Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 69.5% → 93.0%

Time: 51.5s

Alternatives: 26

Speedup: 1.6×

• 47.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 69.5% 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: 93.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 + x2 \cdot 2\\ t_1 := \mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)\\ \mathbf{if}\;x1 \leq -5.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, t_0, x2 \cdot -2\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 5.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{x1 \cdot \left(x1 \cdot 3\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \mathsf{fma}\left(x1, x1 \cdot \frac{t_1}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{3}}, \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{t_1}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(x1 \cdot \left(-6 + \frac{t_1}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{2}}\right) + 4 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(4, x2 \cdot \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(3, x1 \cdot \left(x1 \cdot t_0\right), x2 \cdot -6\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ 3.0 (* x2 2.0))) (t_1 (fma x1 (* x1 3.0) (fma 2.0 x2 (- x1)))))
   (if (<= x1 -5.4e+153)
     (+
      x1
      (+
       (+ x1 (* 4.0 (* -3.0 (* x1 x2))))
       (* 3.0 (- (fma (* x1 x1) t_0 (* x2 -2.0)) x1))))
     (if (<= x1 5.4e+153)
       (+
        x1
        (fma
         3.0
         (/ (- (* x1 (* x1 3.0)) (fma 2.0 x2 x1)) (fma x1 x1 1.0))
         (fma
          x1
          (* x1 (/ t_1 (/ (fma x1 x1 1.0) 3.0)))
          (*
           (fma x1 x1 1.0)
           (+
            x1
            (+
             (* x1 (* x1 -6.0))
             (*
              (/ t_1 (fma x1 x1 1.0))
              (+
               (* x1 (+ -6.0 (/ t_1 (/ (fma x1 x1 1.0) 2.0))))
               (* 4.0 (* x1 x1))))))))))
       (+
        x1
        (fma
         x1
         (fma 4.0 (* x2 (fma 2.0 x2 -3.0)) -2.0)
         (fma 3.0 (* x1 (* x1 t_0)) (* x2 -6.0))))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 + (x2 * 2.0);
	double t_1 = fma(x1, (x1 * 3.0), fma(2.0, x2, -x1));
	double tmp;
	if (x1 <= -5.4e+153) {
		tmp = x1 + ((x1 + (4.0 * (-3.0 * (x1 * x2)))) + (3.0 * (fma((x1 * x1), t_0, (x2 * -2.0)) - x1)));
	} else if (x1 <= 5.4e+153) {
		tmp = x1 + fma(3.0, (((x1 * (x1 * 3.0)) - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), fma(x1, (x1 * (t_1 / (fma(x1, x1, 1.0) / 3.0))), (fma(x1, x1, 1.0) * (x1 + ((x1 * (x1 * -6.0)) + ((t_1 / fma(x1, x1, 1.0)) * ((x1 * (-6.0 + (t_1 / (fma(x1, x1, 1.0) / 2.0)))) + (4.0 * (x1 * x1)))))))));
	} else {
		tmp = x1 + fma(x1, fma(4.0, (x2 * fma(2.0, x2, -3.0)), -2.0), fma(3.0, (x1 * (x1 * t_0)), (x2 * -6.0)));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(3.0 + Float64(x2 * 2.0))
	t_1 = fma(x1, Float64(x1 * 3.0), fma(2.0, x2, Float64(-x1)))
	tmp = 0.0
	if (x1 <= -5.4e+153)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(-3.0 * Float64(x1 * x2)))) + Float64(3.0 * Float64(fma(Float64(x1 * x1), t_0, Float64(x2 * -2.0)) - x1))));
	elseif (x1 <= 5.4e+153)
		tmp = Float64(x1 + fma(3.0, Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), fma(x1, Float64(x1 * Float64(t_1 / Float64(fma(x1, x1, 1.0) / 3.0))), Float64(fma(x1, x1, 1.0) * Float64(x1 + Float64(Float64(x1 * Float64(x1 * -6.0)) + Float64(Float64(t_1 / fma(x1, x1, 1.0)) * Float64(Float64(x1 * Float64(-6.0 + Float64(t_1 / Float64(fma(x1, x1, 1.0) / 2.0)))) + Float64(4.0 * Float64(x1 * x1))))))))));
	else
		tmp = Float64(x1 + fma(x1, fma(4.0, Float64(x2 * fma(2.0, x2, -3.0)), -2.0), fma(3.0, Float64(x1 * Float64(x1 * t_0)), Float64(x2 * -6.0))));
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x1 < -5.4000000000000001e153

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x2 around 0 0.0%

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

   4. Taylor expanded in x1 around 0 87.5%

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

      1. +-commutative 87.5%

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

      2. neg-mul-1 87.5%

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

      3. unsub-neg 87.5%

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

      4. +-commutative 87.5%

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

      5. *-commutative 87.5%

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

      6. fma-def 87.5%

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

      7. unpow2 87.5%

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

      8. cancel-sign-sub-inv 87.5%

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

      9. metadata-eval 87.5%

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

      10. *-commutative 87.5%

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

   6. Simplified 87.5%

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

   if -5.4000000000000001e153 < x1 < 5.4000000000000001e153

   1. Initial program 92.0%

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

   3. Simplified 99.7%

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

   if 5.4000000000000001e153 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 85.7%

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

      1. fma-def 85.7%

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

      2. fma-neg 85.7%

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

      3. fma-neg 85.7%

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

      4. metadata-eval 85.7%

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

      5. metadata-eval 85.7%

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

      6. +-commutative 85.7%

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

      7. *-commutative 85.7%

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

      8. fma-def 85.7%

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

      9. *-commutative 85.7%

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

      10. unpow2 85.7%

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

      11. associate-*l* 85.7%

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

      12. cancel-sign-sub-inv 85.7%

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

      13. metadata-eval 85.7%

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

      14. *-commutative 85.7%

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

   5. Simplified 85.7%

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

4. Final simplification 97.0%

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

Alternative 2: 91.5% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$2), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(N[(x1 + N[(4.0 * N[(-3.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[Power[N[(t$95$1 * N[(t$95$1 * t$95$1), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(t$95$1 + N[(x1 + N[(N[(N[(t$95$0 * 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[(4.0 * t$95$3), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * N[(4.0 * N[(x2 * N[(2.0 * x2 + -3.0), $MachinePrecision]), $MachinePrecision] + -2.0), $MachinePrecision] + N[(3.0 * N[(x1 * N[(x1 * N[(3.0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.1%

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

   3. Taylor expanded in x2 around 0 3.1%

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

   4. Taylor expanded in x1 around 0 25.2%

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

      1. +-commutative 25.2%

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

      2. neg-mul-1 25.2%

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

      3. unsub-neg 25.2%

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

      4. *-commutative 25.2%

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

   6. Simplified 25.2%

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

      1. add-cbrt-cube 89.7%

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

   8. Applied egg-rr 89.7%

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

   if -5.60000000000000037e102 < x1 < 1.35000000000000003e154

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around inf 98.4%

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

   3. Taylor expanded in x1 around 0 99.3%

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

      1. +-commutative 53.5%

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

      2. neg-mul-1 53.5%

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

      3. unsub-neg 53.5%

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

      4. *-commutative 53.5%

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

   5. Simplified 99.3%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 85.7%

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

      1. fma-def 85.7%

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

      2. fma-neg 85.7%

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

      3. fma-neg 85.7%

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

      4. metadata-eval 85.7%

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

      5. metadata-eval 85.7%

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

      6. +-commutative 85.7%

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

      7. *-commutative 85.7%

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

      8. fma-def 85.7%

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

      9. *-commutative 85.7%

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

      10. unpow2 85.7%

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

      11. associate-*l* 85.7%

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

      12. cancel-sign-sub-inv 85.7%

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

      13. metadata-eval 85.7%

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

      14. *-commutative 85.7%

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

   5. Simplified 85.7%

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

4. Final simplification 96.4%

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

Alternative 3: 91.5% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$2), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(N[(x1 + N[(4.0 * N[(-3.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[Power[N[(t$95$1 * N[(t$95$1 * t$95$1), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(t$95$1 + N[(x1 + N[(N[(N[(t$95$0 * 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[(4.0 * t$95$3), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x2 * -6.0), $MachinePrecision] + N[(3.0 * N[(N[Power[x1, 2.0], $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.1%

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

   3. Taylor expanded in x2 around 0 3.1%

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

   4. Taylor expanded in x1 around 0 25.2%

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

      1. +-commutative 25.2%

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

      2. neg-mul-1 25.2%

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

      3. unsub-neg 25.2%

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

      4. *-commutative 25.2%

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

   6. Simplified 25.2%

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

      1. add-cbrt-cube 89.7%

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

   8. Applied egg-rr 89.7%

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

   if -5.60000000000000037e102 < x1 < 1.35000000000000003e154

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around inf 98.4%

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

   3. Taylor expanded in x1 around 0 99.3%

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

      1. +-commutative 53.5%

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

      2. neg-mul-1 53.5%

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

      3. unsub-neg 53.5%

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

      4. *-commutative 53.5%

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

   5. Simplified 99.3%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 85.7%

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

4. Final simplification 96.4%

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

Alternative 4: 92.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(x2 \cdot 2 + t_0\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -1.32 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + x2 \cdot 2, x2 \cdot -2\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 3 \cdot \frac{\left(t_0 - x2 \cdot 2\right) - x1}{t_1}\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(\left(t_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right)\right) + 3 \cdot t_0\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right) + \left(x2 \cdot -6 + 3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ (* x2 2.0) t_0) x1) t_1)))
   (if (<= x1 -1.32e+154)
     (+
      x1
      (+
       (+ x1 (* 4.0 (* -3.0 (* x1 x2))))
       (* 3.0 (- (fma (* x1 x1) (+ 3.0 (* x2 2.0)) (* x2 -2.0)) x1))))
     (if (<= x1 -5.5e+102)
       (+
        x1
        (+
         (+ x1 (* 6.0 (pow x1 4.0)))
         (* 3.0 (/ (- (- t_0 (* x2 2.0)) x1) t_1))))
       (if (<= x1 1.35e+154)
         (+
          x1
          (+
           (* 3.0 (- (* x2 -2.0) x1))
           (+
            x1
            (+
             (+
              (*
               t_1
               (+
                (* (* (* x1 2.0) t_2) (- t_2 3.0))
                (* (* x1 x1) (- (* 4.0 t_2) 6.0))))
              (* 3.0 t_0))
             (* x1 (* x1 x1))))))
         (+
          x1
          (+
           (* x1 (- (* 4.0 (* x2 (- (* x2 2.0) 3.0))) 2.0))
           (+ (* x2 -6.0) (* 3.0 (* (pow x1 2.0) (- 3.0 (* x2 -2.0))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = (((x2 * 2.0) + t_0) - x1) / t_1;
	double tmp;
	if (x1 <= -1.32e+154) {
		tmp = x1 + ((x1 + (4.0 * (-3.0 * (x1 * x2)))) + (3.0 * (fma((x1 * x1), (3.0 + (x2 * 2.0)), (x2 * -2.0)) - x1)));
	} else if (x1 <= -5.5e+102) {
		tmp = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + (3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (3.0 * t_0)) + (x1 * (x1 * x1)))));
	} else {
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0)) + ((x2 * -6.0) + (3.0 * (pow(x1, 2.0) * (3.0 - (x2 * -2.0))))));
	}
	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(Float64(x2 * 2.0) + t_0) - x1) / t_1)
	tmp = 0.0
	if (x1 <= -1.32e+154)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(-3.0 * Float64(x1 * x2)))) + Float64(3.0 * Float64(fma(Float64(x1 * x1), Float64(3.0 + Float64(x2 * 2.0)), Float64(x2 * -2.0)) - x1))));
	elseif (x1 <= -5.5e+102)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_1))));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - x1)) + 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(4.0 * t_2) - 6.0)))) + Float64(3.0 * t_0)) + Float64(x1 * Float64(x1 * x1))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(x2 * 2.0) - 3.0))) - 2.0)) + Float64(Float64(x2 * -6.0) + Float64(3.0 * Float64((x1 ^ 2.0) * Float64(3.0 - Float64(x2 * -2.0)))))));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[x1, -1.32e+154], N[(x1 + N[(N[(x1 + N[(4.0 * N[(-3.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(3.0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5.5e+102], N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] + 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[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x2 * -6.0), $MachinePrecision] + N[(3.0 * N[(N[Power[x1, 2.0], $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.31999999999999998e154

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x2 around 0 0.0%

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

   4. Taylor expanded in x1 around 0 87.5%

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

      1. +-commutative 87.5%

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

      2. neg-mul-1 87.5%

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

      3. unsub-neg 87.5%

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

      4. +-commutative 87.5%

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

      5. *-commutative 87.5%

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

      6. fma-def 87.5%

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

      7. unpow2 87.5%

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

      8. cancel-sign-sub-inv 87.5%

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

      9. metadata-eval 87.5%

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

      10. *-commutative 87.5%

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

   6. Simplified 87.5%

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

   if -1.31999999999999998e154 < x1 < -5.49999999999999981e102

   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 100.0%

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

      1. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   if -5.49999999999999981e102 < x1 < 1.35000000000000003e154

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around inf 98.4%

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

   3. Taylor expanded in x1 around 0 99.3%

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

      1. +-commutative 53.5%

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

      2. neg-mul-1 53.5%

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

      3. unsub-neg 53.5%

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

      4. *-commutative 53.5%

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

   5. Simplified 99.3%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 85.7%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.32 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + x2 \cdot 2, x2 \cdot -2\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right) + \left(x2 \cdot -6 + 3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right)\\ \end{array} \]

Alternative 5: 88.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(x2 \cdot 2 + t_0\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -1.32 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + x2 \cdot 2, x2 \cdot -2\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq -1 \cdot 10^{+105}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 3 \cdot \frac{\left(t_0 - x2 \cdot 2\right) - x1}{t_1}\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+149}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(\left(t_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right)\right) + 3 \cdot t_0\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ (* x2 2.0) t_0) x1) t_1)))
   (if (<= x1 -1.32e+154)
     (+
      x1
      (+
       (+ x1 (* 4.0 (* -3.0 (* x1 x2))))
       (* 3.0 (- (fma (* x1 x1) (+ 3.0 (* x2 2.0)) (* x2 -2.0)) x1))))
     (if (<= x1 -1e+105)
       (+
        x1
        (+
         (+ x1 (* 6.0 (pow x1 4.0)))
         (* 3.0 (/ (- (- t_0 (* x2 2.0)) x1) t_1))))
       (if (<= x1 1.8e+149)
         (+
          x1
          (+
           (* 3.0 (- (* x2 -2.0) x1))
           (+
            x1
            (+
             (+
              (*
               t_1
               (+
                (* (* (* x1 2.0) t_2) (- t_2 3.0))
                (* (* x1 x1) (- (* 4.0 t_2) 6.0))))
              (* 3.0 t_0))
             (* x1 (* x1 x1))))))
         (+
          x1
          (+
           (+ x1 (* 4.0 (* x2 (* x1 (- (* x2 2.0) 3.0)))))
           (* 3.0 (* x2 -2.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = (((x2 * 2.0) + t_0) - x1) / t_1;
	double tmp;
	if (x1 <= -1.32e+154) {
		tmp = x1 + ((x1 + (4.0 * (-3.0 * (x1 * x2)))) + (3.0 * (fma((x1 * x1), (3.0 + (x2 * 2.0)), (x2 * -2.0)) - x1)));
	} else if (x1 <= -1e+105) {
		tmp = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + (3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)));
	} else if (x1 <= 1.8e+149) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (3.0 * t_0)) + (x1 * (x1 * x1)))));
	} else {
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))) + (3.0 * (x2 * -2.0)));
	}
	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(Float64(x2 * 2.0) + t_0) - x1) / t_1)
	tmp = 0.0
	if (x1 <= -1.32e+154)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(-3.0 * Float64(x1 * x2)))) + Float64(3.0 * Float64(fma(Float64(x1 * x1), Float64(3.0 + Float64(x2 * 2.0)), Float64(x2 * -2.0)) - x1))));
	elseif (x1 <= -1e+105)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_1))));
	elseif (x1 <= 1.8e+149)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - x1)) + 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(4.0 * t_2) - 6.0)))) + Float64(3.0 * t_0)) + Float64(x1 * Float64(x1 * x1))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(x2 * 2.0) - 3.0))))) + Float64(3.0 * Float64(x2 * -2.0))));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[x1, -1.32e+154], N[(x1 + N[(N[(x1 + N[(4.0 * N[(-3.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(3.0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1e+105], N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.8e+149], N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] + 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[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.31999999999999998e154

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x2 around 0 0.0%

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

   4. Taylor expanded in x1 around 0 87.5%

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

      1. +-commutative 87.5%

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

      2. neg-mul-1 87.5%

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

      3. unsub-neg 87.5%

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

      4. +-commutative 87.5%

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

      5. *-commutative 87.5%

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

      6. fma-def 87.5%

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

      7. unpow2 87.5%

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

      8. cancel-sign-sub-inv 87.5%

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

      9. metadata-eval 87.5%

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

      10. *-commutative 87.5%

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

   6. Simplified 87.5%

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

   if -1.31999999999999998e154 < x1 < -9.9999999999999994e104

   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 100.0%

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

      1. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   if -9.9999999999999994e104 < x1 < 1.79999999999999997e149

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around inf 98.3%

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

   3. Taylor expanded in x1 around 0 99.3%

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

      1. +-commutative 53.0%

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

      2. neg-mul-1 53.0%

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

      3. unsub-neg 53.0%

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

      4. *-commutative 53.0%

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

   5. Simplified 99.3%

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

   if 1.79999999999999997e149 < x1

   1. Initial program 6.7%

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

   2. Taylor expanded in x1 around 0 6.7%

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

   3. Taylor expanded in x1 around 0 68.8%

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

      1. *-commutative 68.8%

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

   5. Simplified 68.8%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.32 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + x2 \cdot 2, x2 \cdot -2\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq -1 \cdot 10^{+105}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+149}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \]

Alternative 6: 86.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\left(x2 \cdot 2 + t_1\right) - x1}{t_0}\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + x2 \cdot 2, x2 \cdot -2\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+149}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(\left(t_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right)\right) + 3 \cdot t_1\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (/ (- (+ (* x2 2.0) t_1) x1) t_0)))
   (if (<= x1 -5.6e+102)
     (+
      x1
      (+
       (+ x1 (* 4.0 (* -3.0 (* x1 x2))))
       (* 3.0 (- (fma (* x1 x1) (+ 3.0 (* x2 2.0)) (* x2 -2.0)) x1))))
     (if (<= x1 1.8e+149)
       (+
        x1
        (+
         (* 3.0 (- (* x2 -2.0) x1))
         (+
          x1
          (+
           (+
            (*
             t_0
             (+
              (* (* (* x1 2.0) t_2) (- t_2 3.0))
              (* (* x1 x1) (- (* 4.0 t_2) 6.0))))
            (* 3.0 t_1))
           (* x1 (* x1 x1))))))
       (+
        x1
        (+
         (+ x1 (* 4.0 (* x2 (* x1 (- (* x2 2.0) 3.0)))))
         (* 3.0 (* x2 -2.0))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (((x2 * 2.0) + t_1) - x1) / t_0;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + ((x1 + (4.0 * (-3.0 * (x1 * x2)))) + (3.0 * (fma((x1 * x1), (3.0 + (x2 * 2.0)), (x2 * -2.0)) - x1)));
	} else if (x1 <= 1.8e+149) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (((t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (3.0 * t_1)) + (x1 * (x1 * x1)))));
	} else {
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))) + (3.0 * (x2 * -2.0)));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(Float64(Float64(x2 * 2.0) + t_1) - x1) / t_0)
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(-3.0 * Float64(x1 * x2)))) + Float64(3.0 * Float64(fma(Float64(x1 * x1), Float64(3.0 + Float64(x2 * 2.0)), Float64(x2 * -2.0)) - x1))));
	elseif (x1 <= 1.8e+149)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - x1)) + Float64(x1 + Float64(Float64(Float64(t_0 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0)))) + Float64(3.0 * t_1)) + Float64(x1 * Float64(x1 * x1))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(x2 * 2.0) - 3.0))))) + Float64(3.0 * Float64(x2 * -2.0))));
	end
	return 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[(N[(x2 * 2.0), $MachinePrecision] + t$95$1), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(N[(x1 + N[(4.0 * N[(-3.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(3.0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.8e+149], N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(N[(t$95$0 * 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[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.1%

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

   3. Taylor expanded in x2 around 0 3.1%

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

   4. Taylor expanded in x1 around 0 64.5%

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

      1. +-commutative 64.5%

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

      2. neg-mul-1 64.5%

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

      3. unsub-neg 64.5%

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

      4. +-commutative 64.5%

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

      5. *-commutative 64.5%

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

      6. fma-def 64.5%

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

      7. unpow2 64.5%

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

      8. cancel-sign-sub-inv 64.5%

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

      9. metadata-eval 64.5%

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

      10. *-commutative 64.5%

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

   6. Simplified 64.5%

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

   if -5.60000000000000037e102 < x1 < 1.79999999999999997e149

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around inf 98.3%

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

   3. Taylor expanded in x1 around 0 99.3%

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

      1. +-commutative 53.0%

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

      2. neg-mul-1 53.0%

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

      3. unsub-neg 53.0%

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

      4. *-commutative 53.0%

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

   5. Simplified 99.3%

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

   if 1.79999999999999997e149 < x1

   1. Initial program 6.7%

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

   2. Taylor expanded in x1 around 0 6.7%

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

   3. Taylor expanded in x1 around 0 68.8%

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

      1. *-commutative 68.8%

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

   5. Simplified 68.8%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + x2 \cdot 2, x2 \cdot -2\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+149}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \]

Alternative 7: 86.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\left(x2 \cdot 2 + t_1\right) - x1}{t_0}\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right) + x1 \cdot \left(x2 \cdot -12 - 2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+149}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(\left(t_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right)\right) + 3 \cdot t_1\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (/ (- (+ (* x2 2.0) t_1) x1) t_0)))
   (if (<= x1 -5.6e+102)
     (+
      x1
      (+
       (* x2 -6.0)
       (+
        (* 3.0 (* (pow x1 2.0) (- 3.0 (* x2 -2.0))))
        (* x1 (- (* x2 -12.0) 2.0)))))
     (if (<= x1 1.8e+149)
       (+
        x1
        (+
         (* 3.0 (- (* x2 -2.0) x1))
         (+
          x1
          (+
           (+
            (*
             t_0
             (+
              (* (* (* x1 2.0) t_2) (- t_2 3.0))
              (* (* x1 x1) (- (* 4.0 t_2) 6.0))))
            (* 3.0 t_1))
           (* x1 (* x1 x1))))))
       (+
        x1
        (+
         (+ x1 (* 4.0 (* x2 (* x1 (- (* x2 2.0) 3.0)))))
         (* 3.0 (* x2 -2.0))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (((x2 * 2.0) + t_1) - x1) / t_0;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + ((x2 * -6.0) + ((3.0 * (pow(x1, 2.0) * (3.0 - (x2 * -2.0)))) + (x1 * ((x2 * -12.0) - 2.0))));
	} else if (x1 <= 1.8e+149) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (((t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (3.0 * t_1)) + (x1 * (x1 * x1)))));
	} else {
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))) + (3.0 * (x2 * -2.0)));
	}
	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) + 1.0d0
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (((x2 * 2.0d0) + t_1) - x1) / t_0
    if (x1 <= (-5.6d+102)) then
        tmp = x1 + ((x2 * (-6.0d0)) + ((3.0d0 * ((x1 ** 2.0d0) * (3.0d0 - (x2 * (-2.0d0))))) + (x1 * ((x2 * (-12.0d0)) - 2.0d0))))
    else if (x1 <= 1.8d+149) then
        tmp = x1 + ((3.0d0 * ((x2 * (-2.0d0)) - x1)) + (x1 + (((t_0 * ((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * ((4.0d0 * t_2) - 6.0d0)))) + (3.0d0 * t_1)) + (x1 * (x1 * x1)))))
    else
        tmp = x1 + ((x1 + (4.0d0 * (x2 * (x1 * ((x2 * 2.0d0) - 3.0d0))))) + (3.0d0 * (x2 * (-2.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (((x2 * 2.0) + t_1) - x1) / t_0;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + ((x2 * -6.0) + ((3.0 * (Math.pow(x1, 2.0) * (3.0 - (x2 * -2.0)))) + (x1 * ((x2 * -12.0) - 2.0))));
	} else if (x1 <= 1.8e+149) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (((t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (3.0 * t_1)) + (x1 * (x1 * x1)))));
	} else {
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))) + (3.0 * (x2 * -2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = (((x2 * 2.0) + t_1) - x1) / t_0
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 + ((x2 * -6.0) + ((3.0 * (math.pow(x1, 2.0) * (3.0 - (x2 * -2.0)))) + (x1 * ((x2 * -12.0) - 2.0))))
	elif x1 <= 1.8e+149:
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (((t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (3.0 * t_1)) + (x1 * (x1 * x1)))))
	else:
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))) + (3.0 * (x2 * -2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(Float64(Float64(x2 * 2.0) + t_1) - x1) / t_0)
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(Float64(3.0 * Float64((x1 ^ 2.0) * Float64(3.0 - Float64(x2 * -2.0)))) + Float64(x1 * Float64(Float64(x2 * -12.0) - 2.0)))));
	elseif (x1 <= 1.8e+149)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - x1)) + Float64(x1 + Float64(Float64(Float64(t_0 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0)))) + Float64(3.0 * t_1)) + Float64(x1 * Float64(x1 * x1))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(x2 * 2.0) - 3.0))))) + Float64(3.0 * Float64(x2 * -2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * 3.0);
	t_2 = (((x2 * 2.0) + t_1) - x1) / t_0;
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 + ((x2 * -6.0) + ((3.0 * ((x1 ^ 2.0) * (3.0 - (x2 * -2.0)))) + (x1 * ((x2 * -12.0) - 2.0))));
	elseif (x1 <= 1.8e+149)
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (((t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (3.0 * t_1)) + (x1 * (x1 * x1)))));
	else
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))) + (3.0 * (x2 * -2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$1), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(3.0 * N[(N[Power[x1, 2.0], $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.8e+149], N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(N[(t$95$0 * 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[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.1%

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

   3. Taylor expanded in x2 around 0 3.1%

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

   4. Taylor expanded in x1 around 0 64.5%

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

   if -5.60000000000000037e102 < x1 < 1.79999999999999997e149

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around inf 98.3%

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

   3. Taylor expanded in x1 around 0 99.3%

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

      1. +-commutative 53.0%

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

      2. neg-mul-1 53.0%

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

      3. unsub-neg 53.0%

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

      4. *-commutative 53.0%

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

   5. Simplified 99.3%

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

   if 1.79999999999999997e149 < x1

   1. Initial program 6.7%

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

   2. Taylor expanded in x1 around 0 6.7%

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

   3. Taylor expanded in x1 around 0 68.8%

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

      1. *-commutative 68.8%

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

   5. Simplified 68.8%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right) + x1 \cdot \left(x2 \cdot -12 - 2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+149}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \]

Alternative 8: 79.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(x2 \cdot 2 + t_0\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+149}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(\left(t_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right)\right) + 3 \cdot t_0\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ (* x2 2.0) t_0) x1) t_1)))
   (if (<= x1 -5.6e+102)
     (* x1 (+ (* x2 -12.0) -1.0))
     (if (<= x1 1.8e+149)
       (+
        x1
        (+
         (* 3.0 (- (* x2 -2.0) x1))
         (+
          x1
          (+
           (+
            (*
             t_1
             (+
              (* (* (* x1 2.0) t_2) (- t_2 3.0))
              (* (* x1 x1) (- (* 4.0 t_2) 6.0))))
            (* 3.0 t_0))
           (* x1 (* x1 x1))))))
       (+
        x1
        (+
         (+ x1 (* 4.0 (* x2 (* x1 (- (* x2 2.0) 3.0)))))
         (* 3.0 (* x2 -2.0))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = (((x2 * 2.0) + t_0) - x1) / t_1;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 * ((x2 * -12.0) + -1.0);
	} else if (x1 <= 1.8e+149) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (3.0 * t_0)) + (x1 * (x1 * x1)))));
	} else {
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))) + (3.0 * (x2 * -2.0)));
	}
	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 = (((x2 * 2.0d0) + t_0) - x1) / t_1
    if (x1 <= (-5.6d+102)) then
        tmp = x1 * ((x2 * (-12.0d0)) + (-1.0d0))
    else if (x1 <= 1.8d+149) then
        tmp = x1 + ((3.0d0 * ((x2 * (-2.0d0)) - x1)) + (x1 + (((t_1 * ((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * ((4.0d0 * t_2) - 6.0d0)))) + (3.0d0 * t_0)) + (x1 * (x1 * x1)))))
    else
        tmp = x1 + ((x1 + (4.0d0 * (x2 * (x1 * ((x2 * 2.0d0) - 3.0d0))))) + (3.0d0 * (x2 * (-2.0d0))))
    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 = (((x2 * 2.0) + t_0) - x1) / t_1;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 * ((x2 * -12.0) + -1.0);
	} else if (x1 <= 1.8e+149) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (3.0 * t_0)) + (x1 * (x1 * x1)))));
	} else {
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))) + (3.0 * (x2 * -2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = (((x2 * 2.0) + t_0) - x1) / t_1
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 * ((x2 * -12.0) + -1.0)
	elif x1 <= 1.8e+149:
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (3.0 * t_0)) + (x1 * (x1 * x1)))))
	else:
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))) + (3.0 * (x2 * -2.0)))
	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(Float64(x2 * 2.0) + t_0) - x1) / t_1)
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 * Float64(Float64(x2 * -12.0) + -1.0));
	elseif (x1 <= 1.8e+149)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - x1)) + 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(4.0 * t_2) - 6.0)))) + Float64(3.0 * t_0)) + Float64(x1 * Float64(x1 * x1))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(x2 * 2.0) - 3.0))))) + Float64(3.0 * Float64(x2 * -2.0))));
	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 = (((x2 * 2.0) + t_0) - x1) / t_1;
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 * ((x2 * -12.0) + -1.0);
	elseif (x1 <= 1.8e+149)
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (3.0 * t_0)) + (x1 * (x1 * x1)))));
	else
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))) + (3.0 * (x2 * -2.0)));
	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[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.8e+149], N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] + 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[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.1%

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

   3. Taylor expanded in x2 around 0 3.1%

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

   4. Taylor expanded in x1 around 0 25.2%

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

      1. +-commutative 25.2%

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

      2. neg-mul-1 25.2%

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

      3. unsub-neg 25.2%

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

      4. *-commutative 25.2%

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

   6. Simplified 25.2%

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

   7. Taylor expanded in x1 around inf 25.2%

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

   if -5.60000000000000037e102 < x1 < 1.79999999999999997e149

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around inf 98.3%

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

   3. Taylor expanded in x1 around 0 99.3%

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

      1. +-commutative 53.0%

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

      2. neg-mul-1 53.0%

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

      3. unsub-neg 53.0%

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

      4. *-commutative 53.0%

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

   5. Simplified 99.3%

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

   if 1.79999999999999997e149 < x1

   1. Initial program 6.7%

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

   2. Taylor expanded in x1 around 0 6.7%

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

   3. Taylor expanded in x1 around 0 68.8%

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

      1. *-commutative 68.8%

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

   5. Simplified 68.8%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+149}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \]

Alternative 9: 77.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(x2 \cdot 2 + t_0\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+149}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - x2 \cdot 2\right) - x1}{t_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t_0 + t_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ (* x2 2.0) t_0) x1) t_1)))
   (if (<= x1 -5.6e+102)
     (* x1 (+ (* x2 -12.0) -1.0))
     (if (<= x1 1.8e+149)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_0 (* x2 2.0)) x1) t_1))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* 3.0 t_0)
            (*
             t_1
             (+ (* (* (* x1 2.0) t_2) (- t_2 3.0)) (* (* x1 x1) 6.0))))))))
       (+
        x1
        (+
         (+ x1 (* 4.0 (* x2 (* x1 (- (* x2 2.0) 3.0)))))
         (* 3.0 (* x2 -2.0))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = (((x2 * 2.0) + t_0) - x1) / t_1;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 * ((x2 * -12.0) + -1.0);
	} else if (x1 <= 1.8e+149) {
		tmp = x1 + ((3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	} else {
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))) + (3.0 * (x2 * -2.0)));
	}
	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 = (((x2 * 2.0d0) + t_0) - x1) / t_1
    if (x1 <= (-5.6d+102)) then
        tmp = x1 * ((x2 * (-12.0d0)) + (-1.0d0))
    else if (x1 <= 1.8d+149) then
        tmp = x1 + ((3.0d0 * (((t_0 - (x2 * 2.0d0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_0) + (t_1 * ((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * 6.0d0)))))))
    else
        tmp = x1 + ((x1 + (4.0d0 * (x2 * (x1 * ((x2 * 2.0d0) - 3.0d0))))) + (3.0d0 * (x2 * (-2.0d0))))
    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 = (((x2 * 2.0) + t_0) - x1) / t_1;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 * ((x2 * -12.0) + -1.0);
	} else if (x1 <= 1.8e+149) {
		tmp = x1 + ((3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	} else {
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))) + (3.0 * (x2 * -2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = (((x2 * 2.0) + t_0) - x1) / t_1
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 * ((x2 * -12.0) + -1.0)
	elif x1 <= 1.8e+149:
		tmp = x1 + ((3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))))
	else:
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))) + (3.0 * (x2 * -2.0)))
	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(Float64(x2 * 2.0) + t_0) - x1) / t_1)
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 * Float64(Float64(x2 * -12.0) + -1.0));
	elseif (x1 <= 1.8e+149)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_0) + Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * 6.0))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(x2 * 2.0) - 3.0))))) + Float64(3.0 * Float64(x2 * -2.0))));
	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 = (((x2 * 2.0) + t_0) - x1) / t_1;
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 * ((x2 * -12.0) + -1.0);
	elseif (x1 <= 1.8e+149)
		tmp = x1 + ((3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	else
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))) + (3.0 * (x2 * -2.0)));
	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[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.8e+149], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$0), $MachinePrecision] + 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] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.1%

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

   3. Taylor expanded in x2 around 0 3.1%

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

   4. Taylor expanded in x1 around 0 25.2%

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

      1. +-commutative 25.2%

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

      2. neg-mul-1 25.2%

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

      3. unsub-neg 25.2%

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

      4. *-commutative 25.2%

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

   6. Simplified 25.2%

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

   7. Taylor expanded in x1 around inf 25.2%

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

   if -5.60000000000000037e102 < x1 < 1.79999999999999997e149

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around inf 97.0%

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

   3. Taylor expanded in x1 around inf 96.9%

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

   if 1.79999999999999997e149 < x1

   1. Initial program 6.7%

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

   2. Taylor expanded in x1 around 0 6.7%

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

   3. Taylor expanded in x1 around 0 68.8%

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

      1. *-commutative 68.8%

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

   5. Simplified 68.8%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+149}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \]

Alternative 10: 75.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x2 \cdot 2 + t_0\right) - x1}{t_2} - 6\right)\\ t_4 := x1 \cdot \left(x1 \cdot x1\right)\\ t_5 := 3 \cdot \frac{\left(t_0 - x2 \cdot 2\right) - x1}{t_2}\\ t_6 := 3 \cdot t_0\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq -2.3 \cdot 10^{+33}:\\ \;\;\;\;x1 + \left(t_5 + \left(x1 + \left(t_4 + \left(t_6 + t_2 \cdot \left(x1 \cdot 2 + t_3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+149}:\\ \;\;\;\;x1 + \left(t_5 + \left(x1 + \left(t_4 + \left(t_6 + t_2 \cdot \left(t_3 + t_1\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + t_1\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (* 4.0 (* x2 (* x1 (- (* x2 2.0) 3.0)))))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* (* x1 x1) (- (* 4.0 (/ (- (+ (* x2 2.0) t_0) x1) t_2)) 6.0)))
        (t_4 (* x1 (* x1 x1)))
        (t_5 (* 3.0 (/ (- (- t_0 (* x2 2.0)) x1) t_2)))
        (t_6 (* 3.0 t_0)))
   (if (<= x1 -5.6e+102)
     (* x1 (+ (* x2 -12.0) -1.0))
     (if (<= x1 -2.3e+33)
       (+ x1 (+ t_5 (+ x1 (+ t_4 (+ t_6 (* t_2 (+ (* x1 2.0) t_3)))))))
       (if (<= x1 1.8e+149)
         (+ x1 (+ t_5 (+ x1 (+ t_4 (+ t_6 (* t_2 (+ t_3 t_1)))))))
         (+ x1 (+ (+ x1 t_1) (* 3.0 (* x2 -2.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0)));
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = (x1 * x1) * ((4.0 * ((((x2 * 2.0) + t_0) - x1) / t_2)) - 6.0);
	double t_4 = x1 * (x1 * x1);
	double t_5 = 3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_2);
	double t_6 = 3.0 * t_0;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 * ((x2 * -12.0) + -1.0);
	} else if (x1 <= -2.3e+33) {
		tmp = x1 + (t_5 + (x1 + (t_4 + (t_6 + (t_2 * ((x1 * 2.0) + t_3))))));
	} else if (x1 <= 1.8e+149) {
		tmp = x1 + (t_5 + (x1 + (t_4 + (t_6 + (t_2 * (t_3 + t_1))))));
	} else {
		tmp = x1 + ((x1 + t_1) + (3.0 * (x2 * -2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = 4.0d0 * (x2 * (x1 * ((x2 * 2.0d0) - 3.0d0)))
    t_2 = (x1 * x1) + 1.0d0
    t_3 = (x1 * x1) * ((4.0d0 * ((((x2 * 2.0d0) + t_0) - x1) / t_2)) - 6.0d0)
    t_4 = x1 * (x1 * x1)
    t_5 = 3.0d0 * (((t_0 - (x2 * 2.0d0)) - x1) / t_2)
    t_6 = 3.0d0 * t_0
    if (x1 <= (-5.6d+102)) then
        tmp = x1 * ((x2 * (-12.0d0)) + (-1.0d0))
    else if (x1 <= (-2.3d+33)) then
        tmp = x1 + (t_5 + (x1 + (t_4 + (t_6 + (t_2 * ((x1 * 2.0d0) + t_3))))))
    else if (x1 <= 1.8d+149) then
        tmp = x1 + (t_5 + (x1 + (t_4 + (t_6 + (t_2 * (t_3 + t_1))))))
    else
        tmp = x1 + ((x1 + t_1) + (3.0d0 * (x2 * (-2.0d0))))
    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 = 4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0)));
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = (x1 * x1) * ((4.0 * ((((x2 * 2.0) + t_0) - x1) / t_2)) - 6.0);
	double t_4 = x1 * (x1 * x1);
	double t_5 = 3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_2);
	double t_6 = 3.0 * t_0;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 * ((x2 * -12.0) + -1.0);
	} else if (x1 <= -2.3e+33) {
		tmp = x1 + (t_5 + (x1 + (t_4 + (t_6 + (t_2 * ((x1 * 2.0) + t_3))))));
	} else if (x1 <= 1.8e+149) {
		tmp = x1 + (t_5 + (x1 + (t_4 + (t_6 + (t_2 * (t_3 + t_1))))));
	} else {
		tmp = x1 + ((x1 + t_1) + (3.0 * (x2 * -2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = 4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0)))
	t_2 = (x1 * x1) + 1.0
	t_3 = (x1 * x1) * ((4.0 * ((((x2 * 2.0) + t_0) - x1) / t_2)) - 6.0)
	t_4 = x1 * (x1 * x1)
	t_5 = 3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_2)
	t_6 = 3.0 * t_0
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 * ((x2 * -12.0) + -1.0)
	elif x1 <= -2.3e+33:
		tmp = x1 + (t_5 + (x1 + (t_4 + (t_6 + (t_2 * ((x1 * 2.0) + t_3))))))
	elif x1 <= 1.8e+149:
		tmp = x1 + (t_5 + (x1 + (t_4 + (t_6 + (t_2 * (t_3 + t_1))))))
	else:
		tmp = x1 + ((x1 + t_1) + (3.0 * (x2 * -2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(x2 * 2.0) - 3.0))))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(Float64(Float64(Float64(x2 * 2.0) + t_0) - x1) / t_2)) - 6.0))
	t_4 = Float64(x1 * Float64(x1 * x1))
	t_5 = Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_2))
	t_6 = Float64(3.0 * t_0)
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 * Float64(Float64(x2 * -12.0) + -1.0));
	elseif (x1 <= -2.3e+33)
		tmp = Float64(x1 + Float64(t_5 + Float64(x1 + Float64(t_4 + Float64(t_6 + Float64(t_2 * Float64(Float64(x1 * 2.0) + t_3)))))));
	elseif (x1 <= 1.8e+149)
		tmp = Float64(x1 + Float64(t_5 + Float64(x1 + Float64(t_4 + Float64(t_6 + Float64(t_2 * Float64(t_3 + t_1)))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + t_1) + Float64(3.0 * Float64(x2 * -2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = 4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0)));
	t_2 = (x1 * x1) + 1.0;
	t_3 = (x1 * x1) * ((4.0 * ((((x2 * 2.0) + t_0) - x1) / t_2)) - 6.0);
	t_4 = x1 * (x1 * x1);
	t_5 = 3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_2);
	t_6 = 3.0 * t_0;
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 * ((x2 * -12.0) + -1.0);
	elseif (x1 <= -2.3e+33)
		tmp = x1 + (t_5 + (x1 + (t_4 + (t_6 + (t_2 * ((x1 * 2.0) + t_3))))));
	elseif (x1 <= 1.8e+149)
		tmp = x1 + (t_5 + (x1 + (t_4 + (t_6 + (t_2 * (t_3 + t_1))))));
	else
		tmp = x1 + ((x1 + t_1) + (3.0 * (x2 * -2.0)));
	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[(4.0 * N[(x2 * N[(x1 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(3.0 * N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(3.0 * t$95$0), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.3e+33], N[(x1 + N[(t$95$5 + N[(x1 + N[(t$95$4 + N[(t$95$6 + N[(t$95$2 * N[(N[(x1 * 2.0), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.8e+149], N[(x1 + N[(t$95$5 + N[(x1 + N[(t$95$4 + N[(t$95$6 + N[(t$95$2 * N[(t$95$3 + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + t$95$1), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.1%

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

   3. Taylor expanded in x2 around 0 3.1%

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

   4. Taylor expanded in x1 around 0 25.2%

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

      1. +-commutative 25.2%

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

      2. neg-mul-1 25.2%

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

      3. unsub-neg 25.2%

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

      4. *-commutative 25.2%

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

   6. Simplified 25.2%

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

   7. Taylor expanded in x1 around inf 25.2%

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

   if -5.60000000000000037e102 < x1 < -2.30000000000000011e33

   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 75.2%

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

   3. Taylor expanded in x1 around inf 75.2%

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

   4. Taylor expanded in x1 around inf 84.6%

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

      1. *-commutative 84.6%

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

   6. Simplified 84.6%

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

   if -2.30000000000000011e33 < x1 < 1.79999999999999997e149

   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 94.8%

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

   3. Taylor expanded in x1 around inf 94.3%

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

   4. Taylor expanded in x1 around 0 93.8%

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

   if 1.79999999999999997e149 < x1

   1. Initial program 6.7%

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

   2. Taylor expanded in x1 around 0 6.7%

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

   3. Taylor expanded in x1 around 0 68.8%

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

      1. *-commutative 68.8%

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

   5. Simplified 68.8%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq -2.3 \cdot 10^{+33}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+149}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 6\right) + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \]

Alternative 11: 74.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq 2.05 \cdot 10^{+142}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - x2 \cdot 2\right) - x1}{t_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t_0 + t_1 \cdot \left(\left(x1 \cdot x1\right) \cdot 6 + \left(\frac{\left(x2 \cdot 2 + t_0\right) - x1}{t_1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 \cdot 2 - x1\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0))) (t_1 (+ (* x1 x1) 1.0)))
   (if (<= x1 -5.6e+102)
     (* x1 (+ (* x2 -12.0) -1.0))
     (if (<= x1 2.05e+142)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_0 (* x2 2.0)) x1) t_1))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* 3.0 t_0)
            (*
             t_1
             (+
              (* (* x1 x1) 6.0)
              (*
               (- (/ (- (+ (* x2 2.0) t_0) x1) t_1) 3.0)
               (* (* x1 2.0) (- (* x2 2.0) x1))))))))))
       (+
        x1
        (+
         (+ x1 (* 4.0 (* x2 (* x1 (- (* x2 2.0) 3.0)))))
         (* 3.0 (* x2 -2.0))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 * ((x2 * -12.0) + -1.0);
	} else if (x1 <= 2.05e+142) {
		tmp = x1 + ((3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * (((x1 * x1) * 6.0) + ((((((x2 * 2.0) + t_0) - x1) / t_1) - 3.0) * ((x1 * 2.0) * ((x2 * 2.0) - x1)))))))));
	} else {
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))) + (3.0 * (x2 * -2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    if (x1 <= (-5.6d+102)) then
        tmp = x1 * ((x2 * (-12.0d0)) + (-1.0d0))
    else if (x1 <= 2.05d+142) then
        tmp = x1 + ((3.0d0 * (((t_0 - (x2 * 2.0d0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_0) + (t_1 * (((x1 * x1) * 6.0d0) + ((((((x2 * 2.0d0) + t_0) - x1) / t_1) - 3.0d0) * ((x1 * 2.0d0) * ((x2 * 2.0d0) - x1)))))))))
    else
        tmp = x1 + ((x1 + (4.0d0 * (x2 * (x1 * ((x2 * 2.0d0) - 3.0d0))))) + (3.0d0 * (x2 * (-2.0d0))))
    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 tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 * ((x2 * -12.0) + -1.0);
	} else if (x1 <= 2.05e+142) {
		tmp = x1 + ((3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * (((x1 * x1) * 6.0) + ((((((x2 * 2.0) + t_0) - x1) / t_1) - 3.0) * ((x1 * 2.0) * ((x2 * 2.0) - x1)))))))));
	} else {
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))) + (3.0 * (x2 * -2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 * ((x2 * -12.0) + -1.0)
	elif x1 <= 2.05e+142:
		tmp = x1 + ((3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * (((x1 * x1) * 6.0) + ((((((x2 * 2.0) + t_0) - x1) / t_1) - 3.0) * ((x1 * 2.0) * ((x2 * 2.0) - x1)))))))))
	else:
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))) + (3.0 * (x2 * -2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 * Float64(Float64(x2 * -12.0) + -1.0));
	elseif (x1 <= 2.05e+142)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_0) + Float64(t_1 * Float64(Float64(Float64(x1 * x1) * 6.0) + Float64(Float64(Float64(Float64(Float64(Float64(x2 * 2.0) + t_0) - x1) / t_1) - 3.0) * Float64(Float64(x1 * 2.0) * Float64(Float64(x2 * 2.0) - x1))))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(x2 * 2.0) - 3.0))))) + Float64(3.0 * Float64(x2 * -2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * x1) + 1.0;
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 * ((x2 * -12.0) + -1.0);
	elseif (x1 <= 2.05e+142)
		tmp = x1 + ((3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * (((x1 * x1) * 6.0) + ((((((x2 * 2.0) + t_0) - x1) / t_1) - 3.0) * ((x1 * 2.0) * ((x2 * 2.0) - x1)))))))));
	else
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))) + (3.0 * (x2 * -2.0)));
	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]}, If[LessEqual[x1, -5.6e+102], N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.05e+142], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$0), $MachinePrecision] + N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision] + N[(N[(N[(N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision] - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(x2 * 2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.1%

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

   3. Taylor expanded in x2 around 0 3.1%

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

   4. Taylor expanded in x1 around 0 25.2%

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

      1. +-commutative 25.2%

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

      2. neg-mul-1 25.2%

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

      3. unsub-neg 25.2%

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

      4. *-commutative 25.2%

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

   6. Simplified 25.2%

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

   7. Taylor expanded in x1 around inf 25.2%

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

   if -5.60000000000000037e102 < x1 < 2.04999999999999991e142

   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 93.4%

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

   3. Taylor expanded in x1 around inf 92.9%

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

   4. Taylor expanded in x1 around inf 92.8%

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

   if 2.04999999999999991e142 < x1

   1. Initial program 12.5%

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

   2. Taylor expanded in x1 around 0 9.6%

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

   3. Taylor expanded in x1 around 0 67.9%

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

      1. *-commutative 67.9%

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

   5. Simplified 67.9%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq 2.05 \cdot 10^{+142}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6 + \left(\frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 \cdot 2 - x1\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \]

Alternative 12: 74.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := 3 \cdot \frac{\left(t_0 - x2 \cdot 2\right) - x1}{t_1}\\ t_3 := x1 + \left(t_2 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t_0 + t_1 \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x2 \cdot 2 + t_0\right) - x1}{t_1} - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq -6.7:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x1 \leq 530000000:\\ \;\;\;\;x1 + \left(t_2 + \left(x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+149}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* 3.0 (/ (- (- t_0 (* x2 2.0)) x1) t_1)))
        (t_3
         (+
          x1
          (+
           t_2
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* 3.0 t_0)
              (*
               t_1
               (+
                (* x1 2.0)
                (*
                 (* x1 x1)
                 (- (* 4.0 (/ (- (+ (* x2 2.0) t_0) x1) t_1)) 6.0)))))))))))
   (if (<= x1 -5.6e+102)
     (* x1 (+ (* x2 -12.0) -1.0))
     (if (<= x1 -6.7)
       t_3
       (if (<= x1 530000000.0)
         (+ x1 (+ t_2 (+ x1 (* 8.0 (* x2 (* x1 x2))))))
         (if (<= x1 1.8e+149)
           t_3
           (+
            x1
            (+
             (+ x1 (* 4.0 (* x2 (* x1 (- (* x2 2.0) 3.0)))))
             (* 3.0 (* x2 -2.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = 3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1);
	double t_3 = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * ((((x2 * 2.0) + t_0) - x1) / t_1)) - 6.0))))))));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 * ((x2 * -12.0) + -1.0);
	} else if (x1 <= -6.7) {
		tmp = t_3;
	} else if (x1 <= 530000000.0) {
		tmp = x1 + (t_2 + (x1 + (8.0 * (x2 * (x1 * x2)))));
	} else if (x1 <= 1.8e+149) {
		tmp = t_3;
	} else {
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))) + (3.0 * (x2 * -2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = 3.0d0 * (((t_0 - (x2 * 2.0d0)) - x1) / t_1)
    t_3 = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_0) + (t_1 * ((x1 * 2.0d0) + ((x1 * x1) * ((4.0d0 * ((((x2 * 2.0d0) + t_0) - x1) / t_1)) - 6.0d0))))))))
    if (x1 <= (-5.6d+102)) then
        tmp = x1 * ((x2 * (-12.0d0)) + (-1.0d0))
    else if (x1 <= (-6.7d0)) then
        tmp = t_3
    else if (x1 <= 530000000.0d0) then
        tmp = x1 + (t_2 + (x1 + (8.0d0 * (x2 * (x1 * x2)))))
    else if (x1 <= 1.8d+149) then
        tmp = t_3
    else
        tmp = x1 + ((x1 + (4.0d0 * (x2 * (x1 * ((x2 * 2.0d0) - 3.0d0))))) + (3.0d0 * (x2 * (-2.0d0))))
    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 = 3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1);
	double t_3 = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * ((((x2 * 2.0) + t_0) - x1) / t_1)) - 6.0))))))));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 * ((x2 * -12.0) + -1.0);
	} else if (x1 <= -6.7) {
		tmp = t_3;
	} else if (x1 <= 530000000.0) {
		tmp = x1 + (t_2 + (x1 + (8.0 * (x2 * (x1 * x2)))));
	} else if (x1 <= 1.8e+149) {
		tmp = t_3;
	} else {
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))) + (3.0 * (x2 * -2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = 3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)
	t_3 = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * ((((x2 * 2.0) + t_0) - x1) / t_1)) - 6.0))))))))
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 * ((x2 * -12.0) + -1.0)
	elif x1 <= -6.7:
		tmp = t_3
	elif x1 <= 530000000.0:
		tmp = x1 + (t_2 + (x1 + (8.0 * (x2 * (x1 * x2)))))
	elif x1 <= 1.8e+149:
		tmp = t_3
	else:
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))) + (3.0 * (x2 * -2.0)))
	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(3.0 * Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_1))
	t_3 = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_0) + Float64(t_1 * Float64(Float64(x1 * 2.0) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(Float64(Float64(Float64(x2 * 2.0) + t_0) - x1) / t_1)) - 6.0)))))))))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 * Float64(Float64(x2 * -12.0) + -1.0));
	elseif (x1 <= -6.7)
		tmp = t_3;
	elseif (x1 <= 530000000.0)
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(8.0 * Float64(x2 * Float64(x1 * x2))))));
	elseif (x1 <= 1.8e+149)
		tmp = t_3;
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(x2 * 2.0) - 3.0))))) + Float64(3.0 * Float64(x2 * -2.0))));
	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 = 3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1);
	t_3 = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * ((((x2 * 2.0) + t_0) - x1) / t_1)) - 6.0))))))));
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 * ((x2 * -12.0) + -1.0);
	elseif (x1 <= -6.7)
		tmp = t_3;
	elseif (x1 <= 530000000.0)
		tmp = x1 + (t_2 + (x1 + (8.0 * (x2 * (x1 * x2)))));
	elseif (x1 <= 1.8e+149)
		tmp = t_3;
	else
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))) + (3.0 * (x2 * -2.0)));
	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[(3.0 * N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(t$95$2 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$0), $MachinePrecision] + N[(t$95$1 * N[(N[(x1 * 2.0), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -6.7], t$95$3, If[LessEqual[x1, 530000000.0], N[(x1 + N[(t$95$2 + N[(x1 + N[(8.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.8e+149], t$95$3, N[(x1 + N[(N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.1%

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

   3. Taylor expanded in x2 around 0 3.1%

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

   4. Taylor expanded in x1 around 0 25.2%

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

      1. +-commutative 25.2%

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

      2. neg-mul-1 25.2%

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

      3. unsub-neg 25.2%

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

      4. *-commutative 25.2%

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

   6. Simplified 25.2%

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

   7. Taylor expanded in x1 around inf 25.2%

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

   if -5.60000000000000037e102 < x1 < -6.70000000000000018 or 5.3e8 < x1 < 1.79999999999999997e149

   1. Initial program 99.4%

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

   2. Taylor expanded in x1 around 0 81.9%

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

   3. Taylor expanded in x1 around inf 81.9%

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

   4. Taylor expanded in x1 around inf 81.1%

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

      1. *-commutative 81.1%

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

   6. Simplified 81.1%

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

   if -6.70000000000000018 < x1 < 5.3e8

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around inf 97.9%

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

   3. Taylor expanded in x2 around inf 89.0%

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

      1. associate-/l* 89.0%

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

      2. unpow2 89.0%

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

      3. +-commutative 89.0%

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

      4. unpow2 89.0%

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

      5. fma-udef 89.0%

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

   5. Simplified 89.0%

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

   6. Taylor expanded in x1 around 0 88.1%

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

      1. unpow2 88.1%

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

      2. associate-*l* 97.7%

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

   8. Simplified 97.7%

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

   if 1.79999999999999997e149 < x1

   1. Initial program 6.7%

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

   2. Taylor expanded in x1 around 0 6.7%

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

   3. Taylor expanded in x1 around 0 68.8%

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

      1. *-commutative 68.8%

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

   5. Simplified 68.8%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq -6.7:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 530000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+149}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \]

Alternative 13: 65.8% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -7.5 \cdot 10^{+77}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+149}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.4 \cdot 10^{+193}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -7.5e+77)
   (* x1 (+ (* x2 -12.0) -1.0))
   (if (<= x1 1.8e+149)
     (+
      x1
      (+
       (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* x2 2.0)) x1) (+ (* x1 x1) 1.0)))
       (+ x1 (* 8.0 (* x2 (* x1 x2))))))
     (if (<= x1 4.4e+193)
       (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0)))
       (+ x1 (* x1 (+ 1.0 (* 4.0 (* x2 (- (* x2 2.0) 3.0))))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -7.5e+77) {
		tmp = x1 * ((x2 * -12.0) + -1.0);
	} else if (x1 <= 1.8e+149) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (x2 * 2.0)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (8.0 * (x2 * (x1 * x2)))));
	} else if (x1 <= 4.4e+193) {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	} else {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 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 <= (-7.5d+77)) then
        tmp = x1 * ((x2 * (-12.0d0)) + (-1.0d0))
    else if (x1 <= 1.8d+149) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (x2 * 2.0d0)) - x1) / ((x1 * x1) + 1.0d0))) + (x1 + (8.0d0 * (x2 * (x1 * x2)))))
    else if (x1 <= 4.4d+193) then
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    else
        tmp = x1 + (x1 * (1.0d0 + (4.0d0 * (x2 * ((x2 * 2.0d0) - 3.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -7.5e+77) {
		tmp = x1 * ((x2 * -12.0) + -1.0);
	} else if (x1 <= 1.8e+149) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (x2 * 2.0)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (8.0 * (x2 * (x1 * x2)))));
	} else if (x1 <= 4.4e+193) {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	} else {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -7.5e+77:
		tmp = x1 * ((x2 * -12.0) + -1.0)
	elif x1 <= 1.8e+149:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (x2 * 2.0)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (8.0 * (x2 * (x1 * x2)))))
	elif x1 <= 4.4e+193:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	else:
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -7.5e+77)
		tmp = Float64(x1 * Float64(Float64(x2 * -12.0) + -1.0));
	elseif (x1 <= 1.8e+149)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(x2 * 2.0)) - x1) / Float64(Float64(x1 * x1) + 1.0))) + Float64(x1 + Float64(8.0 * Float64(x2 * Float64(x1 * x2))))));
	elseif (x1 <= 4.4e+193)
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(x2 * 2.0) - 3.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -7.5e+77)
		tmp = x1 * ((x2 * -12.0) + -1.0);
	elseif (x1 <= 1.8e+149)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (x2 * 2.0)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (8.0 * (x2 * (x1 * x2)))));
	elseif (x1 <= 4.4e+193)
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	else
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -7.5e+77], N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.8e+149], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(8.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.4e+193], N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * N[(1.0 + N[(4.0 * N[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -7.49999999999999955e77

   1. Initial program 9.3%

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

   2. Taylor expanded in x1 around 0 0.1%

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

   3. Taylor expanded in x2 around 0 3.0%

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

   4. Taylor expanded in x1 around 0 23.2%

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

      1. +-commutative 23.2%

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

      2. neg-mul-1 23.2%

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

      3. unsub-neg 23.2%

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

      4. *-commutative 23.2%

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

   6. Simplified 23.2%

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

   7. Taylor expanded in x1 around inf 23.2%

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

   if -7.49999999999999955e77 < x1 < 1.79999999999999997e149

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around inf 96.9%

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

   3. Taylor expanded in x2 around inf 71.8%

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

      1. associate-/l* 71.8%

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

      2. unpow2 71.8%

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

      3. +-commutative 71.8%

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

      4. unpow2 71.8%

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

      5. fma-udef 71.8%

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

   5. Simplified 71.8%

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

   6. Taylor expanded in x1 around 0 69.4%

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

      1. unpow2 69.4%

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

      2. associate-*l* 76.3%

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

   8. Simplified 76.3%

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

   if 1.79999999999999997e149 < x1 < 4.39999999999999972e193

   1. Initial program 18.2%

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

   2. Taylor expanded in x1 around 0 18.2%

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

   3. Taylor expanded in x1 around 0 5.3%

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

      1. *-commutative 5.3%

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

   5. Simplified 5.3%

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

      1. flip-+ 81.8%

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

   7. Applied egg-rr 81.8%

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

      1. swap-sqr 81.8%

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

      2. metadata-eval 81.8%

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

   9. Simplified 81.8%

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

   if 4.39999999999999972e193 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around inf 80.8%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.5 \cdot 10^{+77}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+149}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.4 \cdot 10^{+193}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\\ \end{array} \]

Alternative 14: 60.1% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{if}\;x1 \leq -1.2 \cdot 10^{+85}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq -1 \cdot 10^{-246} \lor \neg \left(x1 \leq 1.65 \cdot 10^{-230}\right):\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ (* x2 -12.0) -1.0))))
   (if (<= x1 -1.2e+85)
     t_0
     (if (or (<= x1 -1e-246) (not (<= x1 1.65e-230)))
       (+ x1 (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* x2 2.0) 3.0))) 2.0))))
       (+ (* x2 -6.0) t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((x2 * -12.0) + -1.0);
	double tmp;
	if (x1 <= -1.2e+85) {
		tmp = t_0;
	} else if ((x1 <= -1e-246) || !(x1 <= 1.65e-230)) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0)));
	} else {
		tmp = (x2 * -6.0) + t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 * ((x2 * (-12.0d0)) + (-1.0d0))
    if (x1 <= (-1.2d+85)) then
        tmp = t_0
    else if ((x1 <= (-1d-246)) .or. (.not. (x1 <= 1.65d-230))) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((x2 * 2.0d0) - 3.0d0))) - 2.0d0)))
    else
        tmp = (x2 * (-6.0d0)) + t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * ((x2 * -12.0) + -1.0);
	double tmp;
	if (x1 <= -1.2e+85) {
		tmp = t_0;
	} else if ((x1 <= -1e-246) || !(x1 <= 1.65e-230)) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0)));
	} else {
		tmp = (x2 * -6.0) + t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((x2 * -12.0) + -1.0)
	tmp = 0
	if x1 <= -1.2e+85:
		tmp = t_0
	elif (x1 <= -1e-246) or not (x1 <= 1.65e-230):
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0)))
	else:
		tmp = (x2 * -6.0) + t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(x2 * -12.0) + -1.0))
	tmp = 0.0
	if (x1 <= -1.2e+85)
		tmp = t_0;
	elseif ((x1 <= -1e-246) || !(x1 <= 1.65e-230))
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(x2 * 2.0) - 3.0))) - 2.0))));
	else
		tmp = Float64(Float64(x2 * -6.0) + t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((x2 * -12.0) + -1.0);
	tmp = 0.0;
	if (x1 <= -1.2e+85)
		tmp = t_0;
	elseif ((x1 <= -1e-246) || ~((x1 <= 1.65e-230)))
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0)));
	else
		tmp = (x2 * -6.0) + t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.2e+85], t$95$0, If[Or[LessEqual[x1, -1e-246], N[Not[LessEqual[x1, 1.65e-230]], $MachinePrecision]], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.19999999999999998e85

   1. Initial program 7.1%

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

   2. Taylor expanded in x1 around 0 0.1%

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

   3. Taylor expanded in x2 around 0 3.0%

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

   4. Taylor expanded in x1 around 0 23.7%

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

      1. +-commutative 23.7%

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

      2. neg-mul-1 23.7%

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

      3. unsub-neg 23.7%

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

      4. *-commutative 23.7%

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

   6. Simplified 23.7%

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

   7. Taylor expanded in x1 around inf 23.7%

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

   if -1.19999999999999998e85 < x1 < -9.99999999999999956e-247 or 1.64999999999999997e-230 < x1

   1. Initial program 84.1%

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

   2. Taylor expanded in x1 around 0 60.7%

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

   3. Taylor expanded in x1 around 0 67.8%

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

   if -9.99999999999999956e-247 < x1 < 1.64999999999999997e-230

   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 99.5%

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

   3. Taylor expanded in x2 around 0 91.6%

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

   4. Taylor expanded in x1 around 0 91.6%

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

      1. +-commutative 91.6%

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

      2. neg-mul-1 91.6%

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

      3. unsub-neg 91.6%

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

      4. *-commutative 91.6%

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

   6. Simplified 91.6%

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

   7. Taylor expanded in x1 around 0 91.9%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.2 \cdot 10^{+85}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq -1 \cdot 10^{-246} \lor \neg \left(x1 \leq 1.65 \cdot 10^{-230}\right):\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \end{array} \]

Alternative 15: 61.3% accurate, 5.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -1.08 \cdot 10^{+21} \lor \neg \left(x2 \leq 2.6 \cdot 10^{+24}\right):\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \left(x1 + x1 \cdot -3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -1.08e+21) (not (<= x2 2.6e+24)))
   (+
    x1
    (+ (+ x1 (* 4.0 (* x2 (* x1 (- (* x2 2.0) 3.0))))) (* 3.0 (* x2 -2.0))))
   (+ x1 (+ (* x2 (- (* x1 -12.0) 6.0)) (+ x1 (* x1 -3.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.08e+21) || !(x2 <= 2.6e+24)) {
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))) + (3.0 * (x2 * -2.0)));
	} else {
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -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 ((x2 <= (-1.08d+21)) .or. (.not. (x2 <= 2.6d+24))) then
        tmp = x1 + ((x1 + (4.0d0 * (x2 * (x1 * ((x2 * 2.0d0) - 3.0d0))))) + (3.0d0 * (x2 * (-2.0d0))))
    else
        tmp = x1 + ((x2 * ((x1 * (-12.0d0)) - 6.0d0)) + (x1 + (x1 * (-3.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.08e+21) || !(x2 <= 2.6e+24)) {
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))) + (3.0 * (x2 * -2.0)));
	} else {
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -3.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -1.08e+21) or not (x2 <= 2.6e+24):
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))) + (3.0 * (x2 * -2.0)))
	else:
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -3.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -1.08e+21) || !(x2 <= 2.6e+24))
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(x2 * 2.0) - 3.0))))) + Float64(3.0 * Float64(x2 * -2.0))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)) + Float64(x1 + Float64(x1 * -3.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -1.08e+21) || ~((x2 <= 2.6e+24)))
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))) + (3.0 * (x2 * -2.0)));
	else
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -3.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -1.08e+21], N[Not[LessEqual[x2, 2.6e+24]], $MachinePrecision]], N[(x1 + N[(N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -1.08e21 or 2.5999999999999998e24 < x2

   1. Initial program 72.7%

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

   2. Taylor expanded in x1 around 0 58.5%

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

   3. Taylor expanded in x1 around 0 73.3%

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

      1. *-commutative 73.3%

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

   5. Simplified 73.3%

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

   if -1.08e21 < x2 < 2.5999999999999998e24

   1. Initial program 73.9%

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

   2. Taylor expanded in x1 around 0 52.4%

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

   3. Taylor expanded in x2 around 0 52.4%

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

   4. Taylor expanded in x1 around 0 53.6%

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

      1. +-commutative 53.6%

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

      2. neg-mul-1 53.6%

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

      3. unsub-neg 53.6%

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

      4. *-commutative 53.6%

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

   6. Simplified 53.6%

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

   7. Taylor expanded in x2 around 0 54.4%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.08 \cdot 10^{+21} \lor \neg \left(x2 \leq 2.6 \cdot 10^{+24}\right):\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \left(x1 + x1 \cdot -3\right)\right)\\ \end{array} \]

Alternative 16: 64.3% accurate, 5.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.9 \cdot 10^{+84}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.9e+84)
   (* x1 (+ (* x2 -12.0) -1.0))
   (+
    x1
    (+
     (* 3.0 (- (* x2 -2.0) x1))
     (+ x1 (* 4.0 (* x2 (* x1 (- (* x2 2.0) 3.0)))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.9e+84) {
		tmp = x1 * ((x2 * -12.0) + -1.0);
	} else {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 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 <= (-1.9d+84)) then
        tmp = x1 * ((x2 * (-12.0d0)) + (-1.0d0))
    else
        tmp = x1 + ((3.0d0 * ((x2 * (-2.0d0)) - x1)) + (x1 + (4.0d0 * (x2 * (x1 * ((x2 * 2.0d0) - 3.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.9e+84) {
		tmp = x1 * ((x2 * -12.0) + -1.0);
	} else {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.9e+84:
		tmp = x1 * ((x2 * -12.0) + -1.0)
	else:
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.9e+84)
		tmp = Float64(x1 * Float64(Float64(x2 * -12.0) + -1.0));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - x1)) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(x2 * 2.0) - 3.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -1.9e+84)
		tmp = x1 * ((x2 * -12.0) + -1.0);
	else
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.9e+84], N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.9e84

   1. Initial program 7.1%

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

   2. Taylor expanded in x1 around 0 0.1%

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

   3. Taylor expanded in x2 around 0 3.0%

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

   4. Taylor expanded in x1 around 0 23.7%

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

      1. +-commutative 23.7%

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

      2. neg-mul-1 23.7%

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

      3. unsub-neg 23.7%

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

      4. *-commutative 23.7%

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

   6. Simplified 23.7%

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

   7. Taylor expanded in x1 around inf 23.7%

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

   if -1.9e84 < x1

   1. Initial program 86.3%

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

   2. Taylor expanded in x1 around 0 66.1%

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

   3. Taylor expanded in x1 around 0 74.2%

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

      1. +-commutative 49.1%

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

      2. neg-mul-1 49.1%

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

      3. unsub-neg 49.1%

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

      4. *-commutative 49.1%

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

   5. Simplified 74.2%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.9 \cdot 10^{+84}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 17: 52.3% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -1.78 \cdot 10^{+75} \lor \neg \left(x2 \leq 7.2 \cdot 10^{+202}\right):\\ \;\;\;\;x1 + x2 \cdot \left(x2 \cdot \left(x1 \cdot 8\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \left(x1 + x1 \cdot -3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -1.78e+75) (not (<= x2 7.2e+202)))
   (+ x1 (* x2 (* x2 (* x1 8.0))))
   (+ x1 (+ (* x2 (- (* x1 -12.0) 6.0)) (+ x1 (* x1 -3.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.78e+75) || !(x2 <= 7.2e+202)) {
		tmp = x1 + (x2 * (x2 * (x1 * 8.0)));
	} else {
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -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 ((x2 <= (-1.78d+75)) .or. (.not. (x2 <= 7.2d+202))) then
        tmp = x1 + (x2 * (x2 * (x1 * 8.0d0)))
    else
        tmp = x1 + ((x2 * ((x1 * (-12.0d0)) - 6.0d0)) + (x1 + (x1 * (-3.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.78e+75) || !(x2 <= 7.2e+202)) {
		tmp = x1 + (x2 * (x2 * (x1 * 8.0)));
	} else {
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -3.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -1.78e+75) or not (x2 <= 7.2e+202):
		tmp = x1 + (x2 * (x2 * (x1 * 8.0)))
	else:
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -3.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -1.78e+75) || !(x2 <= 7.2e+202))
		tmp = Float64(x1 + Float64(x2 * Float64(x2 * Float64(x1 * 8.0))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)) + Float64(x1 + Float64(x1 * -3.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -1.78e+75) || ~((x2 <= 7.2e+202)))
		tmp = x1 + (x2 * (x2 * (x1 * 8.0)));
	else
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -3.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -1.78e+75], N[Not[LessEqual[x2, 7.2e+202]], $MachinePrecision]], N[(x1 + N[(x2 * N[(x2 * N[(x1 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -1.78e75 or 7.20000000000000016e202 < x2

   1. Initial program 74.4%

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

   2. Taylor expanded in x1 around 0 69.7%

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

   3. Taylor expanded in x2 around inf 67.4%

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

      1. *-commutative 67.4%

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

      2. associate-*r* 67.4%

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

      3. unpow2 67.4%

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

      4. associate-*r* 73.9%

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

      5. *-commutative 73.9%

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

   5. Simplified 73.9%

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

   if -1.78e75 < x2 < 7.20000000000000016e202

   1. Initial program 72.9%

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

   2. Taylor expanded in x1 around 0 50.2%

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

   3. Taylor expanded in x2 around 0 47.6%

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

   4. Taylor expanded in x1 around 0 50.8%

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

      1. +-commutative 50.8%

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

      2. neg-mul-1 50.8%

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

      3. unsub-neg 50.8%

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

      4. *-commutative 50.8%

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

   6. Simplified 50.8%

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

   7. Taylor expanded in x2 around 0 51.3%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.78 \cdot 10^{+75} \lor \neg \left(x2 \leq 7.2 \cdot 10^{+202}\right):\\ \;\;\;\;x1 + x2 \cdot \left(x2 \cdot \left(x1 \cdot 8\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \left(x1 + x1 \cdot -3\right)\right)\\ \end{array} \]

Alternative 18: 44.0% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + 8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{if}\;x2 \leq -4.8 \cdot 10^{+74}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x2 \leq -5.8 \cdot 10^{-134}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 4.2 \cdot 10^{-172}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x2 \leq 3 \cdot 10^{+199}:\\ \;\;\;\;x1 + x2 \cdot \left(x1 \cdot -12 - 6\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* 8.0 (* x1 (* x2 x2))))))
   (if (<= x2 -4.8e+74)
     t_0
     (if (<= x2 -5.8e-134)
       (* x2 -6.0)
       (if (<= x2 4.2e-172)
         (* x1 (+ (* x2 -12.0) -1.0))
         (if (<= x2 3e+199) (+ x1 (* x2 (- (* x1 -12.0) 6.0))) t_0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (8.0 * (x1 * (x2 * x2)));
	double tmp;
	if (x2 <= -4.8e+74) {
		tmp = t_0;
	} else if (x2 <= -5.8e-134) {
		tmp = x2 * -6.0;
	} else if (x2 <= 4.2e-172) {
		tmp = x1 * ((x2 * -12.0) + -1.0);
	} else if (x2 <= 3e+199) {
		tmp = x1 + (x2 * ((x1 * -12.0) - 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) :: tmp
    t_0 = x1 + (8.0d0 * (x1 * (x2 * x2)))
    if (x2 <= (-4.8d+74)) then
        tmp = t_0
    else if (x2 <= (-5.8d-134)) then
        tmp = x2 * (-6.0d0)
    else if (x2 <= 4.2d-172) then
        tmp = x1 * ((x2 * (-12.0d0)) + (-1.0d0))
    else if (x2 <= 3d+199) then
        tmp = x1 + (x2 * ((x1 * (-12.0d0)) - 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 + (8.0 * (x1 * (x2 * x2)));
	double tmp;
	if (x2 <= -4.8e+74) {
		tmp = t_0;
	} else if (x2 <= -5.8e-134) {
		tmp = x2 * -6.0;
	} else if (x2 <= 4.2e-172) {
		tmp = x1 * ((x2 * -12.0) + -1.0);
	} else if (x2 <= 3e+199) {
		tmp = x1 + (x2 * ((x1 * -12.0) - 6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (8.0 * (x1 * (x2 * x2)))
	tmp = 0
	if x2 <= -4.8e+74:
		tmp = t_0
	elif x2 <= -5.8e-134:
		tmp = x2 * -6.0
	elif x2 <= 4.2e-172:
		tmp = x1 * ((x2 * -12.0) + -1.0)
	elif x2 <= 3e+199:
		tmp = x1 + (x2 * ((x1 * -12.0) - 6.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(8.0 * Float64(x1 * Float64(x2 * x2))))
	tmp = 0.0
	if (x2 <= -4.8e+74)
		tmp = t_0;
	elseif (x2 <= -5.8e-134)
		tmp = Float64(x2 * -6.0);
	elseif (x2 <= 4.2e-172)
		tmp = Float64(x1 * Float64(Float64(x2 * -12.0) + -1.0));
	elseif (x2 <= 3e+199)
		tmp = Float64(x1 + Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (8.0 * (x1 * (x2 * x2)));
	tmp = 0.0;
	if (x2 <= -4.8e+74)
		tmp = t_0;
	elseif (x2 <= -5.8e-134)
		tmp = x2 * -6.0;
	elseif (x2 <= 4.2e-172)
		tmp = x1 * ((x2 * -12.0) + -1.0);
	elseif (x2 <= 3e+199)
		tmp = x1 + (x2 * ((x1 * -12.0) - 6.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(8.0 * N[(x1 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x2, -4.8e+74], t$95$0, If[LessEqual[x2, -5.8e-134], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x2, 4.2e-172], N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x2, 3e+199], N[(x1 + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x2 < -4.80000000000000017e74 or 3.0000000000000001e199 < x2

   1. Initial program 74.4%

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

   2. Taylor expanded in x1 around 0 69.7%

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

   3. Taylor expanded in x2 around inf 67.4%

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

      1. *-commutative 67.4%

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

      2. *-commutative 67.4%

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

      3. unpow2 67.4%

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

   5. Simplified 67.4%

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

   if -4.80000000000000017e74 < x2 < -5.79999999999999986e-134

   1. Initial program 82.8%

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

   2. Taylor expanded in x1 around 0 58.8%

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

   3. Taylor expanded in x1 around 0 49.1%

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

      1. *-commutative 49.1%

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

   5. Simplified 49.1%

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

   6. Taylor expanded in x1 around 0 50.2%

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

      1. *-commutative 50.2%

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

   8. Simplified 50.2%

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

   if -5.79999999999999986e-134 < x2 < 4.1999999999999999e-172

   1. Initial program 66.7%

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

   2. Taylor expanded in x1 around 0 48.5%

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

   3. Taylor expanded in x2 around 0 48.5%

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

   4. Taylor expanded in x1 around 0 49.6%

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

      1. +-commutative 49.6%

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

      2. neg-mul-1 49.6%

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

      3. unsub-neg 49.6%

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

      4. *-commutative 49.6%

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

   6. Simplified 49.6%

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

   7. Taylor expanded in x1 around inf 43.3%

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

   if 4.1999999999999999e-172 < x2 < 3.0000000000000001e199

   1. Initial program 73.7%

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

   2. Taylor expanded in x1 around 0 47.9%

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

   3. Taylor expanded in x2 around 0 43.4%

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

   4. Taylor expanded in x1 around 0 49.5%

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

      1. +-commutative 49.5%

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

      2. neg-mul-1 49.5%

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

      3. unsub-neg 49.5%

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

      4. *-commutative 49.5%

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

   6. Simplified 49.5%

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

   7. Taylor expanded in x2 around inf 43.6%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -4.8 \cdot 10^{+74}:\\ \;\;\;\;x1 + 8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{elif}\;x2 \leq -5.8 \cdot 10^{-134}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 4.2 \cdot 10^{-172}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x2 \leq 3 \cdot 10^{+199}:\\ \;\;\;\;x1 + x2 \cdot \left(x1 \cdot -12 - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + 8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \end{array} \]

Alternative 19: 45.7% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + x2 \cdot \left(x2 \cdot \left(x1 \cdot 8\right)\right)\\ \mathbf{if}\;x2 \leq -1.15 \cdot 10^{+70}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x2 \leq -5.3 \cdot 10^{-134}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 9.5 \cdot 10^{-172}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x2 \leq 4 \cdot 10^{+198}:\\ \;\;\;\;x1 + x2 \cdot \left(x1 \cdot -12 - 6\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* x2 (* x2 (* x1 8.0))))))
   (if (<= x2 -1.15e+70)
     t_0
     (if (<= x2 -5.3e-134)
       (* x2 -6.0)
       (if (<= x2 9.5e-172)
         (* x1 (+ (* x2 -12.0) -1.0))
         (if (<= x2 4e+198) (+ x1 (* x2 (- (* x1 -12.0) 6.0))) t_0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x2 * (x2 * (x1 * 8.0)));
	double tmp;
	if (x2 <= -1.15e+70) {
		tmp = t_0;
	} else if (x2 <= -5.3e-134) {
		tmp = x2 * -6.0;
	} else if (x2 <= 9.5e-172) {
		tmp = x1 * ((x2 * -12.0) + -1.0);
	} else if (x2 <= 4e+198) {
		tmp = x1 + (x2 * ((x1 * -12.0) - 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) :: tmp
    t_0 = x1 + (x2 * (x2 * (x1 * 8.0d0)))
    if (x2 <= (-1.15d+70)) then
        tmp = t_0
    else if (x2 <= (-5.3d-134)) then
        tmp = x2 * (-6.0d0)
    else if (x2 <= 9.5d-172) then
        tmp = x1 * ((x2 * (-12.0d0)) + (-1.0d0))
    else if (x2 <= 4d+198) then
        tmp = x1 + (x2 * ((x1 * (-12.0d0)) - 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 + (x2 * (x2 * (x1 * 8.0)));
	double tmp;
	if (x2 <= -1.15e+70) {
		tmp = t_0;
	} else if (x2 <= -5.3e-134) {
		tmp = x2 * -6.0;
	} else if (x2 <= 9.5e-172) {
		tmp = x1 * ((x2 * -12.0) + -1.0);
	} else if (x2 <= 4e+198) {
		tmp = x1 + (x2 * ((x1 * -12.0) - 6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x2 * (x2 * (x1 * 8.0)))
	tmp = 0
	if x2 <= -1.15e+70:
		tmp = t_0
	elif x2 <= -5.3e-134:
		tmp = x2 * -6.0
	elif x2 <= 9.5e-172:
		tmp = x1 * ((x2 * -12.0) + -1.0)
	elif x2 <= 4e+198:
		tmp = x1 + (x2 * ((x1 * -12.0) - 6.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x2 * Float64(x2 * Float64(x1 * 8.0))))
	tmp = 0.0
	if (x2 <= -1.15e+70)
		tmp = t_0;
	elseif (x2 <= -5.3e-134)
		tmp = Float64(x2 * -6.0);
	elseif (x2 <= 9.5e-172)
		tmp = Float64(x1 * Float64(Float64(x2 * -12.0) + -1.0));
	elseif (x2 <= 4e+198)
		tmp = Float64(x1 + Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x2 * (x2 * (x1 * 8.0)));
	tmp = 0.0;
	if (x2 <= -1.15e+70)
		tmp = t_0;
	elseif (x2 <= -5.3e-134)
		tmp = x2 * -6.0;
	elseif (x2 <= 9.5e-172)
		tmp = x1 * ((x2 * -12.0) + -1.0);
	elseif (x2 <= 4e+198)
		tmp = x1 + (x2 * ((x1 * -12.0) - 6.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x2 * N[(x2 * N[(x1 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x2, -1.15e+70], t$95$0, If[LessEqual[x2, -5.3e-134], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x2, 9.5e-172], N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x2, 4e+198], N[(x1 + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x2 < -1.14999999999999997e70 or 4.00000000000000007e198 < x2

   1. Initial program 74.4%

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

   2. Taylor expanded in x1 around 0 69.7%

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

   3. Taylor expanded in x2 around inf 67.4%

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

      1. *-commutative 67.4%

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

      2. associate-*r* 67.4%

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

      3. unpow2 67.4%

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

      4. associate-*r* 73.9%

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

      5. *-commutative 73.9%

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

   5. Simplified 73.9%

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

   if -1.14999999999999997e70 < x2 < -5.30000000000000003e-134

   1. Initial program 82.8%

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

   2. Taylor expanded in x1 around 0 58.8%

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

   3. Taylor expanded in x1 around 0 49.1%

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

      1. *-commutative 49.1%

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

   5. Simplified 49.1%

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

   6. Taylor expanded in x1 around 0 50.2%

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

      1. *-commutative 50.2%

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

   8. Simplified 50.2%

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

   if -5.30000000000000003e-134 < x2 < 9.50000000000000053e-172

   1. Initial program 66.7%

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

   2. Taylor expanded in x1 around 0 48.5%

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

   3. Taylor expanded in x2 around 0 48.5%

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

   4. Taylor expanded in x1 around 0 49.6%

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

      1. +-commutative 49.6%

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

      2. neg-mul-1 49.6%

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

      3. unsub-neg 49.6%

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

      4. *-commutative 49.6%

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

   6. Simplified 49.6%

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

   7. Taylor expanded in x1 around inf 43.3%

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

   if 9.50000000000000053e-172 < x2 < 4.00000000000000007e198

   1. Initial program 73.7%

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

   2. Taylor expanded in x1 around 0 47.9%

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

   3. Taylor expanded in x2 around 0 43.4%

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

   4. Taylor expanded in x1 around 0 49.5%

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

      1. +-commutative 49.5%

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

      2. neg-mul-1 49.5%

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

      3. unsub-neg 49.5%

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

      4. *-commutative 49.5%

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

   6. Simplified 49.5%

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

   7. Taylor expanded in x2 around inf 43.6%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.15 \cdot 10^{+70}:\\ \;\;\;\;x1 + x2 \cdot \left(x2 \cdot \left(x1 \cdot 8\right)\right)\\ \mathbf{elif}\;x2 \leq -5.3 \cdot 10^{-134}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 9.5 \cdot 10^{-172}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x2 \leq 4 \cdot 10^{+198}:\\ \;\;\;\;x1 + x2 \cdot \left(x1 \cdot -12 - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot \left(x2 \cdot \left(x1 \cdot 8\right)\right)\\ \end{array} \]

Alternative 20: 52.4% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -2 \cdot 10^{+75} \lor \neg \left(x2 \leq 5.4 \cdot 10^{+200}\right):\\ \;\;\;\;x1 + x2 \cdot \left(x2 \cdot \left(x1 \cdot 8\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -2e+75) (not (<= x2 5.4e+200)))
   (+ x1 (* x2 (* x2 (* x1 8.0))))
   (+ (* x2 -6.0) (* x1 (+ (* x2 -12.0) -1.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -2e+75) || !(x2 <= 5.4e+200)) {
		tmp = x1 + (x2 * (x2 * (x1 * 8.0)));
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-2d+75)) .or. (.not. (x2 <= 5.4d+200))) then
        tmp = x1 + (x2 * (x2 * (x1 * 8.0d0)))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((x2 * (-12.0d0)) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -2e+75) || !(x2 <= 5.4e+200)) {
		tmp = x1 + (x2 * (x2 * (x1 * 8.0)));
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -2e+75) or not (x2 <= 5.4e+200):
		tmp = x1 + (x2 * (x2 * (x1 * 8.0)))
	else:
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -2e+75) || !(x2 <= 5.4e+200))
		tmp = Float64(x1 + Float64(x2 * Float64(x2 * Float64(x1 * 8.0))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x2 * -12.0) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -2e+75) || ~((x2 <= 5.4e+200)))
		tmp = x1 + (x2 * (x2 * (x1 * 8.0)));
	else
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -2e+75], N[Not[LessEqual[x2, 5.4e+200]], $MachinePrecision]], N[(x1 + N[(x2 * N[(x2 * N[(x1 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -1.99999999999999985e75 or 5.40000000000000031e200 < x2

   1. Initial program 74.4%

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

   2. Taylor expanded in x1 around 0 69.7%

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

   3. Taylor expanded in x2 around inf 67.4%

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

      1. *-commutative 67.4%

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

      2. associate-*r* 67.4%

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

      3. unpow2 67.4%

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

      4. associate-*r* 73.9%

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

      5. *-commutative 73.9%

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

   5. Simplified 73.9%

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

   if -1.99999999999999985e75 < x2 < 5.40000000000000031e200

   1. Initial program 72.9%

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

   2. Taylor expanded in x1 around 0 50.2%

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

   3. Taylor expanded in x2 around 0 47.6%

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

   4. Taylor expanded in x1 around 0 50.8%

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

      1. +-commutative 50.8%

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

      2. neg-mul-1 50.8%

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

      3. unsub-neg 50.8%

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

      4. *-commutative 50.8%

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

   6. Simplified 50.8%

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

   7. Taylor expanded in x1 around 0 51.1%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -2 \cdot 10^{+75} \lor \neg \left(x2 \leq 5.4 \cdot 10^{+200}\right):\\ \;\;\;\;x1 + x2 \cdot \left(x2 \cdot \left(x1 \cdot 8\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \end{array} \]

Alternative 21: 38.2% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -5.5 \cdot 10^{-134} \lor \neg \left(x2 \leq 3.8 \cdot 10^{-172}\right):\\ \;\;\;\;x1 + x2 \cdot \left(x1 \cdot -12 - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -5.5e-134) (not (<= x2 3.8e-172)))
   (+ x1 (* x2 (- (* x1 -12.0) 6.0)))
   (* x1 (+ (* x2 -12.0) -1.0))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -5.5e-134) || !(x2 <= 3.8e-172)) {
		tmp = x1 + (x2 * ((x1 * -12.0) - 6.0));
	} else {
		tmp = x1 * ((x2 * -12.0) + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-5.5d-134)) .or. (.not. (x2 <= 3.8d-172))) then
        tmp = x1 + (x2 * ((x1 * (-12.0d0)) - 6.0d0))
    else
        tmp = x1 * ((x2 * (-12.0d0)) + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -5.5e-134) || !(x2 <= 3.8e-172)) {
		tmp = x1 + (x2 * ((x1 * -12.0) - 6.0));
	} else {
		tmp = x1 * ((x2 * -12.0) + -1.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -5.5e-134) or not (x2 <= 3.8e-172):
		tmp = x1 + (x2 * ((x1 * -12.0) - 6.0))
	else:
		tmp = x1 * ((x2 * -12.0) + -1.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -5.5e-134) || !(x2 <= 3.8e-172))
		tmp = Float64(x1 + Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)));
	else
		tmp = Float64(x1 * Float64(Float64(x2 * -12.0) + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -5.5e-134) || ~((x2 <= 3.8e-172)))
		tmp = x1 + (x2 * ((x1 * -12.0) - 6.0));
	else
		tmp = x1 * ((x2 * -12.0) + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -5.5e-134], N[Not[LessEqual[x2, 3.8e-172]], $MachinePrecision]], N[(x1 + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -5.5000000000000002e-134 or 3.79999999999999987e-172 < x2

   1. Initial program 75.7%

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

   2. Taylor expanded in x1 around 0 57.8%

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

   3. Taylor expanded in x2 around 0 37.3%

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

   4. Taylor expanded in x1 around 0 43.2%

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

      1. +-commutative 43.2%

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

      2. neg-mul-1 43.2%

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

      3. unsub-neg 43.2%

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

      4. *-commutative 43.2%

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

   6. Simplified 43.2%

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

   7. Taylor expanded in x2 around inf 39.3%

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

   if -5.5000000000000002e-134 < x2 < 3.79999999999999987e-172

   1. Initial program 66.7%

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

   2. Taylor expanded in x1 around 0 48.5%

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

   3. Taylor expanded in x2 around 0 48.5%

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

   4. Taylor expanded in x1 around 0 49.6%

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

      1. +-commutative 49.6%

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

      2. neg-mul-1 49.6%

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

      3. unsub-neg 49.6%

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

      4. *-commutative 49.6%

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

   6. Simplified 49.6%

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

   7. Taylor expanded in x1 around inf 43.3%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -5.5 \cdot 10^{-134} \lor \neg \left(x2 \leq 3.8 \cdot 10^{-172}\right):\\ \;\;\;\;x1 + x2 \cdot \left(x1 \cdot -12 - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \end{array} \]

Alternative 22: 35.7% accurate, 11.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.55 \cdot 10^{-138} \lor \neg \left(x1 \leq 8.4 \cdot 10^{-70}\right):\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -2.55e-138) (not (<= x1 8.4e-70)))
   (* x1 (+ (* x2 -12.0) -1.0))
   (* x2 -6.0)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -2.55e-138) || !(x1 <= 8.4e-70)) {
		tmp = x1 * ((x2 * -12.0) + -1.0);
	} 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 <= (-2.55d-138)) .or. (.not. (x1 <= 8.4d-70))) then
        tmp = x1 * ((x2 * (-12.0d0)) + (-1.0d0))
    else
        tmp = x2 * (-6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -2.55e-138) || !(x1 <= 8.4e-70)) {
		tmp = x1 * ((x2 * -12.0) + -1.0);
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -2.55e-138) or not (x1 <= 8.4e-70):
		tmp = x1 * ((x2 * -12.0) + -1.0)
	else:
		tmp = x2 * -6.0
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -2.55e-138) || !(x1 <= 8.4e-70))
		tmp = Float64(x1 * Float64(Float64(x2 * -12.0) + -1.0));
	else
		tmp = Float64(x2 * -6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -2.55e-138) || ~((x1 <= 8.4e-70)))
		tmp = x1 * ((x2 * -12.0) + -1.0);
	else
		tmp = x2 * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -2.55e-138], N[Not[LessEqual[x1, 8.4e-70]], $MachinePrecision]], N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(x2 * -6.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -2.5500000000000001e-138 or 8.4000000000000004e-70 < x1

   1. Initial program 61.7%

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

   2. Taylor expanded in x1 around 0 35.6%

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

   3. Taylor expanded in x2 around 0 20.0%

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

   4. Taylor expanded in x1 around 0 26.8%

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

      1. +-commutative 26.8%

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

      2. neg-mul-1 26.8%

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

      3. unsub-neg 26.8%

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

      4. *-commutative 26.8%

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

   6. Simplified 26.8%

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

   7. Taylor expanded in x1 around inf 23.0%

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

   if -2.5500000000000001e-138 < x1 < 8.4000000000000004e-70

   1. Initial program 99.4%

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

   2. Taylor expanded in x1 around 0 99.4%

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

   3. Taylor expanded in x1 around 0 67.0%

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

      1. *-commutative 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in x1 around 0 67.5%

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

      1. *-commutative 67.5%

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

   8. Simplified 67.5%

      \[\leadsto \color{blue}{x2 \cdot -6} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.55 \cdot 10^{-138} \lor \neg \left(x1 \leq 8.4 \cdot 10^{-70}\right):\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]

Alternative 23: 32.2% accurate, 13.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -7.6 \cdot 10^{-134}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 2.5 \cdot 10^{-171}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 -7.6e-134)
   (* x2 -6.0)
   (if (<= x2 2.5e-171) (- x1) (+ x1 (* x2 -6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= -7.6e-134) {
		tmp = x2 * -6.0;
	} else if (x2 <= 2.5e-171) {
		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 <= (-7.6d-134)) then
        tmp = x2 * (-6.0d0)
    else if (x2 <= 2.5d-171) 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 <= -7.6e-134) {
		tmp = x2 * -6.0;
	} else if (x2 <= 2.5e-171) {
		tmp = -x1;
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= -7.6e-134:
		tmp = x2 * -6.0
	elif x2 <= 2.5e-171:
		tmp = -x1
	else:
		tmp = x1 + (x2 * -6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= -7.6e-134)
		tmp = Float64(x2 * -6.0);
	elseif (x2 <= 2.5e-171)
		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 <= -7.6e-134)
		tmp = x2 * -6.0;
	elseif (x2 <= 2.5e-171)
		tmp = -x1;
	else
		tmp = x1 + (x2 * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, -7.6e-134], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x2, 2.5e-171], (-x1), N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -7.60000000000000006e-134

   1. Initial program 83.3%

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

   2. Taylor expanded in x1 around 0 67.4%

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

   3. Taylor expanded in x1 around 0 35.6%

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

      1. *-commutative 35.6%

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

   5. Simplified 35.6%

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

   6. Taylor expanded in x1 around 0 36.1%

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

      1. *-commutative 36.1%

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

   8. Simplified 36.1%

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

   if -7.60000000000000006e-134 < x2 < 2.49999999999999996e-171

   1. Initial program 66.7%

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

   2. Taylor expanded in x1 around 0 48.5%

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

   3. Taylor expanded in x2 around 0 48.5%

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

   4. Taylor expanded in x1 around 0 49.6%

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

      1. +-commutative 49.6%

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

      2. neg-mul-1 49.6%

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

      3. unsub-neg 49.6%

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

      4. *-commutative 49.6%

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

   6. Simplified 49.6%

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

   7. Taylor expanded in x2 around 0 42.8%

      \[\leadsto \color{blue}{-3 \cdot x1 + 2 \cdot x1} \]
   8. Step-by-step derivation

      1. distribute-rgt-out 43.3%

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

      2. metadata-eval 43.3%

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

      3. *-commutative 43.3%

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

      4. neg-mul-1 43.3%

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

   9. Simplified 43.3%

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

   if 2.49999999999999996e-171 < x2

   1. Initial program 70.7%

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

   2. Taylor expanded in x1 around 0 51.5%

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

   3. Taylor expanded in x1 around 0 30.2%

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

      1. *-commutative 30.2%

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

   5. Simplified 30.2%

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

4. Final simplification 35.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -7.6 \cdot 10^{-134}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 2.5 \cdot 10^{-171}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \]

Alternative 24: 31.9% accurate, 17.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -6.5 \cdot 10^{-134}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 2.7 \cdot 10^{-171}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 -6.5e-134) (* x2 -6.0) (if (<= x2 2.7e-171) (- x1) (* x2 -6.0))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= -6.5e-134) {
		tmp = x2 * -6.0;
	} else if (x2 <= 2.7e-171) {
		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 <= (-6.5d-134)) then
        tmp = x2 * (-6.0d0)
    else if (x2 <= 2.7d-171) 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 <= -6.5e-134) {
		tmp = x2 * -6.0;
	} else if (x2 <= 2.7e-171) {
		tmp = -x1;
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= -6.5e-134:
		tmp = x2 * -6.0
	elif x2 <= 2.7e-171:
		tmp = -x1
	else:
		tmp = x2 * -6.0
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= -6.5e-134)
		tmp = Float64(x2 * -6.0);
	elseif (x2 <= 2.7e-171)
		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 <= -6.5e-134)
		tmp = x2 * -6.0;
	elseif (x2 <= 2.7e-171)
		tmp = -x1;
	else
		tmp = x2 * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, -6.5e-134], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x2, 2.7e-171], (-x1), N[(x2 * -6.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x2 < -6.4999999999999998e-134 or 2.70000000000000014e-171 < x2

   1. Initial program 75.7%

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

   2. Taylor expanded in x1 around 0 57.8%

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

   3. Taylor expanded in x1 around 0 32.3%

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

      1. *-commutative 32.3%

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

   5. Simplified 32.3%

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

   6. Taylor expanded in x1 around 0 32.0%

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

      1. *-commutative 32.0%

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

   8. Simplified 32.0%

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

   if -6.4999999999999998e-134 < x2 < 2.70000000000000014e-171

   1. Initial program 66.7%

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

   2. Taylor expanded in x1 around 0 48.5%

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

   3. Taylor expanded in x2 around 0 48.5%

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

   4. Taylor expanded in x1 around 0 49.6%

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

      1. +-commutative 49.6%

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

      2. neg-mul-1 49.6%

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

      3. unsub-neg 49.6%

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

      4. *-commutative 49.6%

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

   6. Simplified 49.6%

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

   7. Taylor expanded in x2 around 0 42.8%

      \[\leadsto \color{blue}{-3 \cdot x1 + 2 \cdot x1} \]
   8. Step-by-step derivation

      1. distribute-rgt-out 43.3%

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

      2. metadata-eval 43.3%

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

      3. *-commutative 43.3%

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

      4. neg-mul-1 43.3%

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

   9. Simplified 43.3%

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

4. Final simplification 35.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -6.5 \cdot 10^{-134}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 2.7 \cdot 10^{-171}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]

Alternative 25: 13.8% 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 73.3%

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

2. Taylor expanded in x1 around 0 55.3%

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

3. Taylor expanded in x2 around 0 40.3%

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

4. Taylor expanded in x1 around 0 44.9%

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

   1. +-commutative 44.9%

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

   2. neg-mul-1 44.9%

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

   3. unsub-neg 44.9%

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

   4. *-commutative 44.9%

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

6. Simplified 44.9%

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

7. Taylor expanded in x2 around 0 15.8%

   \[\leadsto \color{blue}{-3 \cdot x1 + 2 \cdot x1} \]
8. Step-by-step derivation

   1. distribute-rgt-out 16.0%

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

   2. metadata-eval 16.0%

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

   3. *-commutative 16.0%

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

   4. neg-mul-1 16.0%

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

9. Simplified 16.0%

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

10. Final simplification 16.0%

    \[\leadsto -x1 \]

Alternative 26: 3.3% accurate, 127.0× speedup

Math

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

FPCore

(FPCore (x1 x2) :precision binary64 x1)

C

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

Fortran

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

Java

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

Python

def code(x1, x2):
	return x1

Julia

function code(x1, x2)
	return x1
end

MATLAB

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

Wolfram

code[x1_, x2_] := x1

Derivation

1. Initial program 73.3%

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

2. Taylor expanded in x1 around 0 55.3%

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

3. Taylor expanded in x1 around 0 25.6%

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

   1. *-commutative 25.6%

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

5. Simplified 25.6%

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

6. Taylor expanded in x1 around inf 3.2%

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

7. Final simplification 3.2%

   \[\leadsto x1 \]

Reproduce

herbie shell --seed 2023194 
(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))))))