Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.2% → 99.5%

Time: 57.6s

Alternatives: 24

Speedup: 3.2×

• 46.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 70.2% 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

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+156}:\\ \;\;\;\;x1 + \left(\left(x1 + -4 \cdot {x1}^{5}\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+123}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{x1 \cdot \left(x1 \cdot 3\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \mathsf{fma}\left(x1, x1 \cdot \frac{t_0}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{3}}, \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{t_0}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(x1 \cdot \left(-6 + \frac{t_0}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{2}}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 + 3\right) - x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (fma x1 (* x1 3.0) (fma 2.0 x2 (- x1)))))
   (if (<= x1 -1e+156)
     (+ x1 (+ (+ x1 (* -4.0 (pow x1 5.0))) (* 3.0 (* x2 -2.0))))
     (if (<= x1 2e+123)
       (+
        x1
        (fma
         3.0
         (/ (- (* x1 (* x1 3.0)) (fma 2.0 x2 x1)) (fma x1 x1 1.0))
         (fma
          x1
          (* x1 (/ t_0 (/ (fma x1 x1 1.0) 3.0)))
          (*
           (fma x1 x1 1.0)
           (+
            x1
            (+
             (* x1 (* x1 -6.0))
             (*
              (/ t_0 (fma x1 x1 1.0))
              (+
               (* x1 (+ -6.0 (/ t_0 (/ (fma x1 x1 1.0) 2.0))))
               (* (* x1 x1) 4.0)))))))))
       (+ x1 (+ x1 (* 3.0 (- (* (* x1 x1) (+ x1 3.0)) x1))))))))

C

double code(double x1, double x2) {
	double t_0 = fma(x1, (x1 * 3.0), fma(2.0, x2, -x1));
	double tmp;
	if (x1 <= -1e+156) {
		tmp = x1 + ((x1 + (-4.0 * pow(x1, 5.0))) + (3.0 * (x2 * -2.0)));
	} else if (x1 <= 2e+123) {
		tmp = x1 + fma(3.0, (((x1 * (x1 * 3.0)) - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), fma(x1, (x1 * (t_0 / (fma(x1, x1, 1.0) / 3.0))), (fma(x1, x1, 1.0) * (x1 + ((x1 * (x1 * -6.0)) + ((t_0 / fma(x1, x1, 1.0)) * ((x1 * (-6.0 + (t_0 / (fma(x1, x1, 1.0) / 2.0)))) + ((x1 * x1) * 4.0))))))));
	} else {
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = fma(x1, Float64(x1 * 3.0), fma(2.0, x2, Float64(-x1)))
	tmp = 0.0
	if (x1 <= -1e+156)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(-4.0 * (x1 ^ 5.0))) + Float64(3.0 * Float64(x2 * -2.0))));
	elseif (x1 <= 2e+123)
		tmp = Float64(x1 + fma(3.0, Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), fma(x1, Float64(x1 * Float64(t_0 / Float64(fma(x1, x1, 1.0) / 3.0))), Float64(fma(x1, x1, 1.0) * Float64(x1 + Float64(Float64(x1 * Float64(x1 * -6.0)) + Float64(Float64(t_0 / fma(x1, x1, 1.0)) * Float64(Float64(x1 * Float64(-6.0 + Float64(t_0 / Float64(fma(x1, x1, 1.0) / 2.0)))) + Float64(Float64(x1 * x1) * 4.0)))))))));
	else
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(Float64(Float64(x1 * x1) * Float64(x1 + 3.0)) - x1))));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision] + N[(2.0 * x2 + (-x1)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1e+156], N[(x1 + N[(N[(x1 + N[(-4.0 * N[Power[x1, 5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+123], N[(x1 + N[(3.0 * N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2 + x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * N[(t$95$0 / N[(N[(x1 * x1 + 1.0), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1 + 1.0), $MachinePrecision] * N[(x1 + N[(N[(x1 * N[(x1 * -6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x1 * N[(-6.0 + N[(t$95$0 / N[(N[(x1 * x1 + 1.0), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 + N[(3.0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -9.9999999999999998e155

   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%

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

      1. +-commutative 0.0%

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

      2. neg-mul-1 0.0%

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

      3. unsub-neg 0.0%

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

      4. *-commutative 0.0%

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

   4. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 0.0%

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

      1. *-commutative 0.0%

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

   7. Simplified 0.0%

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

   8. Taylor expanded in x1 around inf 100.0%

      \[\leadsto x1 + \left(\left(\color{blue}{-4 \cdot {x1}^{5}} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   if -9.9999999999999998e155 < x1 < 1.99999999999999996e123

   1. Initial program 91.8%

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

   3. Simplified 99.6%

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

   if 1.99999999999999996e123 < x1

   1. Initial program 11.6%

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

   2. Taylor expanded in x1 around 0 5.0%

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

   3. Taylor expanded in x1 around 0 83.7%

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

      1. +-commutative 83.7%

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

      2. mul-1-neg 83.7%

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

      3. unsub-neg 83.7%

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

      4. *-commutative 83.7%

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

      5. fma-def 83.7%

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

      6. +-commutative 83.7%

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

      7. cube-mult 83.7%

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

      8. unpow2 83.7%

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

      9. distribute-rgt-out 97.7%

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

      10. unpow2 97.7%

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

      11. *-commutative 97.7%

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

   5. Simplified 97.7%

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

   6. Taylor expanded in x2 around 0 100.0%

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

      1. unpow2 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+156}:\\ \;\;\;\;x1 + \left(\left(x1 + -4 \cdot {x1}^{5}\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+123}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{x1 \cdot \left(x1 \cdot 3\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \mathsf{fma}\left(x1, x1 \cdot \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{3}}, \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(x1 \cdot \left(-6 + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{2}}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 + 3\right) - x1\right)\right)\\ \end{array} \]

Alternative 2: 96.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := 1 + x1 \cdot x1\\ t_3 := 3 \cdot \frac{\left(t_1 - x2 \cdot 2\right) - x1}{t_2}\\ t_4 := \frac{\left(t_1 + x2 \cdot 2\right) - x1}{t_2}\\ t_5 := \left(x1 \cdot 2\right) \cdot t_4\\ t_6 := t_1 \cdot t_4\\ t_7 := x1 + \left(t_3 + \left(x1 + \left(t_0 + \left(t_6 + t_2 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot t_4 - 6\right) + t_5 \cdot \left(2 \cdot \frac{x2}{x1 \cdot x1} + \left(\frac{-1}{x1} - \frac{3}{x1 \cdot x1}\right)\right)\right)\right)\right)\right)\right)\\ t_8 := x2 \cdot 2 - x1\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+103}:\\ \;\;\;\;x1 + \left(\left(x1 + -4 \cdot {x1}^{5}\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq -1.4:\\ \;\;\;\;t_7\\ \mathbf{elif}\;x1 \leq 0.86:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + \left(t_0 + \left(t_6 + t_2 \cdot \left(t_5 \cdot \left(t_8 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_8 - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5.8 \cdot 10^{+82}:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ 1.0 (* x1 x1)))
        (t_3 (* 3.0 (/ (- (- t_1 (* x2 2.0)) x1) t_2)))
        (t_4 (/ (- (+ t_1 (* x2 2.0)) x1) t_2))
        (t_5 (* (* x1 2.0) t_4))
        (t_6 (* t_1 t_4))
        (t_7
         (+
          x1
          (+
           t_3
           (+
            x1
            (+
             t_0
             (+
              t_6
              (*
               t_2
               (+
                (* (* x1 x1) (- (* 4.0 t_4) 6.0))
                (*
                 t_5
                 (+
                  (* 2.0 (/ x2 (* x1 x1)))
                  (- (/ -1.0 x1) (/ 3.0 (* x1 x1)))))))))))))
        (t_8 (- (* x2 2.0) x1)))
   (if (<= x1 -1e+103)
     (+ x1 (+ (+ x1 (* -4.0 (pow x1 5.0))) (* 3.0 (* x2 -2.0))))
     (if (<= x1 -1.4)
       t_7
       (if (<= x1 0.86)
         (+
          x1
          (+
           t_3
           (+
            x1
            (+
             t_0
             (+
              t_6
              (*
               t_2
               (+ (* t_5 (- t_8 3.0)) (* (* x1 x1) (- (* 4.0 t_8) 6.0)))))))))
         (if (<= x1 5.8e+82)
           t_7
           (+ x1 (* 3.0 (* x1 (* x1 (+ x1 (+ 3.0 (* x2 2.0)))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = 1.0 + (x1 * x1);
	double t_3 = 3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_2);
	double t_4 = ((t_1 + (x2 * 2.0)) - x1) / t_2;
	double t_5 = (x1 * 2.0) * t_4;
	double t_6 = t_1 * t_4;
	double t_7 = x1 + (t_3 + (x1 + (t_0 + (t_6 + (t_2 * (((x1 * x1) * ((4.0 * t_4) - 6.0)) + (t_5 * ((2.0 * (x2 / (x1 * x1))) + ((-1.0 / x1) - (3.0 / (x1 * x1)))))))))));
	double t_8 = (x2 * 2.0) - x1;
	double tmp;
	if (x1 <= -1e+103) {
		tmp = x1 + ((x1 + (-4.0 * pow(x1, 5.0))) + (3.0 * (x2 * -2.0)));
	} else if (x1 <= -1.4) {
		tmp = t_7;
	} else if (x1 <= 0.86) {
		tmp = x1 + (t_3 + (x1 + (t_0 + (t_6 + (t_2 * ((t_5 * (t_8 - 3.0)) + ((x1 * x1) * ((4.0 * t_8) - 6.0))))))));
	} else if (x1 <= 5.8e+82) {
		tmp = t_7;
	} else {
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: tmp
    t_0 = x1 * (x1 * x1)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = 1.0d0 + (x1 * x1)
    t_3 = 3.0d0 * (((t_1 - (x2 * 2.0d0)) - x1) / t_2)
    t_4 = ((t_1 + (x2 * 2.0d0)) - x1) / t_2
    t_5 = (x1 * 2.0d0) * t_4
    t_6 = t_1 * t_4
    t_7 = x1 + (t_3 + (x1 + (t_0 + (t_6 + (t_2 * (((x1 * x1) * ((4.0d0 * t_4) - 6.0d0)) + (t_5 * ((2.0d0 * (x2 / (x1 * x1))) + (((-1.0d0) / x1) - (3.0d0 / (x1 * x1)))))))))))
    t_8 = (x2 * 2.0d0) - x1
    if (x1 <= (-1d+103)) then
        tmp = x1 + ((x1 + ((-4.0d0) * (x1 ** 5.0d0))) + (3.0d0 * (x2 * (-2.0d0))))
    else if (x1 <= (-1.4d0)) then
        tmp = t_7
    else if (x1 <= 0.86d0) then
        tmp = x1 + (t_3 + (x1 + (t_0 + (t_6 + (t_2 * ((t_5 * (t_8 - 3.0d0)) + ((x1 * x1) * ((4.0d0 * t_8) - 6.0d0))))))))
    else if (x1 <= 5.8d+82) then
        tmp = t_7
    else
        tmp = x1 + (3.0d0 * (x1 * (x1 * (x1 + (3.0d0 + (x2 * 2.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = 1.0 + (x1 * x1);
	double t_3 = 3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_2);
	double t_4 = ((t_1 + (x2 * 2.0)) - x1) / t_2;
	double t_5 = (x1 * 2.0) * t_4;
	double t_6 = t_1 * t_4;
	double t_7 = x1 + (t_3 + (x1 + (t_0 + (t_6 + (t_2 * (((x1 * x1) * ((4.0 * t_4) - 6.0)) + (t_5 * ((2.0 * (x2 / (x1 * x1))) + ((-1.0 / x1) - (3.0 / (x1 * x1)))))))))));
	double t_8 = (x2 * 2.0) - x1;
	double tmp;
	if (x1 <= -1e+103) {
		tmp = x1 + ((x1 + (-4.0 * Math.pow(x1, 5.0))) + (3.0 * (x2 * -2.0)));
	} else if (x1 <= -1.4) {
		tmp = t_7;
	} else if (x1 <= 0.86) {
		tmp = x1 + (t_3 + (x1 + (t_0 + (t_6 + (t_2 * ((t_5 * (t_8 - 3.0)) + ((x1 * x1) * ((4.0 * t_8) - 6.0))))))));
	} else if (x1 <= 5.8e+82) {
		tmp = t_7;
	} else {
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = x1 * (x1 * 3.0)
	t_2 = 1.0 + (x1 * x1)
	t_3 = 3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_2)
	t_4 = ((t_1 + (x2 * 2.0)) - x1) / t_2
	t_5 = (x1 * 2.0) * t_4
	t_6 = t_1 * t_4
	t_7 = x1 + (t_3 + (x1 + (t_0 + (t_6 + (t_2 * (((x1 * x1) * ((4.0 * t_4) - 6.0)) + (t_5 * ((2.0 * (x2 / (x1 * x1))) + ((-1.0 / x1) - (3.0 / (x1 * x1)))))))))))
	t_8 = (x2 * 2.0) - x1
	tmp = 0
	if x1 <= -1e+103:
		tmp = x1 + ((x1 + (-4.0 * math.pow(x1, 5.0))) + (3.0 * (x2 * -2.0)))
	elif x1 <= -1.4:
		tmp = t_7
	elif x1 <= 0.86:
		tmp = x1 + (t_3 + (x1 + (t_0 + (t_6 + (t_2 * ((t_5 * (t_8 - 3.0)) + ((x1 * x1) * ((4.0 * t_8) - 6.0))))))))
	elif x1 <= 5.8e+82:
		tmp = t_7
	else:
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))))
	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(1.0 + Float64(x1 * x1))
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(x2 * 2.0)) - x1) / t_2))
	t_4 = Float64(Float64(Float64(t_1 + Float64(x2 * 2.0)) - x1) / t_2)
	t_5 = Float64(Float64(x1 * 2.0) * t_4)
	t_6 = Float64(t_1 * t_4)
	t_7 = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(t_0 + Float64(t_6 + Float64(t_2 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_4) - 6.0)) + Float64(t_5 * Float64(Float64(2.0 * Float64(x2 / Float64(x1 * x1))) + Float64(Float64(-1.0 / x1) - Float64(3.0 / Float64(x1 * x1))))))))))))
	t_8 = Float64(Float64(x2 * 2.0) - x1)
	tmp = 0.0
	if (x1 <= -1e+103)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(-4.0 * (x1 ^ 5.0))) + Float64(3.0 * Float64(x2 * -2.0))));
	elseif (x1 <= -1.4)
		tmp = t_7;
	elseif (x1 <= 0.86)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(t_0 + Float64(t_6 + Float64(t_2 * Float64(Float64(t_5 * Float64(t_8 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_8) - 6.0)))))))));
	elseif (x1 <= 5.8e+82)
		tmp = t_7;
	else
		tmp = Float64(x1 + Float64(3.0 * Float64(x1 * Float64(x1 * Float64(x1 + Float64(3.0 + Float64(x2 * 2.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = x1 * (x1 * 3.0);
	t_2 = 1.0 + (x1 * x1);
	t_3 = 3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_2);
	t_4 = ((t_1 + (x2 * 2.0)) - x1) / t_2;
	t_5 = (x1 * 2.0) * t_4;
	t_6 = t_1 * t_4;
	t_7 = x1 + (t_3 + (x1 + (t_0 + (t_6 + (t_2 * (((x1 * x1) * ((4.0 * t_4) - 6.0)) + (t_5 * ((2.0 * (x2 / (x1 * x1))) + ((-1.0 / x1) - (3.0 / (x1 * x1)))))))))));
	t_8 = (x2 * 2.0) - x1;
	tmp = 0.0;
	if (x1 <= -1e+103)
		tmp = x1 + ((x1 + (-4.0 * (x1 ^ 5.0))) + (3.0 * (x2 * -2.0)));
	elseif (x1 <= -1.4)
		tmp = t_7;
	elseif (x1 <= 0.86)
		tmp = x1 + (t_3 + (x1 + (t_0 + (t_6 + (t_2 * ((t_5 * (t_8 - 3.0)) + ((x1 * x1) * ((4.0 * t_8) - 6.0))))))));
	elseif (x1 <= 5.8e+82)
		tmp = t_7;
	else
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	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[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(t$95$1 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$1 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$1 * t$95$4), $MachinePrecision]}, Block[{t$95$7 = N[(x1 + N[(t$95$3 + N[(x1 + N[(t$95$0 + N[(t$95$6 + N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$4), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$5 * N[(N[(2.0 * N[(x2 / N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-1.0 / x1), $MachinePrecision] - N[(3.0 / N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(N[(x2 * 2.0), $MachinePrecision] - x1), $MachinePrecision]}, If[LessEqual[x1, -1e+103], N[(x1 + N[(N[(x1 + N[(-4.0 * N[Power[x1, 5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.4], t$95$7, If[LessEqual[x1, 0.86], N[(x1 + N[(t$95$3 + N[(x1 + N[(t$95$0 + N[(t$95$6 + N[(t$95$2 * N[(N[(t$95$5 * N[(t$95$8 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$8), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.8e+82], t$95$7, N[(x1 + N[(3.0 * N[(x1 * N[(x1 * N[(x1 + N[(3.0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1e103

   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%

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

      1. +-commutative 0.0%

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

      2. neg-mul-1 0.0%

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

      3. unsub-neg 0.0%

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

      4. *-commutative 0.0%

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

   4. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 0.0%

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

      1. *-commutative 0.0%

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

   7. Simplified 0.0%

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

   8. Taylor expanded in x1 around inf 100.0%

      \[\leadsto x1 + \left(\left(\color{blue}{-4 \cdot {x1}^{5}} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   if -1e103 < x1 < -1.3999999999999999 or 0.859999999999999987 < x1 < 5.8000000000000003e82

   1. Initial program 99.0%

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

      1. fma-def 99.0%

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

      2. *-commutative 99.0%

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

      3. fma-def 99.1%

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

      4. add-cube-cbrt 98.8%

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

   3. Applied egg-rr 98.8%

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

   4. Taylor expanded in x1 around inf 96.4%

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

      1. unpow2 96.4%

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

      2. associate-*r/ 96.4%

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

      3. metadata-eval 96.4%

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

      4. unpow2 96.4%

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

   6. Simplified 96.4%

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

   if -1.3999999999999999 < x1 < 0.859999999999999987

   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 99.2%

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

      1. +-commutative 99.2%

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

      2. neg-mul-1 99.2%

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

      3. unsub-neg 99.2%

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

      4. *-commutative 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in x1 around 0 99.2%

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

      1. +-commutative 99.2%

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

      2. neg-mul-1 99.2%

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

      3. unsub-neg 99.2%

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

      4. *-commutative 99.2%

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

   7. Simplified 99.2%

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

   if 5.8000000000000003e82 < x1

   1. Initial program 24.5%

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

   2. Taylor expanded in x1 around 0 11.9%

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

   3. Taylor expanded in x1 around 0 81.1%

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

      1. +-commutative 81.1%

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

      2. mul-1-neg 81.1%

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

      3. unsub-neg 81.1%

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

      4. *-commutative 81.1%

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

      5. fma-def 81.1%

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

      6. +-commutative 81.1%

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

      7. cube-mult 81.1%

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

      8. unpow2 81.1%

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

      9. distribute-rgt-out 92.5%

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

      10. unpow2 92.5%

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

      11. *-commutative 92.5%

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

   5. Simplified 92.5%

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

   6. Taylor expanded in x1 around inf 81.1%

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

      1. distribute-lft-out 81.1%

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

      2. *-commutative 81.1%

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

      3. unpow3 81.1%

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

      4. unpow2 81.1%

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

      5. distribute-lft-in 96.2%

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

      6. +-commutative 96.2%

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

      7. unpow2 96.2%

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

      8. associate-*l* 96.2%

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

      9. *-commutative 96.2%

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

      10. cancel-sign-sub-inv 96.2%

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

      11. metadata-eval 96.2%

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

      12. *-commutative 96.2%

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

   8. Simplified 96.2%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+103}:\\ \;\;\;\;x1 + \left(\left(x1 + -4 \cdot {x1}^{5}\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq -1.4:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \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) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(2 \cdot \frac{x2}{x1 \cdot x1} + \left(\frac{-1}{x1} - \frac{3}{x1 \cdot x1}\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.86:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \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) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(\left(x2 \cdot 2 - x1\right) - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(x2 \cdot 2 - x1\right) - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5.8 \cdot 10^{+82}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \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) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(2 \cdot \frac{x2}{x1 \cdot x1} + \left(\frac{-1}{x1} - \frac{3}{x1 \cdot x1}\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \end{array} \]

Alternative 3: 96.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 1 + x1 \cdot x1\\ t_2 := \frac{\left(t_0 + x2 \cdot 2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+103}:\\ \;\;\;\;x1 + \left(\left(x1 + -4 \cdot {x1}^{5}\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 5.8 \cdot 10^{+82}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right)\right) + t_0 \cdot t_2\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(t_0 - x2 \cdot 2\right) - x1}{t_1}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ 1.0 (* x1 x1)))
        (t_2 (/ (- (+ t_0 (* x2 2.0)) x1) t_1)))
   (if (<= x1 -1e+103)
     (+ x1 (+ (+ x1 (* -4.0 (pow x1 5.0))) (* 3.0 (* x2 -2.0))))
     (if (<= x1 5.8e+82)
       (+
        x1
        (+
         (+
          x1
          (+
           (+
            (*
             t_1
             (+
              (* (* (* x1 2.0) t_2) (- t_2 3.0))
              (* (* x1 x1) (- (* 4.0 t_2) 6.0))))
            (* t_0 t_2))
           (* x1 (* x1 x1))))
         (* 3.0 (/ (- (- t_0 (* x2 2.0)) x1) t_1))))
       (+ x1 (* 3.0 (* x1 (* x1 (+ x1 (+ 3.0 (* x2 2.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 1.0 + (x1 * x1);
	double t_2 = ((t_0 + (x2 * 2.0)) - x1) / t_1;
	double tmp;
	if (x1 <= -1e+103) {
		tmp = x1 + ((x1 + (-4.0 * pow(x1, 5.0))) + (3.0 * (x2 * -2.0)));
	} else if (x1 <= 5.8e+82) {
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)));
	} else {
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = 1.0d0 + (x1 * x1)
    t_2 = ((t_0 + (x2 * 2.0d0)) - x1) / t_1
    if (x1 <= (-1d+103)) then
        tmp = x1 + ((x1 + ((-4.0d0) * (x1 ** 5.0d0))) + (3.0d0 * (x2 * (-2.0d0))))
    else if (x1 <= 5.8d+82) then
        tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * ((4.0d0 * t_2) - 6.0d0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0d0 * (((t_0 - (x2 * 2.0d0)) - x1) / t_1)))
    else
        tmp = x1 + (3.0d0 * (x1 * (x1 * (x1 + (3.0d0 + (x2 * 2.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 1.0 + (x1 * x1);
	double t_2 = ((t_0 + (x2 * 2.0)) - x1) / t_1;
	double tmp;
	if (x1 <= -1e+103) {
		tmp = x1 + ((x1 + (-4.0 * Math.pow(x1, 5.0))) + (3.0 * (x2 * -2.0)));
	} else if (x1 <= 5.8e+82) {
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)));
	} else {
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = 1.0 + (x1 * x1)
	t_2 = ((t_0 + (x2 * 2.0)) - x1) / t_1
	tmp = 0
	if x1 <= -1e+103:
		tmp = x1 + ((x1 + (-4.0 * math.pow(x1, 5.0))) + (3.0 * (x2 * -2.0)))
	elif x1 <= 5.8e+82:
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)))
	else:
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(1.0 + Float64(x1 * x1))
	t_2 = Float64(Float64(Float64(t_0 + Float64(x2 * 2.0)) - x1) / t_1)
	tmp = 0.0
	if (x1 <= -1e+103)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(-4.0 * (x1 ^ 5.0))) + Float64(3.0 * Float64(x2 * -2.0))));
	elseif (x1 <= 5.8e+82)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0)))) + Float64(t_0 * t_2)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_1))));
	else
		tmp = Float64(x1 + Float64(3.0 * Float64(x1 * Float64(x1 * Float64(x1 + Float64(3.0 + Float64(x2 * 2.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = 1.0 + (x1 * x1);
	t_2 = ((t_0 + (x2 * 2.0)) - x1) / t_1;
	tmp = 0.0;
	if (x1 <= -1e+103)
		tmp = x1 + ((x1 + (-4.0 * (x1 ^ 5.0))) + (3.0 * (x2 * -2.0)));
	elseif (x1 <= 5.8e+82)
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)));
	else
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[x1, -1e+103], N[(x1 + N[(N[(x1 + N[(-4.0 * N[Power[x1, 5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.8e+82], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(3.0 * N[(x1 * N[(x1 * N[(x1 + N[(3.0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1e103

   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%

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

      1. +-commutative 0.0%

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

      2. neg-mul-1 0.0%

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

      3. unsub-neg 0.0%

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

      4. *-commutative 0.0%

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

   4. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 0.0%

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

      1. *-commutative 0.0%

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

   7. Simplified 0.0%

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

   8. Taylor expanded in x1 around inf 100.0%

      \[\leadsto x1 + \left(\left(\color{blue}{-4 \cdot {x1}^{5}} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   if -1e103 < x1 < 5.8000000000000003e82

   1. Initial program 99.2%

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

   if 5.8000000000000003e82 < x1

   1. Initial program 24.5%

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

   2. Taylor expanded in x1 around 0 11.9%

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

   3. Taylor expanded in x1 around 0 81.1%

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

      1. +-commutative 81.1%

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

      2. mul-1-neg 81.1%

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

      3. unsub-neg 81.1%

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

      4. *-commutative 81.1%

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

      5. fma-def 81.1%

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

      6. +-commutative 81.1%

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

      7. cube-mult 81.1%

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

      8. unpow2 81.1%

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

      9. distribute-rgt-out 92.5%

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

      10. unpow2 92.5%

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

      11. *-commutative 92.5%

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

   5. Simplified 92.5%

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

   6. Taylor expanded in x1 around inf 81.1%

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

      1. distribute-lft-out 81.1%

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

      2. *-commutative 81.1%

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

      3. unpow3 81.1%

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

      4. unpow2 81.1%

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

      5. distribute-lft-in 96.2%

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

      6. +-commutative 96.2%

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

      7. unpow2 96.2%

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

      8. associate-*l* 96.2%

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

      9. *-commutative 96.2%

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

      10. cancel-sign-sub-inv 96.2%

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

      11. metadata-eval 96.2%

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

      12. *-commutative 96.2%

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

   8. Simplified 96.2%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+103}:\\ \;\;\;\;x1 + \left(\left(x1 + -4 \cdot {x1}^{5}\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 5.8 \cdot 10^{+82}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(1 + x1 \cdot x1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \end{array} \]

Alternative 4: 79.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 1 + x1 \cdot x1\\ t_2 := \frac{\left(t_0 + x2 \cdot 2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102} \lor \neg \left(x1 \leq 5.8 \cdot 10^{+82}\right):\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - x2 \cdot 2\right) - x1}{t_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right)\right) + t_0 \cdot \left(x2 \cdot 2\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ 1.0 (* x1 x1)))
        (t_2 (/ (- (+ t_0 (* x2 2.0)) x1) t_1)))
   (if (or (<= x1 -5.5e+102) (not (<= x1 5.8e+82)))
     (+ x1 (* 3.0 (* x1 (* x1 (+ x1 (+ 3.0 (* x2 2.0)))))))
     (+
      x1
      (+
       (* 3.0 (/ (- (- t_0 (* x2 2.0)) x1) t_1))
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (*
           t_1
           (+
            (* (* (* x1 2.0) t_2) (- t_2 3.0))
            (* (* x1 x1) (- (* 4.0 t_2) 6.0))))
          (* t_0 (* x2 2.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 1.0 + (x1 * x1);
	double t_2 = ((t_0 + (x2 * 2.0)) - x1) / t_1;
	double tmp;
	if ((x1 <= -5.5e+102) || !(x1 <= 5.8e+82)) {
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (t_0 * (x2 * 2.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = 1.0d0 + (x1 * x1)
    t_2 = ((t_0 + (x2 * 2.0d0)) - x1) / t_1
    if ((x1 <= (-5.5d+102)) .or. (.not. (x1 <= 5.8d+82))) then
        tmp = x1 + (3.0d0 * (x1 * (x1 * (x1 + (3.0d0 + (x2 * 2.0d0))))))
    else
        tmp = x1 + ((3.0d0 * (((t_0 - (x2 * 2.0d0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * ((4.0d0 * t_2) - 6.0d0)))) + (t_0 * (x2 * 2.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 1.0 + (x1 * x1);
	double t_2 = ((t_0 + (x2 * 2.0)) - x1) / t_1;
	double tmp;
	if ((x1 <= -5.5e+102) || !(x1 <= 5.8e+82)) {
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (t_0 * (x2 * 2.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = 1.0 + (x1 * x1)
	t_2 = ((t_0 + (x2 * 2.0)) - x1) / t_1
	tmp = 0
	if (x1 <= -5.5e+102) or not (x1 <= 5.8e+82):
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))))
	else:
		tmp = x1 + ((3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (t_0 * (x2 * 2.0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(1.0 + Float64(x1 * x1))
	t_2 = Float64(Float64(Float64(t_0 + Float64(x2 * 2.0)) - x1) / t_1)
	tmp = 0.0
	if ((x1 <= -5.5e+102) || !(x1 <= 5.8e+82))
		tmp = Float64(x1 + Float64(3.0 * Float64(x1 * Float64(x1 * Float64(x1 + Float64(3.0 + Float64(x2 * 2.0)))))));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0)))) + Float64(t_0 * Float64(x2 * 2.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = 1.0 + (x1 * x1);
	t_2 = ((t_0 + (x2 * 2.0)) - x1) / t_1;
	tmp = 0.0;
	if ((x1 <= -5.5e+102) || ~((x1 <= 5.8e+82)))
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	else
		tmp = x1 + ((3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (t_0 * (x2 * 2.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[x1, -5.5e+102], N[Not[LessEqual[x1, 5.8e+82]], $MachinePrecision]], N[(x1 + N[(3.0 * N[(x1 * N[(x1 * N[(x1 + N[(3.0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -5.49999999999999981e102 or 5.8000000000000003e82 < x1

   1. Initial program 14.0%

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

   2. Taylor expanded in x1 around 0 6.8%

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

   3. Taylor expanded in x1 around 0 46.2%

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

      1. +-commutative 46.2%

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

      2. mul-1-neg 46.2%

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

      3. unsub-neg 46.2%

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

      4. *-commutative 46.2%

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

      5. fma-def 46.2%

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

      6. +-commutative 46.2%

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

      7. cube-mult 46.2%

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

      8. unpow2 46.2%

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

      9. distribute-rgt-out 52.7%

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

      10. unpow2 52.7%

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

      11. *-commutative 52.7%

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

   5. Simplified 52.7%

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

   6. Taylor expanded in x1 around inf 46.2%

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

      1. distribute-lft-out 46.2%

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

      2. *-commutative 46.2%

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

      3. unpow3 46.2%

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

      4. unpow2 46.2%

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

      5. distribute-lft-in 59.1%

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

      6. +-commutative 59.1%

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

      7. unpow2 59.1%

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

      8. associate-*l* 59.1%

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

      9. *-commutative 59.1%

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

      10. cancel-sign-sub-inv 59.1%

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

      11. metadata-eval 59.1%

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

      12. *-commutative 59.1%

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

   8. Simplified 59.1%

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

   if -5.49999999999999981e102 < x1 < 5.8000000000000003e82

   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 93.0%

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

      1. *-commutative 90.7%

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

   4. Simplified 93.0%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102} \lor \neg \left(x1 \leq 5.8 \cdot 10^{+82}\right):\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(1 + x1 \cdot x1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 \cdot 2\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 5: 78.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 1 + x1 \cdot x1\\ t_2 := \frac{\left(t_0 + x2 \cdot 2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -3.4 \cdot 10^{+84}:\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+110}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - x2 \cdot 2\right) - x1}{t_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_0 \cdot t_2 + t_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 + 3\right) - x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ 1.0 (* x1 x1)))
        (t_2 (/ (- (+ t_0 (* x2 2.0)) x1) t_1)))
   (if (<= x1 -3.4e+84)
     (+ x1 (* 3.0 (* x1 (* x1 (+ x1 (+ 3.0 (* x2 2.0)))))))
     (if (<= x1 5e+110)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_0 (* x2 2.0)) x1) t_1))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* t_0 t_2)
            (*
             t_1
             (+
              (* (* x1 x1) (- (* 4.0 t_2) 6.0))
              (* (* (* x1 2.0) t_2) (- (* x2 2.0) 3.0)))))))))
       (+ x1 (+ x1 (* 3.0 (- (* (* x1 x1) (+ x1 3.0)) x1))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 1.0 + (x1 * x1);
	double t_2 = ((t_0 + (x2 * 2.0)) - x1) / t_1;
	double tmp;
	if (x1 <= -3.4e+84) {
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	} else if (x1 <= 5e+110) {
		tmp = x1 + ((3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((x1 * x1) * ((4.0 * t_2) - 6.0)) + (((x1 * 2.0) * t_2) * ((x2 * 2.0) - 3.0))))))));
	} else {
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = 1.0d0 + (x1 * x1)
    t_2 = ((t_0 + (x2 * 2.0d0)) - x1) / t_1
    if (x1 <= (-3.4d+84)) then
        tmp = x1 + (3.0d0 * (x1 * (x1 * (x1 + (3.0d0 + (x2 * 2.0d0))))))
    else if (x1 <= 5d+110) then
        tmp = x1 + ((3.0d0 * (((t_0 - (x2 * 2.0d0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((x1 * x1) * ((4.0d0 * t_2) - 6.0d0)) + (((x1 * 2.0d0) * t_2) * ((x2 * 2.0d0) - 3.0d0))))))))
    else
        tmp = x1 + (x1 + (3.0d0 * (((x1 * x1) * (x1 + 3.0d0)) - x1)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 1.0 + (x1 * x1);
	double t_2 = ((t_0 + (x2 * 2.0)) - x1) / t_1;
	double tmp;
	if (x1 <= -3.4e+84) {
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	} else if (x1 <= 5e+110) {
		tmp = x1 + ((3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((x1 * x1) * ((4.0 * t_2) - 6.0)) + (((x1 * 2.0) * t_2) * ((x2 * 2.0) - 3.0))))))));
	} else {
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = 1.0 + (x1 * x1)
	t_2 = ((t_0 + (x2 * 2.0)) - x1) / t_1
	tmp = 0
	if x1 <= -3.4e+84:
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))))
	elif x1 <= 5e+110:
		tmp = x1 + ((3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((x1 * x1) * ((4.0 * t_2) - 6.0)) + (((x1 * 2.0) * t_2) * ((x2 * 2.0) - 3.0))))))))
	else:
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(1.0 + Float64(x1 * x1))
	t_2 = Float64(Float64(Float64(t_0 + Float64(x2 * 2.0)) - x1) / t_1)
	tmp = 0.0
	if (x1 <= -3.4e+84)
		tmp = Float64(x1 + Float64(3.0 * Float64(x1 * Float64(x1 * Float64(x1 + Float64(3.0 + Float64(x2 * 2.0)))))));
	elseif (x1 <= 5e+110)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * t_2) + Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0)) + Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(Float64(x2 * 2.0) - 3.0)))))))));
	else
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(Float64(Float64(x1 * x1) * Float64(x1 + 3.0)) - x1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = 1.0 + (x1 * x1);
	t_2 = ((t_0 + (x2 * 2.0)) - x1) / t_1;
	tmp = 0.0;
	if (x1 <= -3.4e+84)
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	elseif (x1 <= 5e+110)
		tmp = x1 + ((3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((x1 * x1) * ((4.0 * t_2) - 6.0)) + (((x1 * 2.0) * t_2) * ((x2 * 2.0) - 3.0))))))));
	else
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[x1, -3.4e+84], N[(x1 + N[(3.0 * N[(x1 * N[(x1 * N[(x1 + N[(3.0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+110], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * t$95$2), $MachinePrecision] + N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 + N[(3.0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.3999999999999998e84

   1. Initial program 2.4%

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

   2. Taylor expanded in x1 around 0 0.1%

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

   3. Taylor expanded in x1 around 0 0.0%

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

      1. +-commutative 0.0%

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

      2. mul-1-neg 0.0%

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

      3. unsub-neg 0.0%

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

      4. *-commutative 0.0%

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

      5. fma-def 0.0%

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

      6. +-commutative 0.0%

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

      7. cube-mult 0.0%

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

      8. unpow2 0.0%

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

      9. distribute-rgt-out 0.0%

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

      10. unpow2 0.0%

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

      11. *-commutative 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in x1 around inf 2.4%

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

      1. distribute-lft-out 2.4%

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

      2. *-commutative 2.4%

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

      3. unpow3 2.4%

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

      4. unpow2 2.4%

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

      5. distribute-lft-in 12.2%

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

      6. +-commutative 12.2%

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

      7. unpow2 12.2%

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

      8. associate-*l* 12.2%

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

      9. *-commutative 12.2%

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

      10. cancel-sign-sub-inv 12.2%

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

      11. metadata-eval 12.2%

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

      12. *-commutative 12.2%

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

   8. Simplified 12.2%

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

   if -3.3999999999999998e84 < x1 < 4.99999999999999978e110

   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 90.8%

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

      1. *-commutative 90.8%

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

   4. Simplified 90.8%

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

   if 4.99999999999999978e110 < x1

   1. Initial program 22.0%

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

   2. Taylor expanded in x1 around 0 10.5%

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

   3. Taylor expanded in x1 around 0 82.0%

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

      1. +-commutative 82.0%

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

      2. mul-1-neg 82.0%

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

      3. unsub-neg 82.0%

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

      4. *-commutative 82.0%

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

      5. fma-def 82.0%

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

      6. +-commutative 82.0%

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

      7. cube-mult 82.0%

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

      8. unpow2 82.0%

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

      9. distribute-rgt-out 94.0%

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

      10. unpow2 94.0%

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

      11. *-commutative 94.0%

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

   5. Simplified 94.0%

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

   6. Taylor expanded in x2 around 0 98.0%

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

      1. unpow2 98.0%

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

   8. Simplified 98.0%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.4 \cdot 10^{+84}:\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+110}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 + 3\right) - x1\right)\right)\\ \end{array} \]

Alternative 6: 80.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + x1 \cdot x1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\left(t_1 + x2 \cdot 2\right) - x1}{t_0}\\ \mathbf{if}\;x1 \leq -8 \cdot 10^{+102}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot 6}\\ \mathbf{elif}\;x1 \leq 5.8 \cdot 10^{+82}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_1 - x2 \cdot 2\right) - x1}{t_0} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right)\right) + t_1 \cdot \left(x2 \cdot 2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (/ (- (+ t_1 (* x2 2.0)) x1) t_0)))
   (if (<= x1 -8e+102)
     (/ (fma x1 x1 (* (* x2 x2) -36.0)) (+ x1 (* x2 6.0)))
     (if (<= x1 5.8e+82)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_1 (* x2 2.0)) x1) t_0))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (*
             t_0
             (+
              (* (* (* x1 2.0) t_2) (- t_2 3.0))
              (* (* x1 x1) (- (* 4.0 t_2) 6.0))))
            (* t_1 (* x2 2.0)))))))
       (+ x1 (* 3.0 (* x1 (* x1 (+ x1 (+ 3.0 (* x2 2.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = 1.0 + (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (x2 * 2.0)) - x1) / t_0;
	double tmp;
	if (x1 <= -8e+102) {
		tmp = fma(x1, x1, ((x2 * x2) * -36.0)) / (x1 + (x2 * 6.0));
	} else if (x1 <= 5.8e+82) {
		tmp = x1 + ((3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (t_1 * (x2 * 2.0))))));
	} else {
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(1.0 + Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(Float64(t_1 + Float64(x2 * 2.0)) - x1) / t_0)
	tmp = 0.0
	if (x1 <= -8e+102)
		tmp = Float64(fma(x1, x1, Float64(Float64(x2 * x2) * -36.0)) / Float64(x1 + Float64(x2 * 6.0)));
	elseif (x1 <= 5.8e+82)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(x2 * 2.0)) - x1) / t_0)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0)))) + Float64(t_1 * Float64(x2 * 2.0)))))));
	else
		tmp = Float64(x1 + Float64(3.0 * Float64(x1 * Float64(x1 * Float64(x1 + Float64(3.0 + Float64(x2 * 2.0)))))));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$1 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[LessEqual[x1, -8e+102], N[(N[(x1 * x1 + N[(N[(x2 * x2), $MachinePrecision] * -36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.8e+82], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$1 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(3.0 * N[(x1 * N[(x1 * N[(x1 + N[(3.0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -7.99999999999999982e102

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.1%

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

   3. Taylor expanded in x1 around 0 0.2%

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

      1. *-commutative 0.2%

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

   5. Simplified 0.2%

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

      1. flip-+ 0.1%

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

   7. Applied egg-rr 0.1%

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

      1. fma-neg 10.1%

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

      2. swap-sqr 10.1%

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

      3. unpow2 10.1%

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

      4. distribute-rgt-neg-in 10.1%

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

      5. unpow2 10.1%

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

      6. metadata-eval 10.1%

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

      7. metadata-eval 10.1%

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

      8. *-commutative 10.1%

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

      9. cancel-sign-sub-inv 10.1%

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

      10. metadata-eval 10.1%

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

      11. *-commutative 10.1%

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

   9. Simplified 10.1%

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

   if -7.99999999999999982e102 < x1 < 5.8000000000000003e82

   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 93.0%

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

      1. *-commutative 90.7%

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

   4. Simplified 93.0%

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

   if 5.8000000000000003e82 < x1

   1. Initial program 24.5%

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

   2. Taylor expanded in x1 around 0 11.9%

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

   3. Taylor expanded in x1 around 0 81.1%

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

      1. +-commutative 81.1%

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

      2. mul-1-neg 81.1%

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

      3. unsub-neg 81.1%

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

      4. *-commutative 81.1%

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

      5. fma-def 81.1%

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

      6. +-commutative 81.1%

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

      7. cube-mult 81.1%

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

      8. unpow2 81.1%

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

      9. distribute-rgt-out 92.5%

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

      10. unpow2 92.5%

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

      11. *-commutative 92.5%

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

   5. Simplified 92.5%

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

   6. Taylor expanded in x1 around inf 81.1%

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

      1. distribute-lft-out 81.1%

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

      2. *-commutative 81.1%

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

      3. unpow3 81.1%

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

      4. unpow2 81.1%

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

      5. distribute-lft-in 96.2%

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

      6. +-commutative 96.2%

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

      7. unpow2 96.2%

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

      8. associate-*l* 96.2%

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

      9. *-commutative 96.2%

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

      10. cancel-sign-sub-inv 96.2%

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

      11. metadata-eval 96.2%

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

      12. *-commutative 96.2%

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

   8. Simplified 96.2%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -8 \cdot 10^{+102}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot 6}\\ \mathbf{elif}\;x1 \leq 5.8 \cdot 10^{+82}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(1 + x1 \cdot x1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 \cdot 2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \end{array} \]

Alternative 7: 94.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + x1 \cdot x1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\left(t_1 + x2 \cdot 2\right) - x1}{t_0}\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+93}:\\ \;\;\;\;x1 + \left(\left(x1 + -4 \cdot {x1}^{5}\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 5.8 \cdot 10^{+82}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_1 - x2 \cdot 2\right) - x1}{t_0} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right)\right) + t_1 \cdot \left(x2 \cdot 2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (/ (- (+ t_1 (* x2 2.0)) x1) t_0)))
   (if (<= x1 -5e+93)
     (+ x1 (+ (+ x1 (* -4.0 (pow x1 5.0))) (* 3.0 (* x2 -2.0))))
     (if (<= x1 5.8e+82)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_1 (* x2 2.0)) x1) t_0))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (*
             t_0
             (+
              (* (* (* x1 2.0) t_2) (- t_2 3.0))
              (* (* x1 x1) (- (* 4.0 t_2) 6.0))))
            (* t_1 (* x2 2.0)))))))
       (+ x1 (* 3.0 (* x1 (* x1 (+ x1 (+ 3.0 (* x2 2.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = 1.0 + (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (x2 * 2.0)) - x1) / t_0;
	double tmp;
	if (x1 <= -5e+93) {
		tmp = x1 + ((x1 + (-4.0 * pow(x1, 5.0))) + (3.0 * (x2 * -2.0)));
	} else if (x1 <= 5.8e+82) {
		tmp = x1 + ((3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (t_1 * (x2 * 2.0))))));
	} else {
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = 1.0d0 + (x1 * x1)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = ((t_1 + (x2 * 2.0d0)) - x1) / t_0
    if (x1 <= (-5d+93)) then
        tmp = x1 + ((x1 + ((-4.0d0) * (x1 ** 5.0d0))) + (3.0d0 * (x2 * (-2.0d0))))
    else if (x1 <= 5.8d+82) then
        tmp = x1 + ((3.0d0 * (((t_1 - (x2 * 2.0d0)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * ((4.0d0 * t_2) - 6.0d0)))) + (t_1 * (x2 * 2.0d0))))))
    else
        tmp = x1 + (3.0d0 * (x1 * (x1 * (x1 + (3.0d0 + (x2 * 2.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 1.0 + (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (x2 * 2.0)) - x1) / t_0;
	double tmp;
	if (x1 <= -5e+93) {
		tmp = x1 + ((x1 + (-4.0 * Math.pow(x1, 5.0))) + (3.0 * (x2 * -2.0)));
	} else if (x1 <= 5.8e+82) {
		tmp = x1 + ((3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (t_1 * (x2 * 2.0))))));
	} else {
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 1.0 + (x1 * x1)
	t_1 = x1 * (x1 * 3.0)
	t_2 = ((t_1 + (x2 * 2.0)) - x1) / t_0
	tmp = 0
	if x1 <= -5e+93:
		tmp = x1 + ((x1 + (-4.0 * math.pow(x1, 5.0))) + (3.0 * (x2 * -2.0)))
	elif x1 <= 5.8e+82:
		tmp = x1 + ((3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (t_1 * (x2 * 2.0))))))
	else:
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(1.0 + Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(Float64(t_1 + Float64(x2 * 2.0)) - x1) / t_0)
	tmp = 0.0
	if (x1 <= -5e+93)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(-4.0 * (x1 ^ 5.0))) + Float64(3.0 * Float64(x2 * -2.0))));
	elseif (x1 <= 5.8e+82)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(x2 * 2.0)) - x1) / t_0)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0)))) + Float64(t_1 * Float64(x2 * 2.0)))))));
	else
		tmp = Float64(x1 + Float64(3.0 * Float64(x1 * Float64(x1 * Float64(x1 + Float64(3.0 + Float64(x2 * 2.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 1.0 + (x1 * x1);
	t_1 = x1 * (x1 * 3.0);
	t_2 = ((t_1 + (x2 * 2.0)) - x1) / t_0;
	tmp = 0.0;
	if (x1 <= -5e+93)
		tmp = x1 + ((x1 + (-4.0 * (x1 ^ 5.0))) + (3.0 * (x2 * -2.0)));
	elseif (x1 <= 5.8e+82)
		tmp = x1 + ((3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (t_1 * (x2 * 2.0))))));
	else
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$1 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[LessEqual[x1, -5e+93], N[(x1 + N[(N[(x1 + N[(-4.0 * N[Power[x1, 5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.8e+82], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$1 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(3.0 * N[(x1 * N[(x1 * N[(x1 + N[(3.0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.0000000000000001e93

   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%

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

      1. +-commutative 0.0%

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

      2. neg-mul-1 0.0%

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

      3. unsub-neg 0.0%

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

      4. *-commutative 0.0%

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

   4. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 0.0%

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

      1. *-commutative 0.0%

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

   7. Simplified 0.0%

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

   8. Taylor expanded in x1 around inf 100.0%

      \[\leadsto x1 + \left(\left(\color{blue}{-4 \cdot {x1}^{5}} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   if -5.0000000000000001e93 < x1 < 5.8000000000000003e82

   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 93.0%

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

      1. *-commutative 90.7%

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

   4. Simplified 93.0%

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

   if 5.8000000000000003e82 < x1

   1. Initial program 24.5%

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

   2. Taylor expanded in x1 around 0 11.9%

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

   3. Taylor expanded in x1 around 0 81.1%

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

      1. +-commutative 81.1%

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

      2. mul-1-neg 81.1%

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

      3. unsub-neg 81.1%

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

      4. *-commutative 81.1%

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

      5. fma-def 81.1%

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

      6. +-commutative 81.1%

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

      7. cube-mult 81.1%

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

      8. unpow2 81.1%

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

      9. distribute-rgt-out 92.5%

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

      10. unpow2 92.5%

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

      11. *-commutative 92.5%

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

   5. Simplified 92.5%

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

   6. Taylor expanded in x1 around inf 81.1%

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

      1. distribute-lft-out 81.1%

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

      2. *-commutative 81.1%

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

      3. unpow3 81.1%

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

      4. unpow2 81.1%

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

      5. distribute-lft-in 96.2%

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

      6. +-commutative 96.2%

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

      7. unpow2 96.2%

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

      8. associate-*l* 96.2%

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

      9. *-commutative 96.2%

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

      10. cancel-sign-sub-inv 96.2%

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

      11. metadata-eval 96.2%

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

      12. *-commutative 96.2%

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

   8. Simplified 96.2%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+93}:\\ \;\;\;\;x1 + \left(\left(x1 + -4 \cdot {x1}^{5}\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 5.8 \cdot 10^{+82}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(1 + x1 \cdot x1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 \cdot 2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \end{array} \]

Alternative 8: 79.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + x1 \cdot x1\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := 3 \cdot \frac{\left(t_2 - x2 \cdot 2\right) - x1}{t_0}\\ t_4 := \frac{\left(t_2 + x2 \cdot 2\right) - x1}{t_0}\\ t_5 := \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_4 - 6\right)\\ t_6 := t_2 \cdot t_4\\ t_7 := t_4 - 3\\ t_8 := x2 \cdot 2 - x1\\ \mathbf{if}\;x1 \leq -3.4 \cdot 10^{+84}:\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -22000000000:\\ \;\;\;\;x1 + \left(\left(x1 + \left(t_1 + \left(t_6 + t_0 \cdot \left(t_5 + t_7 \cdot \left(\left(x1 \cdot 2\right) \cdot t_8\right)\right)\right)\right)\right) + \left(9 - \frac{3}{x1}\right)\right)\\ \mathbf{elif}\;x1 \leq 170:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + \left(t_1 + \left(t_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_4\right) \cdot t_7 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_8 - 6\right)\right) + t_2 \cdot t_8\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+123}:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + \left(t_1 + \left(t_6 + t_0 \cdot \left(t_5 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 + 3\right) - x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* x1 x1)))
        (t_1 (* x1 (* x1 x1)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (* 3.0 (/ (- (- t_2 (* x2 2.0)) x1) t_0)))
        (t_4 (/ (- (+ t_2 (* x2 2.0)) x1) t_0))
        (t_5 (* (* x1 x1) (- (* 4.0 t_4) 6.0)))
        (t_6 (* t_2 t_4))
        (t_7 (- t_4 3.0))
        (t_8 (- (* x2 2.0) x1)))
   (if (<= x1 -3.4e+84)
     (+ x1 (* 3.0 (* x1 (* x1 (+ x1 (+ 3.0 (* x2 2.0)))))))
     (if (<= x1 -22000000000.0)
       (+
        x1
        (+
         (+ x1 (+ t_1 (+ t_6 (* t_0 (+ t_5 (* t_7 (* (* x1 2.0) t_8)))))))
         (- 9.0 (/ 3.0 x1))))
       (if (<= x1 170.0)
         (+
          x1
          (+
           t_3
           (+
            x1
            (+
             t_1
             (+
              (*
               t_0
               (+
                (* (* (* x1 2.0) t_4) t_7)
                (* (* x1 x1) (- (* 4.0 t_8) 6.0))))
              (* t_2 t_8))))))
         (if (<= x1 2e+123)
           (+
            x1
            (+
             t_3
             (+
              x1
              (+
               t_1
               (+
                t_6
                (* t_0 (+ t_5 (* 4.0 (* x2 (* x1 (- (* x2 2.0) 3.0)))))))))))
           (+ x1 (+ x1 (* 3.0 (- (* (* x1 x1) (+ x1 3.0)) x1))))))))))

C

double code(double x1, double x2) {
	double t_0 = 1.0 + (x1 * x1);
	double t_1 = x1 * (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 3.0 * (((t_2 - (x2 * 2.0)) - x1) / t_0);
	double t_4 = ((t_2 + (x2 * 2.0)) - x1) / t_0;
	double t_5 = (x1 * x1) * ((4.0 * t_4) - 6.0);
	double t_6 = t_2 * t_4;
	double t_7 = t_4 - 3.0;
	double t_8 = (x2 * 2.0) - x1;
	double tmp;
	if (x1 <= -3.4e+84) {
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	} else if (x1 <= -22000000000.0) {
		tmp = x1 + ((x1 + (t_1 + (t_6 + (t_0 * (t_5 + (t_7 * ((x1 * 2.0) * t_8))))))) + (9.0 - (3.0 / x1)));
	} else if (x1 <= 170.0) {
		tmp = x1 + (t_3 + (x1 + (t_1 + ((t_0 * ((((x1 * 2.0) * t_4) * t_7) + ((x1 * x1) * ((4.0 * t_8) - 6.0)))) + (t_2 * t_8)))));
	} else if (x1 <= 2e+123) {
		tmp = x1 + (t_3 + (x1 + (t_1 + (t_6 + (t_0 * (t_5 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))))))));
	} else {
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: tmp
    t_0 = 1.0d0 + (x1 * x1)
    t_1 = x1 * (x1 * x1)
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = 3.0d0 * (((t_2 - (x2 * 2.0d0)) - x1) / t_0)
    t_4 = ((t_2 + (x2 * 2.0d0)) - x1) / t_0
    t_5 = (x1 * x1) * ((4.0d0 * t_4) - 6.0d0)
    t_6 = t_2 * t_4
    t_7 = t_4 - 3.0d0
    t_8 = (x2 * 2.0d0) - x1
    if (x1 <= (-3.4d+84)) then
        tmp = x1 + (3.0d0 * (x1 * (x1 * (x1 + (3.0d0 + (x2 * 2.0d0))))))
    else if (x1 <= (-22000000000.0d0)) then
        tmp = x1 + ((x1 + (t_1 + (t_6 + (t_0 * (t_5 + (t_7 * ((x1 * 2.0d0) * t_8))))))) + (9.0d0 - (3.0d0 / x1)))
    else if (x1 <= 170.0d0) then
        tmp = x1 + (t_3 + (x1 + (t_1 + ((t_0 * ((((x1 * 2.0d0) * t_4) * t_7) + ((x1 * x1) * ((4.0d0 * t_8) - 6.0d0)))) + (t_2 * t_8)))))
    else if (x1 <= 2d+123) then
        tmp = x1 + (t_3 + (x1 + (t_1 + (t_6 + (t_0 * (t_5 + (4.0d0 * (x2 * (x1 * ((x2 * 2.0d0) - 3.0d0))))))))))
    else
        tmp = x1 + (x1 + (3.0d0 * (((x1 * x1) * (x1 + 3.0d0)) - x1)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 1.0 + (x1 * x1);
	double t_1 = x1 * (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 3.0 * (((t_2 - (x2 * 2.0)) - x1) / t_0);
	double t_4 = ((t_2 + (x2 * 2.0)) - x1) / t_0;
	double t_5 = (x1 * x1) * ((4.0 * t_4) - 6.0);
	double t_6 = t_2 * t_4;
	double t_7 = t_4 - 3.0;
	double t_8 = (x2 * 2.0) - x1;
	double tmp;
	if (x1 <= -3.4e+84) {
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	} else if (x1 <= -22000000000.0) {
		tmp = x1 + ((x1 + (t_1 + (t_6 + (t_0 * (t_5 + (t_7 * ((x1 * 2.0) * t_8))))))) + (9.0 - (3.0 / x1)));
	} else if (x1 <= 170.0) {
		tmp = x1 + (t_3 + (x1 + (t_1 + ((t_0 * ((((x1 * 2.0) * t_4) * t_7) + ((x1 * x1) * ((4.0 * t_8) - 6.0)))) + (t_2 * t_8)))));
	} else if (x1 <= 2e+123) {
		tmp = x1 + (t_3 + (x1 + (t_1 + (t_6 + (t_0 * (t_5 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))))))));
	} else {
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 1.0 + (x1 * x1)
	t_1 = x1 * (x1 * x1)
	t_2 = x1 * (x1 * 3.0)
	t_3 = 3.0 * (((t_2 - (x2 * 2.0)) - x1) / t_0)
	t_4 = ((t_2 + (x2 * 2.0)) - x1) / t_0
	t_5 = (x1 * x1) * ((4.0 * t_4) - 6.0)
	t_6 = t_2 * t_4
	t_7 = t_4 - 3.0
	t_8 = (x2 * 2.0) - x1
	tmp = 0
	if x1 <= -3.4e+84:
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))))
	elif x1 <= -22000000000.0:
		tmp = x1 + ((x1 + (t_1 + (t_6 + (t_0 * (t_5 + (t_7 * ((x1 * 2.0) * t_8))))))) + (9.0 - (3.0 / x1)))
	elif x1 <= 170.0:
		tmp = x1 + (t_3 + (x1 + (t_1 + ((t_0 * ((((x1 * 2.0) * t_4) * t_7) + ((x1 * x1) * ((4.0 * t_8) - 6.0)))) + (t_2 * t_8)))))
	elif x1 <= 2e+123:
		tmp = x1 + (t_3 + (x1 + (t_1 + (t_6 + (t_0 * (t_5 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))))))))
	else:
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(1.0 + Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * x1))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(x2 * 2.0)) - x1) / t_0))
	t_4 = Float64(Float64(Float64(t_2 + Float64(x2 * 2.0)) - x1) / t_0)
	t_5 = Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_4) - 6.0))
	t_6 = Float64(t_2 * t_4)
	t_7 = Float64(t_4 - 3.0)
	t_8 = Float64(Float64(x2 * 2.0) - x1)
	tmp = 0.0
	if (x1 <= -3.4e+84)
		tmp = Float64(x1 + Float64(3.0 * Float64(x1 * Float64(x1 * Float64(x1 + Float64(3.0 + Float64(x2 * 2.0)))))));
	elseif (x1 <= -22000000000.0)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(t_1 + Float64(t_6 + Float64(t_0 * Float64(t_5 + Float64(t_7 * Float64(Float64(x1 * 2.0) * t_8))))))) + Float64(9.0 - Float64(3.0 / x1))));
	elseif (x1 <= 170.0)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(t_1 + Float64(Float64(t_0 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_4) * t_7) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_8) - 6.0)))) + Float64(t_2 * t_8))))));
	elseif (x1 <= 2e+123)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(t_1 + Float64(t_6 + Float64(t_0 * Float64(t_5 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(x2 * 2.0) - 3.0)))))))))));
	else
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(Float64(Float64(x1 * x1) * Float64(x1 + 3.0)) - x1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 1.0 + (x1 * x1);
	t_1 = x1 * (x1 * x1);
	t_2 = x1 * (x1 * 3.0);
	t_3 = 3.0 * (((t_2 - (x2 * 2.0)) - x1) / t_0);
	t_4 = ((t_2 + (x2 * 2.0)) - x1) / t_0;
	t_5 = (x1 * x1) * ((4.0 * t_4) - 6.0);
	t_6 = t_2 * t_4;
	t_7 = t_4 - 3.0;
	t_8 = (x2 * 2.0) - x1;
	tmp = 0.0;
	if (x1 <= -3.4e+84)
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	elseif (x1 <= -22000000000.0)
		tmp = x1 + ((x1 + (t_1 + (t_6 + (t_0 * (t_5 + (t_7 * ((x1 * 2.0) * t_8))))))) + (9.0 - (3.0 / x1)));
	elseif (x1 <= 170.0)
		tmp = x1 + (t_3 + (x1 + (t_1 + ((t_0 * ((((x1 * 2.0) * t_4) * t_7) + ((x1 * x1) * ((4.0 * t_8) - 6.0)))) + (t_2 * t_8)))));
	elseif (x1 <= 2e+123)
		tmp = x1 + (t_3 + (x1 + (t_1 + (t_6 + (t_0 * (t_5 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))))))));
	else
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(t$95$2 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$2 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$4), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$2 * t$95$4), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$4 - 3.0), $MachinePrecision]}, Block[{t$95$8 = N[(N[(x2 * 2.0), $MachinePrecision] - x1), $MachinePrecision]}, If[LessEqual[x1, -3.4e+84], N[(x1 + N[(3.0 * N[(x1 * N[(x1 * N[(x1 + N[(3.0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -22000000000.0], N[(x1 + N[(N[(x1 + N[(t$95$1 + N[(t$95$6 + N[(t$95$0 * N[(t$95$5 + N[(t$95$7 * N[(N[(x1 * 2.0), $MachinePrecision] * t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(9.0 - N[(3.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 170.0], N[(x1 + N[(t$95$3 + N[(x1 + N[(t$95$1 + N[(N[(t$95$0 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * t$95$7), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$8), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+123], N[(x1 + N[(t$95$3 + N[(x1 + N[(t$95$1 + N[(t$95$6 + N[(t$95$0 * N[(t$95$5 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 + N[(3.0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -3.3999999999999998e84

   1. Initial program 2.4%

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

   2. Taylor expanded in x1 around 0 0.1%

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

   3. Taylor expanded in x1 around 0 0.0%

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

      1. +-commutative 0.0%

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

      2. mul-1-neg 0.0%

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

      3. unsub-neg 0.0%

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

      4. *-commutative 0.0%

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

      5. fma-def 0.0%

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

      6. +-commutative 0.0%

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

      7. cube-mult 0.0%

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

      8. unpow2 0.0%

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

      9. distribute-rgt-out 0.0%

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

      10. unpow2 0.0%

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

      11. *-commutative 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in x1 around inf 2.4%

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

      1. distribute-lft-out 2.4%

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

      2. *-commutative 2.4%

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

      3. unpow3 2.4%

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

      4. unpow2 2.4%

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

      5. distribute-lft-in 12.2%

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

      6. +-commutative 12.2%

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

      7. unpow2 12.2%

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

      8. associate-*l* 12.2%

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

      9. *-commutative 12.2%

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

      10. cancel-sign-sub-inv 12.2%

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

      11. metadata-eval 12.2%

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

      12. *-commutative 12.2%

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

   8. Simplified 12.2%

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

   if -3.3999999999999998e84 < x1 < -2.2e10

   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 81.9%

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

      1. +-commutative 35.2%

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

      2. neg-mul-1 35.2%

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

      3. unsub-neg 35.2%

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

      4. *-commutative 35.2%

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

   4. Simplified 81.9%

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

   5. Taylor expanded in x1 around inf 81.9%

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

      1. associate-*r/ 81.9%

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

      2. metadata-eval 81.9%

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

   7. Simplified 81.9%

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

   if -2.2e10 < 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 97.5%

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

      1. +-commutative 97.5%

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

      2. neg-mul-1 97.5%

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

      3. unsub-neg 97.5%

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

      4. *-commutative 97.5%

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

   4. Simplified 97.5%

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

   5. Taylor expanded in x1 around 0 97.5%

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

      1. +-commutative 97.5%

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

      2. neg-mul-1 97.5%

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

      3. unsub-neg 97.5%

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

      4. *-commutative 97.5%

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

   7. Simplified 97.5%

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

   if 170 < x1 < 1.99999999999999996e123

   1. Initial program 93.1%

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

   2. Taylor expanded in x1 around 0 75.4%

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

      1. +-commutative 20.2%

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

      2. neg-mul-1 20.2%

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

      3. unsub-neg 20.2%

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

      4. *-commutative 20.2%

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

   4. Simplified 75.4%

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

   5. Taylor expanded in x1 around 0 81.3%

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

   if 1.99999999999999996e123 < x1

   1. Initial program 11.6%

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

   2. Taylor expanded in x1 around 0 5.0%

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

   3. Taylor expanded in x1 around 0 83.7%

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

      1. +-commutative 83.7%

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

      2. mul-1-neg 83.7%

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

      3. unsub-neg 83.7%

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

      4. *-commutative 83.7%

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

      5. fma-def 83.7%

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

      6. +-commutative 83.7%

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

      7. cube-mult 83.7%

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

      8. unpow2 83.7%

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

      9. distribute-rgt-out 97.7%

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

      10. unpow2 97.7%

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

      11. *-commutative 97.7%

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

   5. Simplified 97.7%

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

   6. Taylor expanded in x2 around 0 100.0%

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

      1. unpow2 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.4 \cdot 10^{+84}:\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -22000000000:\\ \;\;\;\;x1 + \left(\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) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 \cdot 2 - x1\right)\right)\right)\right)\right)\right) + \left(9 - \frac{3}{x1}\right)\right)\\ \mathbf{elif}\;x1 \leq 170:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(1 + x1 \cdot x1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(x2 \cdot 2 - x1\right) - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 \cdot 2 - x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+123}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \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) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 6\right) + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 + 3\right) - x1\right)\right)\\ \end{array} \]

Alternative 9: 78.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + x1 \cdot x1\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := 3 \cdot \frac{\left(t_2 - x2 \cdot 2\right) - x1}{t_0}\\ t_4 := \frac{\left(t_2 + x2 \cdot 2\right) - x1}{t_0}\\ t_5 := \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_4 - 6\right)\\ t_6 := t_2 \cdot t_4\\ \mathbf{if}\;x1 \leq -3.4 \cdot 10^{+84}:\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3.6 \cdot 10^{+28}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(t_1 + \left(t_6 + t_0 \cdot \left(t_5 + \left(t_4 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 \cdot 2 - x1\right)\right)\right)\right)\right)\right) + \left(9 - \frac{3}{x1}\right)\right)\\ \mathbf{elif}\;x1 \leq 200:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + 8 \cdot \frac{x2}{\frac{x1 + \frac{1}{x1}}{x2}}\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+123}:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + \left(t_1 + \left(t_6 + t_0 \cdot \left(t_5 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 + 3\right) - x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* x1 x1)))
        (t_1 (* x1 (* x1 x1)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (* 3.0 (/ (- (- t_2 (* x2 2.0)) x1) t_0)))
        (t_4 (/ (- (+ t_2 (* x2 2.0)) x1) t_0))
        (t_5 (* (* x1 x1) (- (* 4.0 t_4) 6.0)))
        (t_6 (* t_2 t_4)))
   (if (<= x1 -3.4e+84)
     (+ x1 (* 3.0 (* x1 (* x1 (+ x1 (+ 3.0 (* x2 2.0)))))))
     (if (<= x1 -3.6e+28)
       (+
        x1
        (+
         (+
          x1
          (+
           t_1
           (+
            t_6
            (* t_0 (+ t_5 (* (- t_4 3.0) (* (* x1 2.0) (- (* x2 2.0) x1))))))))
         (- 9.0 (/ 3.0 x1))))
       (if (<= x1 200.0)
         (+ x1 (+ t_3 (+ x1 (* 8.0 (/ x2 (/ (+ x1 (/ 1.0 x1)) x2))))))
         (if (<= x1 2e+123)
           (+
            x1
            (+
             t_3
             (+
              x1
              (+
               t_1
               (+
                t_6
                (* t_0 (+ t_5 (* 4.0 (* x2 (* x1 (- (* x2 2.0) 3.0)))))))))))
           (+ x1 (+ x1 (* 3.0 (- (* (* x1 x1) (+ x1 3.0)) x1))))))))))

C

double code(double x1, double x2) {
	double t_0 = 1.0 + (x1 * x1);
	double t_1 = x1 * (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 3.0 * (((t_2 - (x2 * 2.0)) - x1) / t_0);
	double t_4 = ((t_2 + (x2 * 2.0)) - x1) / t_0;
	double t_5 = (x1 * x1) * ((4.0 * t_4) - 6.0);
	double t_6 = t_2 * t_4;
	double tmp;
	if (x1 <= -3.4e+84) {
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	} else if (x1 <= -3.6e+28) {
		tmp = x1 + ((x1 + (t_1 + (t_6 + (t_0 * (t_5 + ((t_4 - 3.0) * ((x1 * 2.0) * ((x2 * 2.0) - x1)))))))) + (9.0 - (3.0 / x1)));
	} else if (x1 <= 200.0) {
		tmp = x1 + (t_3 + (x1 + (8.0 * (x2 / ((x1 + (1.0 / x1)) / x2)))));
	} else if (x1 <= 2e+123) {
		tmp = x1 + (t_3 + (x1 + (t_1 + (t_6 + (t_0 * (t_5 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))))))));
	} else {
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = 1.0d0 + (x1 * x1)
    t_1 = x1 * (x1 * x1)
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = 3.0d0 * (((t_2 - (x2 * 2.0d0)) - x1) / t_0)
    t_4 = ((t_2 + (x2 * 2.0d0)) - x1) / t_0
    t_5 = (x1 * x1) * ((4.0d0 * t_4) - 6.0d0)
    t_6 = t_2 * t_4
    if (x1 <= (-3.4d+84)) then
        tmp = x1 + (3.0d0 * (x1 * (x1 * (x1 + (3.0d0 + (x2 * 2.0d0))))))
    else if (x1 <= (-3.6d+28)) then
        tmp = x1 + ((x1 + (t_1 + (t_6 + (t_0 * (t_5 + ((t_4 - 3.0d0) * ((x1 * 2.0d0) * ((x2 * 2.0d0) - x1)))))))) + (9.0d0 - (3.0d0 / x1)))
    else if (x1 <= 200.0d0) then
        tmp = x1 + (t_3 + (x1 + (8.0d0 * (x2 / ((x1 + (1.0d0 / x1)) / x2)))))
    else if (x1 <= 2d+123) then
        tmp = x1 + (t_3 + (x1 + (t_1 + (t_6 + (t_0 * (t_5 + (4.0d0 * (x2 * (x1 * ((x2 * 2.0d0) - 3.0d0))))))))))
    else
        tmp = x1 + (x1 + (3.0d0 * (((x1 * x1) * (x1 + 3.0d0)) - x1)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 1.0 + (x1 * x1);
	double t_1 = x1 * (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 3.0 * (((t_2 - (x2 * 2.0)) - x1) / t_0);
	double t_4 = ((t_2 + (x2 * 2.0)) - x1) / t_0;
	double t_5 = (x1 * x1) * ((4.0 * t_4) - 6.0);
	double t_6 = t_2 * t_4;
	double tmp;
	if (x1 <= -3.4e+84) {
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	} else if (x1 <= -3.6e+28) {
		tmp = x1 + ((x1 + (t_1 + (t_6 + (t_0 * (t_5 + ((t_4 - 3.0) * ((x1 * 2.0) * ((x2 * 2.0) - x1)))))))) + (9.0 - (3.0 / x1)));
	} else if (x1 <= 200.0) {
		tmp = x1 + (t_3 + (x1 + (8.0 * (x2 / ((x1 + (1.0 / x1)) / x2)))));
	} else if (x1 <= 2e+123) {
		tmp = x1 + (t_3 + (x1 + (t_1 + (t_6 + (t_0 * (t_5 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))))))));
	} else {
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 1.0 + (x1 * x1)
	t_1 = x1 * (x1 * x1)
	t_2 = x1 * (x1 * 3.0)
	t_3 = 3.0 * (((t_2 - (x2 * 2.0)) - x1) / t_0)
	t_4 = ((t_2 + (x2 * 2.0)) - x1) / t_0
	t_5 = (x1 * x1) * ((4.0 * t_4) - 6.0)
	t_6 = t_2 * t_4
	tmp = 0
	if x1 <= -3.4e+84:
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))))
	elif x1 <= -3.6e+28:
		tmp = x1 + ((x1 + (t_1 + (t_6 + (t_0 * (t_5 + ((t_4 - 3.0) * ((x1 * 2.0) * ((x2 * 2.0) - x1)))))))) + (9.0 - (3.0 / x1)))
	elif x1 <= 200.0:
		tmp = x1 + (t_3 + (x1 + (8.0 * (x2 / ((x1 + (1.0 / x1)) / x2)))))
	elif x1 <= 2e+123:
		tmp = x1 + (t_3 + (x1 + (t_1 + (t_6 + (t_0 * (t_5 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))))))))
	else:
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(1.0 + Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * x1))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(x2 * 2.0)) - x1) / t_0))
	t_4 = Float64(Float64(Float64(t_2 + Float64(x2 * 2.0)) - x1) / t_0)
	t_5 = Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_4) - 6.0))
	t_6 = Float64(t_2 * t_4)
	tmp = 0.0
	if (x1 <= -3.4e+84)
		tmp = Float64(x1 + Float64(3.0 * Float64(x1 * Float64(x1 * Float64(x1 + Float64(3.0 + Float64(x2 * 2.0)))))));
	elseif (x1 <= -3.6e+28)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(t_1 + Float64(t_6 + Float64(t_0 * Float64(t_5 + Float64(Float64(t_4 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(Float64(x2 * 2.0) - x1)))))))) + Float64(9.0 - Float64(3.0 / x1))));
	elseif (x1 <= 200.0)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(8.0 * Float64(x2 / Float64(Float64(x1 + Float64(1.0 / x1)) / x2))))));
	elseif (x1 <= 2e+123)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(t_1 + Float64(t_6 + Float64(t_0 * Float64(t_5 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(x2 * 2.0) - 3.0)))))))))));
	else
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(Float64(Float64(x1 * x1) * Float64(x1 + 3.0)) - x1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 1.0 + (x1 * x1);
	t_1 = x1 * (x1 * x1);
	t_2 = x1 * (x1 * 3.0);
	t_3 = 3.0 * (((t_2 - (x2 * 2.0)) - x1) / t_0);
	t_4 = ((t_2 + (x2 * 2.0)) - x1) / t_0;
	t_5 = (x1 * x1) * ((4.0 * t_4) - 6.0);
	t_6 = t_2 * t_4;
	tmp = 0.0;
	if (x1 <= -3.4e+84)
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	elseif (x1 <= -3.6e+28)
		tmp = x1 + ((x1 + (t_1 + (t_6 + (t_0 * (t_5 + ((t_4 - 3.0) * ((x1 * 2.0) * ((x2 * 2.0) - x1)))))))) + (9.0 - (3.0 / x1)));
	elseif (x1 <= 200.0)
		tmp = x1 + (t_3 + (x1 + (8.0 * (x2 / ((x1 + (1.0 / x1)) / x2)))));
	elseif (x1 <= 2e+123)
		tmp = x1 + (t_3 + (x1 + (t_1 + (t_6 + (t_0 * (t_5 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))))))));
	else
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(t$95$2 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$2 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$4), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$2 * t$95$4), $MachinePrecision]}, If[LessEqual[x1, -3.4e+84], N[(x1 + N[(3.0 * N[(x1 * N[(x1 * N[(x1 + N[(3.0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -3.6e+28], N[(x1 + N[(N[(x1 + N[(t$95$1 + N[(t$95$6 + N[(t$95$0 * N[(t$95$5 + N[(N[(t$95$4 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(x2 * 2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(9.0 - N[(3.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 200.0], N[(x1 + N[(t$95$3 + N[(x1 + N[(8.0 * N[(x2 / N[(N[(x1 + N[(1.0 / x1), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+123], N[(x1 + N[(t$95$3 + N[(x1 + N[(t$95$1 + N[(t$95$6 + N[(t$95$0 * N[(t$95$5 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 + N[(3.0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -3.3999999999999998e84

   1. Initial program 2.4%

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

   2. Taylor expanded in x1 around 0 0.1%

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

   3. Taylor expanded in x1 around 0 0.0%

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

      1. +-commutative 0.0%

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

      2. mul-1-neg 0.0%

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

      3. unsub-neg 0.0%

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

      4. *-commutative 0.0%

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

      5. fma-def 0.0%

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

      6. +-commutative 0.0%

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

      7. cube-mult 0.0%

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

      8. unpow2 0.0%

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

      9. distribute-rgt-out 0.0%

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

      10. unpow2 0.0%

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

      11. *-commutative 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in x1 around inf 2.4%

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

      1. distribute-lft-out 2.4%

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

      2. *-commutative 2.4%

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

      3. unpow3 2.4%

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

      4. unpow2 2.4%

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

      5. distribute-lft-in 12.2%

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

      6. +-commutative 12.2%

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

      7. unpow2 12.2%

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

      8. associate-*l* 12.2%

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

      9. *-commutative 12.2%

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

      10. cancel-sign-sub-inv 12.2%

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

      11. metadata-eval 12.2%

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

      12. *-commutative 12.2%

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

   8. Simplified 12.2%

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

   if -3.3999999999999998e84 < x1 < -3.5999999999999999e28

   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 91.9%

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

      1. +-commutative 34.5%

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

      2. neg-mul-1 34.5%

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

      3. unsub-neg 34.5%

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

      4. *-commutative 34.5%

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

   4. Simplified 91.9%

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

   5. Taylor expanded in x1 around inf 91.9%

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

      1. associate-*r/ 91.9%

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

      2. metadata-eval 91.9%

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

   7. Simplified 91.9%

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

   if -3.5999999999999999e28 < x1 < 200

   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 x2 around inf 83.2%

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

      1. associate-/l* 83.2%

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

      2. unpow2 83.2%

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

      3. +-commutative 83.2%

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

      4. unpow2 83.2%

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

      5. fma-udef 83.2%

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

   4. Simplified 83.2%

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

   5. Taylor expanded in x1 around 0 83.2%

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

   6. Taylor expanded in x2 around 0 83.2%

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

      1. unpow2 83.2%

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

      2. associate-/l* 95.9%

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

   8. Simplified 95.9%

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

   if 200 < x1 < 1.99999999999999996e123

   1. Initial program 93.1%

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

   2. Taylor expanded in x1 around 0 75.4%

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

      1. +-commutative 20.2%

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

      2. neg-mul-1 20.2%

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

      3. unsub-neg 20.2%

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

      4. *-commutative 20.2%

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

   4. Simplified 75.4%

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

   5. Taylor expanded in x1 around 0 81.3%

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

   if 1.99999999999999996e123 < x1

   1. Initial program 11.6%

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

   2. Taylor expanded in x1 around 0 5.0%

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

   3. Taylor expanded in x1 around 0 83.7%

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

      1. +-commutative 83.7%

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

      2. mul-1-neg 83.7%

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

      3. unsub-neg 83.7%

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

      4. *-commutative 83.7%

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

      5. fma-def 83.7%

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

      6. +-commutative 83.7%

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

      7. cube-mult 83.7%

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

      8. unpow2 83.7%

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

      9. distribute-rgt-out 97.7%

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

      10. unpow2 97.7%

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

      11. *-commutative 97.7%

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

   5. Simplified 97.7%

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

   6. Taylor expanded in x2 around 0 100.0%

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

      1. unpow2 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.4 \cdot 10^{+84}:\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3.6 \cdot 10^{+28}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 \cdot 2 - x1\right)\right)\right)\right)\right)\right) + \left(9 - \frac{3}{x1}\right)\right)\\ \mathbf{elif}\;x1 \leq 200:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + 8 \cdot \frac{x2}{\frac{x1 + \frac{1}{x1}}{x2}}\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+123}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 6\right) + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 + 3\right) - x1\right)\right)\\ \end{array} \]

Alternative 10: 78.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 1 + x1 \cdot x1\\ t_2 := \frac{\left(t_0 + x2 \cdot 2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -3.4 \cdot 10^{+84}:\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+123}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - x2 \cdot 2\right) - x1}{t_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_0 \cdot t_2 + t_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right) + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 + 3\right) - x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ 1.0 (* x1 x1)))
        (t_2 (/ (- (+ t_0 (* x2 2.0)) x1) t_1)))
   (if (<= x1 -3.4e+84)
     (+ x1 (* 3.0 (* x1 (* x1 (+ x1 (+ 3.0 (* x2 2.0)))))))
     (if (<= x1 2e+123)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_0 (* x2 2.0)) x1) t_1))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* t_0 t_2)
            (*
             t_1
             (+
              (* (* x1 x1) (- (* 4.0 t_2) 6.0))
              (* 4.0 (* x2 (* x1 (- (* x2 2.0) 3.0)))))))))))
       (+ x1 (+ x1 (* 3.0 (- (* (* x1 x1) (+ x1 3.0)) x1))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 1.0 + (x1 * x1);
	double t_2 = ((t_0 + (x2 * 2.0)) - x1) / t_1;
	double tmp;
	if (x1 <= -3.4e+84) {
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	} else if (x1 <= 2e+123) {
		tmp = x1 + ((3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((x1 * x1) * ((4.0 * t_2) - 6.0)) + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))))))));
	} else {
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = 1.0d0 + (x1 * x1)
    t_2 = ((t_0 + (x2 * 2.0d0)) - x1) / t_1
    if (x1 <= (-3.4d+84)) then
        tmp = x1 + (3.0d0 * (x1 * (x1 * (x1 + (3.0d0 + (x2 * 2.0d0))))))
    else if (x1 <= 2d+123) then
        tmp = x1 + ((3.0d0 * (((t_0 - (x2 * 2.0d0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((x1 * x1) * ((4.0d0 * t_2) - 6.0d0)) + (4.0d0 * (x2 * (x1 * ((x2 * 2.0d0) - 3.0d0))))))))))
    else
        tmp = x1 + (x1 + (3.0d0 * (((x1 * x1) * (x1 + 3.0d0)) - x1)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 1.0 + (x1 * x1);
	double t_2 = ((t_0 + (x2 * 2.0)) - x1) / t_1;
	double tmp;
	if (x1 <= -3.4e+84) {
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	} else if (x1 <= 2e+123) {
		tmp = x1 + ((3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((x1 * x1) * ((4.0 * t_2) - 6.0)) + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))))))));
	} else {
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = 1.0 + (x1 * x1)
	t_2 = ((t_0 + (x2 * 2.0)) - x1) / t_1
	tmp = 0
	if x1 <= -3.4e+84:
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))))
	elif x1 <= 2e+123:
		tmp = x1 + ((3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((x1 * x1) * ((4.0 * t_2) - 6.0)) + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))))))))
	else:
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(1.0 + Float64(x1 * x1))
	t_2 = Float64(Float64(Float64(t_0 + Float64(x2 * 2.0)) - x1) / t_1)
	tmp = 0.0
	if (x1 <= -3.4e+84)
		tmp = Float64(x1 + Float64(3.0 * Float64(x1 * Float64(x1 * Float64(x1 + Float64(3.0 + Float64(x2 * 2.0)))))));
	elseif (x1 <= 2e+123)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * t_2) + Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0)) + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(x2 * 2.0) - 3.0)))))))))));
	else
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(Float64(Float64(x1 * x1) * Float64(x1 + 3.0)) - x1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = 1.0 + (x1 * x1);
	t_2 = ((t_0 + (x2 * 2.0)) - x1) / t_1;
	tmp = 0.0;
	if (x1 <= -3.4e+84)
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	elseif (x1 <= 2e+123)
		tmp = x1 + ((3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((x1 * x1) * ((4.0 * t_2) - 6.0)) + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))))))));
	else
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[x1, -3.4e+84], N[(x1 + N[(3.0 * N[(x1 * N[(x1 * N[(x1 + N[(3.0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+123], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * t$95$2), $MachinePrecision] + N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x2 * N[(x1 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 + N[(3.0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.3999999999999998e84

   1. Initial program 2.4%

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

   2. Taylor expanded in x1 around 0 0.1%

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

   3. Taylor expanded in x1 around 0 0.0%

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

      1. +-commutative 0.0%

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

      2. mul-1-neg 0.0%

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

      3. unsub-neg 0.0%

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

      4. *-commutative 0.0%

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

      5. fma-def 0.0%

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

      6. +-commutative 0.0%

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

      7. cube-mult 0.0%

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

      8. unpow2 0.0%

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

      9. distribute-rgt-out 0.0%

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

      10. unpow2 0.0%

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

      11. *-commutative 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in x1 around inf 2.4%

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

      1. distribute-lft-out 2.4%

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

      2. *-commutative 2.4%

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

      3. unpow3 2.4%

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

      4. unpow2 2.4%

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

      5. distribute-lft-in 12.2%

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

      6. +-commutative 12.2%

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

      7. unpow2 12.2%

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

      8. associate-*l* 12.2%

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

      9. *-commutative 12.2%

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

      10. cancel-sign-sub-inv 12.2%

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

      11. metadata-eval 12.2%

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

      12. *-commutative 12.2%

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

   8. Simplified 12.2%

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

   if -3.3999999999999998e84 < x1 < 1.99999999999999996e123

   1. Initial program 98.1%

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

   2. Taylor expanded in x1 around 0 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 77.3%

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

      2. neg-mul-1 77.3%

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

      3. unsub-neg 77.3%

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

      4. *-commutative 77.3%

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

   4. Simplified 91.2%

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

   5. Taylor expanded in x1 around 0 90.5%

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

   if 1.99999999999999996e123 < x1

   1. Initial program 11.6%

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

   2. Taylor expanded in x1 around 0 5.0%

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

   3. Taylor expanded in x1 around 0 83.7%

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

      1. +-commutative 83.7%

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

      2. mul-1-neg 83.7%

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

      3. unsub-neg 83.7%

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

      4. *-commutative 83.7%

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

      5. fma-def 83.7%

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

      6. +-commutative 83.7%

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

      7. cube-mult 83.7%

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

      8. unpow2 83.7%

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

      9. distribute-rgt-out 97.7%

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

      10. unpow2 97.7%

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

      11. *-commutative 97.7%

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

   5. Simplified 97.7%

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

   6. Taylor expanded in x2 around 0 100.0%

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

      1. unpow2 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.4 \cdot 10^{+84}:\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+123}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 6\right) + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 + 3\right) - x1\right)\right)\\ \end{array} \]

Alternative 11: 70.0% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.1 \cdot 10^{+77} \lor \neg \left(x1 \leq 7.6 \cdot 10^{+81}\right):\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -1.1e+77) (not (<= x1 7.6e+81)))
   (+ x1 (* 3.0 (* x1 (* x1 (+ x1 (+ 3.0 (* x2 2.0)))))))
   (+
    x1
    (+
     (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* x2 2.0)) x1) (+ 1.0 (* x1 x1))))
     (+ x1 (* 4.0 (* x2 (* x1 (- (* x2 2.0) 3.0)))))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -1.1e+77) || !(x1 <= 7.6e+81)) {
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	} else {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (x2 * 2.0)) - x1) / (1.0 + (x1 * x1)))) + (x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-1.1d+77)) .or. (.not. (x1 <= 7.6d+81))) then
        tmp = x1 + (3.0d0 * (x1 * (x1 * (x1 + (3.0d0 + (x2 * 2.0d0))))))
    else
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (x2 * 2.0d0)) - x1) / (1.0d0 + (x1 * x1)))) + (x1 + (4.0d0 * (x2 * (x1 * ((x2 * 2.0d0) - 3.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -1.1e+77) || !(x1 <= 7.6e+81)) {
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	} else {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (x2 * 2.0)) - x1) / (1.0 + (x1 * x1)))) + (x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -1.1e+77) or not (x1 <= 7.6e+81):
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))))
	else:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (x2 * 2.0)) - x1) / (1.0 + (x1 * x1)))) + (x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -1.1e+77) || !(x1 <= 7.6e+81))
		tmp = Float64(x1 + Float64(3.0 * Float64(x1 * Float64(x1 * Float64(x1 + Float64(3.0 + Float64(x2 * 2.0)))))));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(x2 * 2.0)) - x1) / Float64(1.0 + Float64(x1 * x1)))) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(x2 * 2.0) - 3.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -1.1e+77) || ~((x1 <= 7.6e+81)))
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	else
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (x2 * 2.0)) - x1) / (1.0 + (x1 * x1)))) + (x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -1.1e+77], N[Not[LessEqual[x1, 7.6e+81]], $MachinePrecision]], N[(x1 + N[(3.0 * N[(x1 * N[(x1 * N[(x1 + N[(3.0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.1e77 or 7.599999999999999e81 < x1

   1. Initial program 17.5%

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

   2. Taylor expanded in x1 around 0 6.6%

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

   3. Taylor expanded in x1 around 0 44.4%

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

      1. +-commutative 44.4%

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

      2. mul-1-neg 44.4%

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

      3. unsub-neg 44.4%

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

      4. *-commutative 44.4%

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

      5. fma-def 44.4%

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

      6. +-commutative 44.4%

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

      7. cube-mult 44.4%

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

      8. unpow2 44.4%

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

      9. distribute-rgt-out 50.6%

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

      10. unpow2 50.6%

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

      11. *-commutative 50.6%

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

   5. Simplified 50.6%

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

   6. Taylor expanded in x1 around inf 45.5%

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

      1. distribute-lft-out 45.5%

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

      2. *-commutative 45.5%

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

      3. unpow3 45.5%

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

      4. unpow2 45.5%

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

      5. distribute-lft-in 57.9%

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

      6. +-commutative 57.9%

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

      7. unpow2 57.9%

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

      8. associate-*l* 57.9%

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

      9. *-commutative 57.9%

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

      10. cancel-sign-sub-inv 57.9%

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

      11. metadata-eval 57.9%

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

      12. *-commutative 57.9%

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

   8. Simplified 57.9%

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

   if -1.1e77 < x1 < 7.599999999999999e81

   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 82.3%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.1 \cdot 10^{+77} \lor \neg \left(x1 \leq 7.6 \cdot 10^{+81}\right):\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 12: 71.1% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.75 \cdot 10^{+76} \lor \neg \left(x1 \leq 7.6 \cdot 10^{+81}\right):\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + 8 \cdot \frac{x2}{\frac{x1 + \frac{1}{x1}}{x2}}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -1.75e+76) (not (<= x1 7.6e+81)))
   (+ x1 (* 3.0 (* x1 (* x1 (+ x1 (+ 3.0 (* x2 2.0)))))))
   (+
    x1
    (+
     (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* x2 2.0)) x1) (+ 1.0 (* x1 x1))))
     (+ x1 (* 8.0 (/ x2 (/ (+ x1 (/ 1.0 x1)) x2))))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -1.75e+76) || !(x1 <= 7.6e+81)) {
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	} else {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (x2 * 2.0)) - x1) / (1.0 + (x1 * x1)))) + (x1 + (8.0 * (x2 / ((x1 + (1.0 / x1)) / x2)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-1.75d+76)) .or. (.not. (x1 <= 7.6d+81))) then
        tmp = x1 + (3.0d0 * (x1 * (x1 * (x1 + (3.0d0 + (x2 * 2.0d0))))))
    else
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (x2 * 2.0d0)) - x1) / (1.0d0 + (x1 * x1)))) + (x1 + (8.0d0 * (x2 / ((x1 + (1.0d0 / x1)) / x2)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -1.75e+76) || !(x1 <= 7.6e+81)) {
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	} else {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (x2 * 2.0)) - x1) / (1.0 + (x1 * x1)))) + (x1 + (8.0 * (x2 / ((x1 + (1.0 / x1)) / x2)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -1.75e+76) or not (x1 <= 7.6e+81):
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))))
	else:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (x2 * 2.0)) - x1) / (1.0 + (x1 * x1)))) + (x1 + (8.0 * (x2 / ((x1 + (1.0 / x1)) / x2)))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -1.75e+76) || !(x1 <= 7.6e+81))
		tmp = Float64(x1 + Float64(3.0 * Float64(x1 * Float64(x1 * Float64(x1 + Float64(3.0 + Float64(x2 * 2.0)))))));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(x2 * 2.0)) - x1) / Float64(1.0 + Float64(x1 * x1)))) + Float64(x1 + Float64(8.0 * Float64(x2 / Float64(Float64(x1 + Float64(1.0 / x1)) / x2))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -1.75e+76) || ~((x1 <= 7.6e+81)))
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	else
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (x2 * 2.0)) - x1) / (1.0 + (x1 * x1)))) + (x1 + (8.0 * (x2 / ((x1 + (1.0 / x1)) / x2)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -1.75e+76], N[Not[LessEqual[x1, 7.6e+81]], $MachinePrecision]], N[(x1 + N[(3.0 * N[(x1 * N[(x1 * N[(x1 + N[(3.0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(8.0 * N[(x2 / N[(N[(x1 + N[(1.0 / x1), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.75e76 or 7.599999999999999e81 < x1

   1. Initial program 17.5%

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

   2. Taylor expanded in x1 around 0 6.6%

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

   3. Taylor expanded in x1 around 0 44.4%

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

      1. +-commutative 44.4%

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

      2. mul-1-neg 44.4%

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

      3. unsub-neg 44.4%

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

      4. *-commutative 44.4%

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

      5. fma-def 44.4%

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

      6. +-commutative 44.4%

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

      7. cube-mult 44.4%

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

      8. unpow2 44.4%

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

      9. distribute-rgt-out 50.6%

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

      10. unpow2 50.6%

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

      11. *-commutative 50.6%

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

   5. Simplified 50.6%

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

   6. Taylor expanded in x1 around inf 45.5%

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

      1. distribute-lft-out 45.5%

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

      2. *-commutative 45.5%

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

      3. unpow3 45.5%

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

      4. unpow2 45.5%

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

      5. distribute-lft-in 57.9%

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

      6. +-commutative 57.9%

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

      7. unpow2 57.9%

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

      8. associate-*l* 57.9%

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

      9. *-commutative 57.9%

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

      10. cancel-sign-sub-inv 57.9%

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

      11. metadata-eval 57.9%

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

      12. *-commutative 57.9%

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

   8. Simplified 57.9%

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

   if -1.75e76 < x1 < 7.599999999999999e81

   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 x2 around inf 73.7%

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

      1. associate-/l* 74.3%

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

      2. unpow2 74.3%

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

      3. +-commutative 74.3%

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

      4. unpow2 74.3%

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

      5. fma-udef 74.3%

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

   4. Simplified 74.3%

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

   5. Taylor expanded in x1 around 0 74.3%

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

   6. Taylor expanded in x2 around 0 74.3%

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

      1. unpow2 74.3%

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

      2. associate-/l* 84.4%

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

   8. Simplified 84.4%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.75 \cdot 10^{+76} \lor \neg \left(x1 \leq 7.6 \cdot 10^{+81}\right):\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + 8 \cdot \frac{x2}{\frac{x1 + \frac{1}{x1}}{x2}}\right)\right)\\ \end{array} \]

Alternative 13: 63.3% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right) + x2 \cdot -6\right)\\ \mathbf{if}\;x1 \leq -1.6 \cdot 10^{-201}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 2.3 \cdot 10^{-209}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 7.6 \cdot 10^{+81}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (+
          x1
          (+ (* x1 (- (* 4.0 (* x2 (- (* x2 2.0) 3.0))) 2.0)) (* x2 -6.0)))))
   (if (<= x1 -1.6e-201)
     t_0
     (if (<= x1 2.3e-209)
       (+ x1 (* x2 -6.0))
       (if (<= x1 7.6e+81)
         t_0
         (+ x1 (* 3.0 (* x1 (* x1 (+ x1 (+ 3.0 (* x2 2.0))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0)) + (x2 * -6.0));
	double tmp;
	if (x1 <= -1.6e-201) {
		tmp = t_0;
	} else if (x1 <= 2.3e-209) {
		tmp = x1 + (x2 * -6.0);
	} else if (x1 <= 7.6e+81) {
		tmp = t_0;
	} else {
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + ((x1 * ((4.0d0 * (x2 * ((x2 * 2.0d0) - 3.0d0))) - 2.0d0)) + (x2 * (-6.0d0)))
    if (x1 <= (-1.6d-201)) then
        tmp = t_0
    else if (x1 <= 2.3d-209) then
        tmp = x1 + (x2 * (-6.0d0))
    else if (x1 <= 7.6d+81) then
        tmp = t_0
    else
        tmp = x1 + (3.0d0 * (x1 * (x1 * (x1 + (3.0d0 + (x2 * 2.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0)) + (x2 * -6.0));
	double tmp;
	if (x1 <= -1.6e-201) {
		tmp = t_0;
	} else if (x1 <= 2.3e-209) {
		tmp = x1 + (x2 * -6.0);
	} else if (x1 <= 7.6e+81) {
		tmp = t_0;
	} else {
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0)) + (x2 * -6.0))
	tmp = 0
	if x1 <= -1.6e-201:
		tmp = t_0
	elif x1 <= 2.3e-209:
		tmp = x1 + (x2 * -6.0)
	elif x1 <= 7.6e+81:
		tmp = t_0
	else:
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(x2 * 2.0) - 3.0))) - 2.0)) + Float64(x2 * -6.0)))
	tmp = 0.0
	if (x1 <= -1.6e-201)
		tmp = t_0;
	elseif (x1 <= 2.3e-209)
		tmp = Float64(x1 + Float64(x2 * -6.0));
	elseif (x1 <= 7.6e+81)
		tmp = t_0;
	else
		tmp = Float64(x1 + Float64(3.0 * Float64(x1 * Float64(x1 * Float64(x1 + Float64(3.0 + Float64(x2 * 2.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0)) + (x2 * -6.0));
	tmp = 0.0;
	if (x1 <= -1.6e-201)
		tmp = t_0;
	elseif (x1 <= 2.3e-209)
		tmp = x1 + (x2 * -6.0);
	elseif (x1 <= 7.6e+81)
		tmp = t_0;
	else
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.6e-201], t$95$0, If[LessEqual[x1, 2.3e-209], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7.6e+81], t$95$0, N[(x1 + N[(3.0 * N[(x1 * N[(x1 * N[(x1 + N[(3.0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.6000000000000001e-201 or 2.3e-209 < x1 < 7.599999999999999e81

   1. Initial program 75.7%

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

   2. Taylor expanded in x1 around 0 58.0%

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

   3. Taylor expanded in x1 around 0 55.1%

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

   if -1.6000000000000001e-201 < x1 < 2.3e-209

   1. Initial program 99.5%

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

   2. Taylor expanded in x1 around 0 99.5%

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

   3. Taylor expanded in x1 around 0 86.3%

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

      1. *-commutative 86.3%

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

   5. Simplified 86.3%

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

   if 7.599999999999999e81 < x1

   1. Initial program 25.9%

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

   2. Taylor expanded in x1 around 0 11.8%

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

   3. Taylor expanded in x1 around 0 79.8%

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

      1. +-commutative 79.8%

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

      2. mul-1-neg 79.8%

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

      3. unsub-neg 79.8%

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

      4. *-commutative 79.8%

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

      5. fma-def 79.8%

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

      6. +-commutative 79.8%

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

      7. cube-mult 79.8%

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

      8. unpow2 79.8%

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

      9. distribute-rgt-out 90.9%

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

      10. unpow2 90.9%

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

      11. *-commutative 90.9%

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

   5. Simplified 90.9%

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

   6. Taylor expanded in x1 around inf 79.8%

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

      1. distribute-lft-out 79.8%

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

      2. *-commutative 79.8%

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

      3. unpow3 79.8%

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

      4. unpow2 79.8%

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

      5. distribute-lft-in 94.6%

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

      6. +-commutative 94.6%

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

      7. unpow2 94.6%

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

      8. associate-*l* 94.6%

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

      9. *-commutative 94.6%

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

      10. cancel-sign-sub-inv 94.6%

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

      11. metadata-eval 94.6%

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

      12. *-commutative 94.6%

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

   8. Simplified 94.6%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.6 \cdot 10^{-201}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 2.3 \cdot 10^{-209}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 7.6 \cdot 10^{+81}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right) + x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \end{array} \]

Alternative 14: 64.8% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x2 \cdot 2 - 3\\ t_1 := x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot t_0\right) - 2\right) + x2 \cdot -6\right)\\ \mathbf{if}\;x1 \leq -6.8 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq 1.32 \cdot 10^{-194}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot t_0\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 9 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* x2 2.0) 3.0))
        (t_1 (+ x1 (+ (* x1 (- (* 4.0 (* x2 t_0)) 2.0)) (* x2 -6.0)))))
   (if (<= x1 -6.8e-196)
     t_1
     (if (<= x1 1.32e-194)
       (+ x1 (+ (* 3.0 (* x2 -2.0)) (+ x1 (* 4.0 (* x2 (* x1 t_0))))))
       (if (<= x1 9e+81)
         t_1
         (+ x1 (* 3.0 (* x1 (* x1 (+ x1 (+ 3.0 (* x2 2.0))))))))))))

C

double code(double x1, double x2) {
	double t_0 = (x2 * 2.0) - 3.0;
	double t_1 = x1 + ((x1 * ((4.0 * (x2 * t_0)) - 2.0)) + (x2 * -6.0));
	double tmp;
	if (x1 <= -6.8e-196) {
		tmp = t_1;
	} else if (x1 <= 1.32e-194) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (4.0 * (x2 * (x1 * t_0)))));
	} else if (x1 <= 9e+81) {
		tmp = t_1;
	} else {
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (x2 * 2.0d0) - 3.0d0
    t_1 = x1 + ((x1 * ((4.0d0 * (x2 * t_0)) - 2.0d0)) + (x2 * (-6.0d0)))
    if (x1 <= (-6.8d-196)) then
        tmp = t_1
    else if (x1 <= 1.32d-194) then
        tmp = x1 + ((3.0d0 * (x2 * (-2.0d0))) + (x1 + (4.0d0 * (x2 * (x1 * t_0)))))
    else if (x1 <= 9d+81) then
        tmp = t_1
    else
        tmp = x1 + (3.0d0 * (x1 * (x1 * (x1 + (3.0d0 + (x2 * 2.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x2 * 2.0) - 3.0;
	double t_1 = x1 + ((x1 * ((4.0 * (x2 * t_0)) - 2.0)) + (x2 * -6.0));
	double tmp;
	if (x1 <= -6.8e-196) {
		tmp = t_1;
	} else if (x1 <= 1.32e-194) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (4.0 * (x2 * (x1 * t_0)))));
	} else if (x1 <= 9e+81) {
		tmp = t_1;
	} else {
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x2 * 2.0) - 3.0
	t_1 = x1 + ((x1 * ((4.0 * (x2 * t_0)) - 2.0)) + (x2 * -6.0))
	tmp = 0
	if x1 <= -6.8e-196:
		tmp = t_1
	elif x1 <= 1.32e-194:
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (4.0 * (x2 * (x1 * t_0)))))
	elif x1 <= 9e+81:
		tmp = t_1
	else:
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x2 * 2.0) - 3.0)
	t_1 = Float64(x1 + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * t_0)) - 2.0)) + Float64(x2 * -6.0)))
	tmp = 0.0
	if (x1 <= -6.8e-196)
		tmp = t_1;
	elseif (x1 <= 1.32e-194)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(x2 * -2.0)) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * t_0))))));
	elseif (x1 <= 9e+81)
		tmp = t_1;
	else
		tmp = Float64(x1 + Float64(3.0 * Float64(x1 * Float64(x1 * Float64(x1 + Float64(3.0 + Float64(x2 * 2.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x2 * 2.0) - 3.0;
	t_1 = x1 + ((x1 * ((4.0 * (x2 * t_0)) - 2.0)) + (x2 * -6.0));
	tmp = 0.0;
	if (x1 <= -6.8e-196)
		tmp = t_1;
	elseif (x1 <= 1.32e-194)
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (4.0 * (x2 * (x1 * t_0)))));
	elseif (x1 <= 9e+81)
		tmp = t_1;
	else
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(N[(x1 * N[(N[(4.0 * N[(x2 * t$95$0), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -6.8e-196], t$95$1, If[LessEqual[x1, 1.32e-194], N[(x1 + N[(N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x2 * N[(x1 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 9e+81], t$95$1, N[(x1 + N[(3.0 * N[(x1 * N[(x1 * N[(x1 + N[(3.0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -6.8e-196 or 1.32e-194 < x1 < 9.00000000000000034e81

   1. Initial program 74.5%

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

   2. Taylor expanded in x1 around 0 55.9%

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

   3. Taylor expanded in x1 around 0 54.1%

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

   if -6.8e-196 < x1 < 1.32e-194

   1. Initial program 99.6%

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

   2. Taylor expanded in x1 around 0 99.6%

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

   3. Taylor expanded in x1 around 0 96.3%

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

      1. *-commutative 96.3%

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

   5. Simplified 96.3%

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

   if 9.00000000000000034e81 < x1

   1. Initial program 25.9%

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

   2. Taylor expanded in x1 around 0 11.8%

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

   3. Taylor expanded in x1 around 0 79.8%

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

      1. +-commutative 79.8%

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

      2. mul-1-neg 79.8%

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

      3. unsub-neg 79.8%

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

      4. *-commutative 79.8%

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

      5. fma-def 79.8%

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

      6. +-commutative 79.8%

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

      7. cube-mult 79.8%

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

      8. unpow2 79.8%

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

      9. distribute-rgt-out 90.9%

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

      10. unpow2 90.9%

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

      11. *-commutative 90.9%

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

   5. Simplified 90.9%

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

   6. Taylor expanded in x1 around inf 79.8%

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

      1. distribute-lft-out 79.8%

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

      2. *-commutative 79.8%

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

      3. unpow3 79.8%

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

      4. unpow2 79.8%

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

      5. distribute-lft-in 94.6%

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

      6. +-commutative 94.6%

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

      7. unpow2 94.6%

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

      8. associate-*l* 94.6%

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

      9. *-commutative 94.6%

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

      10. cancel-sign-sub-inv 94.6%

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

      11. metadata-eval 94.6%

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

      12. *-commutative 94.6%

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

   8. Simplified 94.6%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6.8 \cdot 10^{-196}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 1.32 \cdot 10^{-194}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 9 \cdot 10^{+81}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right) + x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \end{array} \]

Alternative 15: 69.1% accurate, 5.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq 9.5 \cdot 10^{+81}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 9.5e+81)
   (+
    x1
    (+
     (+ x1 (* 4.0 (* x2 (* x1 (- (* x2 2.0) 3.0)))))
     (* 3.0 (- (* x2 -2.0) x1))))
   (+ x1 (* 3.0 (* x1 (* x1 (+ x1 (+ 3.0 (* x2 2.0)))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= 9.5e+81) {
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= 9.5d+81) then
        tmp = x1 + ((x1 + (4.0d0 * (x2 * (x1 * ((x2 * 2.0d0) - 3.0d0))))) + (3.0d0 * ((x2 * (-2.0d0)) - x1)))
    else
        tmp = x1 + (3.0d0 * (x1 * (x1 * (x1 + (3.0d0 + (x2 * 2.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= 9.5e+81) {
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= 9.5e+81:
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))) + (3.0 * ((x2 * -2.0) - x1)))
	else:
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= 9.5e+81)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(x2 * 2.0) - 3.0))))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	else
		tmp = Float64(x1 + Float64(3.0 * Float64(x1 * Float64(x1 * Float64(x1 + Float64(3.0 + Float64(x2 * 2.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= 9.5e+81)
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((x2 * 2.0) - 3.0))))) + (3.0 * ((x2 * -2.0) - x1)));
	else
		tmp = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, 9.5e+81], N[(x1 + N[(N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(3.0 * N[(x1 * N[(x1 * N[(x1 + N[(3.0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < 9.50000000000000083e81

   1. Initial program 79.6%

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

   2. Taylor expanded in x1 around 0 64.8%

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

   3. Taylor expanded in x1 around 0 64.9%

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

      1. +-commutative 64.9%

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

      2. mul-1-neg 64.9%

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

      3. unsub-neg 64.9%

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

      4. *-commutative 64.9%

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

   5. Simplified 64.9%

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

   if 9.50000000000000083e81 < x1

   1. Initial program 25.9%

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

   2. Taylor expanded in x1 around 0 11.8%

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

   3. Taylor expanded in x1 around 0 79.8%

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

      1. +-commutative 79.8%

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

      2. mul-1-neg 79.8%

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

      3. unsub-neg 79.8%

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

      4. *-commutative 79.8%

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

      5. fma-def 79.8%

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

      6. +-commutative 79.8%

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

      7. cube-mult 79.8%

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

      8. unpow2 79.8%

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

      9. distribute-rgt-out 90.9%

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

      10. unpow2 90.9%

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

      11. *-commutative 90.9%

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

   5. Simplified 90.9%

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

   6. Taylor expanded in x1 around inf 79.8%

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

      1. distribute-lft-out 79.8%

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

      2. *-commutative 79.8%

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

      3. unpow3 79.8%

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

      4. unpow2 79.8%

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

      5. distribute-lft-in 94.6%

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

      6. +-commutative 94.6%

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

      7. unpow2 94.6%

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

      8. associate-*l* 94.6%

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

      9. *-commutative 94.6%

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

      10. cancel-sign-sub-inv 94.6%

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

      11. metadata-eval 94.6%

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

      12. *-commutative 94.6%

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

   8. Simplified 94.6%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq 9.5 \cdot 10^{+81}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \end{array} \]

Alternative 16: 50.0% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \frac{\left(x2 \cdot x2\right) \cdot 8}{x1 + \frac{1}{x1}}\\ t_1 := x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq -1.55 \cdot 10^{-69}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 6.4 \cdot 10^{-84}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 7.6 \cdot 10^{+81}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (/ (* (* x2 x2) 8.0) (+ x1 (/ 1.0 x1)))))
        (t_1 (+ x1 (* 3.0 (* x1 (* x1 (+ x1 (+ 3.0 (* x2 2.0)))))))))
   (if (<= x1 -1.35e+78)
     t_1
     (if (<= x1 -1.55e-69)
       t_0
       (if (<= x1 6.4e-84) (+ x1 (* x2 -6.0)) (if (<= x1 7.6e+81) t_0 t_1))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (((x2 * x2) * 8.0) / (x1 + (1.0 / x1)));
	double t_1 = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	double tmp;
	if (x1 <= -1.35e+78) {
		tmp = t_1;
	} else if (x1 <= -1.55e-69) {
		tmp = t_0;
	} else if (x1 <= 6.4e-84) {
		tmp = x1 + (x2 * -6.0);
	} else if (x1 <= 7.6e+81) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x1 + (((x2 * x2) * 8.0d0) / (x1 + (1.0d0 / x1)))
    t_1 = x1 + (3.0d0 * (x1 * (x1 * (x1 + (3.0d0 + (x2 * 2.0d0))))))
    if (x1 <= (-1.35d+78)) then
        tmp = t_1
    else if (x1 <= (-1.55d-69)) then
        tmp = t_0
    else if (x1 <= 6.4d-84) then
        tmp = x1 + (x2 * (-6.0d0))
    else if (x1 <= 7.6d+81) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (((x2 * x2) * 8.0) / (x1 + (1.0 / x1)));
	double t_1 = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	double tmp;
	if (x1 <= -1.35e+78) {
		tmp = t_1;
	} else if (x1 <= -1.55e-69) {
		tmp = t_0;
	} else if (x1 <= 6.4e-84) {
		tmp = x1 + (x2 * -6.0);
	} else if (x1 <= 7.6e+81) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (((x2 * x2) * 8.0) / (x1 + (1.0 / x1)))
	t_1 = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))))
	tmp = 0
	if x1 <= -1.35e+78:
		tmp = t_1
	elif x1 <= -1.55e-69:
		tmp = t_0
	elif x1 <= 6.4e-84:
		tmp = x1 + (x2 * -6.0)
	elif x1 <= 7.6e+81:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(Float64(x2 * x2) * 8.0) / Float64(x1 + Float64(1.0 / x1))))
	t_1 = Float64(x1 + Float64(3.0 * Float64(x1 * Float64(x1 * Float64(x1 + Float64(3.0 + Float64(x2 * 2.0)))))))
	tmp = 0.0
	if (x1 <= -1.35e+78)
		tmp = t_1;
	elseif (x1 <= -1.55e-69)
		tmp = t_0;
	elseif (x1 <= 6.4e-84)
		tmp = Float64(x1 + Float64(x2 * -6.0));
	elseif (x1 <= 7.6e+81)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (((x2 * x2) * 8.0) / (x1 + (1.0 / x1)));
	t_1 = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	tmp = 0.0;
	if (x1 <= -1.35e+78)
		tmp = t_1;
	elseif (x1 <= -1.55e-69)
		tmp = t_0;
	elseif (x1 <= 6.4e-84)
		tmp = x1 + (x2 * -6.0);
	elseif (x1 <= 7.6e+81)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(N[(x2 * x2), $MachinePrecision] * 8.0), $MachinePrecision] / N[(x1 + N[(1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(3.0 * N[(x1 * N[(x1 * N[(x1 + N[(3.0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.35e+78], t$95$1, If[LessEqual[x1, -1.55e-69], t$95$0, If[LessEqual[x1, 6.4e-84], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7.6e+81], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.35000000000000002e78 or 7.599999999999999e81 < x1

   1. Initial program 17.5%

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

   2. Taylor expanded in x1 around 0 6.6%

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

   3. Taylor expanded in x1 around 0 44.4%

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

      1. +-commutative 44.4%

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

      2. mul-1-neg 44.4%

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

      3. unsub-neg 44.4%

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

      4. *-commutative 44.4%

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

      5. fma-def 44.4%

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

      6. +-commutative 44.4%

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

      7. cube-mult 44.4%

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

      8. unpow2 44.4%

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

      9. distribute-rgt-out 50.6%

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

      10. unpow2 50.6%

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

      11. *-commutative 50.6%

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

   5. Simplified 50.6%

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

   6. Taylor expanded in x1 around inf 45.5%

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

      1. distribute-lft-out 45.5%

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

      2. *-commutative 45.5%

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

      3. unpow3 45.5%

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

      4. unpow2 45.5%

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

      5. distribute-lft-in 57.9%

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

      6. +-commutative 57.9%

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

      7. unpow2 57.9%

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

      8. associate-*l* 57.9%

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

      9. *-commutative 57.9%

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

      10. cancel-sign-sub-inv 57.9%

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

      11. metadata-eval 57.9%

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

      12. *-commutative 57.9%

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

   8. Simplified 57.9%

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

   if -1.35000000000000002e78 < x1 < -1.55e-69 or 6.3999999999999999e-84 < x1 < 7.599999999999999e81

   1. Initial program 98.9%

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

   2. Taylor expanded in x2 around inf 62.9%

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

      1. associate-/l* 64.2%

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

      2. unpow2 64.2%

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

      3. +-commutative 64.2%

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

      4. unpow2 64.2%

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

      5. fma-udef 64.2%

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

   4. Simplified 64.2%

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

   5. Taylor expanded in x1 around 0 64.3%

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

   6. Taylor expanded in x2 around inf 37.8%

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

      1. associate-*r/ 37.8%

         \[\leadsto x1 + \color{blue}{\frac{8 \cdot {x2}^{2}}{x1 + \frac{1}{x1}}} \]

      2. unpow2 37.8%

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

   8. Simplified 37.8%

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

   if -1.55e-69 < x1 < 6.3999999999999999e-84

   1. Initial program 99.5%

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

   2. Taylor expanded in x1 around 0 99.5%

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

   3. Taylor expanded in x1 around 0 65.1%

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

      1. *-commutative 65.1%

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

   5. Simplified 65.1%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+78}:\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.55 \cdot 10^{-69}:\\ \;\;\;\;x1 + \frac{\left(x2 \cdot x2\right) \cdot 8}{x1 + \frac{1}{x1}}\\ \mathbf{elif}\;x1 \leq 6.4 \cdot 10^{-84}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 7.6 \cdot 10^{+81}:\\ \;\;\;\;x1 + \frac{\left(x2 \cdot x2\right) \cdot 8}{x1 + \frac{1}{x1}}\\ \mathbf{else}:\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \end{array} \]

Alternative 17: 49.1% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -6.8 \cdot 10^{+74}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq -4.3 \cdot 10^{-73}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - \frac{3 + \left(x2 \cdot x2\right) \cdot -8}{x1}\right)\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{-86}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 7.6 \cdot 10^{+81}:\\ \;\;\;\;x1 + \frac{\left(x2 \cdot x2\right) \cdot 8}{x1 + \frac{1}{x1}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* 3.0 (* x1 (* x1 (+ x1 (+ 3.0 (* x2 2.0)))))))))
   (if (<= x1 -6.8e+74)
     t_0
     (if (<= x1 -4.3e-73)
       (+ x1 (+ 9.0 (- x1 (/ (+ 3.0 (* (* x2 x2) -8.0)) x1))))
       (if (<= x1 4.5e-86)
         (+ x1 (* x2 -6.0))
         (if (<= x1 7.6e+81)
           (+ x1 (/ (* (* x2 x2) 8.0) (+ x1 (/ 1.0 x1))))
           t_0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	double tmp;
	if (x1 <= -6.8e+74) {
		tmp = t_0;
	} else if (x1 <= -4.3e-73) {
		tmp = x1 + (9.0 + (x1 - ((3.0 + ((x2 * x2) * -8.0)) / x1)));
	} else if (x1 <= 4.5e-86) {
		tmp = x1 + (x2 * -6.0);
	} else if (x1 <= 7.6e+81) {
		tmp = x1 + (((x2 * x2) * 8.0) / (x1 + (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) :: tmp
    t_0 = x1 + (3.0d0 * (x1 * (x1 * (x1 + (3.0d0 + (x2 * 2.0d0))))))
    if (x1 <= (-6.8d+74)) then
        tmp = t_0
    else if (x1 <= (-4.3d-73)) then
        tmp = x1 + (9.0d0 + (x1 - ((3.0d0 + ((x2 * x2) * (-8.0d0))) / x1)))
    else if (x1 <= 4.5d-86) then
        tmp = x1 + (x2 * (-6.0d0))
    else if (x1 <= 7.6d+81) then
        tmp = x1 + (((x2 * x2) * 8.0d0) / (x1 + (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 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	double tmp;
	if (x1 <= -6.8e+74) {
		tmp = t_0;
	} else if (x1 <= -4.3e-73) {
		tmp = x1 + (9.0 + (x1 - ((3.0 + ((x2 * x2) * -8.0)) / x1)));
	} else if (x1 <= 4.5e-86) {
		tmp = x1 + (x2 * -6.0);
	} else if (x1 <= 7.6e+81) {
		tmp = x1 + (((x2 * x2) * 8.0) / (x1 + (1.0 / x1)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))))
	tmp = 0
	if x1 <= -6.8e+74:
		tmp = t_0
	elif x1 <= -4.3e-73:
		tmp = x1 + (9.0 + (x1 - ((3.0 + ((x2 * x2) * -8.0)) / x1)))
	elif x1 <= 4.5e-86:
		tmp = x1 + (x2 * -6.0)
	elif x1 <= 7.6e+81:
		tmp = x1 + (((x2 * x2) * 8.0) / (x1 + (1.0 / x1)))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(3.0 * Float64(x1 * Float64(x1 * Float64(x1 + Float64(3.0 + Float64(x2 * 2.0)))))))
	tmp = 0.0
	if (x1 <= -6.8e+74)
		tmp = t_0;
	elseif (x1 <= -4.3e-73)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 - Float64(Float64(3.0 + Float64(Float64(x2 * x2) * -8.0)) / x1))));
	elseif (x1 <= 4.5e-86)
		tmp = Float64(x1 + Float64(x2 * -6.0));
	elseif (x1 <= 7.6e+81)
		tmp = Float64(x1 + Float64(Float64(Float64(x2 * x2) * 8.0) / Float64(x1 + Float64(1.0 / x1))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (3.0 * (x1 * (x1 * (x1 + (3.0 + (x2 * 2.0))))));
	tmp = 0.0;
	if (x1 <= -6.8e+74)
		tmp = t_0;
	elseif (x1 <= -4.3e-73)
		tmp = x1 + (9.0 + (x1 - ((3.0 + ((x2 * x2) * -8.0)) / x1)));
	elseif (x1 <= 4.5e-86)
		tmp = x1 + (x2 * -6.0);
	elseif (x1 <= 7.6e+81)
		tmp = x1 + (((x2 * x2) * 8.0) / (x1 + (1.0 / x1)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(3.0 * N[(x1 * N[(x1 * N[(x1 + N[(3.0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -6.8e+74], t$95$0, If[LessEqual[x1, -4.3e-73], N[(x1 + N[(9.0 + N[(x1 - N[(N[(3.0 + N[(N[(x2 * x2), $MachinePrecision] * -8.0), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.5e-86], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7.6e+81], N[(x1 + N[(N[(N[(x2 * x2), $MachinePrecision] * 8.0), $MachinePrecision] / N[(x1 + N[(1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -6.7999999999999998e74 or 7.599999999999999e81 < x1

   1. Initial program 17.5%

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

   2. Taylor expanded in x1 around 0 6.6%

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

   3. Taylor expanded in x1 around 0 44.4%

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

      1. +-commutative 44.4%

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

      2. mul-1-neg 44.4%

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

      3. unsub-neg 44.4%

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

      4. *-commutative 44.4%

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

      5. fma-def 44.4%

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

      6. +-commutative 44.4%

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

      7. cube-mult 44.4%

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

      8. unpow2 44.4%

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

      9. distribute-rgt-out 50.6%

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

      10. unpow2 50.6%

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

      11. *-commutative 50.6%

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

   5. Simplified 50.6%

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

   6. Taylor expanded in x1 around inf 45.5%

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

      1. distribute-lft-out 45.5%

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

      2. *-commutative 45.5%

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

      3. unpow3 45.5%

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

      4. unpow2 45.5%

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

      5. distribute-lft-in 57.9%

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

      6. +-commutative 57.9%

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

      7. unpow2 57.9%

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

      8. associate-*l* 57.9%

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

      9. *-commutative 57.9%

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

      10. cancel-sign-sub-inv 57.9%

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

      11. metadata-eval 57.9%

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

      12. *-commutative 57.9%

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

   8. Simplified 57.9%

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

   if -6.7999999999999998e74 < x1 < -4.2999999999999999e-73

   1. Initial program 99.0%

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

   2. Taylor expanded in x2 around inf 60.0%

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

      1. associate-/l* 60.0%

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

      2. unpow2 60.0%

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

      3. +-commutative 60.0%

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

      4. unpow2 60.0%

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

      5. fma-udef 60.0%

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

   4. Simplified 60.0%

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

   5. Taylor expanded in x1 around -inf 35.7%

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

      1. mul-1-neg 35.7%

         \[\leadsto x1 + \left(9 + \left(x1 + \color{blue}{\left(-\frac{3 + -8 \cdot {x2}^{2}}{x1}\right)}\right)\right) \]

      2. unsub-neg 35.7%

         \[\leadsto x1 + \left(9 + \color{blue}{\left(x1 - \frac{3 + -8 \cdot {x2}^{2}}{x1}\right)}\right) \]

      3. *-commutative 35.7%

         \[\leadsto x1 + \left(9 + \left(x1 - \frac{3 + \color{blue}{{x2}^{2} \cdot -8}}{x1}\right)\right) \]

      4. unpow2 35.7%

         \[\leadsto x1 + \left(9 + \left(x1 - \frac{3 + \color{blue}{\left(x2 \cdot x2\right)} \cdot -8}{x1}\right)\right) \]

   7. Simplified 35.7%

      \[\leadsto x1 + \color{blue}{\left(9 + \left(x1 - \frac{3 + \left(x2 \cdot x2\right) \cdot -8}{x1}\right)\right)} \]

   if -4.2999999999999999e-73 < x1 < 4.4999999999999998e-86

   1. Initial program 99.5%

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

   2. Taylor expanded in x1 around 0 99.5%

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

   3. Taylor expanded in x1 around 0 65.8%

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

      1. *-commutative 65.8%

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

   5. Simplified 65.8%

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

   if 4.4999999999999998e-86 < x1 < 7.599999999999999e81

   1. Initial program 98.8%

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

   2. Taylor expanded in x2 around inf 65.6%

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

      1. associate-/l* 67.8%

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

      2. unpow2 67.8%

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

      3. +-commutative 67.8%

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

      4. unpow2 67.8%

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

      5. fma-udef 67.8%

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

   4. Simplified 67.8%

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

   5. Taylor expanded in x1 around 0 67.8%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\color{blue}{x1 + \frac{1}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   6. Taylor expanded in x2 around inf 38.8%

      \[\leadsto x1 + \color{blue}{8 \cdot \frac{{x2}^{2}}{x1 + \frac{1}{x1}}} \]
   7. Step-by-step derivation

      1. associate-*r/ 38.8%

         \[\leadsto x1 + \color{blue}{\frac{8 \cdot {x2}^{2}}{x1 + \frac{1}{x1}}} \]

      2. unpow2 38.8%

         \[\leadsto x1 + \frac{8 \cdot \color{blue}{\left(x2 \cdot x2\right)}}{x1 + \frac{1}{x1}} \]

   8. Simplified 38.8%

      \[\leadsto x1 + \color{blue}{\frac{8 \cdot \left(x2 \cdot x2\right)}{x1 + \frac{1}{x1}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6.8 \cdot 10^{+74}:\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -4.3 \cdot 10^{-73}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - \frac{3 + \left(x2 \cdot x2\right) \cdot -8}{x1}\right)\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{-86}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 7.6 \cdot 10^{+81}:\\ \;\;\;\;x1 + \frac{\left(x2 \cdot x2\right) \cdot 8}{x1 + \frac{1}{x1}}\\ \mathbf{else}:\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 + \left(3 + x2 \cdot 2\right)\right)\right)\right)\\ \end{array} \]

Alternative 18: 50.9% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \mathbf{if}\;x2 \leq -1.16 \cdot 10^{+117}:\\ \;\;\;\;x1 + \left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ \mathbf{elif}\;x2 \leq -3.2 \cdot 10^{-71}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x2 \leq 2.6 \cdot 10^{-136}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 + 3\right) - x1\right)\right)\\ \mathbf{elif}\;x2 \leq 1.55 \cdot 10^{+109}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0)))))
   (if (<= x2 -1.16e+117)
     (+ x1 (* (* x2 x2) (* x1 8.0)))
     (if (<= x2 -3.2e-71)
       t_0
       (if (<= x2 2.6e-136)
         (+ x1 (+ x1 (* 3.0 (- (* (* x1 x1) (+ x1 3.0)) x1))))
         (if (<= x2 1.55e+109)
           t_0
           (+ x1 (* x1 (+ 1.0 (* 4.0 (* x2 (- (* x2 2.0) 3.0))))))))))))

C

double code(double x1, double x2) {
	double t_0 = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	double tmp;
	if (x2 <= -1.16e+117) {
		tmp = x1 + ((x2 * x2) * (x1 * 8.0));
	} else if (x2 <= -3.2e-71) {
		tmp = t_0;
	} else if (x2 <= 2.6e-136) {
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	} else if (x2 <= 1.55e+109) {
		tmp = t_0;
	} else {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    if (x2 <= (-1.16d+117)) then
        tmp = x1 + ((x2 * x2) * (x1 * 8.0d0))
    else if (x2 <= (-3.2d-71)) then
        tmp = t_0
    else if (x2 <= 2.6d-136) then
        tmp = x1 + (x1 + (3.0d0 * (((x1 * x1) * (x1 + 3.0d0)) - x1)))
    else if (x2 <= 1.55d+109) then
        tmp = t_0
    else
        tmp = x1 + (x1 * (1.0d0 + (4.0d0 * (x2 * ((x2 * 2.0d0) - 3.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	double tmp;
	if (x2 <= -1.16e+117) {
		tmp = x1 + ((x2 * x2) * (x1 * 8.0));
	} else if (x2 <= -3.2e-71) {
		tmp = t_0;
	} else if (x2 <= 2.6e-136) {
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	} else if (x2 <= 1.55e+109) {
		tmp = t_0;
	} else {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	tmp = 0
	if x2 <= -1.16e+117:
		tmp = x1 + ((x2 * x2) * (x1 * 8.0))
	elif x2 <= -3.2e-71:
		tmp = t_0
	elif x2 <= 2.6e-136:
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)))
	elif x2 <= 1.55e+109:
		tmp = t_0
	else:
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)))
	tmp = 0.0
	if (x2 <= -1.16e+117)
		tmp = Float64(x1 + Float64(Float64(x2 * x2) * Float64(x1 * 8.0)));
	elseif (x2 <= -3.2e-71)
		tmp = t_0;
	elseif (x2 <= 2.6e-136)
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(Float64(Float64(x1 * x1) * Float64(x1 + 3.0)) - x1))));
	elseif (x2 <= 1.55e+109)
		tmp = t_0;
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(x2 * 2.0) - 3.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	tmp = 0.0;
	if (x2 <= -1.16e+117)
		tmp = x1 + ((x2 * x2) * (x1 * 8.0));
	elseif (x2 <= -3.2e-71)
		tmp = t_0;
	elseif (x2 <= 2.6e-136)
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	elseif (x2 <= 1.55e+109)
		tmp = t_0;
	else
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x2, -1.16e+117], N[(x1 + N[(N[(x2 * x2), $MachinePrecision] * N[(x1 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x2, -3.2e-71], t$95$0, If[LessEqual[x2, 2.6e-136], N[(x1 + N[(x1 + N[(3.0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x2, 1.55e+109], t$95$0, N[(x1 + N[(x1 * N[(1.0 + N[(4.0 * N[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x2 < -1.1600000000000001e117

   1. Initial program 82.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 82.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x2 around inf 69.3%

      \[\leadsto x1 + \color{blue}{8 \cdot \left({x2}^{2} \cdot x1\right)} \]
   4. Step-by-step derivation

      1. *-commutative 69.3%

         \[\leadsto x1 + \color{blue}{\left({x2}^{2} \cdot x1\right) \cdot 8} \]

      2. associate-*l* 69.3%

         \[\leadsto x1 + \color{blue}{{x2}^{2} \cdot \left(x1 \cdot 8\right)} \]

      3. unpow2 69.3%

         \[\leadsto x1 + \color{blue}{\left(x2 \cdot x2\right)} \cdot \left(x1 \cdot 8\right) \]

   5. Simplified 69.3%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)} \]

   if -1.1600000000000001e117 < x2 < -3.1999999999999999e-71 or 2.59999999999999997e-136 < x2 < 1.54999999999999996e109

   1. Initial program 68.5%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 47.4%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 42.9%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 42.9%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 42.9%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
   6. Step-by-step derivation

      1. flip-+ 55.3%

         \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]

   7. Applied egg-rr 55.3%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]
   8. Step-by-step derivation

      1. swap-sqr 55.2%

         \[\leadsto \frac{x1 \cdot x1 - \color{blue}{\left(x2 \cdot x2\right) \cdot \left(-6 \cdot -6\right)}}{x1 - x2 \cdot -6} \]

      2. metadata-eval 55.2%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot \color{blue}{36}}{x1 - x2 \cdot -6} \]

   9. Simplified 55.2%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}} \]

   if -3.1999999999999999e-71 < x2 < 2.59999999999999997e-136

   1. Initial program 62.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 46.7%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 72.4%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + {x1}^{3}\right)\right)\right)}\right) \]
   4. Step-by-step derivation

      1. +-commutative 72.4%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + {x1}^{3}\right)\right) + -1 \cdot x1\right)}\right) \]

      2. mul-1-neg 72.4%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + {x1}^{3}\right)\right) + \color{blue}{\left(-x1\right)}\right)\right) \]

      3. unsub-neg 72.4%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + {x1}^{3}\right)\right) - x1\right)}\right) \]

      4. *-commutative 72.4%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{x2 \cdot -2} + \left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + {x1}^{3}\right)\right) - x1\right)\right) \]

      5. fma-def 72.4%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left(x2, -2, \left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + {x1}^{3}\right)} - x1\right)\right) \]

      6. +-commutative 72.4%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x2, -2, \color{blue}{{x1}^{3} + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}}\right) - x1\right)\right) \]

      7. cube-mult 72.4%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x2, -2, \color{blue}{x1 \cdot \left(x1 \cdot x1\right)} + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)\right) \]

      8. unpow2 72.4%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x2, -2, x1 \cdot \color{blue}{{x1}^{2}} + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)\right) \]

      9. distribute-rgt-out 72.4%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x2, -2, \color{blue}{{x1}^{2} \cdot \left(x1 + \left(3 - -2 \cdot x2\right)\right)}\right) - x1\right)\right) \]

      10. unpow2 72.4%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x2, -2, \color{blue}{\left(x1 \cdot x1\right)} \cdot \left(x1 + \left(3 - -2 \cdot x2\right)\right)\right) - x1\right)\right) \]

      11. *-commutative 72.4%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x2, -2, \left(x1 \cdot x1\right) \cdot \left(x1 + \left(3 - \color{blue}{x2 \cdot -2}\right)\right)\right) - x1\right)\right) \]

   5. Simplified 72.4%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\mathsf{fma}\left(x2, -2, \left(x1 \cdot x1\right) \cdot \left(x1 + \left(3 - x2 \cdot -2\right)\right)\right) - x1\right)}\right) \]

   6. Taylor expanded in x2 around 0 64.4%

      \[\leadsto x1 + \color{blue}{\left(x1 + 3 \cdot \left({x1}^{2} \cdot \left(3 + x1\right) - x1\right)\right)} \]
   7. Step-by-step derivation

      1. unpow2 64.4%

         \[\leadsto x1 + \left(x1 + 3 \cdot \left(\color{blue}{\left(x1 \cdot x1\right)} \cdot \left(3 + x1\right) - x1\right)\right) \]

   8. Simplified 64.4%

      \[\leadsto x1 + \color{blue}{\left(x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 + x1\right) - x1\right)\right)} \]

   if 1.54999999999999996e109 < x2

   1. Initial program 68.8%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 62.3%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around inf 50.1%

      \[\leadsto x1 + \color{blue}{x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.16 \cdot 10^{+117}:\\ \;\;\;\;x1 + \left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ \mathbf{elif}\;x2 \leq -3.2 \cdot 10^{-71}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \mathbf{elif}\;x2 \leq 2.6 \cdot 10^{-136}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 + 3\right) - x1\right)\right)\\ \mathbf{elif}\;x2 \leq 1.55 \cdot 10^{+109}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\\ \end{array} \]

Alternative 19: 40.8% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -6.2 \cdot 10^{-68}:\\ \;\;\;\;x1 + \frac{\left(x2 \cdot x2\right) \cdot 8}{x1 + \frac{1}{x1}}\\ \mathbf{elif}\;x1 \leq 6.4 \cdot 10^{-84}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -6.2e-68)
   (+ x1 (/ (* (* x2 x2) 8.0) (+ x1 (/ 1.0 x1))))
   (if (<= x1 6.4e-84) (+ x1 (* x2 -6.0)) (+ x1 (* (* x2 x2) (* x1 8.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -6.2e-68) {
		tmp = x1 + (((x2 * x2) * 8.0) / (x1 + (1.0 / x1)));
	} else if (x1 <= 6.4e-84) {
		tmp = x1 + (x2 * -6.0);
	} else {
		tmp = x1 + ((x2 * x2) * (x1 * 8.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-6.2d-68)) then
        tmp = x1 + (((x2 * x2) * 8.0d0) / (x1 + (1.0d0 / x1)))
    else if (x1 <= 6.4d-84) then
        tmp = x1 + (x2 * (-6.0d0))
    else
        tmp = x1 + ((x2 * x2) * (x1 * 8.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -6.2e-68) {
		tmp = x1 + (((x2 * x2) * 8.0) / (x1 + (1.0 / x1)));
	} else if (x1 <= 6.4e-84) {
		tmp = x1 + (x2 * -6.0);
	} else {
		tmp = x1 + ((x2 * x2) * (x1 * 8.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -6.2e-68:
		tmp = x1 + (((x2 * x2) * 8.0) / (x1 + (1.0 / x1)))
	elif x1 <= 6.4e-84:
		tmp = x1 + (x2 * -6.0)
	else:
		tmp = x1 + ((x2 * x2) * (x1 * 8.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -6.2e-68)
		tmp = Float64(x1 + Float64(Float64(Float64(x2 * x2) * 8.0) / Float64(x1 + Float64(1.0 / x1))));
	elseif (x1 <= 6.4e-84)
		tmp = Float64(x1 + Float64(x2 * -6.0));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * x2) * Float64(x1 * 8.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -6.2e-68)
		tmp = x1 + (((x2 * x2) * 8.0) / (x1 + (1.0 / x1)));
	elseif (x1 <= 6.4e-84)
		tmp = x1 + (x2 * -6.0);
	else
		tmp = x1 + ((x2 * x2) * (x1 * 8.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -6.2e-68], N[(x1 + N[(N[(N[(x2 * x2), $MachinePrecision] * 8.0), $MachinePrecision] / N[(x1 + N[(1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6.4e-84], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * x2), $MachinePrecision] * N[(x1 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -6.1999999999999999e-68

   1. Initial program 41.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x2 around inf 22.1%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{{x2}^{2} \cdot x1}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   3. Step-by-step derivation

      1. associate-/l* 22.1%

         \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\frac{{x2}^{2}}{\frac{1 + {x1}^{2}}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. unpow2 22.1%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{\color{blue}{x2 \cdot x2}}{\frac{1 + {x1}^{2}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      3. +-commutative 22.1%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{{x1}^{2} + 1}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      4. unpow2 22.1%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{x1 \cdot x1} + 1}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      5. fma-udef 22.1%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Simplified 22.1%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Taylor expanded in x1 around 0 22.1%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\color{blue}{x1 + \frac{1}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   6. Taylor expanded in x2 around inf 13.8%

      \[\leadsto x1 + \color{blue}{8 \cdot \frac{{x2}^{2}}{x1 + \frac{1}{x1}}} \]
   7. Step-by-step derivation

      1. associate-*r/ 13.8%

         \[\leadsto x1 + \color{blue}{\frac{8 \cdot {x2}^{2}}{x1 + \frac{1}{x1}}} \]

      2. unpow2 13.8%

         \[\leadsto x1 + \frac{8 \cdot \color{blue}{\left(x2 \cdot x2\right)}}{x1 + \frac{1}{x1}} \]

   8. Simplified 13.8%

      \[\leadsto x1 + \color{blue}{\frac{8 \cdot \left(x2 \cdot x2\right)}{x1 + \frac{1}{x1}}} \]

   if -6.1999999999999999e-68 < x1 < 6.3999999999999999e-84

   1. Initial program 99.5%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 99.5%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 65.1%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 65.1%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 65.1%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   if 6.3999999999999999e-84 < x1

   1. Initial program 57.8%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 33.8%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x2 around inf 35.8%

      \[\leadsto x1 + \color{blue}{8 \cdot \left({x2}^{2} \cdot x1\right)} \]
   4. Step-by-step derivation

      1. *-commutative 35.8%

         \[\leadsto x1 + \color{blue}{\left({x2}^{2} \cdot x1\right) \cdot 8} \]

      2. associate-*l* 36.6%

         \[\leadsto x1 + \color{blue}{{x2}^{2} \cdot \left(x1 \cdot 8\right)} \]

      3. unpow2 36.6%

         \[\leadsto x1 + \color{blue}{\left(x2 \cdot x2\right)} \cdot \left(x1 \cdot 8\right) \]

   5. Simplified 36.6%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6.2 \cdot 10^{-68}:\\ \;\;\;\;x1 + \frac{\left(x2 \cdot x2\right) \cdot 8}{x1 + \frac{1}{x1}}\\ \mathbf{elif}\;x1 \leq 6.4 \cdot 10^{-84}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ \end{array} \]

Alternative 20: 40.2% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -5.3 \cdot 10^{-73} \lor \neg \left(x1 \leq 3.4 \cdot 10^{-84}\right):\\ \;\;\;\;x1 + \left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -5.3e-73) (not (<= x1 3.4e-84)))
   (+ x1 (* (* x2 x2) (* x1 8.0)))
   (+ x1 (* x2 -6.0))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -5.3e-73) || !(x1 <= 3.4e-84)) {
		tmp = x1 + ((x2 * x2) * (x1 * 8.0));
	} 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 ((x1 <= (-5.3d-73)) .or. (.not. (x1 <= 3.4d-84))) then
        tmp = x1 + ((x2 * x2) * (x1 * 8.0d0))
    else
        tmp = x1 + (x2 * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -5.3e-73) || !(x1 <= 3.4e-84)) {
		tmp = x1 + ((x2 * x2) * (x1 * 8.0));
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -5.3e-73) or not (x1 <= 3.4e-84):
		tmp = x1 + ((x2 * x2) * (x1 * 8.0))
	else:
		tmp = x1 + (x2 * -6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -5.3e-73) || !(x1 <= 3.4e-84))
		tmp = Float64(x1 + Float64(Float64(x2 * x2) * Float64(x1 * 8.0)));
	else
		tmp = Float64(x1 + Float64(x2 * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -5.3e-73) || ~((x1 <= 3.4e-84)))
		tmp = x1 + ((x2 * x2) * (x1 * 8.0));
	else
		tmp = x1 + (x2 * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -5.3e-73], N[Not[LessEqual[x1, 3.4e-84]], $MachinePrecision]], N[(x1 + N[(N[(x2 * x2), $MachinePrecision] * N[(x1 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -5.29999999999999972e-73 or 3.40000000000000021e-84 < x1

   1. Initial program 51.1%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 28.3%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x2 around inf 25.9%

      \[\leadsto x1 + \color{blue}{8 \cdot \left({x2}^{2} \cdot x1\right)} \]
   4. Step-by-step derivation

      1. *-commutative 25.9%

         \[\leadsto x1 + \color{blue}{\left({x2}^{2} \cdot x1\right) \cdot 8} \]

      2. associate-*l* 26.4%

         \[\leadsto x1 + \color{blue}{{x2}^{2} \cdot \left(x1 \cdot 8\right)} \]

      3. unpow2 26.4%

         \[\leadsto x1 + \color{blue}{\left(x2 \cdot x2\right)} \cdot \left(x1 \cdot 8\right) \]

   5. Simplified 26.4%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)} \]

   if -5.29999999999999972e-73 < x1 < 3.40000000000000021e-84

   1. Initial program 99.5%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 99.5%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 65.1%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 65.1%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 65.1%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.3 \cdot 10^{-73} \lor \neg \left(x1 \leq 3.4 \cdot 10^{-84}\right):\\ \;\;\;\;x1 + \left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \]

Alternative 21: 26.6% accurate, 25.4× speedup

Math

\[\begin{array}{l} \\ x1 + x2 \cdot -6 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (+ x1 (* x2 -6.0)))

C

double code(double x1, double x2) {
	return x1 + (x2 * -6.0);
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x1 + (x2 * (-6.0d0))
end function

Java

public static double code(double x1, double x2) {
	return x1 + (x2 * -6.0);
}

Python

def code(x1, x2):
	return x1 + (x2 * -6.0)

Julia

function code(x1, x2)
	return Float64(x1 + Float64(x2 * -6.0))
end

MATLAB

function tmp = code(x1, x2)
	tmp = x1 + (x2 * -6.0);
end

Wolfram

code[x1_, x2_] := N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 68.3%

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

2. Taylor expanded in x1 around 0 53.6%

   \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

3. Taylor expanded in x1 around 0 26.8%

   \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
4. Step-by-step derivation

   1. *-commutative 26.8%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

5. Simplified 26.8%

   \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

6. Final simplification 26.8%

   \[\leadsto x1 + x2 \cdot -6 \]

Alternative 22: 3.3% accurate, 42.3× speedup

Math

\[\begin{array}{l} \\ x1 + x1 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (+ x1 x1))

C

double code(double x1, double x2) {
	return x1 + x1;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x1 + x1
end function

Java

public static double code(double x1, double x2) {
	return x1 + x1;
}

Python

def code(x1, x2):
	return x1 + x1

Julia

function code(x1, x2)
	return Float64(x1 + x1)
end

MATLAB

function tmp = code(x1, x2)
	tmp = x1 + x1;
end

Wolfram

code[x1_, x2_] := N[(x1 + x1), $MachinePrecision]

Derivation

1. Initial program 68.3%

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

2. Taylor expanded in x2 around inf 48.3%

   \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{{x2}^{2} \cdot x1}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Step-by-step derivation

   1. associate-/l* 47.5%

      \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\frac{{x2}^{2}}{\frac{1 + {x1}^{2}}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. unpow2 47.5%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{\color{blue}{x2 \cdot x2}}{\frac{1 + {x1}^{2}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. +-commutative 47.5%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{{x1}^{2} + 1}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. unpow2 47.5%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{x1 \cdot x1} + 1}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. fma-udef 47.5%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

4. Simplified 47.5%

   \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

5. Taylor expanded in x1 around inf 3.6%

   \[\leadsto x1 + \color{blue}{\left(9 + x1\right)} \]
6. Step-by-step derivation

   1. +-commutative 3.6%

      \[\leadsto x1 + \color{blue}{\left(x1 + 9\right)} \]

7. Simplified 3.6%

   \[\leadsto x1 + \color{blue}{\left(x1 + 9\right)} \]

8. Taylor expanded in x1 around inf 3.5%

   \[\leadsto \color{blue}{2 \cdot x1} \]
9. Step-by-step derivation

   1. count-2 3.5%

      \[\leadsto \color{blue}{x1 + x1} \]

10. Simplified 3.5%

    \[\leadsto \color{blue}{x1 + x1} \]

11. Final simplification 3.5%

    \[\leadsto x1 + x1 \]

Alternative 23: 3.5% accurate, 127.0× speedup

Math

\[\begin{array}{l} \\ 9 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 9.0)

C

double code(double x1, double x2) {
	return 9.0;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = 9.0d0
end function

Java

public static double code(double x1, double x2) {
	return 9.0;
}

Python

def code(x1, x2):
	return 9.0

Julia

function code(x1, x2)
	return 9.0
end

MATLAB

function tmp = code(x1, x2)
	tmp = 9.0;
end

Wolfram

code[x1_, x2_] := 9.0

Derivation

1. Initial program 68.3%

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

2. Taylor expanded in x2 around inf 48.3%

   \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{{x2}^{2} \cdot x1}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Step-by-step derivation

   1. associate-/l* 47.5%

      \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\frac{{x2}^{2}}{\frac{1 + {x1}^{2}}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. unpow2 47.5%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{\color{blue}{x2 \cdot x2}}{\frac{1 + {x1}^{2}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. +-commutative 47.5%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{{x1}^{2} + 1}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. unpow2 47.5%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{x1 \cdot x1} + 1}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. fma-udef 47.5%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

4. Simplified 47.5%

   \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

5. Taylor expanded in x1 around inf 3.6%

   \[\leadsto x1 + \color{blue}{\left(9 + x1\right)} \]
6. Step-by-step derivation

   1. +-commutative 3.6%

      \[\leadsto x1 + \color{blue}{\left(x1 + 9\right)} \]

7. Simplified 3.6%

   \[\leadsto x1 + \color{blue}{\left(x1 + 9\right)} \]

8. Taylor expanded in x1 around 0 3.4%

   \[\leadsto \color{blue}{9} \]

9. Final simplification 3.4%

   \[\leadsto 9 \]

Alternative 24: 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 68.3%

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

2. Taylor expanded in x1 around 0 53.6%

   \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

3. Taylor expanded in x1 around 0 26.8%

   \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
4. Step-by-step derivation

   1. *-commutative 26.8%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

5. Simplified 26.8%

   \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

6. Taylor expanded in x1 around inf 3.4%

   \[\leadsto \color{blue}{x1} \]

7. Final simplification 3.4%

   \[\leadsto x1 \]

Reproduce

herbie shell --seed 2023228 
(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))))))