           t_3
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* t_1 (/ (- (+ t_1 (* 2.0 x2)) x1) t_2))
              (* t_2 (* x1 (* x1 6.0))))))))))
   (if (<= x1 -5.6e+102)
     (- (/ x1 (/ t_0 x1)) (/ 36.0 (/ t_0 (* x2 x2))))
     (if (<= x1 -5.2e+16)
       t_4
       (if (<= x1 16200000000.0)
         (+ x1 (+ t_3 (+ x1 (* 4.0 (* x2 (+ (* x1 (* 2.0 x2)) (* x1 -3.0)))))))
         (if (<= x1 1.35e+154)
           t_4
           (/ (- (* 36.0 (* x2 x2)) (* x1 x1)) (- (* x2 -6.0) x1))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x2 * 6.0);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double t_4 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((t_1 + (2.0 * x2)) - x1) / t_2)) + (t_2 * (x1 * (x1 * 6.0)))))));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = (x1 / (t_0 / x1)) - (36.0 / (t_0 / (x2 * x2)));
	} else if (x1 <= -5.2e+16) {
		tmp = t_4;
	} else if (x1 <= 16200000000.0) {
		tmp = x1 + (t_3 + (x1 + (4.0 * (x2 * ((x1 * (2.0 * x2)) + (x1 * -3.0))))));
	} else if (x1 <= 1.35e+154) {
		tmp = t_4;
	} else {
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = x1 + (x2 * 6.0d0)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = 3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_2)
    t_4 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((t_1 + (2.0d0 * x2)) - x1) / t_2)) + (t_2 * (x1 * (x1 * 6.0d0)))))))
    if (x1 <= (-5.6d+102)) then
        tmp = (x1 / (t_0 / x1)) - (36.0d0 / (t_0 / (x2 * x2)))
    else if (x1 <= (-5.2d+16)) then
        tmp = t_4
    else if (x1 <= 16200000000.0d0) then
        tmp = x1 + (t_3 + (x1 + (4.0d0 * (x2 * ((x1 * (2.0d0 * x2)) + (x1 * (-3.0d0)))))))
    else if (x1 <= 1.35d+154) then
        tmp = t_4
    else
        tmp = ((36.0d0 * (x2 * x2)) - (x1 * x1)) / ((x2 * (-6.0d0)) - x1)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x2 * 6.0);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double t_4 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((t_1 + (2.0 * x2)) - x1) / t_2)) + (t_2 * (x1 * (x1 * 6.0)))))));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = (x1 / (t_0 / x1)) - (36.0 / (t_0 / (x2 * x2)));
	} else if (x1 <= -5.2e+16) {
		tmp = t_4;
	} else if (x1 <= 16200000000.0) {
		tmp = x1 + (t_3 + (x1 + (4.0 * (x2 * ((x1 * (2.0 * x2)) + (x1 * -3.0))))));
	} else if (x1 <= 1.35e+154) {
		tmp = t_4;
	} else {
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x2 * 6.0)
	t_1 = x1 * (x1 * 3.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)
	t_4 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((t_1 + (2.0 * x2)) - x1) / t_2)) + (t_2 * (x1 * (x1 * 6.0)))))))
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = (x1 / (t_0 / x1)) - (36.0 / (t_0 / (x2 * x2)))
	elif x1 <= -5.2e+16:
		tmp = t_4
	elif x1 <= 16200000000.0:
		tmp = x1 + (t_3 + (x1 + (4.0 * (x2 * ((x1 * (2.0 * x2)) + (x1 * -3.0))))))
	elif x1 <= 1.35e+154:
		tmp = t_4
	else:
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x2 * 6.0))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2))
	t_4 = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_2)) + Float64(t_2 * Float64(x1 * Float64(x1 * 6.0))))))))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(Float64(x1 / Float64(t_0 / x1)) - Float64(36.0 / Float64(t_0 / Float64(x2 * x2))));
	elseif (x1 <= -5.2e+16)
		tmp = t_4;
	elseif (x1 <= 16200000000.0)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(Float64(x1 * Float64(2.0 * x2)) + Float64(x1 * -3.0)))))));
	elseif (x1 <= 1.35e+154)
		tmp = t_4;
	else
		tmp = Float64(Float64(Float64(36.0 * Float64(x2 * x2)) - Float64(x1 * x1)) / Float64(Float64(x2 * -6.0) - x1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x2 * 6.0);
	t_1 = x1 * (x1 * 3.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	t_4 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((t_1 + (2.0 * x2)) - x1) / t_2)) + (t_2 * (x1 * (x1 * 6.0)))))));
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = (x1 / (t_0 / x1)) - (36.0 / (t_0 / (x2 * x2)));
	elseif (x1 <= -5.2e+16)
		tmp = t_4;
	elseif (x1 <= 16200000000.0)
		tmp = x1 + (t_3 + (x1 + (4.0 * (x2 * ((x1 * (2.0 * x2)) + (x1 * -3.0))))));
	elseif (x1 <= 1.35e+154)
		tmp = t_4;
	else
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x2 * 6.0), $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[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(t$95$3 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * N[(x1 * N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(N[(x1 / N[(t$95$0 / x1), $MachinePrecision]), $MachinePrecision] - N[(36.0 / N[(t$95$0 / N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5.2e+16], t$95$4, If[LessEqual[x1, 16200000000.0], N[(x1 + N[(t$95$3 + N[(x1 + N[(4.0 * N[(x2 * N[(N[(x1 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], t$95$4, N[(N[(N[(36.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision] - N[(x1 * x1), $MachinePrecision]), $MachinePrecision] / N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 2.2%

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

   2. Taylor expanded in x1 around 0 2.2%

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

   3. Taylor expanded in x1 around 0 1.0%

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

      1. *-commutative 1.0%

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

   5. Simplified 1.0%

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

      1. flip-+ 6.5%

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

      2. div-sub 6.5%

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

      3. *-commutative 6.5%

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

      4. cancel-sign-sub-inv 6.5%

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

      5. metadata-eval 6.5%

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

      6. *-commutative 6.5%

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

      7. *-commutative 6.5%

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

      8. swap-sqr 6.5%

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

      9. metadata-eval 6.5%

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

      10. *-commutative 6.5%

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

      11. cancel-sign-sub-inv 6.5%

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

      12. metadata-eval 6.5%

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

   7. Applied egg-rr 6.5%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1}{x1 + 6 \cdot x2} - \frac{36 \cdot \left(x2 \cdot x2\right)}{x1 + 6 \cdot x2}} \]
   8. Step-by-step derivation

      1. associate-/l* 26.2%

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

      2. unpow2 26.2%

         \[\leadsto \frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \frac{36 \cdot \color{blue}{{x2}^{2}}}{x1 + 6 \cdot x2} \]

      3. associate-/l* 26.2%

         \[\leadsto \frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \color{blue}{\frac{36}{\frac{x1 + 6 \cdot x2}{{x2}^{2}}}} \]

      4. unpow2 26.2%

         \[\leadsto \frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \frac{36}{\frac{x1 + 6 \cdot x2}{\color{blue}{x2 \cdot x2}}} \]

   9. Simplified 26.2%

      \[\leadsto \color{blue}{\frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \frac{36}{\frac{x1 + 6 \cdot x2}{x2 \cdot x2}}} \]

   if -5.60000000000000037e102 < x1 < -5.2e16 or 1.62e10 < x1 < 1.35000000000000003e154

   1. Initial program 97.8%

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

   2. Taylor expanded in x1 around 0 88.2%

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

   3. Taylor expanded in x1 around 0 85.1%

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

   4. Taylor expanded in x1 around inf 81.4%

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

      1. *-commutative 81.4%

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

      2. unpow2 81.4%

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

      3. associate-*r* 81.5%

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

   6. Simplified 81.5%

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

   if -5.2e16 < x1 < 1.62e10

   1. Initial program 98.5%

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

   2. Taylor expanded in x1 around 0 85.5%

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

      1. associate-*r* 96.2%

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

      2. sub-neg 96.2%

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

      3. metadata-eval 96.2%

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

      4. distribute-rgt-in 96.2%

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

      5. *-commutative 96.2%

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

   4. Applied egg-rr 96.2%

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

      1. *-commutative 96.2%

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

      2. associate-*r* 96.2%

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

      3. associate-*r* 96.2%

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

      4. distribute-rgt-out 96.2%

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

      5. *-commutative 96.2%

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

      6. *-commutative 96.2%

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

   6. Applied egg-rr 96.2%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 6.8%

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

      1. *-commutative 6.8%

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

   5. Simplified 6.8%

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

      1. +-commutative 6.8%

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

      2. flip-+ 74.1%

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

      3. *-commutative 74.1%

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

      4. *-commutative 74.1%

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

      5. swap-sqr 74.1%

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

      6. metadata-eval 74.1%

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

   7. Applied egg-rr 74.1%

      \[\leadsto \color{blue}{\frac{36 \cdot \left(x2 \cdot x2\right) - x1 \cdot x1}{x2 \cdot -6 - x1}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;\frac{x1}{\frac{x1 + x2 \cdot 6}{x1}} - \frac{36}{\frac{x1 + x2 \cdot 6}{x2 \cdot x2}}\\ \mathbf{elif}\;x1 \leq -5.2 \cdot 10^{+16}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 16200000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2\right) + x1 \cdot -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{36 \cdot \left(x2 \cdot x2\right) - x1 \cdot x1}{x2 \cdot -6 - x1}\\ \end{array} \]

Alternative 11: 63.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 36 \cdot \left(x2 \cdot x2\right)\\ t_1 := x1 + x2 \cdot 6\\ \mathbf{if}\;x1 \leq -9 \cdot 10^{+124}:\\ \;\;\;\;\frac{x1}{\frac{t_1}{x1}} - \frac{36}{\frac{t_1}{x2 \cdot x2}}\\ \mathbf{elif}\;x1 \leq -1.45 \cdot 10^{-165}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{-285}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq 3.4 \cdot 10^{+114}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(2 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;\frac{\left(x1 \cdot x1\right) \cdot t_1 - t_1 \cdot t_0}{t_1 \cdot t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0 - x1 \cdot x1}{x2 \cdot -6 - x1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 36.0 (* x2 x2))) (t_1 (+ x1 (* x2 6.0))))
   (if (<= x1 -9e+124)
     (- (/ x1 (/ t_1 x1)) (/ 36.0 (/ t_1 (* x2 x2))))
     (if (<= x1 -1.45e-165)
       (+ (* x2 -6.0) (* x1 (+ -1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))))
       (if (<= x1 1e-285)
         (+ x1 (+ (* x1 -2.0) (* x2 (- (* x1 -12.0) 6.0))))
         (if (<= x1 3.4e+114)
           (+
            x1
            (+
             (*
              3.0
              (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
             (+ x1 (* 4.0 (* 2.0 (* x1 (* x2 x2)))))))
           (if (<= x1 1.35e+154)
             (/ (- (* (* x1 x1) t_1) (* t_1 t_0)) (* t_1 t_1))
             (/ (- t_0 (* x1 x1)) (- (* x2 -6.0) x1)))))))))

C

double code(double x1, double x2) {
	double t_0 = 36.0 * (x2 * x2);
	double t_1 = x1 + (x2 * 6.0);
	double tmp;
	if (x1 <= -9e+124) {
		tmp = (x1 / (t_1 / x1)) - (36.0 / (t_1 / (x2 * x2)));
	} else if (x1 <= -1.45e-165) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	} else if (x1 <= 1e-285) {
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	} else if (x1 <= 3.4e+114) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (2.0 * (x1 * (x2 * x2))))));
	} else if (x1 <= 1.35e+154) {
		tmp = (((x1 * x1) * t_1) - (t_1 * t_0)) / (t_1 * t_1);
	} else {
		tmp = (t_0 - (x1 * x1)) / ((x2 * -6.0) - x1);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 36.0d0 * (x2 * x2)
    t_1 = x1 + (x2 * 6.0d0)
    if (x1 <= (-9d+124)) then
        tmp = (x1 / (t_1 / x1)) - (36.0d0 / (t_1 / (x2 * x2)))
    else if (x1 <= (-1.45d-165)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0)))))
    else if (x1 <= 1d-285) then
        tmp = x1 + ((x1 * (-2.0d0)) + (x2 * ((x1 * (-12.0d0)) - 6.0d0)))
    else if (x1 <= 3.4d+114) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0))) + (x1 + (4.0d0 * (2.0d0 * (x1 * (x2 * x2))))))
    else if (x1 <= 1.35d+154) then
        tmp = (((x1 * x1) * t_1) - (t_1 * t_0)) / (t_1 * t_1)
    else
        tmp = (t_0 - (x1 * x1)) / ((x2 * (-6.0d0)) - x1)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 36.0 * (x2 * x2);
	double t_1 = x1 + (x2 * 6.0);
	double tmp;
	if (x1 <= -9e+124) {
		tmp = (x1 / (t_1 / x1)) - (36.0 / (t_1 / (x2 * x2)));
	} else if (x1 <= -1.45e-165) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	} else if (x1 <= 1e-285) {
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	} else if (x1 <= 3.4e+114) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (2.0 * (x1 * (x2 * x2))))));
	} else if (x1 <= 1.35e+154) {
		tmp = (((x1 * x1) * t_1) - (t_1 * t_0)) / (t_1 * t_1);
	} else {
		tmp = (t_0 - (x1 * x1)) / ((x2 * -6.0) - x1);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 36.0 * (x2 * x2)
	t_1 = x1 + (x2 * 6.0)
	tmp = 0
	if x1 <= -9e+124:
		tmp = (x1 / (t_1 / x1)) - (36.0 / (t_1 / (x2 * x2)))
	elif x1 <= -1.45e-165:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))))
	elif x1 <= 1e-285:
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)))
	elif x1 <= 3.4e+114:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (2.0 * (x1 * (x2 * x2))))))
	elif x1 <= 1.35e+154:
		tmp = (((x1 * x1) * t_1) - (t_1 * t_0)) / (t_1 * t_1)
	else:
		tmp = (t_0 - (x1 * x1)) / ((x2 * -6.0) - x1)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(36.0 * Float64(x2 * x2))
	t_1 = Float64(x1 + Float64(x2 * 6.0))
	tmp = 0.0
	if (x1 <= -9e+124)
		tmp = Float64(Float64(x1 / Float64(t_1 / x1)) - Float64(36.0 / Float64(t_1 / Float64(x2 * x2))));
	elseif (x1 <= -1.45e-165)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))));
	elseif (x1 <= 1e-285)
		tmp = Float64(x1 + Float64(Float64(x1 * -2.0) + Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0))));
	elseif (x1 <= 3.4e+114)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))) + Float64(x1 + Float64(4.0 * Float64(2.0 * Float64(x1 * Float64(x2 * x2)))))));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(Float64(Float64(Float64(x1 * x1) * t_1) - Float64(t_1 * t_0)) / Float64(t_1 * t_1));
	else
		tmp = Float64(Float64(t_0 - Float64(x1 * x1)) / Float64(Float64(x2 * -6.0) - x1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 36.0 * (x2 * x2);
	t_1 = x1 + (x2 * 6.0);
	tmp = 0.0;
	if (x1 <= -9e+124)
		tmp = (x1 / (t_1 / x1)) - (36.0 / (t_1 / (x2 * x2)));
	elseif (x1 <= -1.45e-165)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	elseif (x1 <= 1e-285)
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	elseif (x1 <= 3.4e+114)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (2.0 * (x1 * (x2 * x2))))));
	elseif (x1 <= 1.35e+154)
		tmp = (((x1 * x1) * t_1) - (t_1 * t_0)) / (t_1 * t_1);
	else
		tmp = (t_0 - (x1 * x1)) / ((x2 * -6.0) - x1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(36.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -9e+124], N[(N[(x1 / N[(t$95$1 / x1), $MachinePrecision]), $MachinePrecision] - N[(36.0 / N[(t$95$1 / N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.45e-165], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1e-285], N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.4e+114], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(2.0 * N[(x1 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(N[(N[(N[(x1 * x1), $MachinePrecision] * t$95$1), $MachinePrecision] - N[(t$95$1 * t$95$0), $MachinePrecision]), $MachinePrecision] / N[(t$95$1 * t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision] / N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x1 < -9.0000000000000008e124

   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%

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

   3. Taylor expanded in x1 around 0 1.1%

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

      1. *-commutative 1.1%

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

   5. Simplified 1.1%

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

      1. flip-+ 7.0%

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

      2. div-sub 7.0%

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

      3. *-commutative 7.0%

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

      4. cancel-sign-sub-inv 7.0%

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

      5. metadata-eval 7.0%

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

      6. *-commutative 7.0%

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

      7. *-commutative 7.0%

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

      8. swap-sqr 7.0%

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

      9. metadata-eval 7.0%

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

      10. *-commutative 7.0%

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

      11. cancel-sign-sub-inv 7.0%

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

      12. metadata-eval 7.0%

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

   7. Applied egg-rr 7.0%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1}{x1 + 6 \cdot x2} - \frac{36 \cdot \left(x2 \cdot x2\right)}{x1 + 6 \cdot x2}} \]
   8. Step-by-step derivation

      1. associate-/l* 28.0%

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

      2. unpow2 28.0%

         \[\leadsto \frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \frac{36 \cdot \color{blue}{{x2}^{2}}}{x1 + 6 \cdot x2} \]

      3. associate-/l* 28.0%

         \[\leadsto \frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \color{blue}{\frac{36}{\frac{x1 + 6 \cdot x2}{{x2}^{2}}}} \]

      4. unpow2 28.0%

         \[\leadsto \frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \frac{36}{\frac{x1 + 6 \cdot x2}{\color{blue}{x2 \cdot x2}}} \]

   9. Simplified 28.0%

      \[\leadsto \color{blue}{\frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \frac{36}{\frac{x1 + 6 \cdot x2}{x2 \cdot x2}}} \]

   if -9.0000000000000008e124 < x1 < -1.45e-165

   1. Initial program 95.7%

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

   2. Taylor expanded in x1 around 0 56.1%

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

   3. Taylor expanded in x1 around 0 57.4%

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

      1. fma-def 57.4%

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

      2. associate-*r* 57.4%

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

      3. *-commutative 57.4%

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

      4. fma-neg 57.4%

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

      5. metadata-eval 57.4%

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

      6. fma-neg 57.4%

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

      7. *-commutative 57.4%

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

      8. metadata-eval 57.4%

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

   5. Simplified 57.4%

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

   6. Taylor expanded in x1 around 0 57.4%

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

   if -1.45e-165 < x1 < 1.00000000000000007e-285

   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 78.3%

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

   3. Taylor expanded in x1 around 0 78.7%

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

      1. fma-def 78.9%

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

      2. associate-*r* 78.9%

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

      3. *-commutative 78.9%

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

      4. fma-neg 78.9%

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

      5. metadata-eval 78.9%

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

      6. fma-neg 78.9%

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

      7. *-commutative 78.9%

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

      8. metadata-eval 78.9%

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

   5. Simplified 78.9%

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

   6. Taylor expanded in x2 around 0 99.7%

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

   if 1.00000000000000007e-285 < x1 < 3.4000000000000001e114

   1. Initial program 98.2%

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

   2. Taylor expanded in x1 around 0 76.7%

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

   3. Taylor expanded in x2 around inf 76.7%

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

      1. unpow2 76.7%

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

   5. Simplified 76.7%

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

   if 3.4000000000000001e114 < x1 < 1.35000000000000003e154

   1. Initial program 93.3%

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

   2. Taylor expanded in x1 around 0 16.9%

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

   3. Taylor expanded in x1 around 0 3.9%

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

      1. *-commutative 3.9%

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

   5. Simplified 3.9%

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

      1. flip-+ 3.9%

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

      2. div-sub 3.9%

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

      3. frac-sub 80.0%

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

      4. *-commutative 80.0%

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

      5. cancel-sign-sub-inv 80.0%

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

      6. metadata-eval 80.0%

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

      7. *-commutative 80.0%

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

      8. cancel-sign-sub-inv 80.0%

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

      9. metadata-eval 80.0%

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

      10. *-commutative 80.0%

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

      11. *-commutative 80.0%

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

      12. swap-sqr 80.0%

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

      13. metadata-eval 80.0%

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

   7. Applied egg-rr 80.0%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 6.8%

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

      1. *-commutative 6.8%

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

   5. Simplified 6.8%

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

      1. +-commutative 6.8%

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

      2. flip-+ 74.1%

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

      3. *-commutative 74.1%

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

      4. *-commutative 74.1%

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

      5. swap-sqr 74.1%

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

      6. metadata-eval 74.1%

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

   7. Applied egg-rr 74.1%

      \[\leadsto \color{blue}{\frac{36 \cdot \left(x2 \cdot x2\right) - x1 \cdot x1}{x2 \cdot -6 - x1}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9 \cdot 10^{+124}:\\ \;\;\;\;\frac{x1}{\frac{x1 + x2 \cdot 6}{x1}} - \frac{36}{\frac{x1 + x2 \cdot 6}{x2 \cdot x2}}\\ \mathbf{elif}\;x1 \leq -1.45 \cdot 10^{-165}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{-285}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq 3.4 \cdot 10^{+114}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(2 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;\frac{\left(x1 \cdot x1\right) \cdot \left(x1 + x2 \cdot 6\right) - \left(x1 + x2 \cdot 6\right) \cdot \left(36 \cdot \left(x2 \cdot x2\right)\right)}{\left(x1 + x2 \cdot 6\right) \cdot \left(x1 + x2 \cdot 6\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{36 \cdot \left(x2 \cdot x2\right) - x1 \cdot x1}{x2 \cdot -6 - x1}\\ \end{array} \]

Alternative 12: 62.2% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + x2 \cdot 6\\ \mathbf{if}\;x1 \leq -2.6 \cdot 10^{+125}:\\ \;\;\;\;\frac{x1}{\frac{t_0}{x1}} - \frac{36}{\frac{t_0}{x2 \cdot x2}}\\ \mathbf{elif}\;x1 \leq -8.4 \cdot 10^{-166}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.9 \cdot 10^{-285}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(2 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{36 \cdot \left(x2 \cdot x2\right) - x1 \cdot x1}{x2 \cdot -6 - x1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* x2 6.0))))
   (if (<= x1 -2.6e+125)
     (- (/ x1 (/ t_0 x1)) (/ 36.0 (/ t_0 (* x2 x2))))
     (if (<= x1 -8.4e-166)
       (+ (* x2 -6.0) (* x1 (+ -1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))))
       (if (<= x1 4.9e-285)
         (+ x1 (+ (* x1 -2.0) (* x2 (- (* x1 -12.0) 6.0))))
         (if (<= x1 1.35e+154)
           (+
            x1
            (+
             (*
              3.0
              (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
             (+ x1 (* 4.0 (* 2.0 (* x1 (* x2 x2)))))))
           (/ (- (* 36.0 (* x2 x2)) (* x1 x1)) (- (* x2 -6.0) x1))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x2 * 6.0);
	double tmp;
	if (x1 <= -2.6e+125) {
		tmp = (x1 / (t_0 / x1)) - (36.0 / (t_0 / (x2 * x2)));
	} else if (x1 <= -8.4e-166) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	} else if (x1 <= 4.9e-285) {
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (2.0 * (x1 * (x2 * x2))))));
	} else {
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + (x2 * 6.0d0)
    if (x1 <= (-2.6d+125)) then
        tmp = (x1 / (t_0 / x1)) - (36.0d0 / (t_0 / (x2 * x2)))
    else if (x1 <= (-8.4d-166)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0)))))
    else if (x1 <= 4.9d-285) then
        tmp = x1 + ((x1 * (-2.0d0)) + (x2 * ((x1 * (-12.0d0)) - 6.0d0)))
    else if (x1 <= 1.35d+154) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0))) + (x1 + (4.0d0 * (2.0d0 * (x1 * (x2 * x2))))))
    else
        tmp = ((36.0d0 * (x2 * x2)) - (x1 * x1)) / ((x2 * (-6.0d0)) - x1)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x2 * 6.0);
	double tmp;
	if (x1 <= -2.6e+125) {
		tmp = (x1 / (t_0 / x1)) - (36.0 / (t_0 / (x2 * x2)));
	} else if (x1 <= -8.4e-166) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	} else if (x1 <= 4.9e-285) {
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (2.0 * (x1 * (x2 * x2))))));
	} else {
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x2 * 6.0)
	tmp = 0
	if x1 <= -2.6e+125:
		tmp = (x1 / (t_0 / x1)) - (36.0 / (t_0 / (x2 * x2)))
	elif x1 <= -8.4e-166:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))))
	elif x1 <= 4.9e-285:
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)))
	elif x1 <= 1.35e+154:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (2.0 * (x1 * (x2 * x2))))))
	else:
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x2 * 6.0))
	tmp = 0.0
	if (x1 <= -2.6e+125)
		tmp = Float64(Float64(x1 / Float64(t_0 / x1)) - Float64(36.0 / Float64(t_0 / Float64(x2 * x2))));
	elseif (x1 <= -8.4e-166)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))));
	elseif (x1 <= 4.9e-285)
		tmp = Float64(x1 + Float64(Float64(x1 * -2.0) + Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0))));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))) + Float64(x1 + Float64(4.0 * Float64(2.0 * Float64(x1 * Float64(x2 * x2)))))));
	else
		tmp = Float64(Float64(Float64(36.0 * Float64(x2 * x2)) - Float64(x1 * x1)) / Float64(Float64(x2 * -6.0) - x1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x2 * 6.0);
	tmp = 0.0;
	if (x1 <= -2.6e+125)
		tmp = (x1 / (t_0 / x1)) - (36.0 / (t_0 / (x2 * x2)));
	elseif (x1 <= -8.4e-166)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	elseif (x1 <= 4.9e-285)
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	elseif (x1 <= 1.35e+154)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (2.0 * (x1 * (x2 * x2))))));
	else
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.6e+125], N[(N[(x1 / N[(t$95$0 / x1), $MachinePrecision]), $MachinePrecision] - N[(36.0 / N[(t$95$0 / N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -8.4e-166], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.9e-285], N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(2.0 * N[(x1 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(36.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision] - N[(x1 * x1), $MachinePrecision]), $MachinePrecision] / N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -2.60000000000000003e125

   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%

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

   3. Taylor expanded in x1 around 0 1.1%

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

      1. *-commutative 1.1%

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

   5. Simplified 1.1%

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

      1. flip-+ 7.0%

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

      2. div-sub 7.0%

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

      3. *-commutative 7.0%

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

      4. cancel-sign-sub-inv 7.0%

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

      5. metadata-eval 7.0%

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

      6. *-commutative 7.0%

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

      7. *-commutative 7.0%

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

      8. swap-sqr 7.0%

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

      9. metadata-eval 7.0%

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

      10. *-commutative 7.0%

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

      11. cancel-sign-sub-inv 7.0%

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

      12. metadata-eval 7.0%

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

   7. Applied egg-rr 7.0%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1}{x1 + 6 \cdot x2} - \frac{36 \cdot \left(x2 \cdot x2\right)}{x1 + 6 \cdot x2}} \]
   8. Step-by-step derivation

      1. associate-/l* 28.0%

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

      2. unpow2 28.0%

         \[\leadsto \frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \frac{36 \cdot \color{blue}{{x2}^{2}}}{x1 + 6 \cdot x2} \]

      3. associate-/l* 28.0%

         \[\leadsto \frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \color{blue}{\frac{36}{\frac{x1 + 6 \cdot x2}{{x2}^{2}}}} \]

      4. unpow2 28.0%

         \[\leadsto \frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \frac{36}{\frac{x1 + 6 \cdot x2}{\color{blue}{x2 \cdot x2}}} \]

   9. Simplified 28.0%

      \[\leadsto \color{blue}{\frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \frac{36}{\frac{x1 + 6 \cdot x2}{x2 \cdot x2}}} \]

   if -2.60000000000000003e125 < x1 < -8.3999999999999998e-166

   1. Initial program 95.7%

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

   2. Taylor expanded in x1 around 0 56.1%

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

   3. Taylor expanded in x1 around 0 57.4%

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

      1. fma-def 57.4%

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

      2. associate-*r* 57.4%

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

      3. *-commutative 57.4%

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

      4. fma-neg 57.4%

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

      5. metadata-eval 57.4%

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

      6. fma-neg 57.4%

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

      7. *-commutative 57.4%

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

      8. metadata-eval 57.4%

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

   5. Simplified 57.4%

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

   6. Taylor expanded in x1 around 0 57.4%

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

   if -8.3999999999999998e-166 < x1 < 4.89999999999999975e-285

   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 78.3%

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

   3. Taylor expanded in x1 around 0 78.7%

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

      1. fma-def 78.9%

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

      2. associate-*r* 78.9%

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

      3. *-commutative 78.9%

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

      4. fma-neg 78.9%

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

      5. metadata-eval 78.9%

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

      6. fma-neg 78.9%

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

      7. *-commutative 78.9%

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

      8. metadata-eval 78.9%

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

   5. Simplified 78.9%

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

   6. Taylor expanded in x2 around 0 99.7%

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

   if 4.89999999999999975e-285 < x1 < 1.35000000000000003e154

   1. Initial program 97.5%

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

   2. Taylor expanded in x1 around 0 67.9%

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

   3. Taylor expanded in x2 around inf 67.9%

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

      1. unpow2 67.9%

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

   5. Simplified 67.9%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 6.8%

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

      1. *-commutative 6.8%

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

   5. Simplified 6.8%

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

      1. +-commutative 6.8%

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

      2. flip-+ 74.1%

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

      3. *-commutative 74.1%

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

      4. *-commutative 74.1%

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

      5. swap-sqr 74.1%

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

      6. metadata-eval 74.1%

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

   7. Applied egg-rr 74.1%

      \[\leadsto \color{blue}{\frac{36 \cdot \left(x2 \cdot x2\right) - x1 \cdot x1}{x2 \cdot -6 - x1}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.6 \cdot 10^{+125}:\\ \;\;\;\;\frac{x1}{\frac{x1 + x2 \cdot 6}{x1}} - \frac{36}{\frac{x1 + x2 \cdot 6}{x2 \cdot x2}}\\ \mathbf{elif}\;x1 \leq -8.4 \cdot 10^{-166}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.9 \cdot 10^{-285}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(2 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{36 \cdot \left(x2 \cdot x2\right) - x1 \cdot x1}{x2 \cdot -6 - x1}\\ \end{array} \]

Alternative 13: 68.0% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 36 \cdot \left(x2 \cdot x2\right)\\ t_1 := x1 + x2 \cdot 6\\ \mathbf{if}\;x1 \leq -4.6 \cdot 10^{+124}:\\ \;\;\;\;\frac{x1}{\frac{t_1}{x1}} - \frac{36}{\frac{t_1}{x2 \cdot x2}}\\ \mathbf{elif}\;x1 \leq 3.4 \cdot 10^{+114}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2\right) + x1 \cdot -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;\frac{\left(x1 \cdot x1\right) \cdot t_1 - t_1 \cdot t_0}{t_1 \cdot t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0 - x1 \cdot x1}{x2 \cdot -6 - x1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 36.0 (* x2 x2))) (t_1 (+ x1 (* x2 6.0))))
   (if (<= x1 -4.6e+124)
     (- (/ x1 (/ t_1 x1)) (/ 36.0 (/ t_1 (* x2 x2))))
     (if (<= x1 3.4e+114)
       (+
        x1
        (+
         (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
         (+ x1 (* 4.0 (* x2 (+ (* x1 (* 2.0 x2)) (* x1 -3.0)))))))
       (if (<= x1 1.35e+154)
         (/ (- (* (* x1 x1) t_1) (* t_1 t_0)) (* t_1 t_1))
         (/ (- t_0 (* x1 x1)) (- (* x2 -6.0) x1)))))))

C

double code(double x1, double x2) {
	double t_0 = 36.0 * (x2 * x2);
	double t_1 = x1 + (x2 * 6.0);
	double tmp;
	if (x1 <= -4.6e+124) {
		tmp = (x1 / (t_1 / x1)) - (36.0 / (t_1 / (x2 * x2)));
	} else if (x1 <= 3.4e+114) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x2 * ((x1 * (2.0 * x2)) + (x1 * -3.0))))));
	} else if (x1 <= 1.35e+154) {
		tmp = (((x1 * x1) * t_1) - (t_1 * t_0)) / (t_1 * t_1);
	} else {
		tmp = (t_0 - (x1 * x1)) / ((x2 * -6.0) - x1);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 36.0d0 * (x2 * x2)
    t_1 = x1 + (x2 * 6.0d0)
    if (x1 <= (-4.6d+124)) then
        tmp = (x1 / (t_1 / x1)) - (36.0d0 / (t_1 / (x2 * x2)))
    else if (x1 <= 3.4d+114) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0))) + (x1 + (4.0d0 * (x2 * ((x1 * (2.0d0 * x2)) + (x1 * (-3.0d0)))))))
    else if (x1 <= 1.35d+154) then
        tmp = (((x1 * x1) * t_1) - (t_1 * t_0)) / (t_1 * t_1)
    else
        tmp = (t_0 - (x1 * x1)) / ((x2 * (-6.0d0)) - x1)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 36.0 * (x2 * x2);
	double t_1 = x1 + (x2 * 6.0);
	double tmp;
	if (x1 <= -4.6e+124) {
		tmp = (x1 / (t_1 / x1)) - (36.0 / (t_1 / (x2 * x2)));
	} else if (x1 <= 3.4e+114) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x2 * ((x1 * (2.0 * x2)) + (x1 * -3.0))))));
	} else if (x1 <= 1.35e+154) {
		tmp = (((x1 * x1) * t_1) - (t_1 * t_0)) / (t_1 * t_1);
	} else {
		tmp = (t_0 - (x1 * x1)) / ((x2 * -6.0) - x1);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 36.0 * (x2 * x2)
	t_1 = x1 + (x2 * 6.0)
	tmp = 0
	if x1 <= -4.6e+124:
		tmp = (x1 / (t_1 / x1)) - (36.0 / (t_1 / (x2 * x2)))
	elif x1 <= 3.4e+114:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x2 * ((x1 * (2.0 * x2)) + (x1 * -3.0))))))
	elif x1 <= 1.35e+154:
		tmp = (((x1 * x1) * t_1) - (t_1 * t_0)) / (t_1 * t_1)
	else:
		tmp = (t_0 - (x1 * x1)) / ((x2 * -6.0) - x1)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(36.0 * Float64(x2 * x2))
	t_1 = Float64(x1 + Float64(x2 * 6.0))
	tmp = 0.0
	if (x1 <= -4.6e+124)
		tmp = Float64(Float64(x1 / Float64(t_1 / x1)) - Float64(36.0 / Float64(t_1 / Float64(x2 * x2))));
	elseif (x1 <= 3.4e+114)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(Float64(x1 * Float64(2.0 * x2)) + Float64(x1 * -3.0)))))));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(Float64(Float64(Float64(x1 * x1) * t_1) - Float64(t_1 * t_0)) / Float64(t_1 * t_1));
	else
		tmp = Float64(Float64(t_0 - Float64(x1 * x1)) / Float64(Float64(x2 * -6.0) - x1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 36.0 * (x2 * x2);
	t_1 = x1 + (x2 * 6.0);
	tmp = 0.0;
	if (x1 <= -4.6e+124)
		tmp = (x1 / (t_1 / x1)) - (36.0 / (t_1 / (x2 * x2)));
	elseif (x1 <= 3.4e+114)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x2 * ((x1 * (2.0 * x2)) + (x1 * -3.0))))));
	elseif (x1 <= 1.35e+154)
		tmp = (((x1 * x1) * t_1) - (t_1 * t_0)) / (t_1 * t_1);
	else
		tmp = (t_0 - (x1 * x1)) / ((x2 * -6.0) - x1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(36.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.6e+124], N[(N[(x1 / N[(t$95$1 / x1), $MachinePrecision]), $MachinePrecision] - N[(36.0 / N[(t$95$1 / N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.4e+114], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x2 * N[(N[(x1 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(N[(N[(N[(x1 * x1), $MachinePrecision] * t$95$1), $MachinePrecision] - N[(t$95$1 * t$95$0), $MachinePrecision]), $MachinePrecision] / N[(t$95$1 * t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision] / N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.59999999999999969e124

   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%

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

   3. Taylor expanded in x1 around 0 1.1%

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

      1. *-commutative 1.1%

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

   5. Simplified 1.1%

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

      1. flip-+ 7.0%

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

      2. div-sub 7.0%

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

      3. *-commutative 7.0%

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

      4. cancel-sign-sub-inv 7.0%

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

      5. metadata-eval 7.0%

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

      6. *-commutative 7.0%

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

      7. *-commutative 7.0%

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

      8. swap-sqr 7.0%

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

      9. metadata-eval 7.0%

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

      10. *-commutative 7.0%

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

      11. cancel-sign-sub-inv 7.0%

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

      12. metadata-eval 7.0%

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

   7. Applied egg-rr 7.0%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1}{x1 + 6 \cdot x2} - \frac{36 \cdot \left(x2 \cdot x2\right)}{x1 + 6 \cdot x2}} \]
   8. Step-by-step derivation

      1. associate-/l* 28.0%

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

      2. unpow2 28.0%

         \[\leadsto \frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \frac{36 \cdot \color{blue}{{x2}^{2}}}{x1 + 6 \cdot x2} \]

      3. associate-/l* 28.0%

         \[\leadsto \frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \color{blue}{\frac{36}{\frac{x1 + 6 \cdot x2}{{x2}^{2}}}} \]

      4. unpow2 28.0%

         \[\leadsto \frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \frac{36}{\frac{x1 + 6 \cdot x2}{\color{blue}{x2 \cdot x2}}} \]

   9. Simplified 28.0%

      \[\leadsto \color{blue}{\frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \frac{36}{\frac{x1 + 6 \cdot x2}{x2 \cdot x2}}} \]

   if -4.59999999999999969e124 < x1 < 3.4000000000000001e114

   1. Initial program 97.6%

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

   2. Taylor expanded in x1 around 0 70.2%

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

      1. associate-*r* 78.0%

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

      2. sub-neg 78.0%

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

      3. metadata-eval 78.0%

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

      4. distribute-rgt-in 76.2%

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

      5. *-commutative 76.2%

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

   4. Applied egg-rr 76.2%

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

      1. *-commutative 76.2%

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

      2. associate-*r* 76.2%

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

      3. associate-*r* 76.2%

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

      4. distribute-rgt-out 78.0%

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

      5. *-commutative 78.0%

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

      6. *-commutative 78.0%

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

   6. Applied egg-rr 78.0%

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

   if 3.4000000000000001e114 < x1 < 1.35000000000000003e154

   1. Initial program 93.3%

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

   2. Taylor expanded in x1 around 0 16.9%

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

   3. Taylor expanded in x1 around 0 3.9%

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

      1. *-commutative 3.9%

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

   5. Simplified 3.9%

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

      1. flip-+ 3.9%

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

      2. div-sub 3.9%

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

      3. frac-sub 80.0%

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

      4. *-commutative 80.0%

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

      5. cancel-sign-sub-inv 80.0%

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

      6. metadata-eval 80.0%

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

      7. *-commutative 80.0%

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

      8. cancel-sign-sub-inv 80.0%

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

      9. metadata-eval 80.0%

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

      10. *-commutative 80.0%

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

      11. *-commutative 80.0%

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

      12. swap-sqr 80.0%

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

      13. metadata-eval 80.0%

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

   7. Applied egg-rr 80.0%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 6.8%

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

      1. *-commutative 6.8%

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

   5. Simplified 6.8%

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

      1. +-commutative 6.8%

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

      2. flip-+ 74.1%

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

      3. *-commutative 74.1%

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

      4. *-commutative 74.1%

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

      5. swap-sqr 74.1%

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

      6. metadata-eval 74.1%

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

   7. Applied egg-rr 74.1%

      \[\leadsto \color{blue}{\frac{36 \cdot \left(x2 \cdot x2\right) - x1 \cdot x1}{x2 \cdot -6 - x1}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.6 \cdot 10^{+124}:\\ \;\;\;\;\frac{x1}{\frac{x1 + x2 \cdot 6}{x1}} - \frac{36}{\frac{x1 + x2 \cdot 6}{x2 \cdot x2}}\\ \mathbf{elif}\;x1 \leq 3.4 \cdot 10^{+114}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2\right) + x1 \cdot -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;\frac{\left(x1 \cdot x1\right) \cdot \left(x1 + x2 \cdot 6\right) - \left(x1 + x2 \cdot 6\right) \cdot \left(36 \cdot \left(x2 \cdot x2\right)\right)}{\left(x1 + x2 \cdot 6\right) \cdot \left(x1 + x2 \cdot 6\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{36 \cdot \left(x2 \cdot x2\right) - x1 \cdot x1}{x2 \cdot -6 - x1}\\ \end{array} \]

Alternative 14: 62.2% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x2 \cdot -6 + x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ t_1 := x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq -8.4 \cdot 10^{-166}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 4.9 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq 7.6 \cdot 10^{+147}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{36 \cdot \left(x2 \cdot x2\right) - x1 \cdot x1}{x2 \cdot -6 - x1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x2 -6.0) (* x1 (+ -1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))))))
        (t_1 (+ x1 (+ (* x1 -2.0) (* x2 (- (* x1 -12.0) 6.0))))))
   (if (<= x1 -5.5e+66)
     t_1
     (if (<= x1 -8.4e-166)
       t_0
       (if (<= x1 4.9e-285)
         t_1
         (if (<= x1 7.6e+147)
           t_0
           (/ (- (* 36.0 (* x2 x2)) (* x1 x1)) (- (* x2 -6.0) x1))))))))

C

double code(double x1, double x2) {
	double t_0 = (x2 * -6.0) + (x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	double t_1 = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	double tmp;
	if (x1 <= -5.5e+66) {
		tmp = t_1;
	} else if (x1 <= -8.4e-166) {
		tmp = t_0;
	} else if (x1 <= 4.9e-285) {
		tmp = t_1;
	} else if (x1 <= 7.6e+147) {
		tmp = t_0;
	} else {
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0)))))
    t_1 = x1 + ((x1 * (-2.0d0)) + (x2 * ((x1 * (-12.0d0)) - 6.0d0)))
    if (x1 <= (-5.5d+66)) then
        tmp = t_1
    else if (x1 <= (-8.4d-166)) then
        tmp = t_0
    else if (x1 <= 4.9d-285) then
        tmp = t_1
    else if (x1 <= 7.6d+147) then
        tmp = t_0
    else
        tmp = ((36.0d0 * (x2 * x2)) - (x1 * x1)) / ((x2 * (-6.0d0)) - x1)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x2 * -6.0) + (x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	double t_1 = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	double tmp;
	if (x1 <= -5.5e+66) {
		tmp = t_1;
	} else if (x1 <= -8.4e-166) {
		tmp = t_0;
	} else if (x1 <= 4.9e-285) {
		tmp = t_1;
	} else if (x1 <= 7.6e+147) {
		tmp = t_0;
	} else {
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x2 * -6.0) + (x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))))
	t_1 = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)))
	tmp = 0
	if x1 <= -5.5e+66:
		tmp = t_1
	elif x1 <= -8.4e-166:
		tmp = t_0
	elif x1 <= 4.9e-285:
		tmp = t_1
	elif x1 <= 7.6e+147:
		tmp = t_0
	else:
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))))
	t_1 = Float64(x1 + Float64(Float64(x1 * -2.0) + Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0))))
	tmp = 0.0
	if (x1 <= -5.5e+66)
		tmp = t_1;
	elseif (x1 <= -8.4e-166)
		tmp = t_0;
	elseif (x1 <= 4.9e-285)
		tmp = t_1;
	elseif (x1 <= 7.6e+147)
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(36.0 * Float64(x2 * x2)) - Float64(x1 * x1)) / Float64(Float64(x2 * -6.0) - x1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x2 * -6.0) + (x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	t_1 = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	tmp = 0.0;
	if (x1 <= -5.5e+66)
		tmp = t_1;
	elseif (x1 <= -8.4e-166)
		tmp = t_0;
	elseif (x1 <= 4.9e-285)
		tmp = t_1;
	elseif (x1 <= 7.6e+147)
		tmp = t_0;
	else
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.5e+66], t$95$1, If[LessEqual[x1, -8.4e-166], t$95$0, If[LessEqual[x1, 4.9e-285], t$95$1, If[LessEqual[x1, 7.6e+147], t$95$0, N[(N[(N[(36.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision] - N[(x1 * x1), $MachinePrecision]), $MachinePrecision] / N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.5e66 or -8.3999999999999998e-166 < x1 < 4.89999999999999975e-285

   1. Initial program 43.5%

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

   2. Taylor expanded in x1 around 0 28.7%

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

   3. Taylor expanded in x1 around 0 30.7%

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

      1. fma-def 30.7%

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

      2. associate-*r* 30.7%

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

      3. *-commutative 30.7%

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

      4. fma-neg 30.7%

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

      5. metadata-eval 30.7%

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

      6. fma-neg 30.7%

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

      7. *-commutative 30.7%

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

      8. metadata-eval 30.7%

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

   5. Simplified 30.7%

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

   6. Taylor expanded in x2 around 0 49.3%

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

   if -5.5e66 < x1 < -8.3999999999999998e-166 or 4.89999999999999975e-285 < x1 < 7.59999999999999941e147

   1. Initial program 98.0%

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

   2. Taylor expanded in x1 around 0 68.6%

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

   3. Taylor expanded in x1 around 0 68.5%

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

      1. fma-def 69.3%

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

      2. associate-*r* 69.3%

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

      3. *-commutative 69.3%

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

      4. fma-neg 69.3%

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

      5. metadata-eval 69.3%

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

      6. fma-neg 69.3%

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

      7. *-commutative 69.3%

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

      8. metadata-eval 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in x1 around 0 68.5%

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

   if 7.59999999999999941e147 < x1

   1. Initial program 12.9%

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

   2. Taylor expanded in x1 around 0 0.6%

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

   3. Taylor expanded in x1 around 0 6.5%

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

      1. *-commutative 6.5%

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

   5. Simplified 6.5%

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

      1. +-commutative 6.5%

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

      2. flip-+ 65.1%

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

      3. *-commutative 65.1%

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

      4. *-commutative 65.1%

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

      5. swap-sqr 65.1%

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

      6. metadata-eval 65.1%

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

   7. Applied egg-rr 65.1%

      \[\leadsto \color{blue}{\frac{36 \cdot \left(x2 \cdot x2\right) - x1 \cdot x1}{x2 \cdot -6 - x1}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+66}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq -8.4 \cdot 10^{-166}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.9 \cdot 10^{-285}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq 7.6 \cdot 10^{+147}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{36 \cdot \left(x2 \cdot x2\right) - x1 \cdot x1}{x2 \cdot -6 - x1}\\ \end{array} \]

Alternative 15: 61.8% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x2 \cdot -6 + x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ t_1 := x1 + x2 \cdot 6\\ \mathbf{if}\;x1 \leq -5.4 \cdot 10^{+124}:\\ \;\;\;\;\frac{x1}{\frac{t_1}{x1}} - \frac{36}{\frac{t_1}{x2 \cdot x2}}\\ \mathbf{elif}\;x1 \leq -8.4 \cdot 10^{-166}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 4.9 \cdot 10^{-285}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq 7.6 \cdot 10^{+147}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{36 \cdot \left(x2 \cdot x2\right) - x1 \cdot x1}{x2 \cdot -6 - x1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x2 -6.0) (* x1 (+ -1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))))))
        (t_1 (+ x1 (* x2 6.0))))
   (if (<= x1 -5.4e+124)
     (- (/ x1 (/ t_1 x1)) (/ 36.0 (/ t_1 (* x2 x2))))
     (if (<= x1 -8.4e-166)
       t_0
       (if (<= x1 4.9e-285)
         (+ x1 (+ (* x1 -2.0) (* x2 (- (* x1 -12.0) 6.0))))
         (if (<= x1 7.6e+147)
           t_0
           (/ (- (* 36.0 (* x2 x2)) (* x1 x1)) (- (* x2 -6.0) x1))))))))

C

double code(double x1, double x2) {
	double t_0 = (x2 * -6.0) + (x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	double t_1 = x1 + (x2 * 6.0);
	double tmp;
	if (x1 <= -5.4e+124) {
		tmp = (x1 / (t_1 / x1)) - (36.0 / (t_1 / (x2 * x2)));
	} else if (x1 <= -8.4e-166) {
		tmp = t_0;
	} else if (x1 <= 4.9e-285) {
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	} else if (x1 <= 7.6e+147) {
		tmp = t_0;
	} else {
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0)))))
    t_1 = x1 + (x2 * 6.0d0)
    if (x1 <= (-5.4d+124)) then
        tmp = (x1 / (t_1 / x1)) - (36.0d0 / (t_1 / (x2 * x2)))
    else if (x1 <= (-8.4d-166)) then
        tmp = t_0
    else if (x1 <= 4.9d-285) then
        tmp = x1 + ((x1 * (-2.0d0)) + (x2 * ((x1 * (-12.0d0)) - 6.0d0)))
    else if (x1 <= 7.6d+147) then
        tmp = t_0
    else
        tmp = ((36.0d0 * (x2 * x2)) - (x1 * x1)) / ((x2 * (-6.0d0)) - x1)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x2 * -6.0) + (x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	double t_1 = x1 + (x2 * 6.0);
	double tmp;
	if (x1 <= -5.4e+124) {
		tmp = (x1 / (t_1 / x1)) - (36.0 / (t_1 / (x2 * x2)));
	} else if (x1 <= -8.4e-166) {
		tmp = t_0;
	} else if (x1 <= 4.9e-285) {
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	} else if (x1 <= 7.6e+147) {
		tmp = t_0;
	} else {
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x2 * -6.0) + (x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))))
	t_1 = x1 + (x2 * 6.0)
	tmp = 0
	if x1 <= -5.4e+124:
		tmp = (x1 / (t_1 / x1)) - (36.0 / (t_1 / (x2 * x2)))
	elif x1 <= -8.4e-166:
		tmp = t_0
	elif x1 <= 4.9e-285:
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)))
	elif x1 <= 7.6e+147:
		tmp = t_0
	else:
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))))
	t_1 = Float64(x1 + Float64(x2 * 6.0))
	tmp = 0.0
	if (x1 <= -5.4e+124)
		tmp = Float64(Float64(x1 / Float64(t_1 / x1)) - Float64(36.0 / Float64(t_1 / Float64(x2 * x2))));
	elseif (x1 <= -8.4e-166)
		tmp = t_0;
	elseif (x1 <= 4.9e-285)
		tmp = Float64(x1 + Float64(Float64(x1 * -2.0) + Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0))));
	elseif (x1 <= 7.6e+147)
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(36.0 * Float64(x2 * x2)) - Float64(x1 * x1)) / Float64(Float64(x2 * -6.0) - x1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x2 * -6.0) + (x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	t_1 = x1 + (x2 * 6.0);
	tmp = 0.0;
	if (x1 <= -5.4e+124)
		tmp = (x1 / (t_1 / x1)) - (36.0 / (t_1 / (x2 * x2)));
	elseif (x1 <= -8.4e-166)
		tmp = t_0;
	elseif (x1 <= 4.9e-285)
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	elseif (x1 <= 7.6e+147)
		tmp = t_0;
	else
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.4e+124], N[(N[(x1 / N[(t$95$1 / x1), $MachinePrecision]), $MachinePrecision] - N[(36.0 / N[(t$95$1 / N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -8.4e-166], t$95$0, If[LessEqual[x1, 4.9e-285], N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7.6e+147], t$95$0, N[(N[(N[(36.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision] - N[(x1 * x1), $MachinePrecision]), $MachinePrecision] / N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.39999999999999956e124

   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%

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

   3. Taylor expanded in x1 around 0 1.1%

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

      1. *-commutative 1.1%

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

   5. Simplified 1.1%

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

      1. flip-+ 7.0%

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

      2. div-sub 7.0%

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

      3. *-commutative 7.0%

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

      4. cancel-sign-sub-inv 7.0%

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

      5. metadata-eval 7.0%

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

      6. *-commutative 7.0%

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

      7. *-commutative 7.0%

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

      8. swap-sqr 7.0%

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

      9. metadata-eval 7.0%

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

      10. *-commutative 7.0%

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

      11. cancel-sign-sub-inv 7.0%

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

      12. metadata-eval 7.0%

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

   7. Applied egg-rr 7.0%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1}{x1 + 6 \cdot x2} - \frac{36 \cdot \left(x2 \cdot x2\right)}{x1 + 6 \cdot x2}} \]
   8. Step-by-step derivation

      1. associate-/l* 28.0%

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

      2. unpow2 28.0%

         \[\leadsto \frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \frac{36 \cdot \color{blue}{{x2}^{2}}}{x1 + 6 \cdot x2} \]

      3. associate-/l* 28.0%

         \[\leadsto \frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \color{blue}{\frac{36}{\frac{x1 + 6 \cdot x2}{{x2}^{2}}}} \]

      4. unpow2 28.0%

         \[\leadsto \frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \frac{36}{\frac{x1 + 6 \cdot x2}{\color{blue}{x2 \cdot x2}}} \]

   9. Simplified 28.0%

      \[\leadsto \color{blue}{\frac{x1}{\frac{x1 + 6 \cdot x2}{x1}} - \frac{36}{\frac{x1 + 6 \cdot x2}{x2 \cdot x2}}} \]

   if -5.39999999999999956e124 < x1 < -8.3999999999999998e-166 or 4.89999999999999975e-285 < x1 < 7.59999999999999941e147

   1. Initial program 96.8%

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

   2. Taylor expanded in x1 around 0 65.3%

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

   3. Taylor expanded in x1 around 0 65.2%

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

      1. fma-def 66.0%

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

      2. associate-*r* 66.0%

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

      3. *-commutative 66.0%

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

      4. fma-neg 66.0%

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

      5. metadata-eval 66.0%

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

      6. fma-neg 66.0%

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

      7. *-commutative 66.0%

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

      8. metadata-eval 66.0%

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

   5. Simplified 66.0%

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

   6. Taylor expanded in x1 around 0 65.2%

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

   if -8.3999999999999998e-166 < x1 < 4.89999999999999975e-285

   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 78.3%

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

   3. Taylor expanded in x1 around 0 78.7%

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

      1. fma-def 78.9%

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

      2. associate-*r* 78.9%

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

      3. *-commutative 78.9%

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

      4. fma-neg 78.9%

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

      5. metadata-eval 78.9%

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

      6. fma-neg 78.9%

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

      7. *-commutative 78.9%

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

      8. metadata-eval 78.9%

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

   5. Simplified 78.9%

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

   6. Taylor expanded in x2 around 0 99.7%

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

   if 7.59999999999999941e147 < x1

   1. Initial program 12.9%

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

   2. Taylor expanded in x1 around 0 0.6%

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

   3. Taylor expanded in x1 around 0 6.5%

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

      1. *-commutative 6.5%

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

   5. Simplified 6.5%

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

      1. +-commutative 6.5%

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

      2. flip-+ 65.1%

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

      3. *-commutative 65.1%

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

      4. *-commutative 65.1%

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

      5. swap-sqr 65.1%

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

      6. metadata-eval 65.1%

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

   7. Applied egg-rr 65.1%

      \[\leadsto \color{blue}{\frac{36 \cdot \left(x2 \cdot x2\right) - x1 \cdot x1}{x2 \cdot -6 - x1}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.4 \cdot 10^{+124}:\\ \;\;\;\;\frac{x1}{\frac{x1 + x2 \cdot 6}{x1}} - \frac{36}{\frac{x1 + x2 \cdot 6}{x2 \cdot x2}}\\ \mathbf{elif}\;x1 \leq -8.4 \cdot 10^{-166}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.9 \cdot 10^{-285}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq 7.6 \cdot 10^{+147}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{36 \cdot \left(x2 \cdot x2\right) - x1 \cdot x1}{x2 \cdot -6 - x1}\\ \end{array} \]

Alternative 16: 58.3% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ t_1 := x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{-109}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 1.02 \cdot 10^{-104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq 5.5 \cdot 10^{+147}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{36 \cdot \left(x2 \cdot x2\right) - x1 \cdot x1}{x2 \cdot -6 - x1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ -1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))))
        (t_1 (+ x1 (+ (* x1 -2.0) (* x2 (- (* x1 -12.0) 6.0))))))
   (if (<= x1 -5.5e+66)
     t_1
     (if (<= x1 -5.6e-109)
       t_0
       (if (<= x1 1.02e-104)
         t_1
         (if (<= x1 5.5e+147)
           t_0
           (/ (- (* 36.0 (* x2 x2)) (* x1 x1)) (- (* x2 -6.0) x1))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	double t_1 = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	double tmp;
	if (x1 <= -5.5e+66) {
		tmp = t_1;
	} else if (x1 <= -5.6e-109) {
		tmp = t_0;
	} else if (x1 <= 1.02e-104) {
		tmp = t_1;
	} else if (x1 <= 5.5e+147) {
		tmp = t_0;
	} else {
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x1 * ((-1.0d0) + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))))
    t_1 = x1 + ((x1 * (-2.0d0)) + (x2 * ((x1 * (-12.0d0)) - 6.0d0)))
    if (x1 <= (-5.5d+66)) then
        tmp = t_1
    else if (x1 <= (-5.6d-109)) then
        tmp = t_0
    else if (x1 <= 1.02d-104) then
        tmp = t_1
    else if (x1 <= 5.5d+147) then
        tmp = t_0
    else
        tmp = ((36.0d0 * (x2 * x2)) - (x1 * x1)) / ((x2 * (-6.0d0)) - x1)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	double t_1 = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	double tmp;
	if (x1 <= -5.5e+66) {
		tmp = t_1;
	} else if (x1 <= -5.6e-109) {
		tmp = t_0;
	} else if (x1 <= 1.02e-104) {
		tmp = t_1;
	} else if (x1 <= 5.5e+147) {
		tmp = t_0;
	} else {
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))))
	t_1 = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)))
	tmp = 0
	if x1 <= -5.5e+66:
		tmp = t_1
	elif x1 <= -5.6e-109:
		tmp = t_0
	elif x1 <= 1.02e-104:
		tmp = t_1
	elif x1 <= 5.5e+147:
		tmp = t_0
	else:
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(-1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))))
	t_1 = Float64(x1 + Float64(Float64(x1 * -2.0) + Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0))))
	tmp = 0.0
	if (x1 <= -5.5e+66)
		tmp = t_1;
	elseif (x1 <= -5.6e-109)
		tmp = t_0;
	elseif (x1 <= 1.02e-104)
		tmp = t_1;
	elseif (x1 <= 5.5e+147)
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(36.0 * Float64(x2 * x2)) - Float64(x1 * x1)) / Float64(Float64(x2 * -6.0) - x1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	t_1 = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	tmp = 0.0;
	if (x1 <= -5.5e+66)
		tmp = t_1;
	elseif (x1 <= -5.6e-109)
		tmp = t_0;
	elseif (x1 <= 1.02e-104)
		tmp = t_1;
	elseif (x1 <= 5.5e+147)
		tmp = t_0;
	else
		tmp = ((36.0 * (x2 * x2)) - (x1 * x1)) / ((x2 * -6.0) - x1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(-1.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.5e+66], t$95$1, If[LessEqual[x1, -5.6e-109], t$95$0, If[LessEqual[x1, 1.02e-104], t$95$1, If[LessEqual[x1, 5.5e+147], t$95$0, N[(N[(N[(36.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision] - N[(x1 * x1), $MachinePrecision]), $MachinePrecision] / N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.5e66 or -5.59999999999999958e-109 < x1 < 1.02000000000000001e-104

   1. Initial program 64.1%

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

   2. Taylor expanded in x1 around 0 50.4%

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

   3. Taylor expanded in x1 around 0 51.8%

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

      1. fma-def 52.0%

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

      2. associate-*r* 52.0%

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

      3. *-commutative 52.0%

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

      4. fma-neg 52.0%

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

      5. metadata-eval 52.0%

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

      6. fma-neg 52.0%

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

      7. *-commutative 52.0%

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

      8. metadata-eval 52.0%

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

   5. Simplified 52.0%

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

   6. Taylor expanded in x2 around 0 59.4%

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

   if -5.5e66 < x1 < -5.59999999999999958e-109 or 1.02000000000000001e-104 < x1 < 5.4999999999999997e147

   1. Initial program 97.4%

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

   2. Taylor expanded in x1 around 0 59.6%

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

   3. Taylor expanded in x1 around 0 59.2%

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

      1. fma-def 60.2%

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

      2. associate-*r* 60.2%

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

      3. *-commutative 60.2%

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

      4. fma-neg 60.2%

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

      5. metadata-eval 60.2%

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

      6. fma-neg 60.2%

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

      7. *-commutative 60.2%

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

      8. metadata-eval 60.2%

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

   5. Simplified 60.2%

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

   6. Taylor expanded in x1 around inf 50.7%

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

   if 5.4999999999999997e147 < x1

   1. Initial program 12.9%

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

   2. Taylor expanded in x1 around 0 0.6%

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

   3. Taylor expanded in x1 around 0 6.5%

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

      1. *-commutative 6.5%

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

   5. Simplified 6.5%

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

      1. +-commutative 6.5%

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

      2. flip-+ 65.1%

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

      3. *-commutative 65.1%

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

      4. *-commutative 65.1%

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

      5. swap-sqr 65.1%

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

      6. metadata-eval 65.1%

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

   7. Applied egg-rr 65.1%

      \[\leadsto \color{blue}{\frac{36 \cdot \left(x2 \cdot x2\right) - x1 \cdot x1}{x2 \cdot -6 - x1}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+66}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{-109}:\\ \;\;\;\;x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.02 \cdot 10^{-104}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq 5.5 \cdot 10^{+147}:\\ \;\;\;\;x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{36 \cdot \left(x2 \cdot x2\right) - x1 \cdot x1}{x2 \cdot -6 - x1}\\ \end{array} \]

Alternative 17: 41.1% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ t_1 := x1 + x2 \cdot -6\\ \mathbf{if}\;x2 \leq -1.36 \cdot 10^{+216}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x2 \leq -2.35 \cdot 10^{+126}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq -2.7 \cdot 10^{+57}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x2 \leq -2.8 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x2 \leq 2.2 \cdot 10^{-243}:\\ \;\;\;\;-x1\\ \mathbf{elif}\;x2 \leq 2.2 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* x2 x2) (* x1 8.0))) (t_1 (+ x1 (* x2 -6.0))))
   (if (<= x2 -1.36e+216)
     t_0
     (if (<= x2 -2.35e+126)
       (* x2 -6.0)
       (if (<= x2 -2.7e+57)
         t_0
         (if (<= x2 -2.8e-190)
           t_1
           (if (<= x2 2.2e-243) (- x1) (if (<= x2 2.2e+118) t_1 t_0))))))))

C

double code(double x1, double x2) {
	double t_0 = (x2 * x2) * (x1 * 8.0);
	double t_1 = x1 + (x2 * -6.0);
	double tmp;
	if (x2 <= -1.36e+216) {
		tmp = t_0;
	} else if (x2 <= -2.35e+126) {
		tmp = x2 * -6.0;
	} else if (x2 <= -2.7e+57) {
		tmp = t_0;
	} else if (x2 <= -2.8e-190) {
		tmp = t_1;
	} else if (x2 <= 2.2e-243) {
		tmp = -x1;
	} else if (x2 <= 2.2e+118) {
		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 = (x2 * x2) * (x1 * 8.0d0)
    t_1 = x1 + (x2 * (-6.0d0))
    if (x2 <= (-1.36d+216)) then
        tmp = t_0
    else if (x2 <= (-2.35d+126)) then
        tmp = x2 * (-6.0d0)
    else if (x2 <= (-2.7d+57)) then
        tmp = t_0
    else if (x2 <= (-2.8d-190)) then
        tmp = t_1
    else if (x2 <= 2.2d-243) then
        tmp = -x1
    else if (x2 <= 2.2d+118) 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 = (x2 * x2) * (x1 * 8.0);
	double t_1 = x1 + (x2 * -6.0);
	double tmp;
	if (x2 <= -1.36e+216) {
		tmp = t_0;
	} else if (x2 <= -2.35e+126) {
		tmp = x2 * -6.0;
	} else if (x2 <= -2.7e+57) {
		tmp = t_0;
	} else if (x2 <= -2.8e-190) {
		tmp = t_1;
	} else if (x2 <= 2.2e-243) {
		tmp = -x1;
	} else if (x2 <= 2.2e+118) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x2 * x2) * (x1 * 8.0)
	t_1 = x1 + (x2 * -6.0)
	tmp = 0
	if x2 <= -1.36e+216:
		tmp = t_0
	elif x2 <= -2.35e+126:
		tmp = x2 * -6.0
	elif x2 <= -2.7e+57:
		tmp = t_0
	elif x2 <= -2.8e-190:
		tmp = t_1
	elif x2 <= 2.2e-243:
		tmp = -x1
	elif x2 <= 2.2e+118:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x2 * x2) * Float64(x1 * 8.0))
	t_1 = Float64(x1 + Float64(x2 * -6.0))
	tmp = 0.0
	if (x2 <= -1.36e+216)
		tmp = t_0;
	elseif (x2 <= -2.35e+126)
		tmp = Float64(x2 * -6.0);
	elseif (x2 <= -2.7e+57)
		tmp = t_0;
	elseif (x2 <= -2.8e-190)
		tmp = t_1;
	elseif (x2 <= 2.2e-243)
		tmp = Float64(-x1);
	elseif (x2 <= 2.2e+118)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x2 * x2) * (x1 * 8.0);
	t_1 = x1 + (x2 * -6.0);
	tmp = 0.0;
	if (x2 <= -1.36e+216)
		tmp = t_0;
	elseif (x2 <= -2.35e+126)
		tmp = x2 * -6.0;
	elseif (x2 <= -2.7e+57)
		tmp = t_0;
	elseif (x2 <= -2.8e-190)
		tmp = t_1;
	elseif (x2 <= 2.2e-243)
		tmp = -x1;
	elseif (x2 <= 2.2e+118)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x2 * x2), $MachinePrecision] * N[(x1 * 8.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x2, -1.36e+216], t$95$0, If[LessEqual[x2, -2.35e+126], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x2, -2.7e+57], t$95$0, If[LessEqual[x2, -2.8e-190], t$95$1, If[LessEqual[x2, 2.2e-243], (-x1), If[LessEqual[x2, 2.2e+118], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x2 < -1.36000000000000007e216 or -2.3499999999999999e126 < x2 < -2.6999999999999998e57 or 2.19999999999999986e118 < x2

   1. Initial program 64.0%

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

   2. Taylor expanded in x1 around 0 52.0%

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

      1. associate-*r* 59.2%

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

      2. sub-neg 59.2%

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

      3. metadata-eval 59.2%

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

      4. distribute-rgt-in 54.1%

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

      5. *-commutative 54.1%

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

   4. Applied egg-rr 54.1%

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

   5. Taylor expanded in x1 around inf 58.4%

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

   6. Taylor expanded in x2 around inf 62.4%

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

      1. associate-*r* 62.4%

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

      2. unpow2 62.4%

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

   8. Simplified 62.4%

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

   if -1.36000000000000007e216 < x2 < -2.3499999999999999e126

   1. Initial program 55.5%

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

   2. Taylor expanded in x1 around 0 13.0%

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

   3. Taylor expanded in x1 around 0 42.2%

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

      1. *-commutative 42.2%

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

   5. Simplified 42.2%

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

   6. Taylor expanded in x1 around 0 42.2%

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

      1. *-commutative 42.2%

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

   8. Simplified 42.2%

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

   if -2.6999999999999998e57 < x2 < -2.80000000000000005e-190 or 2.1999999999999999e-243 < x2 < 2.19999999999999986e118

   1. Initial program 79.3%

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

   2. Taylor expanded in x1 around 0 51.6%

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

   3. Taylor expanded in x1 around 0 37.6%

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

      1. *-commutative 37.6%

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

   5. Simplified 37.6%

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

   if -2.80000000000000005e-190 < x2 < 2.1999999999999999e-243

   1. Initial program 64.2%

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

   2. Taylor expanded in x1 around 0 44.7%

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

   3. Taylor expanded in x1 around 0 47.1%

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

      1. fma-def 47.1%

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

      2. associate-*r* 47.1%

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

      3. *-commutative 47.1%

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

      4. fma-neg 47.1%

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

      5. metadata-eval 47.1%

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

      6. fma-neg 47.1%

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

      7. *-commutative 47.1%

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

      8. metadata-eval 47.1%

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

   5. Simplified 47.1%

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

   6. Taylor expanded in x2 around 0 40.5%

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

      1. distribute-rgt1-in 40.5%

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

      2. metadata-eval 40.5%

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

      3. mul-1-neg 40.5%

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

   8. Simplified 40.5%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.36 \cdot 10^{+216}:\\ \;\;\;\;\left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ \mathbf{elif}\;x2 \leq -2.35 \cdot 10^{+126}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq -2.7 \cdot 10^{+57}:\\ \;\;\;\;\left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ \mathbf{elif}\;x2 \leq -2.8 \cdot 10^{-190}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 2.2 \cdot 10^{-243}:\\ \;\;\;\;-x1\\ \mathbf{elif}\;x2 \leq 2.2 \cdot 10^{+118}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;\left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ \end{array} \]

Alternative 18: 47.8% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.45 \cdot 10^{+111}:\\ \;\;\;\;9 + \left(x1 \cdot 2 + -12 \cdot \left(x1 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq -4.6 \cdot 10^{-209} \lor \neg \left(x1 \leq 1.16 \cdot 10^{-160}\right):\\ \;\;\;\;x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.45e+111)
   (+ 9.0 (+ (* x1 2.0) (* -12.0 (* x1 x2))))
   (if (or (<= x1 -4.6e-209) (not (<= x1 1.16e-160)))
     (* x1 (+ -1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))))
     (* x2 -6.0))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.45e+111) {
		tmp = 9.0 + ((x1 * 2.0) + (-12.0 * (x1 * x2)));
	} else if ((x1 <= -4.6e-209) || !(x1 <= 1.16e-160)) {
		tmp = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	} 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 (x1 <= (-1.45d+111)) then
        tmp = 9.0d0 + ((x1 * 2.0d0) + ((-12.0d0) * (x1 * x2)))
    else if ((x1 <= (-4.6d-209)) .or. (.not. (x1 <= 1.16d-160))) then
        tmp = x1 * ((-1.0d0) + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))))
    else
        tmp = x2 * (-6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.45e+111) {
		tmp = 9.0 + ((x1 * 2.0) + (-12.0 * (x1 * x2)));
	} else if ((x1 <= -4.6e-209) || !(x1 <= 1.16e-160)) {
		tmp = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.45e+111:
		tmp = 9.0 + ((x1 * 2.0) + (-12.0 * (x1 * x2)))
	elif (x1 <= -4.6e-209) or not (x1 <= 1.16e-160):
		tmp = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))))
	else:
		tmp = x2 * -6.0
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.45e+111)
		tmp = Float64(9.0 + Float64(Float64(x1 * 2.0) + Float64(-12.0 * Float64(x1 * x2))));
	elseif ((x1 <= -4.6e-209) || !(x1 <= 1.16e-160))
		tmp = Float64(x1 * Float64(-1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))));
	else
		tmp = Float64(x2 * -6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -1.45e+111)
		tmp = 9.0 + ((x1 * 2.0) + (-12.0 * (x1 * x2)));
	elseif ((x1 <= -4.6e-209) || ~((x1 <= 1.16e-160)))
		tmp = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	else
		tmp = x2 * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.45e+111], N[(9.0 + N[(N[(x1 * 2.0), $MachinePrecision] + N[(-12.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x1, -4.6e-209], N[Not[LessEqual[x1, 1.16e-160]], $MachinePrecision]], N[(x1 * N[(-1.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * -6.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.45e111

   1. Initial program 2.2%

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

   2. Taylor expanded in x1 around 0 2.2%

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

      1. associate-*r* 2.2%

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

      2. sub-neg 2.2%

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

      3. metadata-eval 2.2%

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

      4. distribute-rgt-in 2.2%

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

      5. *-commutative 2.2%

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

   4. Applied egg-rr 2.2%

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

   5. Taylor expanded in x1 around inf 2.3%

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

   6. Taylor expanded in x2 around 0 21.8%

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

   if -1.45e111 < x1 < -4.5999999999999999e-209 or 1.16e-160 < x1

   1. Initial program 82.0%

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

   2. Taylor expanded in x1 around 0 51.6%

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

   3. Taylor expanded in x1 around 0 59.3%

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

      1. fma-def 60.0%

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

      2. associate-*r* 60.0%

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

      3. *-commutative 60.0%

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

      4. fma-neg 60.0%

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

      5. metadata-eval 60.0%

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

      6. fma-neg 60.0%

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

      7. *-commutative 60.0%

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

      8. metadata-eval 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in x1 around inf 47.2%

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

   if -4.5999999999999999e-209 < x1 < 1.16e-160

   1. Initial program 99.5%

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

   2. Taylor expanded in x1 around 0 81.9%

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

   3. Taylor expanded in x1 around 0 81.8%

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

      1. *-commutative 81.8%

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

   5. Simplified 81.8%

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

   6. Taylor expanded in x1 around 0 82.0%

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

      1. *-commutative 82.0%

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

   8. Simplified 82.0%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.45 \cdot 10^{+111}:\\ \;\;\;\;9 + \left(x1 \cdot 2 + -12 \cdot \left(x1 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq -4.6 \cdot 10^{-209} \lor \neg \left(x1 \leq 1.16 \cdot 10^{-160}\right):\\ \;\;\;\;x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]

Alternative 19: 54.7% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+66} \lor \neg \left(x1 \leq -2.3 \cdot 10^{-110}\right) \land x1 \leq 8.2 \cdot 10^{-105}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -5e+66) (and (not (<= x1 -2.3e-110)) (<= x1 8.2e-105)))
   (+ x1 (+ (* x1 -2.0) (* x2 (- (* x1 -12.0) 6.0))))
   (* x1 (+ -1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -5e+66) || (!(x1 <= -2.3e-110) && (x1 <= 8.2e-105))) {
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	} else {
		tmp = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-5d+66)) .or. (.not. (x1 <= (-2.3d-110))) .and. (x1 <= 8.2d-105)) then
        tmp = x1 + ((x1 * (-2.0d0)) + (x2 * ((x1 * (-12.0d0)) - 6.0d0)))
    else
        tmp = x1 * ((-1.0d0) + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -5e+66) || (!(x1 <= -2.3e-110) && (x1 <= 8.2e-105))) {
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	} else {
		tmp = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -5e+66) or (not (x1 <= -2.3e-110) and (x1 <= 8.2e-105)):
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)))
	else:
		tmp = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -5e+66) || (!(x1 <= -2.3e-110) && (x1 <= 8.2e-105)))
		tmp = Float64(x1 + Float64(Float64(x1 * -2.0) + Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0))));
	else
		tmp = Float64(x1 * Float64(-1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -5e+66) || (~((x1 <= -2.3e-110)) && (x1 <= 8.2e-105)))
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	else
		tmp = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -5e+66], And[N[Not[LessEqual[x1, -2.3e-110]], $MachinePrecision], LessEqual[x1, 8.2e-105]]], N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 * N[(-1.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -4.99999999999999991e66 or -2.3000000000000001e-110 < x1 < 8.20000000000000061e-105

   1. Initial program 64.1%

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

   2. Taylor expanded in x1 around 0 50.4%

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

   3. Taylor expanded in x1 around 0 51.8%

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

      1. fma-def 52.0%

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

      2. associate-*r* 52.0%

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

      3. *-commutative 52.0%

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

      4. fma-neg 52.0%

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

      5. metadata-eval 52.0%

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

      6. fma-neg 52.0%

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

      7. *-commutative 52.0%

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

      8. metadata-eval 52.0%

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

   5. Simplified 52.0%

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

   6. Taylor expanded in x2 around 0 59.4%

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

   if -4.99999999999999991e66 < x1 < -2.3000000000000001e-110 or 8.20000000000000061e-105 < x1

   1. Initial program 77.1%

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

   2. Taylor expanded in x1 around 0 45.4%

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

   3. Taylor expanded in x1 around 0 55.1%

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

      1. fma-def 55.9%

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

      2. associate-*r* 55.9%

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

      3. *-commutative 55.9%

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

      4. fma-neg 55.9%

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

      5. metadata-eval 55.9%

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

      6. fma-neg 55.9%

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

      7. *-commutative 55.9%

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

      8. metadata-eval 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in x1 around inf 48.7%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+66} \lor \neg \left(x1 \leq -2.3 \cdot 10^{-110}\right) \land x1 \leq 8.2 \cdot 10^{-105}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \end{array} \]

Alternative 20: 42.6% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -6.8 \cdot 10^{+100}:\\ \;\;\;\;9 + \left(x1 \cdot 2 + -12 \cdot \left(x1 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq -3.4 \cdot 10^{-110}:\\ \;\;\;\;\left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ \mathbf{elif}\;x1 \leq 5.7 \cdot 10^{-158}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x2 \cdot x2\right)\right) \cdot 8\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -6.8e+100)
   (+ 9.0 (+ (* x1 2.0) (* -12.0 (* x1 x2))))
   (if (<= x1 -3.4e-110)
     (* (* x2 x2) (* x1 8.0))
     (if (<= x1 5.7e-158) (* x2 -6.0) (+ x1 (* (* x1 (* x2 x2)) 8.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -6.8e+100) {
		tmp = 9.0 + ((x1 * 2.0) + (-12.0 * (x1 * x2)));
	} else if (x1 <= -3.4e-110) {
		tmp = (x2 * x2) * (x1 * 8.0);
	} else if (x1 <= 5.7e-158) {
		tmp = x2 * -6.0;
	} else {
		tmp = x1 + ((x1 * (x2 * x2)) * 8.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-6.8d+100)) then
        tmp = 9.0d0 + ((x1 * 2.0d0) + ((-12.0d0) * (x1 * x2)))
    else if (x1 <= (-3.4d-110)) then
        tmp = (x2 * x2) * (x1 * 8.0d0)
    else if (x1 <= 5.7d-158) then
        tmp = x2 * (-6.0d0)
    else
        tmp = x1 + ((x1 * (x2 * x2)) * 8.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -6.8e+100) {
		tmp = 9.0 + ((x1 * 2.0) + (-12.0 * (x1 * x2)));
	} else if (x1 <= -3.4e-110) {
		tmp = (x2 * x2) * (x1 * 8.0);
	} else if (x1 <= 5.7e-158) {
		tmp = x2 * -6.0;
	} else {
		tmp = x1 + ((x1 * (x2 * x2)) * 8.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -6.8e+100:
		tmp = 9.0 + ((x1 * 2.0) + (-12.0 * (x1 * x2)))
	elif x1 <= -3.4e-110:
		tmp = (x2 * x2) * (x1 * 8.0)
	elif x1 <= 5.7e-158:
		tmp = x2 * -6.0
	else:
		tmp = x1 + ((x1 * (x2 * x2)) * 8.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -6.8e+100)
		tmp = Float64(9.0 + Float64(Float64(x1 * 2.0) + Float64(-12.0 * Float64(x1 * x2))));
	elseif (x1 <= -3.4e-110)
		tmp = Float64(Float64(x2 * x2) * Float64(x1 * 8.0));
	elseif (x1 <= 5.7e-158)
		tmp = Float64(x2 * -6.0);
	else
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(x2 * x2)) * 8.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -6.8e+100)
		tmp = 9.0 + ((x1 * 2.0) + (-12.0 * (x1 * x2)));
	elseif (x1 <= -3.4e-110)
		tmp = (x2 * x2) * (x1 * 8.0);
	elseif (x1 <= 5.7e-158)
		tmp = x2 * -6.0;
	else
		tmp = x1 + ((x1 * (x2 * x2)) * 8.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -6.8e+100], N[(9.0 + N[(N[(x1 * 2.0), $MachinePrecision] + N[(-12.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -3.4e-110], N[(N[(x2 * x2), $MachinePrecision] * N[(x1 * 8.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.7e-158], N[(x2 * -6.0), $MachinePrecision], N[(x1 + N[(N[(x1 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -6.79999999999999988e100

   1. Initial program 2.2%

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

   2. Taylor expanded in x1 around 0 2.2%

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

      1. associate-*r* 2.2%

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

      2. sub-neg 2.2%

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

      3. metadata-eval 2.2%

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

      4. distribute-rgt-in 2.2%

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

      5. *-commutative 2.2%

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

   4. Applied egg-rr 2.2%

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

   5. Taylor expanded in x1 around inf 2.3%

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

   6. Taylor expanded in x2 around 0 21.8%

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

   if -6.79999999999999988e100 < x1 < -3.4000000000000001e-110

   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 53.1%

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

      1. associate-*r* 57.2%

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

      2. sub-neg 57.2%

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

      3. metadata-eval 57.2%

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

      4. distribute-rgt-in 54.9%

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

      5. *-commutative 54.9%

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

   4. Applied egg-rr 54.9%

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

   5. Taylor expanded in x1 around inf 33.5%

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

   6. Taylor expanded in x2 around inf 31.2%

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

      1. associate-*r* 31.2%

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

      2. unpow2 31.2%

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

   8. Simplified 31.2%

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

   if -3.4000000000000001e-110 < x1 < 5.69999999999999982e-158

   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 0 84.3%

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

   3. Taylor expanded in x1 around 0 68.7%

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

      1. *-commutative 68.7%

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

   5. Simplified 68.7%

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

   6. Taylor expanded in x1 around 0 69.1%

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

      1. *-commutative 69.1%

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

   8. Simplified 69.1%

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

   if 5.69999999999999982e-158 < x1

   1. Initial program 71.2%

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

   2. Taylor expanded in x1 around 0 43.5%

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

   3. Taylor expanded in x2 around inf 41.4%

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

      1. *-commutative 41.4%

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

      2. unpow2 41.4%

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

   5. Simplified 41.4%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(x2 \cdot x2\right)\right) \cdot 8} \]
3. Recombined 4 regimes into one program.

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6.8 \cdot 10^{+100}:\\ \;\;\;\;9 + \left(x1 \cdot 2 + -12 \cdot \left(x1 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq -3.4 \cdot 10^{-110}:\\ \;\;\;\;\left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ \mathbf{elif}\;x1 \leq 5.7 \cdot 10^{-158}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x2 \cdot x2\right)\right) \cdot 8\\ \end{array} \]

Alternative 21: 32.0% accurate, 13.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -2.8 \cdot 10^{-190}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 3 \cdot 10^{-243}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 -2.8e-190)
   (* x2 -6.0)
   (if (<= x2 3e-243) (- x1) (+ x1 (* x2 -6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= -2.8e-190) {
		tmp = x2 * -6.0;
	} else if (x2 <= 3e-243) {
		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 <= (-2.8d-190)) then
        tmp = x2 * (-6.0d0)
    else if (x2 <= 3d-243) 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 <= -2.8e-190) {
		tmp = x2 * -6.0;
	} else if (x2 <= 3e-243) {
		tmp = -x1;
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= -2.8e-190:
		tmp = x2 * -6.0
	elif x2 <= 3e-243:
		tmp = -x1
	else:
		tmp = x1 + (x2 * -6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= -2.8e-190)
		tmp = Float64(x2 * -6.0);
	elseif (x2 <= 3e-243)
		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 <= -2.8e-190)
		tmp = x2 * -6.0;
	elseif (x2 <= 3e-243)
		tmp = -x1;
	else
		tmp = x1 + (x2 * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, -2.8e-190], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x2, 3e-243], (-x1), N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -2.80000000000000005e-190

   1. Initial program 66.4%

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

   2. Taylor expanded in x1 around 0 40.8%

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

   3. Taylor expanded in x1 around 0 27.8%

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

      1. *-commutative 27.8%

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

   5. Simplified 27.8%

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

   6. Taylor expanded in x1 around 0 27.8%

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

      1. *-commutative 27.8%

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

   8. Simplified 27.8%

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

   if -2.80000000000000005e-190 < x2 < 3.0000000000000001e-243

   1. Initial program 64.2%

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

   2. Taylor expanded in x1 around 0 44.7%

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

   3. Taylor expanded in x1 around 0 47.1%

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

      1. fma-def 47.1%

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

      2. associate-*r* 47.1%

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

      3. *-commutative 47.1%

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

      4. fma-neg 47.1%

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

      5. metadata-eval 47.1%

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

      6. fma-neg 47.1%

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

      7. *-commutative 47.1%

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

      8. metadata-eval 47.1%

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

   5. Simplified 47.1%

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

   6. Taylor expanded in x2 around 0 40.5%

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

      1. distribute-rgt1-in 40.5%

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

      2. metadata-eval 40.5%

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

      3. mul-1-neg 40.5%

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

   8. Simplified 40.5%

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

   if 3.0000000000000001e-243 < x2

   1. Initial program 77.0%

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

   2. Taylor expanded in x1 around 0 55.7%

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

   3. Taylor expanded in x1 around 0 25.9%

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

      1. *-commutative 25.9%

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

   5. Simplified 25.9%

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

4. Final simplification 29.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -2.8 \cdot 10^{-190}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 3 \cdot 10^{-243}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \]

Alternative 22: 31.7% accurate, 17.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -2.35 \cdot 10^{-190}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 3 \cdot 10^{-243}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 -2.35e-190) (* x2 -6.0) (if (<= x2 3e-243) (- x1) (* x2 -6.0))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= -2.35e-190) {
		tmp = x2 * -6.0;
	} else if (x2 <= 3e-243) {
		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 <= (-2.35d-190)) then
        tmp = x2 * (-6.0d0)
    else if (x2 <= 3d-243) 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 <= -2.35e-190) {
		tmp = x2 * -6.0;
	} else if (x2 <= 3e-243) {
		tmp = -x1;
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= -2.35e-190:
		tmp = x2 * -6.0
	elif x2 <= 3e-243:
		tmp = -x1
	else:
		tmp = x2 * -6.0
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= -2.35e-190)
		tmp = Float64(x2 * -6.0);
	elseif (x2 <= 3e-243)
		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 <= -2.35e-190)
		tmp = x2 * -6.0;
	elseif (x2 <= 3e-243)
		tmp = -x1;
	else
		tmp = x2 * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, -2.35e-190], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x2, 3e-243], (-x1), N[(x2 * -6.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x2 < -2.3500000000000002e-190 or 3.0000000000000001e-243 < x2

   1. Initial program 71.8%

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

   2. Taylor expanded in x1 around 0 48.5%

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

   3. Taylor expanded in x1 around 0 26.8%

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

      1. *-commutative 26.8%

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

   5. Simplified 26.8%

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

   6. Taylor expanded in x1 around 0 26.7%

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

      1. *-commutative 26.7%

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

   8. Simplified 26.7%

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

   if -2.3500000000000002e-190 < x2 < 3.0000000000000001e-243

   1. Initial program 64.2%

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

   2. Taylor expanded in x1 around 0 44.7%

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

   3. Taylor expanded in x1 around 0 47.1%

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

      1. fma-def 47.1%

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

      2. associate-*r* 47.1%

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

      3. *-commutative 47.1%

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

      4. fma-neg 47.1%

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

      5. metadata-eval 47.1%

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

      6. fma-neg 47.1%

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

      7. *-commutative 47.1%

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

      8. metadata-eval 47.1%

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

   5. Simplified 47.1%

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

   6. Taylor expanded in x2 around 0 40.5%

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

      1. distribute-rgt1-in 40.5%

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

      2. metadata-eval 40.5%

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

      3. mul-1-neg 40.5%

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

   8. Simplified 40.5%

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

4. Final simplification 28.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -2.35 \cdot 10^{-190}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 3 \cdot 10^{-243}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]

Alternative 23: 13.6% 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 70.6%

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

2. Taylor expanded in x1 around 0 47.9%

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

3. Taylor expanded in x1 around 0 53.5%

   \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)} \]
4. Step-by-step derivation

   1. fma-def 53.9%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)} \]

   2. associate-*r* 53.9%

      \[\leadsto x1 + \mathsf{fma}\left(-6, x2, x1 \cdot \left(\color{blue}{\left(4 \cdot x2\right) \cdot \left(2 \cdot x2 - 3\right)} - 2\right)\right) \]

   3. *-commutative 53.9%

      \[\leadsto x1 + \mathsf{fma}\left(-6, x2, x1 \cdot \left(\left(4 \cdot x2\right) \cdot \left(\color{blue}{x2 \cdot 2} - 3\right) - 2\right)\right) \]

   4. fma-neg 53.9%

      \[\leadsto x1 + \mathsf{fma}\left(-6, x2, x1 \cdot \left(\left(4 \cdot x2\right) \cdot \color{blue}{\mathsf{fma}\left(x2, 2, -3\right)} - 2\right)\right) \]

   5. metadata-eval 53.9%

      \[\leadsto x1 + \mathsf{fma}\left(-6, x2, x1 \cdot \left(\left(4 \cdot x2\right) \cdot \mathsf{fma}\left(x2, 2, \color{blue}{-3}\right) - 2\right)\right) \]

   6. fma-neg 53.9%

      \[\leadsto x1 + \mathsf{fma}\left(-6, x2, x1 \cdot \color{blue}{\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(x2, 2, -3\right), -2\right)}\right) \]

   7. *-commutative 53.9%

      \[\leadsto x1 + \mathsf{fma}\left(-6, x2, x1 \cdot \mathsf{fma}\left(\color{blue}{x2 \cdot 4}, \mathsf{fma}\left(x2, 2, -3\right), -2\right)\right) \]

   8. metadata-eval 53.9%

      \[\leadsto x1 + \mathsf{fma}\left(-6, x2, x1 \cdot \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(x2, 2, -3\right), \color{blue}{-2}\right)\right) \]

5. Simplified 53.9%

   \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(x2, 2, -3\right), -2\right)\right)} \]

6. Taylor expanded in x2 around 0 13.0%

   \[\leadsto \color{blue}{x1 + -2 \cdot x1} \]
7. Step-by-step derivation

   1. distribute-rgt1-in 13.0%

      \[\leadsto \color{blue}{\left(-2 + 1\right) \cdot x1} \]

   2. metadata-eval 13.0%

      \[\leadsto \color{blue}{-1} \cdot x1 \]

   3. mul-1-neg 13.0%

      \[\leadsto \color{blue}{-x1} \]

8. Simplified 13.0%

   \[\leadsto \color{blue}{-x1} \]

9. Final simplification 13.0%

   \[\leadsto -x1 \]

Alternative 24: 3.5% accurate, 127.0× speedup

Math

\[\begin{array}{l} \\ 9 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 9.0)

C

double code(double x1, double x2) {
	return 9.0;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = 9.0d0
end function

Java

public static double code(double x1, double x2) {
	return 9.0;
}

Python

def code(x1, x2):
	return 9.0

Julia

function code(x1, x2)
	return 9.0
end

MATLAB

function tmp = code(x1, x2)
	tmp = 9.0;
end

Wolfram

code[x1_, x2_] := 9.0

Derivation

1. Initial program 70.6%

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

2. Taylor expanded in x1 around 0 47.9%

   \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Step-by-step derivation

   1. associate-*r* 53.1%

      \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(\left(x1 \cdot x2\right) \cdot \left(2 \cdot x2 - 3\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. sub-neg 53.1%

      \[\leadsto x1 + \left(\left(4 \cdot \left(\left(x1 \cdot x2\right) \cdot \color{blue}{\left(2 \cdot x2 + \left(-3\right)\right)}\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. metadata-eval 53.1%

      \[\leadsto x1 + \left(\left(4 \cdot \left(\left(x1 \cdot x2\right) \cdot \left(2 \cdot x2 + \color{blue}{-3}\right)\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. distribute-rgt-in 51.5%

      \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(\left(2 \cdot x2\right) \cdot \left(x1 \cdot x2\right) + -3 \cdot \left(x1 \cdot x2\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. *-commutative 51.5%

      \[\leadsto x1 + \left(\left(4 \cdot \left(\color{blue}{\left(x2 \cdot 2\right)} \cdot \left(x1 \cdot x2\right) + -3 \cdot \left(x1 \cdot x2\right)\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

4. Applied egg-rr 51.5%

   \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(\left(x2 \cdot 2\right) \cdot \left(x1 \cdot x2\right) + -3 \cdot \left(x1 \cdot x2\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

5. Taylor expanded in x1 around inf 23.6%

   \[\leadsto x1 + \left(\left(4 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x1 \cdot x2\right) + -3 \cdot \left(x1 \cdot x2\right)\right) + x1\right) + \color{blue}{9}\right) \]

6. Taylor expanded in x1 around 0 3.4%

   \[\leadsto \color{blue}{9} \]

7. Final simplification 3.4%

   \[\leadsto 9 \]

Reproduce

herbie shell --seed 2023297 
(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))))))