Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 69.9% → 99.5%

Time: 48.5s

Alternatives: 22

Speedup: 1.5×

• 46.9% 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: 69.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.3%

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

   3. Simplified 99.6%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around inf 10.7%

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

      1. *-commutative 10.7%

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

   4. Simplified 10.7%

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

   5. Taylor expanded in x1 around inf 98.6%

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

4. Final simplification 99.3%

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

Alternative 2: 99.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.3%

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

   3. Simplified 99.4%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around inf 10.7%

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

      1. *-commutative 10.7%

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

   4. Simplified 10.7%

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

   5. Taylor expanded in x1 around inf 98.6%

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

4. Final simplification 99.1%

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

Alternative 3: 99.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0
	t_3 = x1 + ((x1 + (((t_0 * (((t_2 * (x1 * 2.0)) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (t_1 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)))
	tmp = 0
	if t_3 <= math.inf:
		tmp = t_3
	else:
		tmp = x1 + (x1 + (6.0 * math.pow(x1, 4.0)))
	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(t_1 + Float64(2.0 * x2)) - x1) / t_0)
	t_3 = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_0 * Float64(Float64(Float64(t_2 * Float64(x1 * 2.0)) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)))) + Float64(t_1 * t_2)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_0))))
	tmp = 0.0
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(x1 + Float64(x1 + Float64(6.0 * (x1 ^ 4.0))));
	end
	return tmp
end

MATLAB

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.3%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around inf 10.7%

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

      1. *-commutative 10.7%

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

   4. Simplified 10.7%

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

   5. Taylor expanded in x1 around inf 98.6%

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

4. Final simplification 99.1%

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

Alternative 4: 96.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x1 + 6 \cdot {x1}^{4}\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := t_1 + 2 \cdot x2\\ t_3 := x1 \cdot x1 + 1\\ t_4 := \frac{x1 - t_2}{t_3}\\ t_5 := \frac{t_2 - x1}{t_3}\\ t_6 := x1 \cdot \left(x1 \cdot x1\right)\\ \mathbf{if}\;x1 \leq -1.6 \cdot 10^{+62}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 2.95 \cdot 10^{-8}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - t_1\right)}{t_3} - \left(x1 - \left(\left(t_1 \cdot t_4 + t_3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t_4\right) + \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right) \cdot \left(3 + t_4\right)\right)\right) - t_6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+96}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t_3 \cdot \left(\left(t_5 \cdot \left(x1 \cdot 2\right)\right) \cdot \left(t_5 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t_5 \cdot 4 - 6\right)\right) + t_1 \cdot t_5\right) + t_6\right)\right) + 3 \cdot \left(3 + \frac{-1}{x1}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (+ x1 (* 6.0 (pow x1 4.0)))))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ t_1 (* 2.0 x2)))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (/ (- x1 t_2) t_3))
        (t_5 (/ (- t_2 x1) t_3))
        (t_6 (* x1 (* x1 x1))))
   (if (<= x1 -1.6e+62)
     t_0
     (if (<= x1 2.95e-8)
       (-
        x1
        (-
         (* 3.0 (/ (+ x1 (- (* 2.0 x2) t_1)) t_3))
         (-
          x1
          (-
           (+
            (* t_1 t_4)
            (*
             t_3
             (+
              (* (* x1 x1) (+ 6.0 (* 4.0 t_4)))
              (* (* (* x1 2.0) (- (* 2.0 x2) x1)) (+ 3.0 t_4)))))
           t_6))))
       (if (<= x1 4e+96)
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               t_3
               (+
                (* (* t_5 (* x1 2.0)) (- t_5 3.0))
                (* (* x1 x1) (- (* t_5 4.0) 6.0))))
              (* t_1 t_5))
             t_6))
           (* 3.0 (+ 3.0 (/ -1.0 x1)))))
         t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 + (6.0 * pow(x1, 4.0)));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = t_1 + (2.0 * x2);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = (x1 - t_2) / t_3;
	double t_5 = (t_2 - x1) / t_3;
	double t_6 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -1.6e+62) {
		tmp = t_0;
	} else if (x1 <= 2.95e-8) {
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_3)) - (x1 - (((t_1 * t_4) + (t_3 * (((x1 * x1) * (6.0 + (4.0 * t_4))) + (((x1 * 2.0) * ((2.0 * x2) - x1)) * (3.0 + t_4))))) - t_6)));
	} else if (x1 <= 4e+96) {
		tmp = x1 + ((x1 + (((t_3 * (((t_5 * (x1 * 2.0)) * (t_5 - 3.0)) + ((x1 * x1) * ((t_5 * 4.0) - 6.0)))) + (t_1 * t_5)) + t_6)) + (3.0 * (3.0 + (-1.0 / x1))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: 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 + (6.0d0 * (x1 ** 4.0d0)))
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = t_1 + (2.0d0 * x2)
    t_3 = (x1 * x1) + 1.0d0
    t_4 = (x1 - t_2) / t_3
    t_5 = (t_2 - x1) / t_3
    t_6 = x1 * (x1 * x1)
    if (x1 <= (-1.6d+62)) then
        tmp = t_0
    else if (x1 <= 2.95d-8) then
        tmp = x1 - ((3.0d0 * ((x1 + ((2.0d0 * x2) - t_1)) / t_3)) - (x1 - (((t_1 * t_4) + (t_3 * (((x1 * x1) * (6.0d0 + (4.0d0 * t_4))) + (((x1 * 2.0d0) * ((2.0d0 * x2) - x1)) * (3.0d0 + t_4))))) - t_6)))
    else if (x1 <= 4d+96) then
        tmp = x1 + ((x1 + (((t_3 * (((t_5 * (x1 * 2.0d0)) * (t_5 - 3.0d0)) + ((x1 * x1) * ((t_5 * 4.0d0) - 6.0d0)))) + (t_1 * t_5)) + t_6)) + (3.0d0 * (3.0d0 + ((-1.0d0) / x1))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 + (6.0 * Math.pow(x1, 4.0)));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = t_1 + (2.0 * x2);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = (x1 - t_2) / t_3;
	double t_5 = (t_2 - x1) / t_3;
	double t_6 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -1.6e+62) {
		tmp = t_0;
	} else if (x1 <= 2.95e-8) {
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_3)) - (x1 - (((t_1 * t_4) + (t_3 * (((x1 * x1) * (6.0 + (4.0 * t_4))) + (((x1 * 2.0) * ((2.0 * x2) - x1)) * (3.0 + t_4))))) - t_6)));
	} else if (x1 <= 4e+96) {
		tmp = x1 + ((x1 + (((t_3 * (((t_5 * (x1 * 2.0)) * (t_5 - 3.0)) + ((x1 * x1) * ((t_5 * 4.0) - 6.0)))) + (t_1 * t_5)) + t_6)) + (3.0 * (3.0 + (-1.0 / x1))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 + (6.0 * math.pow(x1, 4.0)))
	t_1 = x1 * (x1 * 3.0)
	t_2 = t_1 + (2.0 * x2)
	t_3 = (x1 * x1) + 1.0
	t_4 = (x1 - t_2) / t_3
	t_5 = (t_2 - x1) / t_3
	t_6 = x1 * (x1 * x1)
	tmp = 0
	if x1 <= -1.6e+62:
		tmp = t_0
	elif x1 <= 2.95e-8:
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_3)) - (x1 - (((t_1 * t_4) + (t_3 * (((x1 * x1) * (6.0 + (4.0 * t_4))) + (((x1 * 2.0) * ((2.0 * x2) - x1)) * (3.0 + t_4))))) - t_6)))
	elif x1 <= 4e+96:
		tmp = x1 + ((x1 + (((t_3 * (((t_5 * (x1 * 2.0)) * (t_5 - 3.0)) + ((x1 * x1) * ((t_5 * 4.0) - 6.0)))) + (t_1 * t_5)) + t_6)) + (3.0 * (3.0 + (-1.0 / x1))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 + Float64(6.0 * (x1 ^ 4.0))))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(t_1 + Float64(2.0 * x2))
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(Float64(x1 - t_2) / t_3)
	t_5 = Float64(Float64(t_2 - x1) / t_3)
	t_6 = Float64(x1 * Float64(x1 * x1))
	tmp = 0.0
	if (x1 <= -1.6e+62)
		tmp = t_0;
	elseif (x1 <= 2.95e-8)
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(Float64(x1 + Float64(Float64(2.0 * x2) - t_1)) / t_3)) - Float64(x1 - Float64(Float64(Float64(t_1 * t_4) + Float64(t_3 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_4))) + Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(2.0 * x2) - x1)) * Float64(3.0 + t_4))))) - t_6))));
	elseif (x1 <= 4e+96)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_3 * Float64(Float64(Float64(t_5 * Float64(x1 * 2.0)) * Float64(t_5 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_5 * 4.0) - 6.0)))) + Float64(t_1 * t_5)) + t_6)) + Float64(3.0 * Float64(3.0 + Float64(-1.0 / x1)))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 + (6.0 * (x1 ^ 4.0)));
	t_1 = x1 * (x1 * 3.0);
	t_2 = t_1 + (2.0 * x2);
	t_3 = (x1 * x1) + 1.0;
	t_4 = (x1 - t_2) / t_3;
	t_5 = (t_2 - x1) / t_3;
	t_6 = x1 * (x1 * x1);
	tmp = 0.0;
	if (x1 <= -1.6e+62)
		tmp = t_0;
	elseif (x1 <= 2.95e-8)
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_3)) - (x1 - (((t_1 * t_4) + (t_3 * (((x1 * x1) * (6.0 + (4.0 * t_4))) + (((x1 * 2.0) * ((2.0 * x2) - x1)) * (3.0 + t_4))))) - t_6)));
	elseif (x1 <= 4e+96)
		tmp = x1 + ((x1 + (((t_3 * (((t_5 * (x1 * 2.0)) * (t_5 - 3.0)) + ((x1 * x1) * ((t_5 * 4.0) - 6.0)))) + (t_1 * t_5)) + t_6)) + (3.0 * (3.0 + (-1.0 / x1))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 - t$95$2), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$2 - x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$6 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.6e+62], t$95$0, If[LessEqual[x1, 2.95e-8], N[(x1 - N[(N[(3.0 * N[(N[(x1 + N[(N[(2.0 * x2), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] - N[(x1 - N[(N[(N[(t$95$1 * t$95$4), $MachinePrecision] + N[(t$95$3 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] * N[(3.0 + t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4e+96], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$3 * N[(N[(N[(t$95$5 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(t$95$5 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$5 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * t$95$5), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(3.0 + N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.59999999999999992e62 or 4.0000000000000002e96 < x1

   1. Initial program 20.2%

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

   2. Taylor expanded in x1 around inf 28.6%

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

      1. *-commutative 28.6%

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

   4. Simplified 28.6%

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

   5. Taylor expanded in x1 around inf 100.0%

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

   if -1.59999999999999992e62 < x1 < 2.9499999999999999e-8

   1. Initial program 98.6%

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

   2. Taylor expanded in x1 around 0 97.5%

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

      1. +-commutative 97.5%

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

      2. mul-1-neg 97.5%

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

      3. unsub-neg 97.5%

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

   4. Simplified 97.5%

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

   if 2.9499999999999999e-8 < x1 < 4.0000000000000002e96

   1. Initial program 99.2%

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

   2. Taylor expanded in x1 around inf 98.5%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.6 \cdot 10^{+62}:\\ \;\;\;\;x1 + \left(x1 + 6 \cdot {x1}^{4}\right)\\ \mathbf{elif}\;x1 \leq 2.95 \cdot 10^{-8}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} - \left(x1 - \left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) + \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+96}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(3 + \frac{-1}{x1}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 6 \cdot {x1}^{4}\right)\\ \end{array} \]

Alternative 5: 96.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x1 + 6 \cdot {x1}^{4}\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := t_1 + 2 \cdot x2\\ t_3 := x1 \cdot x1 + 1\\ t_4 := \frac{x1 - t_2}{t_3}\\ t_5 := \frac{t_2 - x1}{t_3}\\ t_6 := x1 \cdot \left(x1 \cdot x1\right)\\ \mathbf{if}\;x1 \leq -4.8 \cdot 10^{+62}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 2.95 \cdot 10^{-8}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - t_1\right)}{t_3} - \left(x1 - \left(\left(t_1 \cdot t_4 + t_3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t_4\right) + \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right) \cdot \left(3 + t_4\right)\right)\right) - t_6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7 \cdot 10^{+96}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t_3 \cdot \left(\left(t_5 \cdot \left(x1 \cdot 2\right)\right) \cdot \left(t_5 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t_5 \cdot 4 - 6\right)\right) + t_1 \cdot t_5\right) + t_6\right)\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (+ x1 (* 6.0 (pow x1 4.0)))))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ t_1 (* 2.0 x2)))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (/ (- x1 t_2) t_3))
        (t_5 (/ (- t_2 x1) t_3))
        (t_6 (* x1 (* x1 x1))))
   (if (<= x1 -4.8e+62)
     t_0
     (if (<= x1 2.95e-8)
       (-
        x1
        (-
         (* 3.0 (/ (+ x1 (- (* 2.0 x2) t_1)) t_3))
         (-
          x1
          (-
           (+
            (* t_1 t_4)
            (*
             t_3
             (+
              (* (* x1 x1) (+ 6.0 (* 4.0 t_4)))
              (* (* (* x1 2.0) (- (* 2.0 x2) x1)) (+ 3.0 t_4)))))
           t_6))))
       (if (<= x1 7e+96)
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               t_3
               (+
                (* (* t_5 (* x1 2.0)) (- t_5 3.0))
                (* (* x1 x1) (- (* t_5 4.0) 6.0))))
              (* t_1 t_5))
             t_6))
           9.0))
         t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 + (6.0 * pow(x1, 4.0)));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = t_1 + (2.0 * x2);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = (x1 - t_2) / t_3;
	double t_5 = (t_2 - x1) / t_3;
	double t_6 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -4.8e+62) {
		tmp = t_0;
	} else if (x1 <= 2.95e-8) {
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_3)) - (x1 - (((t_1 * t_4) + (t_3 * (((x1 * x1) * (6.0 + (4.0 * t_4))) + (((x1 * 2.0) * ((2.0 * x2) - x1)) * (3.0 + t_4))))) - t_6)));
	} else if (x1 <= 7e+96) {
		tmp = x1 + ((x1 + (((t_3 * (((t_5 * (x1 * 2.0)) * (t_5 - 3.0)) + ((x1 * x1) * ((t_5 * 4.0) - 6.0)))) + (t_1 * t_5)) + t_6)) + 9.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = x1 + (x1 + (6.0d0 * (x1 ** 4.0d0)))
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = t_1 + (2.0d0 * x2)
    t_3 = (x1 * x1) + 1.0d0
    t_4 = (x1 - t_2) / t_3
    t_5 = (t_2 - x1) / t_3
    t_6 = x1 * (x1 * x1)
    if (x1 <= (-4.8d+62)) then
        tmp = t_0
    else if (x1 <= 2.95d-8) then
        tmp = x1 - ((3.0d0 * ((x1 + ((2.0d0 * x2) - t_1)) / t_3)) - (x1 - (((t_1 * t_4) + (t_3 * (((x1 * x1) * (6.0d0 + (4.0d0 * t_4))) + (((x1 * 2.0d0) * ((2.0d0 * x2) - x1)) * (3.0d0 + t_4))))) - t_6)))
    else if (x1 <= 7d+96) then
        tmp = x1 + ((x1 + (((t_3 * (((t_5 * (x1 * 2.0d0)) * (t_5 - 3.0d0)) + ((x1 * x1) * ((t_5 * 4.0d0) - 6.0d0)))) + (t_1 * t_5)) + t_6)) + 9.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 + (6.0 * Math.pow(x1, 4.0)));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = t_1 + (2.0 * x2);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = (x1 - t_2) / t_3;
	double t_5 = (t_2 - x1) / t_3;
	double t_6 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -4.8e+62) {
		tmp = t_0;
	} else if (x1 <= 2.95e-8) {
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_3)) - (x1 - (((t_1 * t_4) + (t_3 * (((x1 * x1) * (6.0 + (4.0 * t_4))) + (((x1 * 2.0) * ((2.0 * x2) - x1)) * (3.0 + t_4))))) - t_6)));
	} else if (x1 <= 7e+96) {
		tmp = x1 + ((x1 + (((t_3 * (((t_5 * (x1 * 2.0)) * (t_5 - 3.0)) + ((x1 * x1) * ((t_5 * 4.0) - 6.0)))) + (t_1 * t_5)) + t_6)) + 9.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 + (6.0 * math.pow(x1, 4.0)))
	t_1 = x1 * (x1 * 3.0)
	t_2 = t_1 + (2.0 * x2)
	t_3 = (x1 * x1) + 1.0
	t_4 = (x1 - t_2) / t_3
	t_5 = (t_2 - x1) / t_3
	t_6 = x1 * (x1 * x1)
	tmp = 0
	if x1 <= -4.8e+62:
		tmp = t_0
	elif x1 <= 2.95e-8:
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_3)) - (x1 - (((t_1 * t_4) + (t_3 * (((x1 * x1) * (6.0 + (4.0 * t_4))) + (((x1 * 2.0) * ((2.0 * x2) - x1)) * (3.0 + t_4))))) - t_6)))
	elif x1 <= 7e+96:
		tmp = x1 + ((x1 + (((t_3 * (((t_5 * (x1 * 2.0)) * (t_5 - 3.0)) + ((x1 * x1) * ((t_5 * 4.0) - 6.0)))) + (t_1 * t_5)) + t_6)) + 9.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 + Float64(6.0 * (x1 ^ 4.0))))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(t_1 + Float64(2.0 * x2))
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(Float64(x1 - t_2) / t_3)
	t_5 = Float64(Float64(t_2 - x1) / t_3)
	t_6 = Float64(x1 * Float64(x1 * x1))
	tmp = 0.0
	if (x1 <= -4.8e+62)
		tmp = t_0;
	elseif (x1 <= 2.95e-8)
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(Float64(x1 + Float64(Float64(2.0 * x2) - t_1)) / t_3)) - Float64(x1 - Float64(Float64(Float64(t_1 * t_4) + Float64(t_3 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_4))) + Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(2.0 * x2) - x1)) * Float64(3.0 + t_4))))) - t_6))));
	elseif (x1 <= 7e+96)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_3 * Float64(Float64(Float64(t_5 * Float64(x1 * 2.0)) * Float64(t_5 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_5 * 4.0) - 6.0)))) + Float64(t_1 * t_5)) + t_6)) + 9.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 + (6.0 * (x1 ^ 4.0)));
	t_1 = x1 * (x1 * 3.0);
	t_2 = t_1 + (2.0 * x2);
	t_3 = (x1 * x1) + 1.0;
	t_4 = (x1 - t_2) / t_3;
	t_5 = (t_2 - x1) / t_3;
	t_6 = x1 * (x1 * x1);
	tmp = 0.0;
	if (x1 <= -4.8e+62)
		tmp = t_0;
	elseif (x1 <= 2.95e-8)
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_3)) - (x1 - (((t_1 * t_4) + (t_3 * (((x1 * x1) * (6.0 + (4.0 * t_4))) + (((x1 * 2.0) * ((2.0 * x2) - x1)) * (3.0 + t_4))))) - t_6)));
	elseif (x1 <= 7e+96)
		tmp = x1 + ((x1 + (((t_3 * (((t_5 * (x1 * 2.0)) * (t_5 - 3.0)) + ((x1 * x1) * ((t_5 * 4.0) - 6.0)))) + (t_1 * t_5)) + t_6)) + 9.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 - t$95$2), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$2 - x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$6 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.8e+62], t$95$0, If[LessEqual[x1, 2.95e-8], N[(x1 - N[(N[(3.0 * N[(N[(x1 + N[(N[(2.0 * x2), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] - N[(x1 - N[(N[(N[(t$95$1 * t$95$4), $MachinePrecision] + N[(t$95$3 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] * N[(3.0 + t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7e+96], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$3 * N[(N[(N[(t$95$5 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(t$95$5 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$5 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * t$95$5), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4.8e62 or 6.9999999999999998e96 < x1

   1. Initial program 20.2%

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

   2. Taylor expanded in x1 around inf 28.6%

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

      1. *-commutative 28.6%

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

   4. Simplified 28.6%

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

   5. Taylor expanded in x1 around inf 100.0%

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

   if -4.8e62 < x1 < 2.9499999999999999e-8

   1. Initial program 98.6%

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

   2. Taylor expanded in x1 around 0 97.5%

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

      1. +-commutative 97.5%

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

      2. mul-1-neg 97.5%

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

      3. unsub-neg 97.5%

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

   4. Simplified 97.5%

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

   if 2.9499999999999999e-8 < x1 < 6.9999999999999998e96

   1. Initial program 99.2%

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

   2. Taylor expanded in x1 around inf 98.0%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.8 \cdot 10^{+62}:\\ \;\;\;\;x1 + \left(x1 + 6 \cdot {x1}^{4}\right)\\ \mathbf{elif}\;x1 \leq 2.95 \cdot 10^{-8}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} - \left(x1 - \left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) + \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7 \cdot 10^{+96}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 6 \cdot {x1}^{4}\right)\\ \end{array} \]

Alternative 6: 95.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 + \left(x1 + 6 \cdot {x1}^{4}\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := t_3 + 2 \cdot x2\\ t_5 := \frac{t_4 - x1}{t_1}\\ t_6 := t_3 \cdot t_5\\ t_7 := \left(x1 \cdot x1\right) \cdot \left(t_5 \cdot 4 - 6\right)\\ \mathbf{if}\;x1 \leq -49000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x1 \leq 2.95 \cdot 10^{-8}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_3 - 2 \cdot x2\right) - x1}{t_1} + \left(x1 + \left(t_0 + \left(t_6 + t_1 \cdot \left(t_7 + \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - t_4}{t_1}\right) \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+96}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t_1 \cdot \left(\left(t_5 \cdot \left(x1 \cdot 2\right)\right) \cdot \left(t_5 - 3\right) + t_7\right) + t_6\right) + t_0\right)\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (+ x1 (+ x1 (* 6.0 (pow x1 4.0)))))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (+ t_3 (* 2.0 x2)))
        (t_5 (/ (- t_4 x1) t_1))
        (t_6 (* t_3 t_5))
        (t_7 (* (* x1 x1) (- (* t_5 4.0) 6.0))))
   (if (<= x1 -49000000000000.0)
     t_2
     (if (<= x1 2.95e-8)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_3 (* 2.0 x2)) x1) t_1))
         (+
          x1
          (+
           t_0
           (+
            t_6
            (*
             t_1
             (+
              t_7
              (* (* (* x1 2.0) (/ (- x1 t_4) t_1)) (- 3.0 (* 2.0 x2))))))))))
       (if (<= x1 5e+96)
         (+
          x1
          (+
           (+
            x1
            (+ (+ (* t_1 (+ (* (* t_5 (* x1 2.0)) (- t_5 3.0)) t_7)) t_6) t_0))
           9.0))
         t_2)))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 + (x1 + (6.0 * pow(x1, 4.0)));
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = t_3 + (2.0 * x2);
	double t_5 = (t_4 - x1) / t_1;
	double t_6 = t_3 * t_5;
	double t_7 = (x1 * x1) * ((t_5 * 4.0) - 6.0);
	double tmp;
	if (x1 <= -49000000000000.0) {
		tmp = t_2;
	} else if (x1 <= 2.95e-8) {
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_1)) + (x1 + (t_0 + (t_6 + (t_1 * (t_7 + (((x1 * 2.0) * ((x1 - t_4) / t_1)) * (3.0 - (2.0 * x2)))))))));
	} else if (x1 <= 5e+96) {
		tmp = x1 + ((x1 + (((t_1 * (((t_5 * (x1 * 2.0)) * (t_5 - 3.0)) + t_7)) + t_6) + t_0)) + 9.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = x1 * (x1 * x1)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = x1 + (x1 + (6.0d0 * (x1 ** 4.0d0)))
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = t_3 + (2.0d0 * x2)
    t_5 = (t_4 - x1) / t_1
    t_6 = t_3 * t_5
    t_7 = (x1 * x1) * ((t_5 * 4.0d0) - 6.0d0)
    if (x1 <= (-49000000000000.0d0)) then
        tmp = t_2
    else if (x1 <= 2.95d-8) then
        tmp = x1 + ((3.0d0 * (((t_3 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + (t_0 + (t_6 + (t_1 * (t_7 + (((x1 * 2.0d0) * ((x1 - t_4) / t_1)) * (3.0d0 - (2.0d0 * x2)))))))))
    else if (x1 <= 5d+96) then
        tmp = x1 + ((x1 + (((t_1 * (((t_5 * (x1 * 2.0d0)) * (t_5 - 3.0d0)) + t_7)) + t_6) + t_0)) + 9.0d0)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 + (x1 + (6.0 * Math.pow(x1, 4.0)));
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = t_3 + (2.0 * x2);
	double t_5 = (t_4 - x1) / t_1;
	double t_6 = t_3 * t_5;
	double t_7 = (x1 * x1) * ((t_5 * 4.0) - 6.0);
	double tmp;
	if (x1 <= -49000000000000.0) {
		tmp = t_2;
	} else if (x1 <= 2.95e-8) {
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_1)) + (x1 + (t_0 + (t_6 + (t_1 * (t_7 + (((x1 * 2.0) * ((x1 - t_4) / t_1)) * (3.0 - (2.0 * x2)))))))));
	} else if (x1 <= 5e+96) {
		tmp = x1 + ((x1 + (((t_1 * (((t_5 * (x1 * 2.0)) * (t_5 - 3.0)) + t_7)) + t_6) + t_0)) + 9.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = (x1 * x1) + 1.0
	t_2 = x1 + (x1 + (6.0 * math.pow(x1, 4.0)))
	t_3 = x1 * (x1 * 3.0)
	t_4 = t_3 + (2.0 * x2)
	t_5 = (t_4 - x1) / t_1
	t_6 = t_3 * t_5
	t_7 = (x1 * x1) * ((t_5 * 4.0) - 6.0)
	tmp = 0
	if x1 <= -49000000000000.0:
		tmp = t_2
	elif x1 <= 2.95e-8:
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_1)) + (x1 + (t_0 + (t_6 + (t_1 * (t_7 + (((x1 * 2.0) * ((x1 - t_4) / t_1)) * (3.0 - (2.0 * x2)))))))))
	elif x1 <= 5e+96:
		tmp = x1 + ((x1 + (((t_1 * (((t_5 * (x1 * 2.0)) * (t_5 - 3.0)) + t_7)) + t_6) + t_0)) + 9.0)
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(x1 + Float64(x1 + Float64(6.0 * (x1 ^ 4.0))))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(t_3 + Float64(2.0 * x2))
	t_5 = Float64(Float64(t_4 - x1) / t_1)
	t_6 = Float64(t_3 * t_5)
	t_7 = Float64(Float64(x1 * x1) * Float64(Float64(t_5 * 4.0) - 6.0))
	tmp = 0.0
	if (x1 <= -49000000000000.0)
		tmp = t_2;
	elseif (x1 <= 2.95e-8)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_3 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(t_0 + Float64(t_6 + Float64(t_1 * Float64(t_7 + Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(x1 - t_4) / t_1)) * Float64(3.0 - Float64(2.0 * x2))))))))));
	elseif (x1 <= 5e+96)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_1 * Float64(Float64(Float64(t_5 * Float64(x1 * 2.0)) * Float64(t_5 - 3.0)) + t_7)) + t_6) + t_0)) + 9.0));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = (x1 * x1) + 1.0;
	t_2 = x1 + (x1 + (6.0 * (x1 ^ 4.0)));
	t_3 = x1 * (x1 * 3.0);
	t_4 = t_3 + (2.0 * x2);
	t_5 = (t_4 - x1) / t_1;
	t_6 = t_3 * t_5;
	t_7 = (x1 * x1) * ((t_5 * 4.0) - 6.0);
	tmp = 0.0;
	if (x1 <= -49000000000000.0)
		tmp = t_2;
	elseif (x1 <= 2.95e-8)
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_1)) + (x1 + (t_0 + (t_6 + (t_1 * (t_7 + (((x1 * 2.0) * ((x1 - t_4) / t_1)) * (3.0 - (2.0 * x2)))))))));
	elseif (x1 <= 5e+96)
		tmp = x1 + ((x1 + (((t_1 * (((t_5 * (x1 * 2.0)) * (t_5 - 3.0)) + t_7)) + t_6) + t_0)) + 9.0);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$4 - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$3 * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$5 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -49000000000000.0], t$95$2, If[LessEqual[x1, 2.95e-8], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$3 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$0 + N[(t$95$6 + N[(t$95$1 * N[(t$95$7 + N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(x1 - t$95$4), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+96], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$1 * N[(N[(N[(t$95$5 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(t$95$5 - 3.0), $MachinePrecision]), $MachinePrecision] + t$95$7), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4.9e13 or 5.0000000000000004e96 < x1

   1. Initial program 29.3%

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

   2. Taylor expanded in x1 around inf 35.6%

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

      1. *-commutative 35.6%

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

   4. Simplified 35.6%

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

   5. Taylor expanded in x1 around inf 98.8%

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

   if -4.9e13 < x1 < 2.9499999999999999e-8

   1. Initial program 98.6%

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

   2. Taylor expanded in x1 around 0 98.1%

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

   if 2.9499999999999999e-8 < x1 < 5.0000000000000004e96

   1. Initial program 99.2%

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

   2. Taylor expanded in x1 around inf 98.0%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -49000000000000:\\ \;\;\;\;x1 + \left(x1 + 6 \cdot {x1}^{4}\right)\\ \mathbf{elif}\;x1 \leq 2.95 \cdot 10^{-8}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+96}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 6 \cdot {x1}^{4}\right)\\ \end{array} \]

Alternative 7: 95.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x1 + 6 \cdot {x1}^{4}\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := t_1 + 2 \cdot x2\\ t_3 := x1 \cdot x1 + 1\\ t_4 := \frac{x1 - t_2}{t_3}\\ t_5 := \frac{t_2 - x1}{t_3}\\ t_6 := x1 \cdot \left(x1 \cdot x1\right)\\ \mathbf{if}\;x1 \leq -155000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 2.95 \cdot 10^{-8}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - t_1\right)}{t_3} + \left(\left(\left(t_1 \cdot t_4 + t_3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t_4\right) + \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right) \cdot \left(3 - 2 \cdot x2\right)\right)\right) - t_6\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 7 \cdot 10^{+96}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t_3 \cdot \left(\left(t_5 \cdot \left(x1 \cdot 2\right)\right) \cdot \left(t_5 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t_5 \cdot 4 - 6\right)\right) + t_1 \cdot t_5\right) + t_6\right)\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (+ x1 (* 6.0 (pow x1 4.0)))))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ t_1 (* 2.0 x2)))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (/ (- x1 t_2) t_3))
        (t_5 (/ (- t_2 x1) t_3))
        (t_6 (* x1 (* x1 x1))))
   (if (<= x1 -155000000000.0)
     t_0
     (if (<= x1 2.95e-8)
       (-
        x1
        (+
         (* 3.0 (/ (+ x1 (- (* 2.0 x2) t_1)) t_3))
         (-
          (-
           (+
            (* t_1 t_4)
            (*
             t_3
             (+
              (* (* x1 x1) (+ 6.0 (* 4.0 t_4)))
              (* (* (* x1 2.0) (- (* 2.0 x2) x1)) (- 3.0 (* 2.0 x2))))))
           t_6)
          x1)))
       (if (<= x1 7e+96)
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               t_3
               (+
                (* (* t_5 (* x1 2.0)) (- t_5 3.0))
                (* (* x1 x1) (- (* t_5 4.0) 6.0))))
              (* t_1 t_5))
             t_6))
           9.0))
         t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 + (6.0 * pow(x1, 4.0)));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = t_1 + (2.0 * x2);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = (x1 - t_2) / t_3;
	double t_5 = (t_2 - x1) / t_3;
	double t_6 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -155000000000.0) {
		tmp = t_0;
	} else if (x1 <= 2.95e-8) {
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_3)) + ((((t_1 * t_4) + (t_3 * (((x1 * x1) * (6.0 + (4.0 * t_4))) + (((x1 * 2.0) * ((2.0 * x2) - x1)) * (3.0 - (2.0 * x2)))))) - t_6) - x1));
	} else if (x1 <= 7e+96) {
		tmp = x1 + ((x1 + (((t_3 * (((t_5 * (x1 * 2.0)) * (t_5 - 3.0)) + ((x1 * x1) * ((t_5 * 4.0) - 6.0)))) + (t_1 * t_5)) + t_6)) + 9.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = x1 + (x1 + (6.0d0 * (x1 ** 4.0d0)))
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = t_1 + (2.0d0 * x2)
    t_3 = (x1 * x1) + 1.0d0
    t_4 = (x1 - t_2) / t_3
    t_5 = (t_2 - x1) / t_3
    t_6 = x1 * (x1 * x1)
    if (x1 <= (-155000000000.0d0)) then
        tmp = t_0
    else if (x1 <= 2.95d-8) then
        tmp = x1 - ((3.0d0 * ((x1 + ((2.0d0 * x2) - t_1)) / t_3)) + ((((t_1 * t_4) + (t_3 * (((x1 * x1) * (6.0d0 + (4.0d0 * t_4))) + (((x1 * 2.0d0) * ((2.0d0 * x2) - x1)) * (3.0d0 - (2.0d0 * x2)))))) - t_6) - x1))
    else if (x1 <= 7d+96) then
        tmp = x1 + ((x1 + (((t_3 * (((t_5 * (x1 * 2.0d0)) * (t_5 - 3.0d0)) + ((x1 * x1) * ((t_5 * 4.0d0) - 6.0d0)))) + (t_1 * t_5)) + t_6)) + 9.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 + (6.0 * Math.pow(x1, 4.0)));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = t_1 + (2.0 * x2);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = (x1 - t_2) / t_3;
	double t_5 = (t_2 - x1) / t_3;
	double t_6 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -155000000000.0) {
		tmp = t_0;
	} else if (x1 <= 2.95e-8) {
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_3)) + ((((t_1 * t_4) + (t_3 * (((x1 * x1) * (6.0 + (4.0 * t_4))) + (((x1 * 2.0) * ((2.0 * x2) - x1)) * (3.0 - (2.0 * x2)))))) - t_6) - x1));
	} else if (x1 <= 7e+96) {
		tmp = x1 + ((x1 + (((t_3 * (((t_5 * (x1 * 2.0)) * (t_5 - 3.0)) + ((x1 * x1) * ((t_5 * 4.0) - 6.0)))) + (t_1 * t_5)) + t_6)) + 9.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 + (6.0 * math.pow(x1, 4.0)))
	t_1 = x1 * (x1 * 3.0)
	t_2 = t_1 + (2.0 * x2)
	t_3 = (x1 * x1) + 1.0
	t_4 = (x1 - t_2) / t_3
	t_5 = (t_2 - x1) / t_3
	t_6 = x1 * (x1 * x1)
	tmp = 0
	if x1 <= -155000000000.0:
		tmp = t_0
	elif x1 <= 2.95e-8:
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_3)) + ((((t_1 * t_4) + (t_3 * (((x1 * x1) * (6.0 + (4.0 * t_4))) + (((x1 * 2.0) * ((2.0 * x2) - x1)) * (3.0 - (2.0 * x2)))))) - t_6) - x1))
	elif x1 <= 7e+96:
		tmp = x1 + ((x1 + (((t_3 * (((t_5 * (x1 * 2.0)) * (t_5 - 3.0)) + ((x1 * x1) * ((t_5 * 4.0) - 6.0)))) + (t_1 * t_5)) + t_6)) + 9.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 + Float64(6.0 * (x1 ^ 4.0))))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(t_1 + Float64(2.0 * x2))
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(Float64(x1 - t_2) / t_3)
	t_5 = Float64(Float64(t_2 - x1) / t_3)
	t_6 = Float64(x1 * Float64(x1 * x1))
	tmp = 0.0
	if (x1 <= -155000000000.0)
		tmp = t_0;
	elseif (x1 <= 2.95e-8)
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(Float64(x1 + Float64(Float64(2.0 * x2) - t_1)) / t_3)) + Float64(Float64(Float64(Float64(t_1 * t_4) + Float64(t_3 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_4))) + Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(2.0 * x2) - x1)) * Float64(3.0 - Float64(2.0 * x2)))))) - t_6) - x1)));
	elseif (x1 <= 7e+96)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_3 * Float64(Float64(Float64(t_5 * Float64(x1 * 2.0)) * Float64(t_5 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_5 * 4.0) - 6.0)))) + Float64(t_1 * t_5)) + t_6)) + 9.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 + (6.0 * (x1 ^ 4.0)));
	t_1 = x1 * (x1 * 3.0);
	t_2 = t_1 + (2.0 * x2);
	t_3 = (x1 * x1) + 1.0;
	t_4 = (x1 - t_2) / t_3;
	t_5 = (t_2 - x1) / t_3;
	t_6 = x1 * (x1 * x1);
	tmp = 0.0;
	if (x1 <= -155000000000.0)
		tmp = t_0;
	elseif (x1 <= 2.95e-8)
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_3)) + ((((t_1 * t_4) + (t_3 * (((x1 * x1) * (6.0 + (4.0 * t_4))) + (((x1 * 2.0) * ((2.0 * x2) - x1)) * (3.0 - (2.0 * x2)))))) - t_6) - x1));
	elseif (x1 <= 7e+96)
		tmp = x1 + ((x1 + (((t_3 * (((t_5 * (x1 * 2.0)) * (t_5 - 3.0)) + ((x1 * x1) * ((t_5 * 4.0) - 6.0)))) + (t_1 * t_5)) + t_6)) + 9.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 - t$95$2), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$2 - x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$6 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -155000000000.0], t$95$0, If[LessEqual[x1, 2.95e-8], N[(x1 - N[(N[(3.0 * N[(N[(x1 + N[(N[(2.0 * x2), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(t$95$1 * t$95$4), $MachinePrecision] + N[(t$95$3 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$6), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7e+96], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$3 * N[(N[(N[(t$95$5 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(t$95$5 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$5 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * t$95$5), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.55e11 or 6.9999999999999998e96 < x1

   1. Initial program 29.3%

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

   2. Taylor expanded in x1 around inf 35.6%

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

      1. *-commutative 35.6%

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

   4. Simplified 35.6%

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

   5. Taylor expanded in x1 around inf 98.8%

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

   if -1.55e11 < x1 < 2.9499999999999999e-8

   1. Initial program 98.6%

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

   2. Taylor expanded in x1 around 0 98.2%

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

      1. +-commutative 98.2%

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

      2. mul-1-neg 98.2%

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

      3. unsub-neg 98.2%

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

   4. Simplified 98.2%

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

   5. Taylor expanded in x1 around 0 98.0%

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

   if 2.9499999999999999e-8 < x1 < 6.9999999999999998e96

   1. Initial program 99.2%

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

   2. Taylor expanded in x1 around inf 98.0%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -155000000000:\\ \;\;\;\;x1 + \left(x1 + 6 \cdot {x1}^{4}\right)\\ \mathbf{elif}\;x1 \leq 2.95 \cdot 10^{-8}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} + \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) + \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right) \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 7 \cdot 10^{+96}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 6 \cdot {x1}^{4}\right)\\ \end{array} \]

Alternative 8: 94.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x1 + 6 \cdot {x1}^{4}\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := t_1 + 2 \cdot x2\\ t_3 := x1 \cdot x1 + 1\\ t_4 := \frac{x1 - t_2}{t_3}\\ t_5 := \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t_4\right)\\ t_6 := x1 \cdot \left(x1 \cdot x1\right)\\ \mathbf{if}\;x1 \leq -145000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 2.95 \cdot 10^{-8}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - t_1\right)}{t_3} + \left(\left(\left(t_1 \cdot t_4 + t_3 \cdot \left(t_5 + \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right) \cdot \left(3 - 2 \cdot x2\right)\right)\right) - t_6\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+96}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(t_6 - \left(t_3 \cdot \left(t_5 + \left(\frac{t_2 - x1}{t_3} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(3 + t_4\right)\right) - t_1 \cdot \left(2 \cdot x2\right)\right)\right)\right) + 3 \cdot \frac{1}{\frac{-0.5}{x2}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (+ x1 (* 6.0 (pow x1 4.0)))))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ t_1 (* 2.0 x2)))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (/ (- x1 t_2) t_3))
        (t_5 (* (* x1 x1) (+ 6.0 (* 4.0 t_4))))
        (t_6 (* x1 (* x1 x1))))
   (if (<= x1 -145000000000.0)
     t_0
     (if (<= x1 2.95e-8)
       (-
        x1
        (+
         (* 3.0 (/ (+ x1 (- (* 2.0 x2) t_1)) t_3))
         (-
          (-
           (+
            (* t_1 t_4)
            (*
             t_3
             (+ t_5 (* (* (* x1 2.0) (- (* 2.0 x2) x1)) (- 3.0 (* 2.0 x2))))))
           t_6)
          x1)))
       (if (<= x1 4e+96)
         (+
          x1
          (+
           (+
            x1
            (-
             t_6
             (-
              (* t_3 (+ t_5 (* (* (/ (- t_2 x1) t_3) (* x1 2.0)) (+ 3.0 t_4))))
              (* t_1 (* 2.0 x2)))))
           (* 3.0 (/ 1.0 (/ -0.5 x2)))))
         t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 + (6.0 * pow(x1, 4.0)));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = t_1 + (2.0 * x2);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = (x1 - t_2) / t_3;
	double t_5 = (x1 * x1) * (6.0 + (4.0 * t_4));
	double t_6 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -145000000000.0) {
		tmp = t_0;
	} else if (x1 <= 2.95e-8) {
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_3)) + ((((t_1 * t_4) + (t_3 * (t_5 + (((x1 * 2.0) * ((2.0 * x2) - x1)) * (3.0 - (2.0 * x2)))))) - t_6) - x1));
	} else if (x1 <= 4e+96) {
		tmp = x1 + ((x1 + (t_6 - ((t_3 * (t_5 + ((((t_2 - x1) / t_3) * (x1 * 2.0)) * (3.0 + t_4)))) - (t_1 * (2.0 * x2))))) + (3.0 * (1.0 / (-0.5 / x2))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = x1 + (x1 + (6.0d0 * (x1 ** 4.0d0)))
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = t_1 + (2.0d0 * x2)
    t_3 = (x1 * x1) + 1.0d0
    t_4 = (x1 - t_2) / t_3
    t_5 = (x1 * x1) * (6.0d0 + (4.0d0 * t_4))
    t_6 = x1 * (x1 * x1)
    if (x1 <= (-145000000000.0d0)) then
        tmp = t_0
    else if (x1 <= 2.95d-8) then
        tmp = x1 - ((3.0d0 * ((x1 + ((2.0d0 * x2) - t_1)) / t_3)) + ((((t_1 * t_4) + (t_3 * (t_5 + (((x1 * 2.0d0) * ((2.0d0 * x2) - x1)) * (3.0d0 - (2.0d0 * x2)))))) - t_6) - x1))
    else if (x1 <= 4d+96) then
        tmp = x1 + ((x1 + (t_6 - ((t_3 * (t_5 + ((((t_2 - x1) / t_3) * (x1 * 2.0d0)) * (3.0d0 + t_4)))) - (t_1 * (2.0d0 * x2))))) + (3.0d0 * (1.0d0 / ((-0.5d0) / x2))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 + (6.0 * Math.pow(x1, 4.0)));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = t_1 + (2.0 * x2);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = (x1 - t_2) / t_3;
	double t_5 = (x1 * x1) * (6.0 + (4.0 * t_4));
	double t_6 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -145000000000.0) {
		tmp = t_0;
	} else if (x1 <= 2.95e-8) {
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_3)) + ((((t_1 * t_4) + (t_3 * (t_5 + (((x1 * 2.0) * ((2.0 * x2) - x1)) * (3.0 - (2.0 * x2)))))) - t_6) - x1));
	} else if (x1 <= 4e+96) {
		tmp = x1 + ((x1 + (t_6 - ((t_3 * (t_5 + ((((t_2 - x1) / t_3) * (x1 * 2.0)) * (3.0 + t_4)))) - (t_1 * (2.0 * x2))))) + (3.0 * (1.0 / (-0.5 / x2))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 + (6.0 * math.pow(x1, 4.0)))
	t_1 = x1 * (x1 * 3.0)
	t_2 = t_1 + (2.0 * x2)
	t_3 = (x1 * x1) + 1.0
	t_4 = (x1 - t_2) / t_3
	t_5 = (x1 * x1) * (6.0 + (4.0 * t_4))
	t_6 = x1 * (x1 * x1)
	tmp = 0
	if x1 <= -145000000000.0:
		tmp = t_0
	elif x1 <= 2.95e-8:
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_3)) + ((((t_1 * t_4) + (t_3 * (t_5 + (((x1 * 2.0) * ((2.0 * x2) - x1)) * (3.0 - (2.0 * x2)))))) - t_6) - x1))
	elif x1 <= 4e+96:
		tmp = x1 + ((x1 + (t_6 - ((t_3 * (t_5 + ((((t_2 - x1) / t_3) * (x1 * 2.0)) * (3.0 + t_4)))) - (t_1 * (2.0 * x2))))) + (3.0 * (1.0 / (-0.5 / x2))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 + Float64(6.0 * (x1 ^ 4.0))))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(t_1 + Float64(2.0 * x2))
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(Float64(x1 - t_2) / t_3)
	t_5 = Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_4)))
	t_6 = Float64(x1 * Float64(x1 * x1))
	tmp = 0.0
	if (x1 <= -145000000000.0)
		tmp = t_0;
	elseif (x1 <= 2.95e-8)
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(Float64(x1 + Float64(Float64(2.0 * x2) - t_1)) / t_3)) + Float64(Float64(Float64(Float64(t_1 * t_4) + Float64(t_3 * Float64(t_5 + Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(2.0 * x2) - x1)) * Float64(3.0 - Float64(2.0 * x2)))))) - t_6) - x1)));
	elseif (x1 <= 4e+96)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(t_6 - Float64(Float64(t_3 * Float64(t_5 + Float64(Float64(Float64(Float64(t_2 - x1) / t_3) * Float64(x1 * 2.0)) * Float64(3.0 + t_4)))) - Float64(t_1 * Float64(2.0 * x2))))) + Float64(3.0 * Float64(1.0 / Float64(-0.5 / x2)))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 + (6.0 * (x1 ^ 4.0)));
	t_1 = x1 * (x1 * 3.0);
	t_2 = t_1 + (2.0 * x2);
	t_3 = (x1 * x1) + 1.0;
	t_4 = (x1 - t_2) / t_3;
	t_5 = (x1 * x1) * (6.0 + (4.0 * t_4));
	t_6 = x1 * (x1 * x1);
	tmp = 0.0;
	if (x1 <= -145000000000.0)
		tmp = t_0;
	elseif (x1 <= 2.95e-8)
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_3)) + ((((t_1 * t_4) + (t_3 * (t_5 + (((x1 * 2.0) * ((2.0 * x2) - x1)) * (3.0 - (2.0 * x2)))))) - t_6) - x1));
	elseif (x1 <= 4e+96)
		tmp = x1 + ((x1 + (t_6 - ((t_3 * (t_5 + ((((t_2 - x1) / t_3) * (x1 * 2.0)) * (3.0 + t_4)))) - (t_1 * (2.0 * x2))))) + (3.0 * (1.0 / (-0.5 / x2))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 - t$95$2), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -145000000000.0], t$95$0, If[LessEqual[x1, 2.95e-8], N[(x1 - N[(N[(3.0 * N[(N[(x1 + N[(N[(2.0 * x2), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(t$95$1 * t$95$4), $MachinePrecision] + N[(t$95$3 * N[(t$95$5 + N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$6), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4e+96], N[(x1 + N[(N[(x1 + N[(t$95$6 - N[(N[(t$95$3 * N[(t$95$5 + N[(N[(N[(N[(t$95$2 - x1), $MachinePrecision] / t$95$3), $MachinePrecision] * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(3.0 + t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(1.0 / N[(-0.5 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.45e11 or 4.0000000000000002e96 < x1

   1. Initial program 29.3%

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

   2. Taylor expanded in x1 around inf 35.6%

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

      1. *-commutative 35.6%

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

   4. Simplified 35.6%

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

   5. Taylor expanded in x1 around inf 98.8%

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

   if -1.45e11 < x1 < 2.9499999999999999e-8

   1. Initial program 98.6%

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

   2. Taylor expanded in x1 around 0 98.2%

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

      1. +-commutative 98.2%

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

      2. mul-1-neg 98.2%

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

      3. unsub-neg 98.2%

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

   4. Simplified 98.2%

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

   5. Taylor expanded in x1 around 0 98.0%

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

   if 2.9499999999999999e-8 < x1 < 4.0000000000000002e96

   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. Step-by-step derivation

      1. fma-def 99.2%

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

      2. clear-num 99.2%

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

      3. associate--l- 99.2%

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

      4. *-commutative 99.2%

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

      5. *-commutative 99.2%

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

      6. inv-pow 99.2%

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

      7. associate-*r* 99.2%

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

      8. *-commutative 99.2%

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

      9. fma-neg 99.2%

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

      10. pow2 99.2%

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

      11. fma-def 99.2%

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

   3. Applied egg-rr 99.2%

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

      1. unpow-1 99.2%

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

      2. fma-udef 99.2%

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

      3. unsub-neg 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in x1 around 0 95.7%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{1}{\color{blue}{\frac{-0.5}{x2}}}\right) \]

   7. Taylor expanded in x1 around 0 88.5%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{\left(2 \cdot x2\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{1}{\frac{-0.5}{x2}}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -145000000000:\\ \;\;\;\;x1 + \left(x1 + 6 \cdot {x1}^{4}\right)\\ \mathbf{elif}\;x1 \leq 2.95 \cdot 10^{-8}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} + \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) + \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right) \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+96}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right) - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right)\right)\right)\right) + 3 \cdot \frac{1}{\frac{-0.5}{x2}}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 6 \cdot {x1}^{4}\right)\\ \end{array} \]

Alternative 9: 76.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := t_0 + 2 \cdot x2\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{x1 - t_1}{t_2}\\ t_4 := \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t_3\right)\\ t_5 := x1 \cdot \left(x1 \cdot x1\right)\\ t_6 := x1 + \left(\left(x1 + \left(t_5 - \left(t_2 \cdot \left(t_4 + \left(\frac{t_1 - x1}{t_2} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(3 + t_3\right)\right) - t_0 \cdot \left(2 \cdot x2\right)\right)\right)\right) + 3 \cdot \frac{1}{\frac{-0.5}{x2}}\right)\\ t_7 := 3 - 2 \cdot x2\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right) - x1\\ \mathbf{elif}\;x1 \leq -0.064:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x1 \leq 2.95 \cdot 10^{-8}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - t_0\right)}{t_2} + \left(\left(\left(t_0 \cdot t_3 + t_2 \cdot \left(t_4 + \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right) \cdot t_7\right)\right) - t_5\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot t_7\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ t_0 (* 2.0 x2)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (/ (- x1 t_1) t_2))
        (t_4 (* (* x1 x1) (+ 6.0 (* 4.0 t_3))))
        (t_5 (* x1 (* x1 x1)))
        (t_6
         (+
          x1
          (+
           (+
            x1
            (-
             t_5
             (-
              (* t_2 (+ t_4 (* (* (/ (- t_1 x1) t_2) (* x1 2.0)) (+ 3.0 t_3))))
              (* t_0 (* 2.0 x2)))))
           (* 3.0 (/ 1.0 (/ -0.5 x2))))))
        (t_7 (- 3.0 (* 2.0 x2))))
   (if (<= x1 -5.6e+102)
     (- (* x2 (- (* x1 -12.0) 6.0)) x1)
     (if (<= x1 -0.064)
       t_6
       (if (<= x1 2.95e-8)
         (-
          x1
          (+
           (* 3.0 (/ (+ x1 (- (* 2.0 x2) t_0)) t_2))
           (-
            (-
             (+
              (* t_0 t_3)
              (* t_2 (+ t_4 (* (* (* x1 2.0) (- (* 2.0 x2) x1)) t_7))))
             t_5)
            x1)))
         (if (<= x1 1.35e+154)
           t_6
           (+ x1 (* x1 (- 1.0 (* 4.0 (* x2 t_7)))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = t_0 + (2.0 * x2);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = (x1 - t_1) / t_2;
	double t_4 = (x1 * x1) * (6.0 + (4.0 * t_3));
	double t_5 = x1 * (x1 * x1);
	double t_6 = x1 + ((x1 + (t_5 - ((t_2 * (t_4 + ((((t_1 - x1) / t_2) * (x1 * 2.0)) * (3.0 + t_3)))) - (t_0 * (2.0 * x2))))) + (3.0 * (1.0 / (-0.5 / x2))));
	double t_7 = 3.0 - (2.0 * x2);
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = (x2 * ((x1 * -12.0) - 6.0)) - x1;
	} else if (x1 <= -0.064) {
		tmp = t_6;
	} else if (x1 <= 2.95e-8) {
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_0)) / t_2)) + ((((t_0 * t_3) + (t_2 * (t_4 + (((x1 * 2.0) * ((2.0 * x2) - x1)) * t_7)))) - t_5) - x1));
	} else if (x1 <= 1.35e+154) {
		tmp = t_6;
	} else {
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * t_7))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = t_0 + (2.0d0 * x2)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = (x1 - t_1) / t_2
    t_4 = (x1 * x1) * (6.0d0 + (4.0d0 * t_3))
    t_5 = x1 * (x1 * x1)
    t_6 = x1 + ((x1 + (t_5 - ((t_2 * (t_4 + ((((t_1 - x1) / t_2) * (x1 * 2.0d0)) * (3.0d0 + t_3)))) - (t_0 * (2.0d0 * x2))))) + (3.0d0 * (1.0d0 / ((-0.5d0) / x2))))
    t_7 = 3.0d0 - (2.0d0 * x2)
    if (x1 <= (-5.6d+102)) then
        tmp = (x2 * ((x1 * (-12.0d0)) - 6.0d0)) - x1
    else if (x1 <= (-0.064d0)) then
        tmp = t_6
    else if (x1 <= 2.95d-8) then
        tmp = x1 - ((3.0d0 * ((x1 + ((2.0d0 * x2) - t_0)) / t_2)) + ((((t_0 * t_3) + (t_2 * (t_4 + (((x1 * 2.0d0) * ((2.0d0 * x2) - x1)) * t_7)))) - t_5) - x1))
    else if (x1 <= 1.35d+154) then
        tmp = t_6
    else
        tmp = x1 + (x1 * (1.0d0 - (4.0d0 * (x2 * t_7))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = t_0 + (2.0 * x2);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = (x1 - t_1) / t_2;
	double t_4 = (x1 * x1) * (6.0 + (4.0 * t_3));
	double t_5 = x1 * (x1 * x1);
	double t_6 = x1 + ((x1 + (t_5 - ((t_2 * (t_4 + ((((t_1 - x1) / t_2) * (x1 * 2.0)) * (3.0 + t_3)))) - (t_0 * (2.0 * x2))))) + (3.0 * (1.0 / (-0.5 / x2))));
	double t_7 = 3.0 - (2.0 * x2);
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = (x2 * ((x1 * -12.0) - 6.0)) - x1;
	} else if (x1 <= -0.064) {
		tmp = t_6;
	} else if (x1 <= 2.95e-8) {
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_0)) / t_2)) + ((((t_0 * t_3) + (t_2 * (t_4 + (((x1 * 2.0) * ((2.0 * x2) - x1)) * t_7)))) - t_5) - x1));
	} else if (x1 <= 1.35e+154) {
		tmp = t_6;
	} else {
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * t_7))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = t_0 + (2.0 * x2)
	t_2 = (x1 * x1) + 1.0
	t_3 = (x1 - t_1) / t_2
	t_4 = (x1 * x1) * (6.0 + (4.0 * t_3))
	t_5 = x1 * (x1 * x1)
	t_6 = x1 + ((x1 + (t_5 - ((t_2 * (t_4 + ((((t_1 - x1) / t_2) * (x1 * 2.0)) * (3.0 + t_3)))) - (t_0 * (2.0 * x2))))) + (3.0 * (1.0 / (-0.5 / x2))))
	t_7 = 3.0 - (2.0 * x2)
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = (x2 * ((x1 * -12.0) - 6.0)) - x1
	elif x1 <= -0.064:
		tmp = t_6
	elif x1 <= 2.95e-8:
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_0)) / t_2)) + ((((t_0 * t_3) + (t_2 * (t_4 + (((x1 * 2.0) * ((2.0 * x2) - x1)) * t_7)))) - t_5) - x1))
	elif x1 <= 1.35e+154:
		tmp = t_6
	else:
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * t_7))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(t_0 + Float64(2.0 * x2))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(x1 - t_1) / t_2)
	t_4 = Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_3)))
	t_5 = Float64(x1 * Float64(x1 * x1))
	t_6 = Float64(x1 + Float64(Float64(x1 + Float64(t_5 - Float64(Float64(t_2 * Float64(t_4 + Float64(Float64(Float64(Float64(t_1 - x1) / t_2) * Float64(x1 * 2.0)) * Float64(3.0 + t_3)))) - Float64(t_0 * Float64(2.0 * x2))))) + Float64(3.0 * Float64(1.0 / Float64(-0.5 / x2)))))
	t_7 = Float64(3.0 - Float64(2.0 * x2))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)) - x1);
	elseif (x1 <= -0.064)
		tmp = t_6;
	elseif (x1 <= 2.95e-8)
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(Float64(x1 + Float64(Float64(2.0 * x2) - t_0)) / t_2)) + Float64(Float64(Float64(Float64(t_0 * t_3) + Float64(t_2 * Float64(t_4 + Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(2.0 * x2) - x1)) * t_7)))) - t_5) - x1)));
	elseif (x1 <= 1.35e+154)
		tmp = t_6;
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 - Float64(4.0 * Float64(x2 * t_7)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = t_0 + (2.0 * x2);
	t_2 = (x1 * x1) + 1.0;
	t_3 = (x1 - t_1) / t_2;
	t_4 = (x1 * x1) * (6.0 + (4.0 * t_3));
	t_5 = x1 * (x1 * x1);
	t_6 = x1 + ((x1 + (t_5 - ((t_2 * (t_4 + ((((t_1 - x1) / t_2) * (x1 * 2.0)) * (3.0 + t_3)))) - (t_0 * (2.0 * x2))))) + (3.0 * (1.0 / (-0.5 / x2))));
	t_7 = 3.0 - (2.0 * x2);
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = (x2 * ((x1 * -12.0) - 6.0)) - x1;
	elseif (x1 <= -0.064)
		tmp = t_6;
	elseif (x1 <= 2.95e-8)
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_0)) / t_2)) + ((((t_0 * t_3) + (t_2 * (t_4 + (((x1 * 2.0) * ((2.0 * x2) - x1)) * t_7)))) - t_5) - x1));
	elseif (x1 <= 1.35e+154)
		tmp = t_6;
	else
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * t_7))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 - t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(x1 + N[(N[(x1 + N[(t$95$5 - N[(N[(t$95$2 * N[(t$95$4 + N[(N[(N[(N[(t$95$1 - x1), $MachinePrecision] / t$95$2), $MachinePrecision] * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(3.0 + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$0 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(1.0 / N[(-0.5 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, -0.064], t$95$6, If[LessEqual[x1, 2.95e-8], N[(x1 - N[(N[(3.0 * N[(N[(x1 + N[(N[(2.0 * x2), $MachinePrecision] - t$95$0), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(t$95$0 * t$95$3), $MachinePrecision] + N[(t$95$2 * N[(t$95$4 + N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$5), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], t$95$6, N[(x1 + N[(x1 * N[(1.0 - N[(4.0 * N[(x2 * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 3.5%

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

      1. fma-def 3.5%

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

      2. fma-neg 3.5%

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

      3. fma-neg 3.5%

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

      4. metadata-eval 3.5%

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

      5. metadata-eval 3.5%

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

   5. Simplified 3.5%

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

   6. Taylor expanded in x1 around 0 3.5%

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

   7. Taylor expanded in x2 around 0 26.6%

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

   if -5.60000000000000037e102 < x1 < -0.064000000000000001 or 2.9499999999999999e-8 < 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. Step-by-step derivation

      1. fma-def 99.3%

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

      2. clear-num 99.3%

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

      3. associate--l- 99.3%

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

      4. *-commutative 99.3%

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

      5. *-commutative 99.3%

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

      6. inv-pow 99.3%

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

      7. associate-*r* 99.3%

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

      8. *-commutative 99.3%

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

      9. fma-neg 99.3%

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

      10. pow2 99.3%

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

      11. fma-def 99.3%

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

   3. Applied egg-rr 99.3%

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

      1. unpow-1 99.3%

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

      2. fma-udef 99.3%

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

      3. unsub-neg 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in x1 around 0 97.5%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{1}{\color{blue}{\frac{-0.5}{x2}}}\right) \]

   7. Taylor expanded in x1 around 0 91.6%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{\left(2 \cdot x2\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{1}{\frac{-0.5}{x2}}\right) \]

   if -0.064000000000000001 < x1 < 2.9499999999999999e-8

   1. Initial program 98.6%

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

   2. Taylor expanded in x1 around 0 98.6%

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

      1. +-commutative 98.6%

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

      2. mul-1-neg 98.6%

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

      3. unsub-neg 98.6%

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

   4. Simplified 98.6%

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

   5. Taylor expanded in x1 around 0 98.6%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around inf 58.6%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right) - x1\\ \mathbf{elif}\;x1 \leq -0.064:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right) - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right)\right)\right)\right) + 3 \cdot \frac{1}{\frac{-0.5}{x2}}\right)\\ \mathbf{elif}\;x1 \leq 2.95 \cdot 10^{-8}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} + \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) + \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right) \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right) - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right)\right)\right)\right) + 3 \cdot \frac{1}{\frac{-0.5}{x2}}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \end{array} \]

Alternative 10: 75.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := 3 - 2 \cdot x2\\ t_3 := x2 \cdot t_2\\ t_4 := x1 \cdot \left(x1 \cdot 3\right)\\ t_5 := t_4 + 2 \cdot x2\\ t_6 := \frac{x1 - t_5}{t_1}\\ t_7 := t_4 \cdot t_6\\ t_8 := \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t_6\right)\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right) - x1\\ \mathbf{elif}\;x1 \leq -3900:\\ \;\;\;\;x1 + \left(3 \cdot \frac{1}{\frac{-0.5}{x2}} + \left(x1 + \left(t_0 - \left(t_7 - \left(\left(\frac{t_5 - x1}{t_1} \cdot \left(x1 \cdot 2\right)\right) \cdot \frac{1}{x1} + t_8\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.95 \cdot 10^{-8}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - t_4\right)}{t_1} + \left(\left(\left(t_7 + t_1 \cdot \left(t_8 + \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right) \cdot t_2\right)\right) - t_0\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_4 - 2 \cdot x2\right) - x1}{t_1} - \left(\left(\left(t_7 + t_1 \cdot \left(4 \cdot \left(x1 \cdot t_3\right) + t_8\right)\right) - t_0\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot t_3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (- 3.0 (* 2.0 x2)))
        (t_3 (* x2 t_2))
        (t_4 (* x1 (* x1 3.0)))
        (t_5 (+ t_4 (* 2.0 x2)))
        (t_6 (/ (- x1 t_5) t_1))
        (t_7 (* t_4 t_6))
        (t_8 (* (* x1 x1) (+ 6.0 (* 4.0 t_6)))))
   (if (<= x1 -5.6e+102)
     (- (* x2 (- (* x1 -12.0) 6.0)) x1)
     (if (<= x1 -3900.0)
       (+
        x1
        (+
         (* 3.0 (/ 1.0 (/ -0.5 x2)))
         (+
          x1
          (-
           t_0
           (-
            t_7
            (*
             (+ (* (* (/ (- t_5 x1) t_1) (* x1 2.0)) (/ 1.0 x1)) t_8)
             (- -1.0 (* x1 x1))))))))
       (if (<= x1 2.95e-8)
         (-
          x1
          (+
           (* 3.0 (/ (+ x1 (- (* 2.0 x2) t_4)) t_1))
           (-
            (-
             (+ t_7 (* t_1 (+ t_8 (* (* (* x1 2.0) (- (* 2.0 x2) x1)) t_2))))
             t_0)
            x1)))
         (if (<= x1 1.35e+154)
           (+
            x1
            (-
             (* 3.0 (/ (- (- t_4 (* 2.0 x2)) x1) t_1))
             (- (- (+ t_7 (* t_1 (+ (* 4.0 (* x1 t_3)) t_8))) t_0) x1)))
           (+ x1 (* x1 (- 1.0 (* 4.0 t_3))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = 3.0 - (2.0 * x2);
	double t_3 = x2 * t_2;
	double t_4 = x1 * (x1 * 3.0);
	double t_5 = t_4 + (2.0 * x2);
	double t_6 = (x1 - t_5) / t_1;
	double t_7 = t_4 * t_6;
	double t_8 = (x1 * x1) * (6.0 + (4.0 * t_6));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = (x2 * ((x1 * -12.0) - 6.0)) - x1;
	} else if (x1 <= -3900.0) {
		tmp = x1 + ((3.0 * (1.0 / (-0.5 / x2))) + (x1 + (t_0 - (t_7 - ((((((t_5 - x1) / t_1) * (x1 * 2.0)) * (1.0 / x1)) + t_8) * (-1.0 - (x1 * x1)))))));
	} else if (x1 <= 2.95e-8) {
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_4)) / t_1)) + (((t_7 + (t_1 * (t_8 + (((x1 * 2.0) * ((2.0 * x2) - x1)) * t_2)))) - t_0) - x1));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((3.0 * (((t_4 - (2.0 * x2)) - x1) / t_1)) - (((t_7 + (t_1 * ((4.0 * (x1 * t_3)) + t_8))) - t_0) - x1));
	} else {
		tmp = x1 + (x1 * (1.0 - (4.0 * t_3)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: tmp
    t_0 = x1 * (x1 * x1)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = 3.0d0 - (2.0d0 * x2)
    t_3 = x2 * t_2
    t_4 = x1 * (x1 * 3.0d0)
    t_5 = t_4 + (2.0d0 * x2)
    t_6 = (x1 - t_5) / t_1
    t_7 = t_4 * t_6
    t_8 = (x1 * x1) * (6.0d0 + (4.0d0 * t_6))
    if (x1 <= (-5.6d+102)) then
        tmp = (x2 * ((x1 * (-12.0d0)) - 6.0d0)) - x1
    else if (x1 <= (-3900.0d0)) then
        tmp = x1 + ((3.0d0 * (1.0d0 / ((-0.5d0) / x2))) + (x1 + (t_0 - (t_7 - ((((((t_5 - x1) / t_1) * (x1 * 2.0d0)) * (1.0d0 / x1)) + t_8) * ((-1.0d0) - (x1 * x1)))))))
    else if (x1 <= 2.95d-8) then
        tmp = x1 - ((3.0d0 * ((x1 + ((2.0d0 * x2) - t_4)) / t_1)) + (((t_7 + (t_1 * (t_8 + (((x1 * 2.0d0) * ((2.0d0 * x2) - x1)) * t_2)))) - t_0) - x1))
    else if (x1 <= 1.35d+154) then
        tmp = x1 + ((3.0d0 * (((t_4 - (2.0d0 * x2)) - x1) / t_1)) - (((t_7 + (t_1 * ((4.0d0 * (x1 * t_3)) + t_8))) - t_0) - x1))
    else
        tmp = x1 + (x1 * (1.0d0 - (4.0d0 * t_3)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = 3.0 - (2.0 * x2);
	double t_3 = x2 * t_2;
	double t_4 = x1 * (x1 * 3.0);
	double t_5 = t_4 + (2.0 * x2);
	double t_6 = (x1 - t_5) / t_1;
	double t_7 = t_4 * t_6;
	double t_8 = (x1 * x1) * (6.0 + (4.0 * t_6));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = (x2 * ((x1 * -12.0) - 6.0)) - x1;
	} else if (x1 <= -3900.0) {
		tmp = x1 + ((3.0 * (1.0 / (-0.5 / x2))) + (x1 + (t_0 - (t_7 - ((((((t_5 - x1) / t_1) * (x1 * 2.0)) * (1.0 / x1)) + t_8) * (-1.0 - (x1 * x1)))))));
	} else if (x1 <= 2.95e-8) {
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_4)) / t_1)) + (((t_7 + (t_1 * (t_8 + (((x1 * 2.0) * ((2.0 * x2) - x1)) * t_2)))) - t_0) - x1));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((3.0 * (((t_4 - (2.0 * x2)) - x1) / t_1)) - (((t_7 + (t_1 * ((4.0 * (x1 * t_3)) + t_8))) - t_0) - x1));
	} else {
		tmp = x1 + (x1 * (1.0 - (4.0 * t_3)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = (x1 * x1) + 1.0
	t_2 = 3.0 - (2.0 * x2)
	t_3 = x2 * t_2
	t_4 = x1 * (x1 * 3.0)
	t_5 = t_4 + (2.0 * x2)
	t_6 = (x1 - t_5) / t_1
	t_7 = t_4 * t_6
	t_8 = (x1 * x1) * (6.0 + (4.0 * t_6))
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = (x2 * ((x1 * -12.0) - 6.0)) - x1
	elif x1 <= -3900.0:
		tmp = x1 + ((3.0 * (1.0 / (-0.5 / x2))) + (x1 + (t_0 - (t_7 - ((((((t_5 - x1) / t_1) * (x1 * 2.0)) * (1.0 / x1)) + t_8) * (-1.0 - (x1 * x1)))))))
	elif x1 <= 2.95e-8:
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_4)) / t_1)) + (((t_7 + (t_1 * (t_8 + (((x1 * 2.0) * ((2.0 * x2) - x1)) * t_2)))) - t_0) - x1))
	elif x1 <= 1.35e+154:
		tmp = x1 + ((3.0 * (((t_4 - (2.0 * x2)) - x1) / t_1)) - (((t_7 + (t_1 * ((4.0 * (x1 * t_3)) + t_8))) - t_0) - x1))
	else:
		tmp = x1 + (x1 * (1.0 - (4.0 * t_3)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(3.0 - Float64(2.0 * x2))
	t_3 = Float64(x2 * t_2)
	t_4 = Float64(x1 * Float64(x1 * 3.0))
	t_5 = Float64(t_4 + Float64(2.0 * x2))
	t_6 = Float64(Float64(x1 - t_5) / t_1)
	t_7 = Float64(t_4 * t_6)
	t_8 = Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_6)))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)) - x1);
	elseif (x1 <= -3900.0)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(1.0 / Float64(-0.5 / x2))) + Float64(x1 + Float64(t_0 - Float64(t_7 - Float64(Float64(Float64(Float64(Float64(Float64(t_5 - x1) / t_1) * Float64(x1 * 2.0)) * Float64(1.0 / x1)) + t_8) * Float64(-1.0 - Float64(x1 * x1))))))));
	elseif (x1 <= 2.95e-8)
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(Float64(x1 + Float64(Float64(2.0 * x2) - t_4)) / t_1)) + Float64(Float64(Float64(t_7 + Float64(t_1 * Float64(t_8 + Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(2.0 * x2) - x1)) * t_2)))) - t_0) - x1)));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_4 - Float64(2.0 * x2)) - x1) / t_1)) - Float64(Float64(Float64(t_7 + Float64(t_1 * Float64(Float64(4.0 * Float64(x1 * t_3)) + t_8))) - t_0) - x1)));
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 - Float64(4.0 * t_3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = (x1 * x1) + 1.0;
	t_2 = 3.0 - (2.0 * x2);
	t_3 = x2 * t_2;
	t_4 = x1 * (x1 * 3.0);
	t_5 = t_4 + (2.0 * x2);
	t_6 = (x1 - t_5) / t_1;
	t_7 = t_4 * t_6;
	t_8 = (x1 * x1) * (6.0 + (4.0 * t_6));
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = (x2 * ((x1 * -12.0) - 6.0)) - x1;
	elseif (x1 <= -3900.0)
		tmp = x1 + ((3.0 * (1.0 / (-0.5 / x2))) + (x1 + (t_0 - (t_7 - ((((((t_5 - x1) / t_1) * (x1 * 2.0)) * (1.0 / x1)) + t_8) * (-1.0 - (x1 * x1)))))));
	elseif (x1 <= 2.95e-8)
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_4)) / t_1)) + (((t_7 + (t_1 * (t_8 + (((x1 * 2.0) * ((2.0 * x2) - x1)) * t_2)))) - t_0) - x1));
	elseif (x1 <= 1.35e+154)
		tmp = x1 + ((3.0 * (((t_4 - (2.0 * x2)) - x1) / t_1)) - (((t_7 + (t_1 * ((4.0 * (x1 * t_3)) + t_8))) - t_0) - x1));
	else
		tmp = x1 + (x1 * (1.0 - (4.0 * t_3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x2 * t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 - t$95$5), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$4 * t$95$6), $MachinePrecision]}, Block[{t$95$8 = N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, -3900.0], N[(x1 + N[(N[(3.0 * N[(1.0 / N[(-0.5 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$0 - N[(t$95$7 - N[(N[(N[(N[(N[(N[(t$95$5 - x1), $MachinePrecision] / t$95$1), $MachinePrecision] * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(1.0 / x1), $MachinePrecision]), $MachinePrecision] + t$95$8), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.95e-8], N[(x1 - N[(N[(3.0 * N[(N[(x1 + N[(N[(2.0 * x2), $MachinePrecision] - t$95$4), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t$95$7 + N[(t$95$1 * N[(t$95$8 + N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$4 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(t$95$7 + N[(t$95$1 * N[(N[(4.0 * N[(x1 * t$95$3), $MachinePrecision]), $MachinePrecision] + t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * N[(1.0 - N[(4.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 5 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 0.0%

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

   3. Taylor expanded in x1 around 0 3.5%

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

      1. fma-def 3.5%

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

      2. fma-neg 3.5%

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

      3. fma-neg 3.5%

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

      4. metadata-eval 3.5%

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

      5. metadata-eval 3.5%

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

   5. Simplified 3.5%

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

   6. Taylor expanded in x1 around 0 3.5%

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

   7. Taylor expanded in x2 around 0 26.6%

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

   if -5.60000000000000037e102 < x1 < -3900

   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. Step-by-step derivation

      1. fma-def 99.2%

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

      2. clear-num 99.2%

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

      3. associate--l- 99.2%

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

      4. *-commutative 99.2%

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

      5. *-commutative 99.2%

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

      6. inv-pow 99.2%

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

      7. associate-*r* 99.2%

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

      8. *-commutative 99.2%

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

      9. fma-neg 99.2%

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

      10. pow2 99.2%

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

      11. fma-def 99.2%

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

   3. Applied egg-rr 99.2%

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

      1. unpow-1 99.2%

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

      2. fma-udef 99.2%

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

      3. unsub-neg 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in x1 around 0 98.9%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{1}{\color{blue}{\frac{-0.5}{x2}}}\right) \]

   7. Taylor expanded in x1 around inf 93.3%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \color{blue}{\frac{-1}{x1}} + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{1}{\frac{-0.5}{x2}}\right) \]

   if -3900 < x1 < 2.9499999999999999e-8

   1. Initial program 98.6%

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

   2. Taylor expanded in x1 around 0 98.6%

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

      1. +-commutative 98.6%

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

      2. mul-1-neg 98.6%

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

      3. unsub-neg 98.6%

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

   4. Simplified 98.6%

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

   5. Taylor expanded in x1 around 0 98.6%

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

   if 2.9499999999999999e-8 < x1 < 1.35000000000000003e154

   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 72.0%

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

      1. +-commutative 72.0%

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

      2. mul-1-neg 72.0%

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

      3. unsub-neg 72.0%

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

   4. Simplified 72.0%

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

   5. Taylor expanded in x1 around 0 72.2%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around inf 58.6%

      \[\leadsto x1 + \color{blue}{x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right) - x1\\ \mathbf{elif}\;x1 \leq -3900:\\ \;\;\;\;x1 + \left(3 \cdot \frac{1}{\frac{-0.5}{x2}} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} - \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot 2\right)\right) \cdot \frac{1}{x1} + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.95 \cdot 10^{-8}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} + \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) + \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right) \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \end{array} \]

Alternative 11: 70.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := x2 \cdot \left(x1 \cdot -12 - 6\right) - x1\\ t_3 := x2 \cdot \left(3 - 2 \cdot x2\right)\\ t_4 := x1 \cdot x1 + 1\\ t_5 := \frac{x1 - \left(t_0 + 2 \cdot x2\right)}{t_4}\\ t_6 := t_4 \cdot \left(4 \cdot \left(x1 \cdot t_3\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t_5\right)\right)\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x1 \leq -1 \cdot 10^{-177}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - t_0\right)}{t_4} - \left(x1 - \left(\left(t_6 - t_0 \cdot \left(2 \cdot x2\right)\right) - t_1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.1 \cdot 10^{-199}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_4} - \left(\left(\left(t_0 \cdot t_5 + t_6\right) - t_1\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot t_3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (* x1 (* x1 x1)))
        (t_2 (- (* x2 (- (* x1 -12.0) 6.0)) x1))
        (t_3 (* x2 (- 3.0 (* 2.0 x2))))
        (t_4 (+ (* x1 x1) 1.0))
        (t_5 (/ (- x1 (+ t_0 (* 2.0 x2))) t_4))
        (t_6 (* t_4 (+ (* 4.0 (* x1 t_3)) (* (* x1 x1) (+ 6.0 (* 4.0 t_5)))))))
   (if (<= x1 -5.6e+102)
     t_2
     (if (<= x1 -1e-177)
       (-
        x1
        (-
         (* 3.0 (/ (+ x1 (- (* 2.0 x2) t_0)) t_4))
         (- x1 (- (- t_6 (* t_0 (* 2.0 x2))) t_1))))
       (if (<= x1 4.1e-199)
         t_2
         (if (<= x1 1.35e+154)
           (+
            x1
            (-
             (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_4))
             (- (- (+ (* t_0 t_5) t_6) t_1) x1)))
           (+ x1 (* x1 (- 1.0 (* 4.0 t_3))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * (x1 * x1);
	double t_2 = (x2 * ((x1 * -12.0) - 6.0)) - x1;
	double t_3 = x2 * (3.0 - (2.0 * x2));
	double t_4 = (x1 * x1) + 1.0;
	double t_5 = (x1 - (t_0 + (2.0 * x2))) / t_4;
	double t_6 = t_4 * ((4.0 * (x1 * t_3)) + ((x1 * x1) * (6.0 + (4.0 * t_5))));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_2;
	} else if (x1 <= -1e-177) {
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_0)) / t_4)) - (x1 - ((t_6 - (t_0 * (2.0 * x2))) - t_1)));
	} else if (x1 <= 4.1e-199) {
		tmp = t_2;
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_4)) - ((((t_0 * t_5) + t_6) - t_1) - x1));
	} else {
		tmp = x1 + (x1 * (1.0 - (4.0 * t_3)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = x1 * (x1 * x1)
    t_2 = (x2 * ((x1 * (-12.0d0)) - 6.0d0)) - x1
    t_3 = x2 * (3.0d0 - (2.0d0 * x2))
    t_4 = (x1 * x1) + 1.0d0
    t_5 = (x1 - (t_0 + (2.0d0 * x2))) / t_4
    t_6 = t_4 * ((4.0d0 * (x1 * t_3)) + ((x1 * x1) * (6.0d0 + (4.0d0 * t_5))))
    if (x1 <= (-5.6d+102)) then
        tmp = t_2
    else if (x1 <= (-1d-177)) then
        tmp = x1 - ((3.0d0 * ((x1 + ((2.0d0 * x2) - t_0)) / t_4)) - (x1 - ((t_6 - (t_0 * (2.0d0 * x2))) - t_1)))
    else if (x1 <= 4.1d-199) then
        tmp = t_2
    else if (x1 <= 1.35d+154) then
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_4)) - ((((t_0 * t_5) + t_6) - t_1) - x1))
    else
        tmp = x1 + (x1 * (1.0d0 - (4.0d0 * t_3)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * (x1 * x1);
	double t_2 = (x2 * ((x1 * -12.0) - 6.0)) - x1;
	double t_3 = x2 * (3.0 - (2.0 * x2));
	double t_4 = (x1 * x1) + 1.0;
	double t_5 = (x1 - (t_0 + (2.0 * x2))) / t_4;
	double t_6 = t_4 * ((4.0 * (x1 * t_3)) + ((x1 * x1) * (6.0 + (4.0 * t_5))));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_2;
	} else if (x1 <= -1e-177) {
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_0)) / t_4)) - (x1 - ((t_6 - (t_0 * (2.0 * x2))) - t_1)));
	} else if (x1 <= 4.1e-199) {
		tmp = t_2;
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_4)) - ((((t_0 * t_5) + t_6) - t_1) - x1));
	} else {
		tmp = x1 + (x1 * (1.0 - (4.0 * t_3)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = x1 * (x1 * x1)
	t_2 = (x2 * ((x1 * -12.0) - 6.0)) - x1
	t_3 = x2 * (3.0 - (2.0 * x2))
	t_4 = (x1 * x1) + 1.0
	t_5 = (x1 - (t_0 + (2.0 * x2))) / t_4
	t_6 = t_4 * ((4.0 * (x1 * t_3)) + ((x1 * x1) * (6.0 + (4.0 * t_5))))
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = t_2
	elif x1 <= -1e-177:
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_0)) / t_4)) - (x1 - ((t_6 - (t_0 * (2.0 * x2))) - t_1)))
	elif x1 <= 4.1e-199:
		tmp = t_2
	elif x1 <= 1.35e+154:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_4)) - ((((t_0 * t_5) + t_6) - t_1) - x1))
	else:
		tmp = x1 + (x1 * (1.0 - (4.0 * t_3)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(x1 * Float64(x1 * x1))
	t_2 = Float64(Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)) - x1)
	t_3 = Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))
	t_4 = Float64(Float64(x1 * x1) + 1.0)
	t_5 = Float64(Float64(x1 - Float64(t_0 + Float64(2.0 * x2))) / t_4)
	t_6 = Float64(t_4 * Float64(Float64(4.0 * Float64(x1 * t_3)) + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_5)))))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = t_2;
	elseif (x1 <= -1e-177)
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(Float64(x1 + Float64(Float64(2.0 * x2) - t_0)) / t_4)) - Float64(x1 - Float64(Float64(t_6 - Float64(t_0 * Float64(2.0 * x2))) - t_1))));
	elseif (x1 <= 4.1e-199)
		tmp = t_2;
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_4)) - Float64(Float64(Float64(Float64(t_0 * t_5) + t_6) - t_1) - x1)));
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 - Float64(4.0 * t_3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = x1 * (x1 * x1);
	t_2 = (x2 * ((x1 * -12.0) - 6.0)) - x1;
	t_3 = x2 * (3.0 - (2.0 * x2));
	t_4 = (x1 * x1) + 1.0;
	t_5 = (x1 - (t_0 + (2.0 * x2))) / t_4;
	t_6 = t_4 * ((4.0 * (x1 * t_3)) + ((x1 * x1) * (6.0 + (4.0 * t_5))));
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = t_2;
	elseif (x1 <= -1e-177)
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_0)) / t_4)) - (x1 - ((t_6 - (t_0 * (2.0 * x2))) - t_1)));
	elseif (x1 <= 4.1e-199)
		tmp = t_2;
	elseif (x1 <= 1.35e+154)
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_4)) - ((((t_0 * t_5) + t_6) - t_1) - x1));
	else
		tmp = x1 + (x1 * (1.0 - (4.0 * t_3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$3 = N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 - N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$4 * N[(N[(4.0 * N[(x1 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], t$95$2, If[LessEqual[x1, -1e-177], N[(x1 - N[(N[(3.0 * N[(N[(x1 + N[(N[(2.0 * x2), $MachinePrecision] - t$95$0), $MachinePrecision]), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision] - N[(x1 - N[(N[(t$95$6 - N[(t$95$0 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.1e-199], t$95$2, If[LessEqual[x1, 1.35e+154], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(t$95$0 * t$95$5), $MachinePrecision] + t$95$6), $MachinePrecision] - t$95$1), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * N[(1.0 - N[(4.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.60000000000000037e102 or -9.99999999999999952e-178 < x1 < 4.10000000000000022e-199

   1. Initial program 52.7%

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

   2. Taylor expanded in x1 around 0 39.5%

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

   3. Taylor expanded in x1 around 0 41.2%

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

      1. fma-def 41.2%

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

      2. fma-neg 41.2%

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

      3. fma-neg 41.2%

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

      4. metadata-eval 41.2%

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

      5. metadata-eval 41.2%

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

   5. Simplified 41.2%

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

   6. Taylor expanded in x1 around 0 41.2%

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

   7. Taylor expanded in x2 around 0 62.9%

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

   if -5.60000000000000037e102 < x1 < -9.99999999999999952e-178

   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 96.6%

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

      1. +-commutative 96.6%

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

      2. mul-1-neg 96.6%

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

      3. unsub-neg 96.6%

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

   4. Simplified 96.6%

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

   5. Taylor expanded in x1 around 0 89.5%

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

   6. Taylor expanded in x1 around 0 89.6%

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

   if 4.10000000000000022e-199 < 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 0 86.3%

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

      1. +-commutative 86.3%

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

      2. mul-1-neg 86.3%

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

      3. unsub-neg 86.3%

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

   4. Simplified 86.3%

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

   5. Taylor expanded in x1 around 0 79.1%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around inf 58.6%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right) - x1\\ \mathbf{elif}\;x1 \leq -1 \cdot 10^{-177}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} - \left(x1 - \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right) - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.1 \cdot 10^{-199}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right) - x1\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \end{array} \]

Alternative 12: 71.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x2 \cdot \left(x1 \cdot -12 - 6\right) - x1\\ t_2 := x1 \cdot \left(x1 \cdot x1\right)\\ t_3 := x2 \cdot \left(3 - 2 \cdot x2\right)\\ t_4 := 4 \cdot t_3\\ t_5 := 4 \cdot \left(x1 \cdot t_3\right)\\ t_6 := x1 \cdot \left(x1 \cdot 3\right)\\ t_7 := t_6 + 2 \cdot x2\\ t_8 := \frac{x1 - t_7}{t_0}\\ t_9 := \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t_8\right)\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq -4000:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(t_2 + \left(t_6 \cdot \frac{t_7 - x1}{t_0} - t_0 \cdot \left(t_9 - x1 \cdot 2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -8 \cdot 10^{-178}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(t_4 - -1\right)\\ \mathbf{elif}\;x1 \leq 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq 170:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_6 - 2 \cdot x2\right) - x1}{t_0} + \left(x1 - t_5\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(9 - \left(\left(\left(t_6 \cdot t_8 + t_0 \cdot \left(t_5 + t_9\right)\right) - t_2\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - t_4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (- (* x2 (- (* x1 -12.0) 6.0)) x1))
        (t_2 (* x1 (* x1 x1)))
        (t_3 (* x2 (- 3.0 (* 2.0 x2))))
        (t_4 (* 4.0 t_3))
        (t_5 (* 4.0 (* x1 t_3)))
        (t_6 (* x1 (* x1 3.0)))
        (t_7 (+ t_6 (* 2.0 x2)))
        (t_8 (/ (- x1 t_7) t_0))
        (t_9 (* (* x1 x1) (+ 6.0 (* 4.0 t_8)))))
   (if (<= x1 -5.6e+102)
     t_1
     (if (<= x1 -4000.0)
       (+
        x1
        (+
         9.0
         (+
          x1
          (+ t_2 (- (* t_6 (/ (- t_7 x1) t_0)) (* t_0 (- t_9 (* x1 2.0))))))))
       (if (<= x1 -8e-178)
         (- (* x2 -6.0) (* x1 (- t_4 -1.0)))
         (if (<= x1 1e-198)
           t_1
           (if (<= x1 170.0)
             (+ x1 (+ (* 3.0 (/ (- (- t_6 (* 2.0 x2)) x1) t_0)) (- x1 t_5)))
             (if (<= x1 1.35e+154)
               (+
                x1
                (- 9.0 (- (- (+ (* t_6 t_8) (* t_0 (+ t_5 t_9))) t_2) x1)))
               (+ x1 (* x1 (- 1.0 t_4)))))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = (x2 * ((x1 * -12.0) - 6.0)) - x1;
	double t_2 = x1 * (x1 * x1);
	double t_3 = x2 * (3.0 - (2.0 * x2));
	double t_4 = 4.0 * t_3;
	double t_5 = 4.0 * (x1 * t_3);
	double t_6 = x1 * (x1 * 3.0);
	double t_7 = t_6 + (2.0 * x2);
	double t_8 = (x1 - t_7) / t_0;
	double t_9 = (x1 * x1) * (6.0 + (4.0 * t_8));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_1;
	} else if (x1 <= -4000.0) {
		tmp = x1 + (9.0 + (x1 + (t_2 + ((t_6 * ((t_7 - x1) / t_0)) - (t_0 * (t_9 - (x1 * 2.0)))))));
	} else if (x1 <= -8e-178) {
		tmp = (x2 * -6.0) - (x1 * (t_4 - -1.0));
	} else if (x1 <= 1e-198) {
		tmp = t_1;
	} else if (x1 <= 170.0) {
		tmp = x1 + ((3.0 * (((t_6 - (2.0 * x2)) - x1) / t_0)) + (x1 - t_5));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + (9.0 - ((((t_6 * t_8) + (t_0 * (t_5 + t_9))) - t_2) - x1));
	} else {
		tmp = x1 + (x1 * (1.0 - t_4));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = (x2 * ((x1 * (-12.0d0)) - 6.0d0)) - x1
    t_2 = x1 * (x1 * x1)
    t_3 = x2 * (3.0d0 - (2.0d0 * x2))
    t_4 = 4.0d0 * t_3
    t_5 = 4.0d0 * (x1 * t_3)
    t_6 = x1 * (x1 * 3.0d0)
    t_7 = t_6 + (2.0d0 * x2)
    t_8 = (x1 - t_7) / t_0
    t_9 = (x1 * x1) * (6.0d0 + (4.0d0 * t_8))
    if (x1 <= (-5.6d+102)) then
        tmp = t_1
    else if (x1 <= (-4000.0d0)) then
        tmp = x1 + (9.0d0 + (x1 + (t_2 + ((t_6 * ((t_7 - x1) / t_0)) - (t_0 * (t_9 - (x1 * 2.0d0)))))))
    else if (x1 <= (-8d-178)) then
        tmp = (x2 * (-6.0d0)) - (x1 * (t_4 - (-1.0d0)))
    else if (x1 <= 1d-198) then
        tmp = t_1
    else if (x1 <= 170.0d0) then
        tmp = x1 + ((3.0d0 * (((t_6 - (2.0d0 * x2)) - x1) / t_0)) + (x1 - t_5))
    else if (x1 <= 1.35d+154) then
        tmp = x1 + (9.0d0 - ((((t_6 * t_8) + (t_0 * (t_5 + t_9))) - t_2) - x1))
    else
        tmp = x1 + (x1 * (1.0d0 - t_4))
    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 = (x2 * ((x1 * -12.0) - 6.0)) - x1;
	double t_2 = x1 * (x1 * x1);
	double t_3 = x2 * (3.0 - (2.0 * x2));
	double t_4 = 4.0 * t_3;
	double t_5 = 4.0 * (x1 * t_3);
	double t_6 = x1 * (x1 * 3.0);
	double t_7 = t_6 + (2.0 * x2);
	double t_8 = (x1 - t_7) / t_0;
	double t_9 = (x1 * x1) * (6.0 + (4.0 * t_8));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_1;
	} else if (x1 <= -4000.0) {
		tmp = x1 + (9.0 + (x1 + (t_2 + ((t_6 * ((t_7 - x1) / t_0)) - (t_0 * (t_9 - (x1 * 2.0)))))));
	} else if (x1 <= -8e-178) {
		tmp = (x2 * -6.0) - (x1 * (t_4 - -1.0));
	} else if (x1 <= 1e-198) {
		tmp = t_1;
	} else if (x1 <= 170.0) {
		tmp = x1 + ((3.0 * (((t_6 - (2.0 * x2)) - x1) / t_0)) + (x1 - t_5));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + (9.0 - ((((t_6 * t_8) + (t_0 * (t_5 + t_9))) - t_2) - x1));
	} else {
		tmp = x1 + (x1 * (1.0 - t_4));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = (x2 * ((x1 * -12.0) - 6.0)) - x1
	t_2 = x1 * (x1 * x1)
	t_3 = x2 * (3.0 - (2.0 * x2))
	t_4 = 4.0 * t_3
	t_5 = 4.0 * (x1 * t_3)
	t_6 = x1 * (x1 * 3.0)
	t_7 = t_6 + (2.0 * x2)
	t_8 = (x1 - t_7) / t_0
	t_9 = (x1 * x1) * (6.0 + (4.0 * t_8))
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = t_1
	elif x1 <= -4000.0:
		tmp = x1 + (9.0 + (x1 + (t_2 + ((t_6 * ((t_7 - x1) / t_0)) - (t_0 * (t_9 - (x1 * 2.0)))))))
	elif x1 <= -8e-178:
		tmp = (x2 * -6.0) - (x1 * (t_4 - -1.0))
	elif x1 <= 1e-198:
		tmp = t_1
	elif x1 <= 170.0:
		tmp = x1 + ((3.0 * (((t_6 - (2.0 * x2)) - x1) / t_0)) + (x1 - t_5))
	elif x1 <= 1.35e+154:
		tmp = x1 + (9.0 - ((((t_6 * t_8) + (t_0 * (t_5 + t_9))) - t_2) - x1))
	else:
		tmp = x1 + (x1 * (1.0 - t_4))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)) - x1)
	t_2 = Float64(x1 * Float64(x1 * x1))
	t_3 = Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))
	t_4 = Float64(4.0 * t_3)
	t_5 = Float64(4.0 * Float64(x1 * t_3))
	t_6 = Float64(x1 * Float64(x1 * 3.0))
	t_7 = Float64(t_6 + Float64(2.0 * x2))
	t_8 = Float64(Float64(x1 - t_7) / t_0)
	t_9 = Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_8)))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = t_1;
	elseif (x1 <= -4000.0)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_2 + Float64(Float64(t_6 * Float64(Float64(t_7 - x1) / t_0)) - Float64(t_0 * Float64(t_9 - Float64(x1 * 2.0))))))));
	elseif (x1 <= -8e-178)
		tmp = Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(t_4 - -1.0)));
	elseif (x1 <= 1e-198)
		tmp = t_1;
	elseif (x1 <= 170.0)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_6 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 - t_5)));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(9.0 - Float64(Float64(Float64(Float64(t_6 * t_8) + Float64(t_0 * Float64(t_5 + t_9))) - t_2) - x1)));
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 - t_4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = (x2 * ((x1 * -12.0) - 6.0)) - x1;
	t_2 = x1 * (x1 * x1);
	t_3 = x2 * (3.0 - (2.0 * x2));
	t_4 = 4.0 * t_3;
	t_5 = 4.0 * (x1 * t_3);
	t_6 = x1 * (x1 * 3.0);
	t_7 = t_6 + (2.0 * x2);
	t_8 = (x1 - t_7) / t_0;
	t_9 = (x1 * x1) * (6.0 + (4.0 * t_8));
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = t_1;
	elseif (x1 <= -4000.0)
		tmp = x1 + (9.0 + (x1 + (t_2 + ((t_6 * ((t_7 - x1) / t_0)) - (t_0 * (t_9 - (x1 * 2.0)))))));
	elseif (x1 <= -8e-178)
		tmp = (x2 * -6.0) - (x1 * (t_4 - -1.0));
	elseif (x1 <= 1e-198)
		tmp = t_1;
	elseif (x1 <= 170.0)
		tmp = x1 + ((3.0 * (((t_6 - (2.0 * x2)) - x1) / t_0)) + (x1 - t_5));
	elseif (x1 <= 1.35e+154)
		tmp = x1 + (9.0 - ((((t_6 * t_8) + (t_0 * (t_5 + t_9))) - t_2) - x1));
	else
		tmp = x1 + (x1 * (1.0 - t_4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(4.0 * t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(4.0 * N[(x1 * t$95$3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$6 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(N[(x1 - t$95$7), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$9 = N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], t$95$1, If[LessEqual[x1, -4000.0], N[(x1 + N[(9.0 + N[(x1 + N[(t$95$2 + N[(N[(t$95$6 * N[(N[(t$95$7 - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] - N[(t$95$0 * N[(t$95$9 - N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -8e-178], N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(t$95$4 - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1e-198], t$95$1, If[LessEqual[x1, 170.0], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$6 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 - t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(9.0 - N[(N[(N[(N[(t$95$6 * t$95$8), $MachinePrecision] + N[(t$95$0 * N[(t$95$5 + t$95$9), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * N[(1.0 - t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x1 < -5.60000000000000037e102 or -7.9999999999999996e-178 < x1 < 9.9999999999999991e-199

   1. Initial program 52.7%

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

   2. Taylor expanded in x1 around 0 39.5%

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

   3. Taylor expanded in x1 around 0 41.2%

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

      1. fma-def 41.2%

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

      2. fma-neg 41.2%

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

      3. fma-neg 41.2%

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

      4. metadata-eval 41.2%

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

      5. metadata-eval 41.2%

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

   5. Simplified 41.2%

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

   6. Taylor expanded in x1 around 0 41.2%

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

   7. Taylor expanded in x2 around 0 62.9%

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

   if -5.60000000000000037e102 < x1 < -4e3

   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 91.7%

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

      1. +-commutative 91.7%

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

      2. mul-1-neg 91.7%

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

      3. unsub-neg 91.7%

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

   4. Simplified 91.7%

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

   5. Taylor expanded in x1 around inf 91.7%

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

   6. Taylor expanded in x1 around inf 91.2%

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

      1. *-commutative 91.2%

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

   8. Simplified 91.2%

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

   if -4e3 < x1 < -7.9999999999999996e-178

   1. Initial program 99.1%

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

   2. Taylor expanded in x1 around 0 90.3%

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

   3. Taylor expanded in x1 around 0 91.0%

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

      1. fma-def 91.1%

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

      2. fma-neg 91.1%

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

      3. fma-neg 91.1%

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

      4. metadata-eval 91.1%

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

      5. metadata-eval 91.1%

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

   5. Simplified 91.1%

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

   6. Taylor expanded in x1 around 0 91.0%

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

   if 9.9999999999999991e-199 < x1 < 170

   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 84.6%

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

   if 170 < x1 < 1.35000000000000003e154

   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 73.0%

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

      1. +-commutative 73.0%

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

      2. mul-1-neg 73.0%

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

      3. unsub-neg 73.0%

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

   4. Simplified 73.0%

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

   5. Taylor expanded in x1 around 0 73.3%

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

   6. Taylor expanded in x1 around inf 73.3%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around inf 58.6%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right) - x1\\ \mathbf{elif}\;x1 \leq -4000:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - x1 \cdot 2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -8 \cdot 10^{-178}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq 10^{-198}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right) - x1\\ \mathbf{elif}\;x1 \leq 170:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(9 - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \end{array} \]

Alternative 13: 69.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x2 \cdot \left(x1 \cdot -12 - 6\right) - x1\\ t_3 := x2 \cdot \left(3 - 2 \cdot x2\right)\\ t_4 := x1 - \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - t_0\right)}{t_1} - \left(x1 - \left(\left(t_1 \cdot \left(4 \cdot \left(x1 \cdot t_3\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(t_0 + 2 \cdot x2\right)}{t_1}\right)\right) - t_0 \cdot \left(2 \cdot x2\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x1 \leq -6.5 \cdot 10^{-179}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x1 \leq 9 \cdot 10^{-199}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot t_3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (- (* x2 (- (* x1 -12.0) 6.0)) x1))
        (t_3 (* x2 (- 3.0 (* 2.0 x2))))
        (t_4
         (-
          x1
          (-
           (* 3.0 (/ (+ x1 (- (* 2.0 x2) t_0)) t_1))
           (-
            x1
            (-
             (-
              (*
               t_1
               (+
                (* 4.0 (* x1 t_3))
                (*
                 (* x1 x1)
                 (+ 6.0 (* 4.0 (/ (- x1 (+ t_0 (* 2.0 x2))) t_1))))))
              (* t_0 (* 2.0 x2)))
             (* x1 (* x1 x1))))))))
   (if (<= x1 -5.6e+102)
     t_2
     (if (<= x1 -6.5e-179)
       t_4
       (if (<= x1 9e-199)
         t_2
         (if (<= x1 1.35e+154) t_4 (+ x1 (* x1 (- 1.0 (* 4.0 t_3))))))))))

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 * ((x1 * -12.0) - 6.0)) - x1;
	double t_3 = x2 * (3.0 - (2.0 * x2));
	double t_4 = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_0)) / t_1)) - (x1 - (((t_1 * ((4.0 * (x1 * t_3)) + ((x1 * x1) * (6.0 + (4.0 * ((x1 - (t_0 + (2.0 * x2))) / t_1)))))) - (t_0 * (2.0 * x2))) - (x1 * (x1 * x1)))));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_2;
	} else if (x1 <= -6.5e-179) {
		tmp = t_4;
	} else if (x1 <= 9e-199) {
		tmp = t_2;
	} else if (x1 <= 1.35e+154) {
		tmp = t_4;
	} else {
		tmp = x1 + (x1 * (1.0 - (4.0 * t_3)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = (x2 * ((x1 * (-12.0d0)) - 6.0d0)) - x1
    t_3 = x2 * (3.0d0 - (2.0d0 * x2))
    t_4 = x1 - ((3.0d0 * ((x1 + ((2.0d0 * x2) - t_0)) / t_1)) - (x1 - (((t_1 * ((4.0d0 * (x1 * t_3)) + ((x1 * x1) * (6.0d0 + (4.0d0 * ((x1 - (t_0 + (2.0d0 * x2))) / t_1)))))) - (t_0 * (2.0d0 * x2))) - (x1 * (x1 * x1)))))
    if (x1 <= (-5.6d+102)) then
        tmp = t_2
    else if (x1 <= (-6.5d-179)) then
        tmp = t_4
    else if (x1 <= 9d-199) then
        tmp = t_2
    else if (x1 <= 1.35d+154) then
        tmp = t_4
    else
        tmp = x1 + (x1 * (1.0d0 - (4.0d0 * t_3)))
    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 * ((x1 * -12.0) - 6.0)) - x1;
	double t_3 = x2 * (3.0 - (2.0 * x2));
	double t_4 = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_0)) / t_1)) - (x1 - (((t_1 * ((4.0 * (x1 * t_3)) + ((x1 * x1) * (6.0 + (4.0 * ((x1 - (t_0 + (2.0 * x2))) / t_1)))))) - (t_0 * (2.0 * x2))) - (x1 * (x1 * x1)))));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_2;
	} else if (x1 <= -6.5e-179) {
		tmp = t_4;
	} else if (x1 <= 9e-199) {
		tmp = t_2;
	} else if (x1 <= 1.35e+154) {
		tmp = t_4;
	} else {
		tmp = x1 + (x1 * (1.0 - (4.0 * t_3)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = (x2 * ((x1 * -12.0) - 6.0)) - x1
	t_3 = x2 * (3.0 - (2.0 * x2))
	t_4 = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_0)) / t_1)) - (x1 - (((t_1 * ((4.0 * (x1 * t_3)) + ((x1 * x1) * (6.0 + (4.0 * ((x1 - (t_0 + (2.0 * x2))) / t_1)))))) - (t_0 * (2.0 * x2))) - (x1 * (x1 * x1)))))
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = t_2
	elif x1 <= -6.5e-179:
		tmp = t_4
	elif x1 <= 9e-199:
		tmp = t_2
	elif x1 <= 1.35e+154:
		tmp = t_4
	else:
		tmp = x1 + (x1 * (1.0 - (4.0 * t_3)))
	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(x2 * Float64(Float64(x1 * -12.0) - 6.0)) - x1)
	t_3 = Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))
	t_4 = Float64(x1 - Float64(Float64(3.0 * Float64(Float64(x1 + Float64(Float64(2.0 * x2) - t_0)) / t_1)) - Float64(x1 - Float64(Float64(Float64(t_1 * Float64(Float64(4.0 * Float64(x1 * t_3)) + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * Float64(Float64(x1 - Float64(t_0 + Float64(2.0 * x2))) / t_1)))))) - Float64(t_0 * Float64(2.0 * x2))) - Float64(x1 * Float64(x1 * x1))))))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = t_2;
	elseif (x1 <= -6.5e-179)
		tmp = t_4;
	elseif (x1 <= 9e-199)
		tmp = t_2;
	elseif (x1 <= 1.35e+154)
		tmp = t_4;
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 - Float64(4.0 * t_3))));
	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 * ((x1 * -12.0) - 6.0)) - x1;
	t_3 = x2 * (3.0 - (2.0 * x2));
	t_4 = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_0)) / t_1)) - (x1 - (((t_1 * ((4.0 * (x1 * t_3)) + ((x1 * x1) * (6.0 + (4.0 * ((x1 - (t_0 + (2.0 * x2))) / t_1)))))) - (t_0 * (2.0 * x2))) - (x1 * (x1 * x1)))));
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = t_2;
	elseif (x1 <= -6.5e-179)
		tmp = t_4;
	elseif (x1 <= 9e-199)
		tmp = t_2;
	elseif (x1 <= 1.35e+154)
		tmp = t_4;
	else
		tmp = x1 + (x1 * (1.0 - (4.0 * t_3)));
	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[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$3 = N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 - N[(N[(3.0 * N[(N[(x1 + N[(N[(2.0 * x2), $MachinePrecision] - t$95$0), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(x1 - N[(N[(N[(t$95$1 * N[(N[(4.0 * N[(x1 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * N[(N[(x1 - N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$0 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], t$95$2, If[LessEqual[x1, -6.5e-179], t$95$4, If[LessEqual[x1, 9e-199], t$95$2, If[LessEqual[x1, 1.35e+154], t$95$4, N[(x1 + N[(x1 * N[(1.0 - N[(4.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.60000000000000037e102 or -6.49999999999999996e-179 < x1 < 8.99999999999999995e-199

   1. Initial program 52.7%

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

   2. Taylor expanded in x1 around 0 39.5%

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

   3. Taylor expanded in x1 around 0 41.2%

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

      1. fma-def 41.2%

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

      2. fma-neg 41.2%

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

      3. fma-neg 41.2%

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

      4. metadata-eval 41.2%

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

      5. metadata-eval 41.2%

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

   5. Simplified 41.2%

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

   6. Taylor expanded in x1 around 0 41.2%

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

   7. Taylor expanded in x2 around 0 62.9%

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

   if -5.60000000000000037e102 < x1 < -6.49999999999999996e-179 or 8.99999999999999995e-199 < 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 0 90.8%

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

      1. +-commutative 90.8%

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

      2. mul-1-neg 90.8%

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

      3. unsub-neg 90.8%

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

   4. Simplified 90.8%

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

   5. Taylor expanded in x1 around 0 83.6%

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

   6. Taylor expanded in x1 around 0 83.0%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around inf 58.6%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right) - x1\\ \mathbf{elif}\;x1 \leq -6.5 \cdot 10^{-179}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} - \left(x1 - \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right) - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 9 \cdot 10^{-199}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right) - x1\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} - \left(x1 - \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right) - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \end{array} \]

Alternative 14: 70.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x2 \cdot \left(3 - 2 \cdot x2\right)\\ t_2 := 4 \cdot t_1\\ t_3 := x2 \cdot \left(x1 \cdot -12 - 6\right) - x1\\ t_4 := x1 \cdot \left(x1 \cdot 3\right)\\ t_5 := t_4 + 2 \cdot x2\\ t_6 := x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_4 \cdot \frac{t_5 - x1}{t_0} - t_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - t_5}{t_0}\right) - x1 \cdot 2\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x1 \leq -4000:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x1 \leq -1.8 \cdot 10^{-175}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(t_2 - -1\right)\\ \mathbf{elif}\;x1 \leq 7 \cdot 10^{-199}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x1 \leq 3.8 \cdot 10^{+47}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_4 - 2 \cdot x2\right) - x1}{t_0} + \left(x1 - 4 \cdot \left(x1 \cdot t_1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - t_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x2 (- 3.0 (* 2.0 x2))))
        (t_2 (* 4.0 t_1))
        (t_3 (- (* x2 (- (* x1 -12.0) 6.0)) x1))
        (t_4 (* x1 (* x1 3.0)))
        (t_5 (+ t_4 (* 2.0 x2)))
        (t_6
         (+
          x1
          (+
           9.0
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (-
              (* t_4 (/ (- t_5 x1) t_0))
              (*
               t_0
               (-
                (* (* x1 x1) (+ 6.0 (* 4.0 (/ (- x1 t_5) t_0))))
                (* x1 2.0))))))))))
   (if (<= x1 -5.6e+102)
     t_3
     (if (<= x1 -4000.0)
       t_6
       (if (<= x1 -1.8e-175)
         (- (* x2 -6.0) (* x1 (- t_2 -1.0)))
         (if (<= x1 7e-199)
           t_3
           (if (<= x1 3.8e+47)
             (+
              x1
              (+
               (* 3.0 (/ (- (- t_4 (* 2.0 x2)) x1) t_0))
               (- x1 (* 4.0 (* x1 t_1)))))
             (if (<= x1 1.35e+154) t_6 (+ x1 (* x1 (- 1.0 t_2)))))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x2 * (3.0 - (2.0 * x2));
	double t_2 = 4.0 * t_1;
	double t_3 = (x2 * ((x1 * -12.0) - 6.0)) - x1;
	double t_4 = x1 * (x1 * 3.0);
	double t_5 = t_4 + (2.0 * x2);
	double t_6 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_4 * ((t_5 - x1) / t_0)) - (t_0 * (((x1 * x1) * (6.0 + (4.0 * ((x1 - t_5) / t_0)))) - (x1 * 2.0)))))));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_3;
	} else if (x1 <= -4000.0) {
		tmp = t_6;
	} else if (x1 <= -1.8e-175) {
		tmp = (x2 * -6.0) - (x1 * (t_2 - -1.0));
	} else if (x1 <= 7e-199) {
		tmp = t_3;
	} else if (x1 <= 3.8e+47) {
		tmp = x1 + ((3.0 * (((t_4 - (2.0 * x2)) - x1) / t_0)) + (x1 - (4.0 * (x1 * t_1))));
	} else if (x1 <= 1.35e+154) {
		tmp = t_6;
	} else {
		tmp = x1 + (x1 * (1.0 - t_2));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x2 * (3.0d0 - (2.0d0 * x2))
    t_2 = 4.0d0 * t_1
    t_3 = (x2 * ((x1 * (-12.0d0)) - 6.0d0)) - x1
    t_4 = x1 * (x1 * 3.0d0)
    t_5 = t_4 + (2.0d0 * x2)
    t_6 = x1 + (9.0d0 + (x1 + ((x1 * (x1 * x1)) + ((t_4 * ((t_5 - x1) / t_0)) - (t_0 * (((x1 * x1) * (6.0d0 + (4.0d0 * ((x1 - t_5) / t_0)))) - (x1 * 2.0d0)))))))
    if (x1 <= (-5.6d+102)) then
        tmp = t_3
    else if (x1 <= (-4000.0d0)) then
        tmp = t_6
    else if (x1 <= (-1.8d-175)) then
        tmp = (x2 * (-6.0d0)) - (x1 * (t_2 - (-1.0d0)))
    else if (x1 <= 7d-199) then
        tmp = t_3
    else if (x1 <= 3.8d+47) then
        tmp = x1 + ((3.0d0 * (((t_4 - (2.0d0 * x2)) - x1) / t_0)) + (x1 - (4.0d0 * (x1 * t_1))))
    else if (x1 <= 1.35d+154) then
        tmp = t_6
    else
        tmp = x1 + (x1 * (1.0d0 - t_2))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x2 * (3.0 - (2.0 * x2));
	double t_2 = 4.0 * t_1;
	double t_3 = (x2 * ((x1 * -12.0) - 6.0)) - x1;
	double t_4 = x1 * (x1 * 3.0);
	double t_5 = t_4 + (2.0 * x2);
	double t_6 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_4 * ((t_5 - x1) / t_0)) - (t_0 * (((x1 * x1) * (6.0 + (4.0 * ((x1 - t_5) / t_0)))) - (x1 * 2.0)))))));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_3;
	} else if (x1 <= -4000.0) {
		tmp = t_6;
	} else if (x1 <= -1.8e-175) {
		tmp = (x2 * -6.0) - (x1 * (t_2 - -1.0));
	} else if (x1 <= 7e-199) {
		tmp = t_3;
	} else if (x1 <= 3.8e+47) {
		tmp = x1 + ((3.0 * (((t_4 - (2.0 * x2)) - x1) / t_0)) + (x1 - (4.0 * (x1 * t_1))));
	} else if (x1 <= 1.35e+154) {
		tmp = t_6;
	} else {
		tmp = x1 + (x1 * (1.0 - t_2));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x2 * (3.0 - (2.0 * x2))
	t_2 = 4.0 * t_1
	t_3 = (x2 * ((x1 * -12.0) - 6.0)) - x1
	t_4 = x1 * (x1 * 3.0)
	t_5 = t_4 + (2.0 * x2)
	t_6 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_4 * ((t_5 - x1) / t_0)) - (t_0 * (((x1 * x1) * (6.0 + (4.0 * ((x1 - t_5) / t_0)))) - (x1 * 2.0)))))))
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = t_3
	elif x1 <= -4000.0:
		tmp = t_6
	elif x1 <= -1.8e-175:
		tmp = (x2 * -6.0) - (x1 * (t_2 - -1.0))
	elif x1 <= 7e-199:
		tmp = t_3
	elif x1 <= 3.8e+47:
		tmp = x1 + ((3.0 * (((t_4 - (2.0 * x2)) - x1) / t_0)) + (x1 - (4.0 * (x1 * t_1))))
	elif x1 <= 1.35e+154:
		tmp = t_6
	else:
		tmp = x1 + (x1 * (1.0 - t_2))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))
	t_2 = Float64(4.0 * t_1)
	t_3 = Float64(Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)) - x1)
	t_4 = Float64(x1 * Float64(x1 * 3.0))
	t_5 = Float64(t_4 + Float64(2.0 * x2))
	t_6 = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_4 * Float64(Float64(t_5 - x1) / t_0)) - Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * Float64(Float64(x1 - t_5) / t_0)))) - Float64(x1 * 2.0))))))))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = t_3;
	elseif (x1 <= -4000.0)
		tmp = t_6;
	elseif (x1 <= -1.8e-175)
		tmp = Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(t_2 - -1.0)));
	elseif (x1 <= 7e-199)
		tmp = t_3;
	elseif (x1 <= 3.8e+47)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_4 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 - Float64(4.0 * Float64(x1 * t_1)))));
	elseif (x1 <= 1.35e+154)
		tmp = t_6;
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 - t_2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x2 * (3.0 - (2.0 * x2));
	t_2 = 4.0 * t_1;
	t_3 = (x2 * ((x1 * -12.0) - 6.0)) - x1;
	t_4 = x1 * (x1 * 3.0);
	t_5 = t_4 + (2.0 * x2);
	t_6 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_4 * ((t_5 - x1) / t_0)) - (t_0 * (((x1 * x1) * (6.0 + (4.0 * ((x1 - t_5) / t_0)))) - (x1 * 2.0)))))));
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = t_3;
	elseif (x1 <= -4000.0)
		tmp = t_6;
	elseif (x1 <= -1.8e-175)
		tmp = (x2 * -6.0) - (x1 * (t_2 - -1.0));
	elseif (x1 <= 7e-199)
		tmp = t_3;
	elseif (x1 <= 3.8e+47)
		tmp = x1 + ((3.0 * (((t_4 - (2.0 * x2)) - x1) / t_0)) + (x1 - (4.0 * (x1 * t_1))));
	elseif (x1 <= 1.35e+154)
		tmp = t_6;
	else
		tmp = x1 + (x1 * (1.0 - t_2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$4 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(x1 + N[(9.0 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$4 * N[(N[(t$95$5 - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] - N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * N[(N[(x1 - t$95$5), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], t$95$3, If[LessEqual[x1, -4000.0], t$95$6, If[LessEqual[x1, -1.8e-175], N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(t$95$2 - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7e-199], t$95$3, If[LessEqual[x1, 3.8e+47], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$4 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 - N[(4.0 * N[(x1 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], t$95$6, N[(x1 + N[(x1 * N[(1.0 - t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -5.60000000000000037e102 or -1.8e-175 < x1 < 6.9999999999999998e-199

   1. Initial program 52.7%

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

   2. Taylor expanded in x1 around 0 39.5%

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

   3. Taylor expanded in x1 around 0 41.2%

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

      1. fma-def 41.2%

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

      2. fma-neg 41.2%

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

      3. fma-neg 41.2%

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

      4. metadata-eval 41.2%

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

      5. metadata-eval 41.2%

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

   5. Simplified 41.2%

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

   6. Taylor expanded in x1 around 0 41.2%

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

   7. Taylor expanded in x2 around 0 62.9%

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

   if -5.60000000000000037e102 < x1 < -4e3 or 3.8000000000000003e47 < x1 < 1.35000000000000003e154

   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 91.2%

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

      1. +-commutative 91.2%

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

      2. mul-1-neg 91.2%

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

      3. unsub-neg 91.2%

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

   4. Simplified 91.2%

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

   5. Taylor expanded in x1 around inf 91.2%

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

   6. Taylor expanded in x1 around inf 95.6%

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

      1. *-commutative 95.6%

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

   8. Simplified 95.6%

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

   if -4e3 < x1 < -1.8e-175

   1. Initial program 99.1%

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

   2. Taylor expanded in x1 around 0 90.3%

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

   3. Taylor expanded in x1 around 0 91.0%

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

      1. fma-def 91.1%

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

      2. fma-neg 91.1%

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

      3. fma-neg 91.1%

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

      4. metadata-eval 91.1%

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

      5. metadata-eval 91.1%

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

   5. Simplified 91.1%

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

   6. Taylor expanded in x1 around 0 91.0%

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

   if 6.9999999999999998e-199 < x1 < 3.8000000000000003e47

   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 71.0%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around inf 58.6%

      \[\leadsto x1 + \color{blue}{x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right) - x1\\ \mathbf{elif}\;x1 \leq -4000:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - x1 \cdot 2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.8 \cdot 10^{-175}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq 7 \cdot 10^{-199}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right) - x1\\ \mathbf{elif}\;x1 \leq 3.8 \cdot 10^{+47}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - x1 \cdot 2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \end{array} \]

Alternative 15: 59.6% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -6.3 \cdot 10^{+84} \lor \neg \left(x1 \leq -6.2 \cdot 10^{-178}\right) \land x1 \leq 1.15 \cdot 10^{-199}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -6.3e+84) (and (not (<= x1 -6.2e-178)) (<= x1 1.15e-199)))
   (- (* x2 (- (* x1 -12.0) 6.0)) x1)
   (- (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))) -1.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -6.3e+84) || (!(x1 <= -6.2e-178) && (x1 <= 1.15e-199))) {
		tmp = (x2 * ((x1 * -12.0) - 6.0)) - x1;
	} else {
		tmp = (x2 * -6.0) - (x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-6.3d+84)) .or. (.not. (x1 <= (-6.2d-178))) .and. (x1 <= 1.15d-199)) then
        tmp = (x2 * ((x1 * (-12.0d0)) - 6.0d0)) - x1
    else
        tmp = (x2 * (-6.0d0)) - (x1 * ((4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))) - (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -6.3e+84) || (!(x1 <= -6.2e-178) && (x1 <= 1.15e-199))) {
		tmp = (x2 * ((x1 * -12.0) - 6.0)) - x1;
	} else {
		tmp = (x2 * -6.0) - (x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - -1.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -6.3e+84) or (not (x1 <= -6.2e-178) and (x1 <= 1.15e-199)):
		tmp = (x2 * ((x1 * -12.0) - 6.0)) - x1
	else:
		tmp = (x2 * -6.0) - (x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - -1.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -6.3e+84) || (!(x1 <= -6.2e-178) && (x1 <= 1.15e-199)))
		tmp = Float64(Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)) - x1);
	else
		tmp = Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))) - -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -6.3e+84) || (~((x1 <= -6.2e-178)) && (x1 <= 1.15e-199)))
		tmp = (x2 * ((x1 * -12.0) - 6.0)) - x1;
	else
		tmp = (x2 * -6.0) - (x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -6.3e+84], And[N[Not[LessEqual[x1, -6.2e-178]], $MachinePrecision], LessEqual[x1, 1.15e-199]]], N[(N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -6.30000000000000013e84 or -6.1999999999999999e-178 < x1 < 1.1500000000000001e-199

   1. Initial program 53.7%

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

   2. Taylor expanded in x1 around 0 38.6%

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

   3. Taylor expanded in x1 around 0 40.3%

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

      1. fma-def 40.4%

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

      2. fma-neg 40.4%

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

      3. fma-neg 40.4%

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

      4. metadata-eval 40.4%

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

      5. metadata-eval 40.4%

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

   5. Simplified 40.4%

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

   6. Taylor expanded in x1 around 0 40.3%

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

   7. Taylor expanded in x2 around 0 61.6%

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

   if -6.30000000000000013e84 < x1 < -6.1999999999999999e-178 or 1.1500000000000001e-199 < x1

   1. Initial program 83.2%

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

   2. Taylor expanded in x1 around 0 50.4%

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

   3. Taylor expanded in x1 around 0 59.5%

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

      1. fma-def 59.6%

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

      2. fma-neg 59.6%

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

      3. fma-neg 59.6%

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

      4. metadata-eval 59.6%

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

      5. metadata-eval 59.6%

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

   5. Simplified 59.6%

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

   6. Taylor expanded in x1 around 0 59.5%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6.3 \cdot 10^{+84} \lor \neg \left(x1 \leq -6.2 \cdot 10^{-178}\right) \land x1 \leq 1.15 \cdot 10^{-199}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - -1\right)\\ \end{array} \]

Alternative 16: 54.8% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.8 \cdot 10^{+87} \lor \neg \left(x1 \leq -1.45 \cdot 10^{-99}\right) \land x1 \leq 1.02 \cdot 10^{-123}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -2.8e+87) (and (not (<= x1 -1.45e-99)) (<= x1 1.02e-123)))
   (- (* x2 (- (* x1 -12.0) 6.0)) x1)
   (* x1 (+ -1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -2.8e+87) || (!(x1 <= -1.45e-99) && (x1 <= 1.02e-123))) {
		tmp = (x2 * ((x1 * -12.0) - 6.0)) - x1;
	} else {
		tmp = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-2.8d+87)) .or. (.not. (x1 <= (-1.45d-99))) .and. (x1 <= 1.02d-123)) then
        tmp = (x2 * ((x1 * (-12.0d0)) - 6.0d0)) - x1
    else
        tmp = x1 * ((-1.0d0) + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -2.8e+87) || (!(x1 <= -1.45e-99) && (x1 <= 1.02e-123))) {
		tmp = (x2 * ((x1 * -12.0) - 6.0)) - x1;
	} else {
		tmp = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -2.8e+87) or (not (x1 <= -1.45e-99) and (x1 <= 1.02e-123)):
		tmp = (x2 * ((x1 * -12.0) - 6.0)) - x1
	else:
		tmp = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -2.8e+87) || (!(x1 <= -1.45e-99) && (x1 <= 1.02e-123)))
		tmp = Float64(Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)) - x1);
	else
		tmp = Float64(x1 * Float64(-1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -2.8e+87) || (~((x1 <= -1.45e-99)) && (x1 <= 1.02e-123)))
		tmp = (x2 * ((x1 * -12.0) - 6.0)) - x1;
	else
		tmp = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -2.8e+87], And[N[Not[LessEqual[x1, -1.45e-99]], $MachinePrecision], LessEqual[x1, 1.02e-123]]], N[(N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], N[(x1 * N[(-1.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -2.80000000000000015e87 or -1.44999999999999993e-99 < x1 < 1.02e-123

   1. Initial program 66.9%

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

   2. Taylor expanded in x1 around 0 53.1%

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

   3. Taylor expanded in x1 around 0 54.5%

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

      1. fma-def 54.5%

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

      2. fma-neg 54.5%

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

      3. fma-neg 54.5%

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

      4. metadata-eval 54.5%

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

      5. metadata-eval 54.5%

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

   5. Simplified 54.5%

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

   6. Taylor expanded in x1 around 0 54.5%

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

   7. Taylor expanded in x2 around 0 67.4%

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

   if -2.80000000000000015e87 < x1 < -1.44999999999999993e-99 or 1.02e-123 < x1

   1. Initial program 78.8%

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

   2. Taylor expanded in x1 around 0 39.8%

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

   3. Taylor expanded in x1 around 0 51.3%

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

      1. fma-def 51.3%

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

      2. fma-neg 51.3%

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

      3. fma-neg 51.3%

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

      4. metadata-eval 51.3%

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

      5. metadata-eval 51.3%

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

   5. Simplified 51.3%

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

   6. Taylor expanded in x1 around inf 45.3%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.8 \cdot 10^{+87} \lor \neg \left(x1 \leq -1.45 \cdot 10^{-99}\right) \land x1 \leq 1.02 \cdot 10^{-123}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \end{array} \]

Alternative 17: 32.4% accurate, 13.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -1.65 \cdot 10^{-169}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 5.8 \cdot 10^{-144}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 -1.65e-169)
   (* x2 -6.0)
   (if (<= x2 5.8e-144) (- x1) (+ x1 (* x2 -6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= -1.65e-169) {
		tmp = x2 * -6.0;
	} else if (x2 <= 5.8e-144) {
		tmp = -x1;
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x2 <= (-1.65d-169)) then
        tmp = x2 * (-6.0d0)
    else if (x2 <= 5.8d-144) then
        tmp = -x1
    else
        tmp = x1 + (x2 * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x2 <= -1.65e-169) {
		tmp = x2 * -6.0;
	} else if (x2 <= 5.8e-144) {
		tmp = -x1;
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= -1.65e-169:
		tmp = x2 * -6.0
	elif x2 <= 5.8e-144:
		tmp = -x1
	else:
		tmp = x1 + (x2 * -6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= -1.65e-169)
		tmp = Float64(x2 * -6.0);
	elseif (x2 <= 5.8e-144)
		tmp = Float64(-x1);
	else
		tmp = Float64(x1 + Float64(x2 * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= -1.65e-169)
		tmp = x2 * -6.0;
	elseif (x2 <= 5.8e-144)
		tmp = -x1;
	else
		tmp = x1 + (x2 * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, -1.65e-169], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x2, 5.8e-144], (-x1), N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -1.65000000000000013e-169

   1. Initial program 76.0%

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

   2. Taylor expanded in x1 around 0 45.8%

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

   3. Taylor expanded in x1 around 0 35.8%

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

      1. *-commutative 35.8%

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

   5. Simplified 35.8%

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

   6. Taylor expanded in x1 around 0 36.0%

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

   if -1.65000000000000013e-169 < x2 < 5.8000000000000004e-144

   1. Initial program 77.6%

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

   2. Taylor expanded in x1 around 0 50.5%

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

   3. Taylor expanded in x1 around 0 51.8%

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

      1. fma-def 51.8%

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

      2. fma-neg 51.8%

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

      3. fma-neg 51.8%

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

      4. metadata-eval 51.8%

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

      5. metadata-eval 51.8%

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

   5. Simplified 51.8%

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

   6. Taylor expanded in x2 around 0 47.6%

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

      1. distribute-rgt1-in 47.6%

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

      2. metadata-eval 47.6%

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

      3. neg-mul-1 47.6%

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

   8. Simplified 47.6%

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

   if 5.8000000000000004e-144 < x2

   1. Initial program 67.4%

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

   2. Taylor expanded in x1 around 0 44.3%

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

   3. Taylor expanded in x1 around 0 32.7%

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

      1. *-commutative 32.7%

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

   5. Simplified 32.7%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.65 \cdot 10^{-169}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 5.8 \cdot 10^{-144}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \]

Alternative 18: 45.0% accurate, 14.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.0%

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

2. Taylor expanded in x1 around 0 46.3%

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

3. Taylor expanded in x1 around 0 52.9%

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

   1. fma-def 52.9%

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

   2. fma-neg 52.9%

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

   3. fma-neg 52.9%

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

   4. metadata-eval 52.9%

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

   5. metadata-eval 52.9%

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

5. Simplified 52.9%

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

6. Taylor expanded in x1 around 0 52.9%

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

7. Taylor expanded in x2 around 0 45.2%

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

8. Final simplification 45.2%

   \[\leadsto x2 \cdot \left(x1 \cdot -12 - 6\right) - x1 \]

Alternative 19: 32.0% accurate, 17.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -4 \cdot 10^{-168} \lor \neg \left(x2 \leq 4.3 \cdot 10^{-131}\right):\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -4e-168) (not (<= x2 4.3e-131))) (* x2 -6.0) (- x1)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -4e-168) || !(x2 <= 4.3e-131)) {
		tmp = x2 * -6.0;
	} else {
		tmp = -x1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-4d-168)) .or. (.not. (x2 <= 4.3d-131))) then
        tmp = x2 * (-6.0d0)
    else
        tmp = -x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -4e-168) || !(x2 <= 4.3e-131)) {
		tmp = x2 * -6.0;
	} else {
		tmp = -x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -4e-168) or not (x2 <= 4.3e-131):
		tmp = x2 * -6.0
	else:
		tmp = -x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -4e-168) || !(x2 <= 4.3e-131))
		tmp = Float64(x2 * -6.0);
	else
		tmp = Float64(-x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -4e-168) || ~((x2 <= 4.3e-131)))
		tmp = x2 * -6.0;
	else
		tmp = -x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -4e-168], N[Not[LessEqual[x2, 4.3e-131]], $MachinePrecision]], N[(x2 * -6.0), $MachinePrecision], (-x1)]

Derivation

1. Split input into 2 regimes

2. if x2 < -4.0000000000000002e-168 or 4.30000000000000019e-131 < x2

   1. Initial program 72.1%

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

   2. Taylor expanded in x1 around 0 45.7%

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

   3. Taylor expanded in x1 around 0 34.6%

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

      1. *-commutative 34.6%

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

   5. Simplified 34.6%

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

   6. Taylor expanded in x1 around 0 34.4%

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

   if -4.0000000000000002e-168 < x2 < 4.30000000000000019e-131

   1. Initial program 75.5%

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

   2. Taylor expanded in x1 around 0 48.2%

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

   3. Taylor expanded in x1 around 0 49.5%

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

      1. fma-def 49.5%

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

      2. fma-neg 49.5%

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

      3. fma-neg 49.5%

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

      4. metadata-eval 49.5%

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

      5. metadata-eval 49.5%

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

   5. Simplified 49.5%

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

   6. Taylor expanded in x2 around 0 45.5%

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

      1. distribute-rgt1-in 45.5%

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

      2. metadata-eval 45.5%

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

      3. neg-mul-1 45.5%

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

   8. Simplified 45.5%

      \[\leadsto \color{blue}{-x1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -4 \cdot 10^{-168} \lor \neg \left(x2 \leq 4.3 \cdot 10^{-131}\right):\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \]

Alternative 20: 38.6% accurate, 25.4× speedup

Math

\[\begin{array}{l} \\ x2 \cdot -6 - x1 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.0%

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

2. Taylor expanded in x1 around 0 46.3%

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

3. Taylor expanded in x1 around 0 52.9%

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

   1. fma-def 52.9%

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

   2. fma-neg 52.9%

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

   3. fma-neg 52.9%

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

   4. metadata-eval 52.9%

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

   5. metadata-eval 52.9%

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

5. Simplified 52.9%

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

6. Taylor expanded in x1 around 0 52.9%

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

7. Taylor expanded in x2 around 0 39.7%

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

   1. mul-1-neg 39.7%

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

9. Simplified 39.7%

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

10. Final simplification 39.7%

    \[\leadsto x2 \cdot -6 - x1 \]

Alternative 21: 13.4% 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 73.0%

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

2. Taylor expanded in x1 around 0 46.3%

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

3. Taylor expanded in x1 around 0 52.9%

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

   1. fma-def 52.9%

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

   2. fma-neg 52.9%

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

   3. fma-neg 52.9%

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

   4. metadata-eval 52.9%

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

   5. metadata-eval 52.9%

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

5. Simplified 52.9%

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

6. Taylor expanded in x2 around 0 14.4%

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

   1. distribute-rgt1-in 14.4%

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

   2. metadata-eval 14.4%

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

   3. neg-mul-1 14.4%

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

8. Simplified 14.4%

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

9. Final simplification 14.4%

   \[\leadsto -x1 \]

Alternative 22: 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 73.0%

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

2. Taylor expanded in x1 around 0 46.3%

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

3. Taylor expanded in x1 around 0 27.5%

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

   1. *-commutative 27.5%

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

5. Simplified 27.5%

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

6. Taylor expanded in x1 around inf 3.3%

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

7. Final simplification 3.3%

   \[\leadsto x1 \]

Reproduce

herbie shell --seed 2023315 
(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))))))