Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.7% → 99.5%

Time: 49.2s

Alternatives: 20

Speedup: 4.4×

• 45.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 70.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (fma x1 (* x1 3.0) (fma 2.0 x2 (- x1)))))
   (if (<= x1 -5e+153)
     (+ x1 (* x1 (* x1 9.0)))
     (if (<= x1 5e+102)
       (+
        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
        (fma
         3.0
         (* x2 -2.0)
         (fma
          x1
          (- (* x1 9.0) 3.0)
          (*
           (fma x1 x1 1.0)
           (+ x1 (* 2.0 (* (- (* x2 4.0) 6.0) (* x1 x2))))))))))))

C

double code(double x1, double x2) {
	double t_0 = fma(x1, (x1 * 3.0), fma(2.0, x2, -x1));
	double tmp;
	if (x1 <= -5e+153) {
		tmp = x1 + (x1 * (x1 * 9.0));
	} else if (x1 <= 5e+102) {
		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 + fma(3.0, (x2 * -2.0), fma(x1, ((x1 * 9.0) - 3.0), (fma(x1, x1, 1.0) * (x1 + (2.0 * (((x2 * 4.0) - 6.0) * (x1 * x2)))))));
	}
	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 <= -5e+153)
		tmp = Float64(x1 + Float64(x1 * Float64(x1 * 9.0)));
	elseif (x1 <= 5e+102)
		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 + fma(3.0, Float64(x2 * -2.0), fma(x1, Float64(Float64(x1 * 9.0) - 3.0), Float64(fma(x1, x1, 1.0) * Float64(x1 + Float64(2.0 * Float64(Float64(Float64(x2 * 4.0) - 6.0) * Float64(x1 * x2))))))));
	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, -5e+153], N[(x1 + N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+102], 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[(3.0 * N[(x2 * -2.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision] + N[(N[(x1 * x1 + 1.0), $MachinePrecision] * N[(x1 + N[(2.0 * N[(N[(N[(x2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision] * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.00000000000000018e153

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 63.0%

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

   4. Taylor expanded in x2 around 0 63.0%

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

      1. *-commutative 63.0%

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

      2. unpow2 63.0%

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

   6. Simplified 63.0%

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

   7. Taylor expanded in x1 around inf 100.0%

      \[\leadsto x1 + \color{blue}{9 \cdot {x1}^{2}} \]
   8. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto x1 + \color{blue}{{x1}^{2} \cdot 9} \]

      2. unpow2 100.0%

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

      3. associate-*r* 100.0%

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

   9. Simplified 100.0%

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

   if -5.00000000000000018e153 < x1 < 5e102

   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 99.7%

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

   if 5e102 < x1

   1. Initial program 17.4%

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

   3. Simplified 17.4%

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

   4. Taylor expanded in x1 around 0 17.4%

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

   5. Taylor expanded in x1 around inf 17.4%

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

   6. Taylor expanded in x1 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 99.8%

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

Alternative 2: 98.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 1 + x1 \cdot x1\\ t_2 := 3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_1}\\ t_3 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -4 \cdot 10^{+156}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -2 \cdot 10^{+104}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + t_2\right)\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(t_2 + \left(x1 + \left(\left(t_1 \cdot \left(\left(t_3 \cdot \left(x1 \cdot 2\right)\right) \cdot \left(t_3 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_3 - 6\right)\right) + t_0 \cdot t_3\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, x2 \cdot -2, \mathsf{fma}\left(x1, x1 \cdot 9 - 3, \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + 2 \cdot \left(\left(x2 \cdot 4 - 6\right) \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ 1.0 (* x1 x1)))
        (t_2 (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1)))
        (t_3 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (if (<= x1 -4e+156)
     (+ x1 (* x1 (* x1 9.0)))
     (if (<= x1 -2e+104)
       (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) t_2))
       (if (<= x1 6e+102)
         (+
          x1
          (+
           t_2
           (+
            x1
            (+
             (+
              (*
               t_1
               (+
                (* (* t_3 (* x1 2.0)) (- t_3 3.0))
                (* (* x1 x1) (- (* 4.0 t_3) 6.0))))
              (* t_0 t_3))
             (* x1 (* x1 x1))))))
         (+
          x1
          (fma
           3.0
           (* x2 -2.0)
           (fma
            x1
            (- (* x1 9.0) 3.0)
            (*
             (fma x1 x1 1.0)
             (+ x1 (* 2.0 (* (- (* x2 4.0) 6.0) (* x1 x2)))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 1.0 + (x1 * x1);
	double t_2 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1);
	double t_3 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if (x1 <= -4e+156) {
		tmp = x1 + (x1 * (x1 * 9.0));
	} else if (x1 <= -2e+104) {
		tmp = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + t_2);
	} else if (x1 <= 6e+102) {
		tmp = x1 + (t_2 + (x1 + (((t_1 * (((t_3 * (x1 * 2.0)) * (t_3 - 3.0)) + ((x1 * x1) * ((4.0 * t_3) - 6.0)))) + (t_0 * t_3)) + (x1 * (x1 * x1)))));
	} else {
		tmp = x1 + fma(3.0, (x2 * -2.0), fma(x1, ((x1 * 9.0) - 3.0), (fma(x1, x1, 1.0) * (x1 + (2.0 * (((x2 * 4.0) - 6.0) * (x1 * x2)))))));
	}
	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(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1))
	t_3 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if (x1 <= -4e+156)
		tmp = Float64(x1 + Float64(x1 * Float64(x1 * 9.0)));
	elseif (x1 <= -2e+104)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + t_2));
	elseif (x1 <= 6e+102)
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(Float64(Float64(t_1 * Float64(Float64(Float64(t_3 * Float64(x1 * 2.0)) * Float64(t_3 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_3) - 6.0)))) + Float64(t_0 * t_3)) + Float64(x1 * Float64(x1 * x1))))));
	else
		tmp = Float64(x1 + fma(3.0, Float64(x2 * -2.0), fma(x1, Float64(Float64(x1 * 9.0) - 3.0), Float64(fma(x1, x1, 1.0) * Float64(x1 + Float64(2.0 * Float64(Float64(Float64(x2 * 4.0) - 6.0) * Float64(x1 * x2))))))));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[x1, -4e+156], N[(x1 + N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2e+104], N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6e+102], N[(x1 + N[(t$95$2 + N[(x1 + N[(N[(N[(t$95$1 * N[(N[(N[(t$95$3 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$3), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(3.0 * N[(x2 * -2.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision] + N[(N[(x1 * x1 + 1.0), $MachinePrecision] * N[(x1 + N[(2.0 * N[(N[(N[(x2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision] * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -3.9999999999999999e156

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 63.0%

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

   4. Taylor expanded in x2 around 0 63.0%

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

      1. *-commutative 63.0%

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

      2. unpow2 63.0%

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

   6. Simplified 63.0%

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

   7. Taylor expanded in x1 around inf 100.0%

      \[\leadsto x1 + \color{blue}{9 \cdot {x1}^{2}} \]
   8. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto x1 + \color{blue}{{x1}^{2} \cdot 9} \]

      2. unpow2 100.0%

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

      3. associate-*r* 100.0%

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

   9. Simplified 100.0%

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

   if -3.9999999999999999e156 < x1 < -2e104

   1. Initial program 6.7%

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

   2. Taylor expanded in x1 around inf 93.3%

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

      1. *-commutative 93.3%

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

   4. Simplified 93.3%

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

   if -2e104 < x1 < 5.9999999999999996e102

   1. Initial program 99.4%

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

   if 5.9999999999999996e102 < x1

   1. Initial program 17.4%

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

   3. Simplified 17.4%

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

   4. Taylor expanded in x1 around 0 17.4%

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

   5. Taylor expanded in x1 around inf 17.4%

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

   6. Taylor expanded in x1 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+156}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -2 \cdot 10^{+104}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1}\right)\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(\left(\left(1 + x1 \cdot x1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, x2 \cdot -2, \mathsf{fma}\left(x1, x1 \cdot 9 - 3, \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + 2 \cdot \left(\left(x2 \cdot 4 - 6\right) \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 3: 95.6% accurate, 0.5× speedup

Math

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

FPCore

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

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

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

Python

def code(x1, x2):
	t_0 = 1.0 + (x1 * x1)
	t_1 = x1 * (x1 * 3.0)
	t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0
	t_3 = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 + (((t_0 * (((t_2 * (x1 * 2.0)) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (t_1 * t_2)) + (x1 * (x1 * x1)))))
	tmp = 0
	if t_3 <= math.inf:
		tmp = t_3
	else:
		tmp = x1 + (x1 * (x1 * 9.0))
	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(2.0 * x2)) - x1) / t_0)
	t_3 = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 + Float64(Float64(Float64(t_0 * Float64(Float64(Float64(t_2 * Float64(x1 * 2.0)) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0)))) + Float64(t_1 * t_2)) + Float64(x1 * Float64(x1 * x1))))))
	tmp = 0.0
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(x1 + Float64(x1 * Float64(x1 * 9.0)));
	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 + (2.0 * x2)) - x1) / t_0;
	t_3 = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 + (((t_0 * (((t_2 * (x1 * 2.0)) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (t_1 * t_2)) + (x1 * (x1 * x1)))));
	tmp = 0.0;
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = x1 + (x1 * (x1 * 9.0));
	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[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(N[(t$95$0 * N[(N[(N[(t$95$2 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, Infinity], t$95$3, N[(x1 + N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 51.2%

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

   4. Taylor expanded in x2 around 0 70.2%

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

      1. *-commutative 70.2%

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

      2. unpow2 70.2%

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

   6. Simplified 70.2%

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

   7. Taylor expanded in x1 around inf 83.7%

      \[\leadsto x1 + \color{blue}{9 \cdot {x1}^{2}} \]
   8. Step-by-step derivation

      1. *-commutative 83.7%

         \[\leadsto x1 + \color{blue}{{x1}^{2} \cdot 9} \]

      2. unpow2 83.7%

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

      3. associate-*r* 83.7%

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

   9. Simplified 83.7%

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

4. Final simplification 94.6%

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

Alternative 4: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 9\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := 1 + x1 \cdot x1\\ t_3 := 3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_2}\\ t_4 := \frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_2}\\ \mathbf{if}\;x1 \leq -4 \cdot 10^{+156}:\\ \;\;\;\;x1 + t_0\\ \mathbf{elif}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + t_3\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+137}:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + \left(\left(t_2 \cdot \left(\left(t_4 \cdot \left(x1 \cdot 2\right)\right) \cdot \left(t_4 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_4 - 6\right)\right) + t_1 \cdot t_4\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + \left(t_0 + x2 \cdot -6\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 9.0)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ 1.0 (* x1 x1)))
        (t_3 (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2)))
        (t_4 (/ (- (+ t_1 (* 2.0 x2)) x1) t_2)))
   (if (<= x1 -4e+156)
     (+ x1 t_0)
     (if (<= x1 -5e+102)
       (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) t_3))
       (if (<= x1 1.8e+137)
         (+
          x1
          (+
           t_3
           (+
            x1
            (+
             (+
              (*
               t_2
               (+
                (* (* t_4 (* x1 2.0)) (- t_4 3.0))
                (* (* x1 x1) (- (* 4.0 t_4) 6.0))))
              (* t_1 t_4))
             (* x1 (* x1 x1))))))
         (+
          x1
          (+
           (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0))
           (+ t_0 (* x2 -6.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 9.0);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = 1.0 + (x1 * x1);
	double t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double t_4 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	double tmp;
	if (x1 <= -4e+156) {
		tmp = x1 + t_0;
	} else if (x1 <= -5e+102) {
		tmp = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + t_3);
	} else if (x1 <= 1.8e+137) {
		tmp = x1 + (t_3 + (x1 + (((t_2 * (((t_4 * (x1 * 2.0)) * (t_4 - 3.0)) + ((x1 * x1) * ((4.0 * t_4) - 6.0)))) + (t_1 * t_4)) + (x1 * (x1 * x1)))));
	} else {
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (t_0 + (x2 * -6.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = x1 * (x1 * 9.0d0)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = 1.0d0 + (x1 * x1)
    t_3 = 3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_2)
    t_4 = ((t_1 + (2.0d0 * x2)) - x1) / t_2
    if (x1 <= (-4d+156)) then
        tmp = x1 + t_0
    else if (x1 <= (-5d+102)) then
        tmp = x1 + ((x1 + (6.0d0 * (x1 ** 4.0d0))) + t_3)
    else if (x1 <= 1.8d+137) then
        tmp = x1 + (t_3 + (x1 + (((t_2 * (((t_4 * (x1 * 2.0d0)) * (t_4 - 3.0d0)) + ((x1 * x1) * ((4.0d0 * t_4) - 6.0d0)))) + (t_1 * t_4)) + (x1 * (x1 * x1)))))
    else
        tmp = x1 + ((x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)) + (t_0 + (x2 * (-6.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 9.0);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = 1.0 + (x1 * x1);
	double t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double t_4 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	double tmp;
	if (x1 <= -4e+156) {
		tmp = x1 + t_0;
	} else if (x1 <= -5e+102) {
		tmp = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + t_3);
	} else if (x1 <= 1.8e+137) {
		tmp = x1 + (t_3 + (x1 + (((t_2 * (((t_4 * (x1 * 2.0)) * (t_4 - 3.0)) + ((x1 * x1) * ((4.0 * t_4) - 6.0)))) + (t_1 * t_4)) + (x1 * (x1 * x1)))));
	} else {
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (t_0 + (x2 * -6.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 9.0)
	t_1 = x1 * (x1 * 3.0)
	t_2 = 1.0 + (x1 * x1)
	t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)
	t_4 = ((t_1 + (2.0 * x2)) - x1) / t_2
	tmp = 0
	if x1 <= -4e+156:
		tmp = x1 + t_0
	elif x1 <= -5e+102:
		tmp = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + t_3)
	elif x1 <= 1.8e+137:
		tmp = x1 + (t_3 + (x1 + (((t_2 * (((t_4 * (x1 * 2.0)) * (t_4 - 3.0)) + ((x1 * x1) * ((4.0 * t_4) - 6.0)))) + (t_1 * t_4)) + (x1 * (x1 * x1)))))
	else:
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (t_0 + (x2 * -6.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 9.0))
	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(2.0 * x2)) - x1) / t_2))
	t_4 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_2)
	tmp = 0.0
	if (x1 <= -4e+156)
		tmp = Float64(x1 + t_0);
	elseif (x1 <= -5e+102)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + t_3));
	elseif (x1 <= 1.8e+137)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(Float64(Float64(t_2 * Float64(Float64(Float64(t_4 * Float64(x1 * 2.0)) * Float64(t_4 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_4) - 6.0)))) + Float64(t_1 * t_4)) + Float64(x1 * Float64(x1 * x1))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0)) + Float64(t_0 + Float64(x2 * -6.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 9.0);
	t_1 = x1 * (x1 * 3.0);
	t_2 = 1.0 + (x1 * x1);
	t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	t_4 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	tmp = 0.0;
	if (x1 <= -4e+156)
		tmp = x1 + t_0;
	elseif (x1 <= -5e+102)
		tmp = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + t_3);
	elseif (x1 <= 1.8e+137)
		tmp = x1 + (t_3 + (x1 + (((t_2 * (((t_4 * (x1 * 2.0)) * (t_4 - 3.0)) + ((x1 * x1) * ((4.0 * t_4) - 6.0)))) + (t_1 * t_4)) + (x1 * (x1 * x1)))));
	else
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (t_0 + (x2 * -6.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 9.0), $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[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[x1, -4e+156], N[(x1 + t$95$0), $MachinePrecision], If[LessEqual[x1, -5e+102], N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.8e+137], N[(x1 + N[(t$95$3 + N[(x1 + N[(N[(N[(t$95$2 * N[(N[(N[(t$95$4 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$4), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -3.9999999999999999e156

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 63.0%

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

   4. Taylor expanded in x2 around 0 63.0%

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

      1. *-commutative 63.0%

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

      2. unpow2 63.0%

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

   6. Simplified 63.0%

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

   7. Taylor expanded in x1 around inf 100.0%

      \[\leadsto x1 + \color{blue}{9 \cdot {x1}^{2}} \]
   8. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto x1 + \color{blue}{{x1}^{2} \cdot 9} \]

      2. unpow2 100.0%

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

      3. associate-*r* 100.0%

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

   9. Simplified 100.0%

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

   if -3.9999999999999999e156 < x1 < -5e102

   1. Initial program 6.7%

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

   2. Taylor expanded in x1 around inf 93.3%

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

      1. *-commutative 93.3%

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

   4. Simplified 93.3%

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

   if -5e102 < x1 < 1.8e137

   1. Initial program 99.4%

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

   if 1.8e137 < x1

   1. Initial program 7.3%

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

   2. Taylor expanded in x1 around 0 7.3%

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

   3. Taylor expanded in x1 around 0 58.5%

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

   4. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. unpow2 100.0%

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

      3. associate-*l* 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+156}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1}\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+137}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(\left(\left(1 + x1 \cdot x1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + \left(x1 \cdot \left(x1 \cdot 9\right) + x2 \cdot -6\right)\right)\\ \end{array} \]

Alternative 5: 93.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 9\right)\\ t_1 := 1 + x1 \cdot x1\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \frac{\left(t_2 + 2 \cdot x2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -1.6 \cdot 10^{+135}:\\ \;\;\;\;x1 + t_0\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+137}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_2 - 2 \cdot x2\right) - x1}{t_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_1 \cdot \left(\left(t_3 \cdot \left(x1 \cdot 2\right)\right) \cdot \left(t_3 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_3 - 6\right)\right) + 3 \cdot t_2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + \left(t_0 + x2 \cdot -6\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 9.0)))
        (t_1 (+ 1.0 (* x1 x1)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (/ (- (+ t_2 (* 2.0 x2)) x1) t_1)))
   (if (<= x1 -1.6e+135)
     (+ x1 t_0)
     (if (<= x1 1.8e+137)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_1))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (*
             t_1
             (+
              (* (* t_3 (* x1 2.0)) (- t_3 3.0))
              (* (* x1 x1) (- (* 4.0 t_3) 6.0))))
            (* 3.0 t_2))))))
       (+
        x1
        (+
         (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0))
         (+ t_0 (* x2 -6.0))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 9.0);
	double t_1 = 1.0 + (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = ((t_2 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if (x1 <= -1.6e+135) {
		tmp = x1 + t_0;
	} else if (x1 <= 1.8e+137) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((t_3 * (x1 * 2.0)) * (t_3 - 3.0)) + ((x1 * x1) * ((4.0 * t_3) - 6.0)))) + (3.0 * t_2)))));
	} else {
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (t_0 + (x2 * -6.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x1 * (x1 * 9.0d0)
    t_1 = 1.0d0 + (x1 * x1)
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = ((t_2 + (2.0d0 * x2)) - x1) / t_1
    if (x1 <= (-1.6d+135)) then
        tmp = x1 + t_0
    else if (x1 <= 1.8d+137) then
        tmp = x1 + ((3.0d0 * (((t_2 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((t_3 * (x1 * 2.0d0)) * (t_3 - 3.0d0)) + ((x1 * x1) * ((4.0d0 * t_3) - 6.0d0)))) + (3.0d0 * t_2)))))
    else
        tmp = x1 + ((x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)) + (t_0 + (x2 * (-6.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 9.0);
	double t_1 = 1.0 + (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = ((t_2 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if (x1 <= -1.6e+135) {
		tmp = x1 + t_0;
	} else if (x1 <= 1.8e+137) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((t_3 * (x1 * 2.0)) * (t_3 - 3.0)) + ((x1 * x1) * ((4.0 * t_3) - 6.0)))) + (3.0 * t_2)))));
	} else {
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (t_0 + (x2 * -6.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 9.0)
	t_1 = 1.0 + (x1 * x1)
	t_2 = x1 * (x1 * 3.0)
	t_3 = ((t_2 + (2.0 * x2)) - x1) / t_1
	tmp = 0
	if x1 <= -1.6e+135:
		tmp = x1 + t_0
	elif x1 <= 1.8e+137:
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((t_3 * (x1 * 2.0)) * (t_3 - 3.0)) + ((x1 * x1) * ((4.0 * t_3) - 6.0)))) + (3.0 * t_2)))))
	else:
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (t_0 + (x2 * -6.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 9.0))
	t_1 = Float64(1.0 + Float64(x1 * x1))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(Float64(t_2 + Float64(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if (x1 <= -1.6e+135)
		tmp = Float64(x1 + t_0);
	elseif (x1 <= 1.8e+137)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * Float64(Float64(Float64(t_3 * Float64(x1 * 2.0)) * Float64(t_3 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_3) - 6.0)))) + Float64(3.0 * t_2))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0)) + Float64(t_0 + Float64(x2 * -6.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 9.0);
	t_1 = 1.0 + (x1 * x1);
	t_2 = x1 * (x1 * 3.0);
	t_3 = ((t_2 + (2.0 * x2)) - x1) / t_1;
	tmp = 0.0;
	if (x1 <= -1.6e+135)
		tmp = x1 + t_0;
	elseif (x1 <= 1.8e+137)
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((t_3 * (x1 * 2.0)) * (t_3 - 3.0)) + ((x1 * x1) * ((4.0 * t_3) - 6.0)))) + (3.0 * t_2)))));
	else
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (t_0 + (x2 * -6.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[x1, -1.6e+135], N[(x1 + t$95$0), $MachinePrecision], If[LessEqual[x1, 1.8e+137], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * N[(N[(N[(t$95$3 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$3), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.59999999999999987e135

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 48.2%

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

   4. Taylor expanded in x2 around 0 48.2%

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

      1. *-commutative 48.2%

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

      2. unpow2 48.2%

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

   6. Simplified 48.2%

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

   7. Taylor expanded in x1 around inf 77.2%

      \[\leadsto x1 + \color{blue}{9 \cdot {x1}^{2}} \]
   8. Step-by-step derivation

      1. *-commutative 77.2%

         \[\leadsto x1 + \color{blue}{{x1}^{2} \cdot 9} \]

      2. unpow2 77.2%

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

      3. associate-*r* 77.2%

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

   9. Simplified 77.2%

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

   if -1.59999999999999987e135 < x1 < 1.8e137

   1. Initial program 96.6%

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

   2. Taylor expanded in x1 around inf 95.9%

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

   if 1.8e137 < x1

   1. Initial program 7.3%

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

   2. Taylor expanded in x1 around 0 7.3%

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

   3. Taylor expanded in x1 around 0 58.5%

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

   4. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. unpow2 100.0%

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

      3. associate-*l* 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.6 \cdot 10^{+135}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+137}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(1 + x1 \cdot x1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + \left(x1 \cdot \left(x1 \cdot 9\right) + x2 \cdot -6\right)\right)\\ \end{array} \]

Alternative 6: 90.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 1 + x1 \cdot x1\\ t_2 := x1 \cdot \left(x1 \cdot 9\right)\\ t_3 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -1.6 \cdot 10^{+135}:\\ \;\;\;\;x1 + t_2\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+137}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t_0 + t_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot t_3 - 6\right) + \left(t_3 - 3\right) \cdot \left(\left(2 \cdot x2 - x1\right) \cdot \left(x1 \cdot 2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + \left(t_2 + x2 \cdot -6\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ 1.0 (* x1 x1)))
        (t_2 (* x1 (* x1 9.0)))
        (t_3 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (if (<= x1 -1.6e+135)
     (+ x1 t_2)
     (if (<= x1 1.8e+137)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* 3.0 t_0)
            (*
             t_1
             (+
              (* (* x1 x1) (- (* 4.0 t_3) 6.0))
              (* (- t_3 3.0) (* (- (* 2.0 x2) x1) (* x1 2.0))))))))))
       (+
        x1
        (+
         (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0))
         (+ t_2 (* x2 -6.0))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 1.0 + (x1 * x1);
	double t_2 = x1 * (x1 * 9.0);
	double t_3 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if (x1 <= -1.6e+135) {
		tmp = x1 + t_2;
	} else if (x1 <= 1.8e+137) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * (((x1 * x1) * ((4.0 * t_3) - 6.0)) + ((t_3 - 3.0) * (((2.0 * x2) - x1) * (x1 * 2.0)))))))));
	} else {
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (t_2 + (x2 * -6.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = 1.0d0 + (x1 * x1)
    t_2 = x1 * (x1 * 9.0d0)
    t_3 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    if (x1 <= (-1.6d+135)) then
        tmp = x1 + t_2
    else if (x1 <= 1.8d+137) then
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_0) + (t_1 * (((x1 * x1) * ((4.0d0 * t_3) - 6.0d0)) + ((t_3 - 3.0d0) * (((2.0d0 * x2) - x1) * (x1 * 2.0d0)))))))))
    else
        tmp = x1 + ((x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)) + (t_2 + (x2 * (-6.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 1.0 + (x1 * x1);
	double t_2 = x1 * (x1 * 9.0);
	double t_3 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if (x1 <= -1.6e+135) {
		tmp = x1 + t_2;
	} else if (x1 <= 1.8e+137) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * (((x1 * x1) * ((4.0 * t_3) - 6.0)) + ((t_3 - 3.0) * (((2.0 * x2) - x1) * (x1 * 2.0)))))))));
	} else {
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (t_2 + (x2 * -6.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = 1.0 + (x1 * x1)
	t_2 = x1 * (x1 * 9.0)
	t_3 = ((t_0 + (2.0 * x2)) - x1) / t_1
	tmp = 0
	if x1 <= -1.6e+135:
		tmp = x1 + t_2
	elif x1 <= 1.8e+137:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * (((x1 * x1) * ((4.0 * t_3) - 6.0)) + ((t_3 - 3.0) * (((2.0 * x2) - x1) * (x1 * 2.0)))))))))
	else:
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (t_2 + (x2 * -6.0)))
	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(x1 * Float64(x1 * 9.0))
	t_3 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if (x1 <= -1.6e+135)
		tmp = Float64(x1 + t_2);
	elseif (x1 <= 1.8e+137)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_0) + Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_3) - 6.0)) + Float64(Float64(t_3 - 3.0) * Float64(Float64(Float64(2.0 * x2) - x1) * Float64(x1 * 2.0))))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0)) + Float64(t_2 + Float64(x2 * -6.0))));
	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 = x1 * (x1 * 9.0);
	t_3 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	tmp = 0.0;
	if (x1 <= -1.6e+135)
		tmp = x1 + t_2;
	elseif (x1 <= 1.8e+137)
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * (((x1 * x1) * ((4.0 * t_3) - 6.0)) + ((t_3 - 3.0) * (((2.0 * x2) - x1) * (x1 * 2.0)))))))));
	else
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (t_2 + (x2 * -6.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[x1, -1.6e+135], N[(x1 + t$95$2), $MachinePrecision], If[LessEqual[x1, 1.8e+137], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$0), $MachinePrecision] + N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$3), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$3 - 3.0), $MachinePrecision] * N[(N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision] * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.59999999999999987e135

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 48.2%

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

   4. Taylor expanded in x2 around 0 48.2%

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

      1. *-commutative 48.2%

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

      2. unpow2 48.2%

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

   6. Simplified 48.2%

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

   7. Taylor expanded in x1 around inf 77.2%

      \[\leadsto x1 + \color{blue}{9 \cdot {x1}^{2}} \]
   8. Step-by-step derivation

      1. *-commutative 77.2%

         \[\leadsto x1 + \color{blue}{{x1}^{2} \cdot 9} \]

      2. unpow2 77.2%

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

      3. associate-*r* 77.2%

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

   9. Simplified 77.2%

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

   if -1.59999999999999987e135 < x1 < 1.8e137

   1. Initial program 96.6%

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

   2. Taylor expanded in x1 around 0 93.0%

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

   3. Taylor expanded in x1 around inf 92.8%

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

   if 1.8e137 < x1

   1. Initial program 7.3%

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

   2. Taylor expanded in x1 around 0 7.3%

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

   3. Taylor expanded in x1 around 0 58.5%

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

   4. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. unpow2 100.0%

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

      3. associate-*l* 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.6 \cdot 10^{+135}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+137}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(1 + x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} - 3\right) \cdot \left(\left(2 \cdot x2 - x1\right) \cdot \left(x1 \cdot 2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + \left(x1 \cdot \left(x1 \cdot 9\right) + x2 \cdot -6\right)\right)\\ \end{array} \]

Alternative 7: 89.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot \left(x1 \cdot 9\right)\\ t_2 := 1 + x1 \cdot x1\\ t_3 := 2 \cdot x2 - 3\\ \mathbf{if}\;x1 \leq -1.65 \cdot 10^{+135}:\\ \;\;\;\;x1 + t_1\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+137}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_2} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t_0 + t_2 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_2} - 6\right) + 4 \cdot \left(x2 \cdot \left(x1 \cdot t_3\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot t_3\right) - 2\right) + \left(t_1 + x2 \cdot -6\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (* x1 (* x1 9.0)))
        (t_2 (+ 1.0 (* x1 x1)))
        (t_3 (- (* 2.0 x2) 3.0)))
   (if (<= x1 -1.65e+135)
     (+ x1 t_1)
     (if (<= x1 1.8e+137)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_2))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* 3.0 t_0)
            (*
             t_2
             (+
              (* (* x1 x1) (- (* 4.0 (/ (- (+ t_0 (* 2.0 x2)) x1) t_2)) 6.0))
              (* 4.0 (* x2 (* x1 t_3))))))))))
       (+ x1 (+ (* x1 (- (* 4.0 (* x2 t_3)) 2.0)) (+ t_1 (* x2 -6.0))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * (x1 * 9.0);
	double t_2 = 1.0 + (x1 * x1);
	double t_3 = (2.0 * x2) - 3.0;
	double tmp;
	if (x1 <= -1.65e+135) {
		tmp = x1 + t_1;
	} else if (x1 <= 1.8e+137) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_2 * (((x1 * x1) * ((4.0 * (((t_0 + (2.0 * x2)) - x1) / t_2)) - 6.0)) + (4.0 * (x2 * (x1 * t_3)))))))));
	} else {
		tmp = x1 + ((x1 * ((4.0 * (x2 * t_3)) - 2.0)) + (t_1 + (x2 * -6.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = x1 * (x1 * 9.0d0)
    t_2 = 1.0d0 + (x1 * x1)
    t_3 = (2.0d0 * x2) - 3.0d0
    if (x1 <= (-1.65d+135)) then
        tmp = x1 + t_1
    else if (x1 <= 1.8d+137) then
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_2)) + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_0) + (t_2 * (((x1 * x1) * ((4.0d0 * (((t_0 + (2.0d0 * x2)) - x1) / t_2)) - 6.0d0)) + (4.0d0 * (x2 * (x1 * t_3)))))))))
    else
        tmp = x1 + ((x1 * ((4.0d0 * (x2 * t_3)) - 2.0d0)) + (t_1 + (x2 * (-6.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * (x1 * 9.0);
	double t_2 = 1.0 + (x1 * x1);
	double t_3 = (2.0 * x2) - 3.0;
	double tmp;
	if (x1 <= -1.65e+135) {
		tmp = x1 + t_1;
	} else if (x1 <= 1.8e+137) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_2 * (((x1 * x1) * ((4.0 * (((t_0 + (2.0 * x2)) - x1) / t_2)) - 6.0)) + (4.0 * (x2 * (x1 * t_3)))))))));
	} else {
		tmp = x1 + ((x1 * ((4.0 * (x2 * t_3)) - 2.0)) + (t_1 + (x2 * -6.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = x1 * (x1 * 9.0)
	t_2 = 1.0 + (x1 * x1)
	t_3 = (2.0 * x2) - 3.0
	tmp = 0
	if x1 <= -1.65e+135:
		tmp = x1 + t_1
	elif x1 <= 1.8e+137:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_2 * (((x1 * x1) * ((4.0 * (((t_0 + (2.0 * x2)) - x1) / t_2)) - 6.0)) + (4.0 * (x2 * (x1 * t_3)))))))))
	else:
		tmp = x1 + ((x1 * ((4.0 * (x2 * t_3)) - 2.0)) + (t_1 + (x2 * -6.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(x1 * Float64(x1 * 9.0))
	t_2 = Float64(1.0 + Float64(x1 * x1))
	t_3 = Float64(Float64(2.0 * x2) - 3.0)
	tmp = 0.0
	if (x1 <= -1.65e+135)
		tmp = Float64(x1 + t_1);
	elseif (x1 <= 1.8e+137)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_2)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_0) + Float64(t_2 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_2)) - 6.0)) + Float64(4.0 * Float64(x2 * Float64(x1 * t_3))))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * t_3)) - 2.0)) + Float64(t_1 + Float64(x2 * -6.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = x1 * (x1 * 9.0);
	t_2 = 1.0 + (x1 * x1);
	t_3 = (2.0 * x2) - 3.0;
	tmp = 0.0;
	if (x1 <= -1.65e+135)
		tmp = x1 + t_1;
	elseif (x1 <= 1.8e+137)
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_2 * (((x1 * x1) * ((4.0 * (((t_0 + (2.0 * x2)) - x1) / t_2)) - 6.0)) + (4.0 * (x2 * (x1 * t_3)))))))));
	else
		tmp = x1 + ((x1 * ((4.0 * (x2 * t_3)) - 2.0)) + (t_1 + (x2 * -6.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, If[LessEqual[x1, -1.65e+135], N[(x1 + t$95$1), $MachinePrecision], If[LessEqual[x1, 1.8e+137], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$0), $MachinePrecision] + N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x2 * N[(x1 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 * N[(N[(4.0 * N[(x2 * t$95$3), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.65e135

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 48.2%

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

   4. Taylor expanded in x2 around 0 48.2%

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

      1. *-commutative 48.2%

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

      2. unpow2 48.2%

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

   6. Simplified 48.2%

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

   7. Taylor expanded in x1 around inf 77.2%

      \[\leadsto x1 + \color{blue}{9 \cdot {x1}^{2}} \]
   8. Step-by-step derivation

      1. *-commutative 77.2%

         \[\leadsto x1 + \color{blue}{{x1}^{2} \cdot 9} \]

      2. unpow2 77.2%

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

      3. associate-*r* 77.2%

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

   9. Simplified 77.2%

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

   if -1.65e135 < x1 < 1.8e137

   1. Initial program 96.6%

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

   2. Taylor expanded in x1 around 0 93.0%

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

   3. Taylor expanded in x1 around inf 92.8%

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

   4. Taylor expanded in x1 around 0 92.6%

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

   if 1.8e137 < x1

   1. Initial program 7.3%

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

   2. Taylor expanded in x1 around 0 7.3%

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

   3. Taylor expanded in x1 around 0 58.5%

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

   4. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. unpow2 100.0%

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

      3. associate-*l* 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.65 \cdot 10^{+135}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+137}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(1 + x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} - 6\right) + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + \left(x1 \cdot \left(x1 \cdot 9\right) + x2 \cdot -6\right)\right)\\ \end{array} \]

Alternative 8: 90.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 2 \cdot x2 - 3\\ t_2 := x1 \cdot \left(x1 \cdot 9\right)\\ t_3 := 1 + x1 \cdot x1\\ t_4 := 3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_3}\\ t_5 := x1 + \left(t_4 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t_0 + t_3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_3} - 6\right) + x1 \cdot 2\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -1.6 \cdot 10^{+135}:\\ \;\;\;\;x1 + t_2\\ \mathbf{elif}\;x1 \leq -40:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x1 \leq 14500:\\ \;\;\;\;x1 + \left(t_4 + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot t_1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+137}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot t_1\right) - 2\right) + \left(t_2 + x2 \cdot -6\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (- (* 2.0 x2) 3.0))
        (t_2 (* x1 (* x1 9.0)))
        (t_3 (+ 1.0 (* x1 x1)))
        (t_4 (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_3)))
        (t_5
         (+
          x1
          (+
           t_4
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* 3.0 t_0)
              (*
               t_3
               (+
                (* (* x1 x1) (- (* 4.0 (/ (- (+ t_0 (* 2.0 x2)) x1) t_3)) 6.0))
                (* x1 2.0))))))))))
   (if (<= x1 -1.6e+135)
     (+ x1 t_2)
     (if (<= x1 -40.0)
       t_5
       (if (<= x1 14500.0)
         (+ x1 (+ t_4 (+ x1 (* 4.0 (* x2 (* x1 t_1))))))
         (if (<= x1 1.8e+137)
           t_5
           (+
            x1
            (+ (* x1 (- (* 4.0 (* x2 t_1)) 2.0)) (+ t_2 (* x2 -6.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (2.0 * x2) - 3.0;
	double t_2 = x1 * (x1 * 9.0);
	double t_3 = 1.0 + (x1 * x1);
	double t_4 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3);
	double t_5 = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_3 * (((x1 * x1) * ((4.0 * (((t_0 + (2.0 * x2)) - x1) / t_3)) - 6.0)) + (x1 * 2.0)))))));
	double tmp;
	if (x1 <= -1.6e+135) {
		tmp = x1 + t_2;
	} else if (x1 <= -40.0) {
		tmp = t_5;
	} else if (x1 <= 14500.0) {
		tmp = x1 + (t_4 + (x1 + (4.0 * (x2 * (x1 * t_1)))));
	} else if (x1 <= 1.8e+137) {
		tmp = t_5;
	} else {
		tmp = x1 + ((x1 * ((4.0 * (x2 * t_1)) - 2.0)) + (t_2 + (x2 * -6.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (2.0d0 * x2) - 3.0d0
    t_2 = x1 * (x1 * 9.0d0)
    t_3 = 1.0d0 + (x1 * x1)
    t_4 = 3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_3)
    t_5 = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_0) + (t_3 * (((x1 * x1) * ((4.0d0 * (((t_0 + (2.0d0 * x2)) - x1) / t_3)) - 6.0d0)) + (x1 * 2.0d0)))))))
    if (x1 <= (-1.6d+135)) then
        tmp = x1 + t_2
    else if (x1 <= (-40.0d0)) then
        tmp = t_5
    else if (x1 <= 14500.0d0) then
        tmp = x1 + (t_4 + (x1 + (4.0d0 * (x2 * (x1 * t_1)))))
    else if (x1 <= 1.8d+137) then
        tmp = t_5
    else
        tmp = x1 + ((x1 * ((4.0d0 * (x2 * t_1)) - 2.0d0)) + (t_2 + (x2 * (-6.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (2.0 * x2) - 3.0;
	double t_2 = x1 * (x1 * 9.0);
	double t_3 = 1.0 + (x1 * x1);
	double t_4 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3);
	double t_5 = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_3 * (((x1 * x1) * ((4.0 * (((t_0 + (2.0 * x2)) - x1) / t_3)) - 6.0)) + (x1 * 2.0)))))));
	double tmp;
	if (x1 <= -1.6e+135) {
		tmp = x1 + t_2;
	} else if (x1 <= -40.0) {
		tmp = t_5;
	} else if (x1 <= 14500.0) {
		tmp = x1 + (t_4 + (x1 + (4.0 * (x2 * (x1 * t_1)))));
	} else if (x1 <= 1.8e+137) {
		tmp = t_5;
	} else {
		tmp = x1 + ((x1 * ((4.0 * (x2 * t_1)) - 2.0)) + (t_2 + (x2 * -6.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (2.0 * x2) - 3.0
	t_2 = x1 * (x1 * 9.0)
	t_3 = 1.0 + (x1 * x1)
	t_4 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3)
	t_5 = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_3 * (((x1 * x1) * ((4.0 * (((t_0 + (2.0 * x2)) - x1) / t_3)) - 6.0)) + (x1 * 2.0)))))))
	tmp = 0
	if x1 <= -1.6e+135:
		tmp = x1 + t_2
	elif x1 <= -40.0:
		tmp = t_5
	elif x1 <= 14500.0:
		tmp = x1 + (t_4 + (x1 + (4.0 * (x2 * (x1 * t_1)))))
	elif x1 <= 1.8e+137:
		tmp = t_5
	else:
		tmp = x1 + ((x1 * ((4.0 * (x2 * t_1)) - 2.0)) + (t_2 + (x2 * -6.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(2.0 * x2) - 3.0)
	t_2 = Float64(x1 * Float64(x1 * 9.0))
	t_3 = Float64(1.0 + Float64(x1 * x1))
	t_4 = Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_3))
	t_5 = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_0) + Float64(t_3 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_3)) - 6.0)) + Float64(x1 * 2.0))))))))
	tmp = 0.0
	if (x1 <= -1.6e+135)
		tmp = Float64(x1 + t_2);
	elseif (x1 <= -40.0)
		tmp = t_5;
	elseif (x1 <= 14500.0)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * t_1))))));
	elseif (x1 <= 1.8e+137)
		tmp = t_5;
	else
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * t_1)) - 2.0)) + Float64(t_2 + Float64(x2 * -6.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (2.0 * x2) - 3.0;
	t_2 = x1 * (x1 * 9.0);
	t_3 = 1.0 + (x1 * x1);
	t_4 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3);
	t_5 = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_3 * (((x1 * x1) * ((4.0 * (((t_0 + (2.0 * x2)) - x1) / t_3)) - 6.0)) + (x1 * 2.0)))))));
	tmp = 0.0;
	if (x1 <= -1.6e+135)
		tmp = x1 + t_2;
	elseif (x1 <= -40.0)
		tmp = t_5;
	elseif (x1 <= 14500.0)
		tmp = x1 + (t_4 + (x1 + (4.0 * (x2 * (x1 * t_1)))));
	elseif (x1 <= 1.8e+137)
		tmp = t_5;
	else
		tmp = x1 + ((x1 * ((4.0 * (x2 * t_1)) - 2.0)) + (t_2 + (x2 * -6.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(t$95$4 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$0), $MachinePrecision] + N[(t$95$3 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.6e+135], N[(x1 + t$95$2), $MachinePrecision], If[LessEqual[x1, -40.0], t$95$5, If[LessEqual[x1, 14500.0], N[(x1 + N[(t$95$4 + N[(x1 + N[(4.0 * N[(x2 * N[(x1 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.8e+137], t$95$5, N[(x1 + N[(N[(x1 * N[(N[(4.0 * N[(x2 * t$95$1), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.59999999999999987e135

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 48.2%

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

   4. Taylor expanded in x2 around 0 48.2%

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

      1. *-commutative 48.2%

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

      2. unpow2 48.2%

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

   6. Simplified 48.2%

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

   7. Taylor expanded in x1 around inf 77.2%

      \[\leadsto x1 + \color{blue}{9 \cdot {x1}^{2}} \]
   8. Step-by-step derivation

      1. *-commutative 77.2%

         \[\leadsto x1 + \color{blue}{{x1}^{2} \cdot 9} \]

      2. unpow2 77.2%

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

      3. associate-*r* 77.2%

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

   9. Simplified 77.2%

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

   if -1.59999999999999987e135 < x1 < -40 or 14500 < x1 < 1.8e137

   1. Initial program 89.0%

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

   2. Taylor expanded in x1 around 0 77.2%

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

   3. Taylor expanded in x1 around inf 82.1%

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

      1. *-commutative 82.1%

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

   5. Simplified 82.1%

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

   6. Taylor expanded in x1 around inf 82.1%

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

   if -40 < x1 < 14500

   1. Initial program 99.4%

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

   2. Taylor expanded in x1 around 0 98.8%

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

   if 1.8e137 < x1

   1. Initial program 7.3%

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

   2. Taylor expanded in x1 around 0 7.3%

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

   3. Taylor expanded in x1 around 0 58.5%

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

   4. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. unpow2 100.0%

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

      3. associate-*l* 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.6 \cdot 10^{+135}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -40:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(1 + x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} - 6\right) + x1 \cdot 2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 14500:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+137}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(1 + x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} - 6\right) + x1 \cdot 2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + \left(x1 \cdot \left(x1 \cdot 9\right) + x2 \cdot -6\right)\right)\\ \end{array} \]

Alternative 9: 89.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 2 \cdot x2 - 3\\ t_2 := x1 \cdot \left(x1 \cdot 9\right)\\ t_3 := 1 + x1 \cdot x1\\ t_4 := t_3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_3} - 6\right) + x1 \cdot 2\right)\\ t_5 := x1 \cdot \left(x1 \cdot x1\right)\\ t_6 := 3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_3}\\ \mathbf{if}\;x1 \leq -1.6 \cdot 10^{+135}:\\ \;\;\;\;x1 + t_2\\ \mathbf{elif}\;x1 \leq -140:\\ \;\;\;\;x1 + \left(t_6 + \left(x1 + \left(t_5 + \left(t_4 + t_0 \cdot \left(2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 14000:\\ \;\;\;\;x1 + \left(t_6 + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot t_1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+137}:\\ \;\;\;\;x1 + \left(t_6 + \left(x1 + \left(t_5 + \left(3 \cdot t_0 + t_4\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot t_1\right) - 2\right) + \left(t_2 + x2 \cdot -6\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (- (* 2.0 x2) 3.0))
        (t_2 (* x1 (* x1 9.0)))
        (t_3 (+ 1.0 (* x1 x1)))
        (t_4
         (*
          t_3
          (+
           (* (* x1 x1) (- (* 4.0 (/ (- (+ t_0 (* 2.0 x2)) x1) t_3)) 6.0))
           (* x1 2.0))))
        (t_5 (* x1 (* x1 x1)))
        (t_6 (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_3))))
   (if (<= x1 -1.6e+135)
     (+ x1 t_2)
     (if (<= x1 -140.0)
       (+ x1 (+ t_6 (+ x1 (+ t_5 (+ t_4 (* t_0 (* 2.0 x2)))))))
       (if (<= x1 14000.0)
         (+ x1 (+ t_6 (+ x1 (* 4.0 (* x2 (* x1 t_1))))))
         (if (<= x1 1.8e+137)
           (+ x1 (+ t_6 (+ x1 (+ t_5 (+ (* 3.0 t_0) t_4)))))
           (+
            x1
            (+ (* x1 (- (* 4.0 (* x2 t_1)) 2.0)) (+ t_2 (* x2 -6.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (2.0 * x2) - 3.0;
	double t_2 = x1 * (x1 * 9.0);
	double t_3 = 1.0 + (x1 * x1);
	double t_4 = t_3 * (((x1 * x1) * ((4.0 * (((t_0 + (2.0 * x2)) - x1) / t_3)) - 6.0)) + (x1 * 2.0));
	double t_5 = x1 * (x1 * x1);
	double t_6 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3);
	double tmp;
	if (x1 <= -1.6e+135) {
		tmp = x1 + t_2;
	} else if (x1 <= -140.0) {
		tmp = x1 + (t_6 + (x1 + (t_5 + (t_4 + (t_0 * (2.0 * x2))))));
	} else if (x1 <= 14000.0) {
		tmp = x1 + (t_6 + (x1 + (4.0 * (x2 * (x1 * t_1)))));
	} else if (x1 <= 1.8e+137) {
		tmp = x1 + (t_6 + (x1 + (t_5 + ((3.0 * t_0) + t_4))));
	} else {
		tmp = x1 + ((x1 * ((4.0 * (x2 * t_1)) - 2.0)) + (t_2 + (x2 * -6.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (2.0d0 * x2) - 3.0d0
    t_2 = x1 * (x1 * 9.0d0)
    t_3 = 1.0d0 + (x1 * x1)
    t_4 = t_3 * (((x1 * x1) * ((4.0d0 * (((t_0 + (2.0d0 * x2)) - x1) / t_3)) - 6.0d0)) + (x1 * 2.0d0))
    t_5 = x1 * (x1 * x1)
    t_6 = 3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_3)
    if (x1 <= (-1.6d+135)) then
        tmp = x1 + t_2
    else if (x1 <= (-140.0d0)) then
        tmp = x1 + (t_6 + (x1 + (t_5 + (t_4 + (t_0 * (2.0d0 * x2))))))
    else if (x1 <= 14000.0d0) then
        tmp = x1 + (t_6 + (x1 + (4.0d0 * (x2 * (x1 * t_1)))))
    else if (x1 <= 1.8d+137) then
        tmp = x1 + (t_6 + (x1 + (t_5 + ((3.0d0 * t_0) + t_4))))
    else
        tmp = x1 + ((x1 * ((4.0d0 * (x2 * t_1)) - 2.0d0)) + (t_2 + (x2 * (-6.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (2.0 * x2) - 3.0;
	double t_2 = x1 * (x1 * 9.0);
	double t_3 = 1.0 + (x1 * x1);
	double t_4 = t_3 * (((x1 * x1) * ((4.0 * (((t_0 + (2.0 * x2)) - x1) / t_3)) - 6.0)) + (x1 * 2.0));
	double t_5 = x1 * (x1 * x1);
	double t_6 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3);
	double tmp;
	if (x1 <= -1.6e+135) {
		tmp = x1 + t_2;
	} else if (x1 <= -140.0) {
		tmp = x1 + (t_6 + (x1 + (t_5 + (t_4 + (t_0 * (2.0 * x2))))));
	} else if (x1 <= 14000.0) {
		tmp = x1 + (t_6 + (x1 + (4.0 * (x2 * (x1 * t_1)))));
	} else if (x1 <= 1.8e+137) {
		tmp = x1 + (t_6 + (x1 + (t_5 + ((3.0 * t_0) + t_4))));
	} else {
		tmp = x1 + ((x1 * ((4.0 * (x2 * t_1)) - 2.0)) + (t_2 + (x2 * -6.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (2.0 * x2) - 3.0
	t_2 = x1 * (x1 * 9.0)
	t_3 = 1.0 + (x1 * x1)
	t_4 = t_3 * (((x1 * x1) * ((4.0 * (((t_0 + (2.0 * x2)) - x1) / t_3)) - 6.0)) + (x1 * 2.0))
	t_5 = x1 * (x1 * x1)
	t_6 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3)
	tmp = 0
	if x1 <= -1.6e+135:
		tmp = x1 + t_2
	elif x1 <= -140.0:
		tmp = x1 + (t_6 + (x1 + (t_5 + (t_4 + (t_0 * (2.0 * x2))))))
	elif x1 <= 14000.0:
		tmp = x1 + (t_6 + (x1 + (4.0 * (x2 * (x1 * t_1)))))
	elif x1 <= 1.8e+137:
		tmp = x1 + (t_6 + (x1 + (t_5 + ((3.0 * t_0) + t_4))))
	else:
		tmp = x1 + ((x1 * ((4.0 * (x2 * t_1)) - 2.0)) + (t_2 + (x2 * -6.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(2.0 * x2) - 3.0)
	t_2 = Float64(x1 * Float64(x1 * 9.0))
	t_3 = Float64(1.0 + Float64(x1 * x1))
	t_4 = Float64(t_3 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_3)) - 6.0)) + Float64(x1 * 2.0)))
	t_5 = Float64(x1 * Float64(x1 * x1))
	t_6 = Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_3))
	tmp = 0.0
	if (x1 <= -1.6e+135)
		tmp = Float64(x1 + t_2);
	elseif (x1 <= -140.0)
		tmp = Float64(x1 + Float64(t_6 + Float64(x1 + Float64(t_5 + Float64(t_4 + Float64(t_0 * Float64(2.0 * x2)))))));
	elseif (x1 <= 14000.0)
		tmp = Float64(x1 + Float64(t_6 + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * t_1))))));
	elseif (x1 <= 1.8e+137)
		tmp = Float64(x1 + Float64(t_6 + Float64(x1 + Float64(t_5 + Float64(Float64(3.0 * t_0) + t_4)))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * t_1)) - 2.0)) + Float64(t_2 + Float64(x2 * -6.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (2.0 * x2) - 3.0;
	t_2 = x1 * (x1 * 9.0);
	t_3 = 1.0 + (x1 * x1);
	t_4 = t_3 * (((x1 * x1) * ((4.0 * (((t_0 + (2.0 * x2)) - x1) / t_3)) - 6.0)) + (x1 * 2.0));
	t_5 = x1 * (x1 * x1);
	t_6 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3);
	tmp = 0.0;
	if (x1 <= -1.6e+135)
		tmp = x1 + t_2;
	elseif (x1 <= -140.0)
		tmp = x1 + (t_6 + (x1 + (t_5 + (t_4 + (t_0 * (2.0 * x2))))));
	elseif (x1 <= 14000.0)
		tmp = x1 + (t_6 + (x1 + (4.0 * (x2 * (x1 * t_1)))));
	elseif (x1 <= 1.8e+137)
		tmp = x1 + (t_6 + (x1 + (t_5 + ((3.0 * t_0) + t_4))));
	else
		tmp = x1 + ((x1 * ((4.0 * (x2 * t_1)) - 2.0)) + (t_2 + (x2 * -6.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.6e+135], N[(x1 + t$95$2), $MachinePrecision], If[LessEqual[x1, -140.0], N[(x1 + N[(t$95$6 + N[(x1 + N[(t$95$5 + N[(t$95$4 + N[(t$95$0 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 14000.0], N[(x1 + N[(t$95$6 + N[(x1 + N[(4.0 * N[(x2 * N[(x1 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.8e+137], N[(x1 + N[(t$95$6 + N[(x1 + N[(t$95$5 + N[(N[(3.0 * t$95$0), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 * N[(N[(4.0 * N[(x2 * t$95$1), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -1.59999999999999987e135

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 48.2%

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

   4. Taylor expanded in x2 around 0 48.2%

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

      1. *-commutative 48.2%

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

      2. unpow2 48.2%

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

   6. Simplified 48.2%

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

   7. Taylor expanded in x1 around inf 77.2%

      \[\leadsto x1 + \color{blue}{9 \cdot {x1}^{2}} \]
   8. Step-by-step derivation

      1. *-commutative 77.2%

         \[\leadsto x1 + \color{blue}{{x1}^{2} \cdot 9} \]

      2. unpow2 77.2%

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

      3. associate-*r* 77.2%

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

   9. Simplified 77.2%

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

   if -1.59999999999999987e135 < x1 < -140

   1. Initial program 79.5%

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

   2. Taylor expanded in x1 around 0 70.9%

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

   3. Taylor expanded in x1 around inf 70.7%

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

      1. *-commutative 70.7%

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

   5. Simplified 70.7%

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

   6. Taylor expanded in x1 around 0 70.7%

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

   if -140 < x1 < 14000

   1. Initial program 99.4%

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

   2. Taylor expanded in x1 around 0 98.8%

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

   if 14000 < x1 < 1.8e137

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 84.1%

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

   3. Taylor expanded in x1 around inf 94.4%

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

      1. *-commutative 94.4%

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

   5. Simplified 94.4%

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

   6. Taylor expanded in x1 around inf 94.4%

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

   if 1.8e137 < x1

   1. Initial program 7.3%

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

   2. Taylor expanded in x1 around 0 7.3%

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

   3. Taylor expanded in x1 around 0 58.5%

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

   4. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. unpow2 100.0%

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

      3. associate-*l* 100.0%

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

   6. Simplified 100.0%

      \[\leadsto x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + \left(-6 \cdot x2 + \color{blue}{x1 \cdot \left(x1 \cdot 9\right)}\right)\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.6 \cdot 10^{+135}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -140:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(1 + x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} - 6\right) + x1 \cdot 2\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 14000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+137}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(1 + x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} - 6\right) + x1 \cdot 2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + \left(x1 \cdot \left(x1 \cdot 9\right) + x2 \cdot -6\right)\right)\\ \end{array} \]

Alternative 10: 89.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 2 \cdot x2 - 3\\ t_2 := x1 \cdot \left(x1 \cdot 9\right)\\ t_3 := 1 + x1 \cdot x1\\ t_4 := t_3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_3} - 6\right) + x1 \cdot 2\right)\\ t_5 := x1 \cdot \left(x1 \cdot x1\right)\\ t_6 := 3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_3}\\ \mathbf{if}\;x1 \leq -1.6 \cdot 10^{+135}:\\ \;\;\;\;x1 + t_2\\ \mathbf{elif}\;x1 \leq -25:\\ \;\;\;\;x1 + \left(t_6 + \left(x1 + \left(t_5 + \left(t_4 + t_0 \cdot \left(2 \cdot x2 - x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7000:\\ \;\;\;\;x1 + \left(t_6 + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot t_1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+137}:\\ \;\;\;\;x1 + \left(t_6 + \left(x1 + \left(t_5 + \left(3 \cdot t_0 + t_4\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot t_1\right) - 2\right) + \left(t_2 + x2 \cdot -6\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (- (* 2.0 x2) 3.0))
        (t_2 (* x1 (* x1 9.0)))
        (t_3 (+ 1.0 (* x1 x1)))
        (t_4
         (*
          t_3
          (+
           (* (* x1 x1) (- (* 4.0 (/ (- (+ t_0 (* 2.0 x2)) x1) t_3)) 6.0))
           (* x1 2.0))))
        (t_5 (* x1 (* x1 x1)))
        (t_6 (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_3))))
   (if (<= x1 -1.6e+135)
     (+ x1 t_2)
     (if (<= x1 -25.0)
       (+ x1 (+ t_6 (+ x1 (+ t_5 (+ t_4 (* t_0 (- (* 2.0 x2) x1)))))))
       (if (<= x1 7000.0)
         (+ x1 (+ t_6 (+ x1 (* 4.0 (* x2 (* x1 t_1))))))
         (if (<= x1 1.8e+137)
           (+ x1 (+ t_6 (+ x1 (+ t_5 (+ (* 3.0 t_0) t_4)))))
           (+
            x1
            (+ (* x1 (- (* 4.0 (* x2 t_1)) 2.0)) (+ t_2 (* x2 -6.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (2.0 * x2) - 3.0;
	double t_2 = x1 * (x1 * 9.0);
	double t_3 = 1.0 + (x1 * x1);
	double t_4 = t_3 * (((x1 * x1) * ((4.0 * (((t_0 + (2.0 * x2)) - x1) / t_3)) - 6.0)) + (x1 * 2.0));
	double t_5 = x1 * (x1 * x1);
	double t_6 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3);
	double tmp;
	if (x1 <= -1.6e+135) {
		tmp = x1 + t_2;
	} else if (x1 <= -25.0) {
		tmp = x1 + (t_6 + (x1 + (t_5 + (t_4 + (t_0 * ((2.0 * x2) - x1))))));
	} else if (x1 <= 7000.0) {
		tmp = x1 + (t_6 + (x1 + (4.0 * (x2 * (x1 * t_1)))));
	} else if (x1 <= 1.8e+137) {
		tmp = x1 + (t_6 + (x1 + (t_5 + ((3.0 * t_0) + t_4))));
	} else {
		tmp = x1 + ((x1 * ((4.0 * (x2 * t_1)) - 2.0)) + (t_2 + (x2 * -6.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (2.0d0 * x2) - 3.0d0
    t_2 = x1 * (x1 * 9.0d0)
    t_3 = 1.0d0 + (x1 * x1)
    t_4 = t_3 * (((x1 * x1) * ((4.0d0 * (((t_0 + (2.0d0 * x2)) - x1) / t_3)) - 6.0d0)) + (x1 * 2.0d0))
    t_5 = x1 * (x1 * x1)
    t_6 = 3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_3)
    if (x1 <= (-1.6d+135)) then
        tmp = x1 + t_2
    else if (x1 <= (-25.0d0)) then
        tmp = x1 + (t_6 + (x1 + (t_5 + (t_4 + (t_0 * ((2.0d0 * x2) - x1))))))
    else if (x1 <= 7000.0d0) then
        tmp = x1 + (t_6 + (x1 + (4.0d0 * (x2 * (x1 * t_1)))))
    else if (x1 <= 1.8d+137) then
        tmp = x1 + (t_6 + (x1 + (t_5 + ((3.0d0 * t_0) + t_4))))
    else
        tmp = x1 + ((x1 * ((4.0d0 * (x2 * t_1)) - 2.0d0)) + (t_2 + (x2 * (-6.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (2.0 * x2) - 3.0;
	double t_2 = x1 * (x1 * 9.0);
	double t_3 = 1.0 + (x1 * x1);
	double t_4 = t_3 * (((x1 * x1) * ((4.0 * (((t_0 + (2.0 * x2)) - x1) / t_3)) - 6.0)) + (x1 * 2.0));
	double t_5 = x1 * (x1 * x1);
	double t_6 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3);
	double tmp;
	if (x1 <= -1.6e+135) {
		tmp = x1 + t_2;
	} else if (x1 <= -25.0) {
		tmp = x1 + (t_6 + (x1 + (t_5 + (t_4 + (t_0 * ((2.0 * x2) - x1))))));
	} else if (x1 <= 7000.0) {
		tmp = x1 + (t_6 + (x1 + (4.0 * (x2 * (x1 * t_1)))));
	} else if (x1 <= 1.8e+137) {
		tmp = x1 + (t_6 + (x1 + (t_5 + ((3.0 * t_0) + t_4))));
	} else {
		tmp = x1 + ((x1 * ((4.0 * (x2 * t_1)) - 2.0)) + (t_2 + (x2 * -6.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (2.0 * x2) - 3.0
	t_2 = x1 * (x1 * 9.0)
	t_3 = 1.0 + (x1 * x1)
	t_4 = t_3 * (((x1 * x1) * ((4.0 * (((t_0 + (2.0 * x2)) - x1) / t_3)) - 6.0)) + (x1 * 2.0))
	t_5 = x1 * (x1 * x1)
	t_6 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3)
	tmp = 0
	if x1 <= -1.6e+135:
		tmp = x1 + t_2
	elif x1 <= -25.0:
		tmp = x1 + (t_6 + (x1 + (t_5 + (t_4 + (t_0 * ((2.0 * x2) - x1))))))
	elif x1 <= 7000.0:
		tmp = x1 + (t_6 + (x1 + (4.0 * (x2 * (x1 * t_1)))))
	elif x1 <= 1.8e+137:
		tmp = x1 + (t_6 + (x1 + (t_5 + ((3.0 * t_0) + t_4))))
	else:
		tmp = x1 + ((x1 * ((4.0 * (x2 * t_1)) - 2.0)) + (t_2 + (x2 * -6.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(2.0 * x2) - 3.0)
	t_2 = Float64(x1 * Float64(x1 * 9.0))
	t_3 = Float64(1.0 + Float64(x1 * x1))
	t_4 = Float64(t_3 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_3)) - 6.0)) + Float64(x1 * 2.0)))
	t_5 = Float64(x1 * Float64(x1 * x1))
	t_6 = Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_3))
	tmp = 0.0
	if (x1 <= -1.6e+135)
		tmp = Float64(x1 + t_2);
	elseif (x1 <= -25.0)
		tmp = Float64(x1 + Float64(t_6 + Float64(x1 + Float64(t_5 + Float64(t_4 + Float64(t_0 * Float64(Float64(2.0 * x2) - x1)))))));
	elseif (x1 <= 7000.0)
		tmp = Float64(x1 + Float64(t_6 + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * t_1))))));
	elseif (x1 <= 1.8e+137)
		tmp = Float64(x1 + Float64(t_6 + Float64(x1 + Float64(t_5 + Float64(Float64(3.0 * t_0) + t_4)))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * t_1)) - 2.0)) + Float64(t_2 + Float64(x2 * -6.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (2.0 * x2) - 3.0;
	t_2 = x1 * (x1 * 9.0);
	t_3 = 1.0 + (x1 * x1);
	t_4 = t_3 * (((x1 * x1) * ((4.0 * (((t_0 + (2.0 * x2)) - x1) / t_3)) - 6.0)) + (x1 * 2.0));
	t_5 = x1 * (x1 * x1);
	t_6 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3);
	tmp = 0.0;
	if (x1 <= -1.6e+135)
		tmp = x1 + t_2;
	elseif (x1 <= -25.0)
		tmp = x1 + (t_6 + (x1 + (t_5 + (t_4 + (t_0 * ((2.0 * x2) - x1))))));
	elseif (x1 <= 7000.0)
		tmp = x1 + (t_6 + (x1 + (4.0 * (x2 * (x1 * t_1)))));
	elseif (x1 <= 1.8e+137)
		tmp = x1 + (t_6 + (x1 + (t_5 + ((3.0 * t_0) + t_4))));
	else
		tmp = x1 + ((x1 * ((4.0 * (x2 * t_1)) - 2.0)) + (t_2 + (x2 * -6.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.6e+135], N[(x1 + t$95$2), $MachinePrecision], If[LessEqual[x1, -25.0], N[(x1 + N[(t$95$6 + N[(x1 + N[(t$95$5 + N[(t$95$4 + N[(t$95$0 * N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7000.0], N[(x1 + N[(t$95$6 + N[(x1 + N[(4.0 * N[(x2 * N[(x1 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.8e+137], N[(x1 + N[(t$95$6 + N[(x1 + N[(t$95$5 + N[(N[(3.0 * t$95$0), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 * N[(N[(4.0 * N[(x2 * t$95$1), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -1.59999999999999987e135

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 48.2%

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

   4. Taylor expanded in x2 around 0 48.2%

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

      1. *-commutative 48.2%

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

      2. unpow2 48.2%

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

   6. Simplified 48.2%

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

   7. Taylor expanded in x1 around inf 77.2%

      \[\leadsto x1 + \color{blue}{9 \cdot {x1}^{2}} \]
   8. Step-by-step derivation

      1. *-commutative 77.2%

         \[\leadsto x1 + \color{blue}{{x1}^{2} \cdot 9} \]

      2. unpow2 77.2%

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

      3. associate-*r* 77.2%

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

   9. Simplified 77.2%

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

   if -1.59999999999999987e135 < x1 < -25

   1. Initial program 79.5%

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

   2. Taylor expanded in x1 around 0 70.9%

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

   3. Taylor expanded in x1 around inf 70.7%

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

      1. *-commutative 70.7%

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

   5. Simplified 70.7%

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

   6. Taylor expanded in x1 around 0 70.8%

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

   if -25 < x1 < 7e3

   1. Initial program 99.4%

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

   2. Taylor expanded in x1 around 0 98.8%

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

   if 7e3 < x1 < 1.8e137

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 84.1%

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

   3. Taylor expanded in x1 around inf 94.4%

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

      1. *-commutative 94.4%

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

   5. Simplified 94.4%

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

   6. Taylor expanded in x1 around inf 94.4%

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

   if 1.8e137 < x1

   1. Initial program 7.3%

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

   2. Taylor expanded in x1 around 0 7.3%

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

   3. Taylor expanded in x1 around 0 58.5%

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

   4. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. unpow2 100.0%

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

      3. associate-*l* 100.0%

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

   6. Simplified 100.0%

      \[\leadsto x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + \left(-6 \cdot x2 + \color{blue}{x1 \cdot \left(x1 \cdot 9\right)}\right)\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.6 \cdot 10^{+135}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -25:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(1 + x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} - 6\right) + x1 \cdot 2\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2 - x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+137}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(1 + x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} - 6\right) + x1 \cdot 2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + \left(x1 \cdot \left(x1 \cdot 9\right) + x2 \cdot -6\right)\right)\\ \end{array} \]

Alternative 11: 88.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot x2 - 3\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot \left(x1 \cdot 9\right)\\ t_3 := 1 + x1 \cdot x1\\ t_4 := 3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_3}\\ t_5 := x1 + \left(t_4 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_1 \cdot \frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_3} + t_3 \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 + t_2\\ \mathbf{elif}\;x1 \leq -18000000:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x1 \leq 13500:\\ \;\;\;\;x1 + \left(t_4 + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot t_0\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+137}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot t_0\right) - 2\right) + \left(t_2 + x2 \cdot -6\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* 2.0 x2) 3.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (* x1 (* x1 9.0)))
        (t_3 (+ 1.0 (* x1 x1)))
        (t_4 (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_3)))
        (t_5
         (+
          x1
          (+
           t_4
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* t_1 (/ (- (+ t_1 (* 2.0 x2)) x1) t_3))
              (* t_3 (+ (* x1 2.0) (* (* x1 x1) 6.0))))))))))
   (if (<= x1 -5.5e+102)
     (+ x1 t_2)
     (if (<= x1 -18000000.0)
       t_5
       (if (<= x1 13500.0)
         (+ x1 (+ t_4 (+ x1 (* 4.0 (* x2 (* x1 t_0))))))
         (if (<= x1 1.8e+137)
           t_5
           (+
            x1
            (+ (* x1 (- (* 4.0 (* x2 t_0)) 2.0)) (+ t_2 (* x2 -6.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = x1 * (x1 * 9.0);
	double t_3 = 1.0 + (x1 * x1);
	double t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_3);
	double t_5 = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((t_1 + (2.0 * x2)) - x1) / t_3)) + (t_3 * ((x1 * 2.0) + ((x1 * x1) * 6.0)))))));
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = x1 + t_2;
	} else if (x1 <= -18000000.0) {
		tmp = t_5;
	} else if (x1 <= 13500.0) {
		tmp = x1 + (t_4 + (x1 + (4.0 * (x2 * (x1 * t_0)))));
	} else if (x1 <= 1.8e+137) {
		tmp = t_5;
	} else {
		tmp = x1 + ((x1 * ((4.0 * (x2 * t_0)) - 2.0)) + (t_2 + (x2 * -6.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = (2.0d0 * x2) - 3.0d0
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = x1 * (x1 * 9.0d0)
    t_3 = 1.0d0 + (x1 * x1)
    t_4 = 3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_3)
    t_5 = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((t_1 + (2.0d0 * x2)) - x1) / t_3)) + (t_3 * ((x1 * 2.0d0) + ((x1 * x1) * 6.0d0)))))))
    if (x1 <= (-5.5d+102)) then
        tmp = x1 + t_2
    else if (x1 <= (-18000000.0d0)) then
        tmp = t_5
    else if (x1 <= 13500.0d0) then
        tmp = x1 + (t_4 + (x1 + (4.0d0 * (x2 * (x1 * t_0)))))
    else if (x1 <= 1.8d+137) then
        tmp = t_5
    else
        tmp = x1 + ((x1 * ((4.0d0 * (x2 * t_0)) - 2.0d0)) + (t_2 + (x2 * (-6.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = x1 * (x1 * 9.0);
	double t_3 = 1.0 + (x1 * x1);
	double t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_3);
	double t_5 = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((t_1 + (2.0 * x2)) - x1) / t_3)) + (t_3 * ((x1 * 2.0) + ((x1 * x1) * 6.0)))))));
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = x1 + t_2;
	} else if (x1 <= -18000000.0) {
		tmp = t_5;
	} else if (x1 <= 13500.0) {
		tmp = x1 + (t_4 + (x1 + (4.0 * (x2 * (x1 * t_0)))));
	} else if (x1 <= 1.8e+137) {
		tmp = t_5;
	} else {
		tmp = x1 + ((x1 * ((4.0 * (x2 * t_0)) - 2.0)) + (t_2 + (x2 * -6.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (2.0 * x2) - 3.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = x1 * (x1 * 9.0)
	t_3 = 1.0 + (x1 * x1)
	t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_3)
	t_5 = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((t_1 + (2.0 * x2)) - x1) / t_3)) + (t_3 * ((x1 * 2.0) + ((x1 * x1) * 6.0)))))))
	tmp = 0
	if x1 <= -5.5e+102:
		tmp = x1 + t_2
	elif x1 <= -18000000.0:
		tmp = t_5
	elif x1 <= 13500.0:
		tmp = x1 + (t_4 + (x1 + (4.0 * (x2 * (x1 * t_0)))))
	elif x1 <= 1.8e+137:
		tmp = t_5
	else:
		tmp = x1 + ((x1 * ((4.0 * (x2 * t_0)) - 2.0)) + (t_2 + (x2 * -6.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(2.0 * x2) - 3.0)
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(x1 * Float64(x1 * 9.0))
	t_3 = Float64(1.0 + Float64(x1 * x1))
	t_4 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_3))
	t_5 = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_3)) + Float64(t_3 * Float64(Float64(x1 * 2.0) + Float64(Float64(x1 * x1) * 6.0))))))))
	tmp = 0.0
	if (x1 <= -5.5e+102)
		tmp = Float64(x1 + t_2);
	elseif (x1 <= -18000000.0)
		tmp = t_5;
	elseif (x1 <= 13500.0)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * t_0))))));
	elseif (x1 <= 1.8e+137)
		tmp = t_5;
	else
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * t_0)) - 2.0)) + Float64(t_2 + Float64(x2 * -6.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (2.0 * x2) - 3.0;
	t_1 = x1 * (x1 * 3.0);
	t_2 = x1 * (x1 * 9.0);
	t_3 = 1.0 + (x1 * x1);
	t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_3);
	t_5 = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((t_1 + (2.0 * x2)) - x1) / t_3)) + (t_3 * ((x1 * 2.0) + ((x1 * x1) * 6.0)))))));
	tmp = 0.0;
	if (x1 <= -5.5e+102)
		tmp = x1 + t_2;
	elseif (x1 <= -18000000.0)
		tmp = t_5;
	elseif (x1 <= 13500.0)
		tmp = x1 + (t_4 + (x1 + (4.0 * (x2 * (x1 * t_0)))));
	elseif (x1 <= 1.8e+137)
		tmp = t_5;
	else
		tmp = x1 + ((x1 * ((4.0 * (x2 * t_0)) - 2.0)) + (t_2 + (x2 * -6.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(t$95$4 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 * N[(N[(x1 * 2.0), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.5e+102], N[(x1 + t$95$2), $MachinePrecision], If[LessEqual[x1, -18000000.0], t$95$5, If[LessEqual[x1, 13500.0], N[(x1 + N[(t$95$4 + N[(x1 + N[(4.0 * N[(x2 * N[(x1 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.8e+137], t$95$5, N[(x1 + N[(N[(x1 * N[(N[(4.0 * N[(x2 * t$95$0), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.49999999999999981e102

   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 2.4%

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

   3. Taylor expanded in x1 around 0 44.0%

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

   4. Taylor expanded in x2 around 0 44.0%

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

      1. *-commutative 44.0%

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

      2. unpow2 44.0%

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

   6. Simplified 44.0%

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

   7. Taylor expanded in x1 around inf 67.0%

      \[\leadsto x1 + \color{blue}{9 \cdot {x1}^{2}} \]
   8. Step-by-step derivation

      1. *-commutative 67.0%

         \[\leadsto x1 + \color{blue}{{x1}^{2} \cdot 9} \]

      2. unpow2 67.0%

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

      3. associate-*r* 67.0%

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

   9. Simplified 67.0%

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

   if -5.49999999999999981e102 < x1 < -1.8e7 or 13500 < x1 < 1.8e137

   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 85.9%

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

   3. Taylor expanded in x1 around inf 91.4%

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

      1. *-commutative 91.4%

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

   5. Simplified 91.4%

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

   6. Taylor expanded in x1 around inf 81.2%

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

   if -1.8e7 < x1 < 13500

   1. Initial program 99.4%

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

   2. Taylor expanded in x1 around 0 98.8%

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

   if 1.8e137 < x1

   1. Initial program 7.3%

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

   2. Taylor expanded in x1 around 0 7.3%

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

   3. Taylor expanded in x1 around 0 58.5%

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

   4. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. unpow2 100.0%

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

      3. associate-*l* 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -18000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 13500:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+137}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + \left(x1 \cdot \left(x1 \cdot 9\right) + x2 \cdot -6\right)\right)\\ \end{array} \]

Alternative 12: 74.4% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;2 \cdot x2 \leq -2 \cdot 10^{+25} \lor \neg \left(2 \cdot x2 \leq 10^{+102}\right):\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + \left(x2 \cdot -6 + 9 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= (* 2.0 x2) -2e+25) (not (<= (* 2.0 x2) 1e+102)))
   (+
    x1
    (+ (+ x1 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0))))) (* 3.0 (* x2 -2.0))))
   (+ x1 (+ (* x1 -2.0) (+ (* x2 -6.0) (* 9.0 (* x1 x1)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (((2.0 * x2) <= -2e+25) || !((2.0 * x2) <= 1e+102)) {
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))) + (3.0 * (x2 * -2.0)));
	} else {
		tmp = x1 + ((x1 * -2.0) + ((x2 * -6.0) + (9.0 * (x1 * x1))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (((2.0d0 * x2) <= (-2d+25)) .or. (.not. ((2.0d0 * x2) <= 1d+102))) then
        tmp = x1 + ((x1 + (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0))))) + (3.0d0 * (x2 * (-2.0d0))))
    else
        tmp = x1 + ((x1 * (-2.0d0)) + ((x2 * (-6.0d0)) + (9.0d0 * (x1 * x1))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (((2.0 * x2) <= -2e+25) || !((2.0 * x2) <= 1e+102)) {
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))) + (3.0 * (x2 * -2.0)));
	} else {
		tmp = x1 + ((x1 * -2.0) + ((x2 * -6.0) + (9.0 * (x1 * x1))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if ((2.0 * x2) <= -2e+25) or not ((2.0 * x2) <= 1e+102):
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))) + (3.0 * (x2 * -2.0)))
	else:
		tmp = x1 + ((x1 * -2.0) + ((x2 * -6.0) + (9.0 * (x1 * x1))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((Float64(2.0 * x2) <= -2e+25) || !(Float64(2.0 * x2) <= 1e+102))
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0))))) + Float64(3.0 * Float64(x2 * -2.0))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 * -2.0) + Float64(Float64(x2 * -6.0) + Float64(9.0 * Float64(x1 * x1)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (((2.0 * x2) <= -2e+25) || ~(((2.0 * x2) <= 1e+102)))
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))) + (3.0 * (x2 * -2.0)));
	else
		tmp = x1 + ((x1 * -2.0) + ((x2 * -6.0) + (9.0 * (x1 * x1))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[N[(2.0 * x2), $MachinePrecision], -2e+25], N[Not[LessEqual[N[(2.0 * x2), $MachinePrecision], 1e+102]], $MachinePrecision]], N[(x1 + N[(N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] + N[(N[(x2 * -6.0), $MachinePrecision] + N[(9.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 2 x2) < -2.00000000000000018e25 or 9.99999999999999977e101 < (*.f64 2 x2)

   1. Initial program 70.4%

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

   2. Taylor expanded in x1 around 0 65.1%

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

   3. Taylor expanded in x1 around 0 80.7%

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

      1. *-commutative 80.7%

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

   5. Simplified 80.7%

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

   if -2.00000000000000018e25 < (*.f64 2 x2) < 9.99999999999999977e101

   1. Initial program 67.5%

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

   2. Taylor expanded in x1 around 0 45.5%

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

   3. Taylor expanded in x1 around 0 69.7%

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

   4. Taylor expanded in x2 around 0 72.5%

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

      1. *-commutative 72.5%

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

      2. unpow2 72.5%

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

   6. Simplified 72.5%

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

   7. Taylor expanded in x2 around 0 73.9%

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

      1. *-commutative 73.9%

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

   9. Simplified 73.9%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;2 \cdot x2 \leq -2 \cdot 10^{+25} \lor \neg \left(2 \cdot x2 \leq 10^{+102}\right):\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + \left(x2 \cdot -6 + 9 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \end{array} \]

Alternative 13: 79.9% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot x2 - 3\\ t_1 := x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{if}\;x1 \leq -7.8 \cdot 10^{+135}:\\ \;\;\;\;x1 + t_1\\ \mathbf{elif}\;x1 \leq 5.7 \cdot 10^{-73}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot t_0\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot t_0\right) - 2\right) + \left(t_1 + x2 \cdot -6\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* 2.0 x2) 3.0)) (t_1 (* x1 (* x1 9.0))))
   (if (<= x1 -7.8e+135)
     (+ x1 t_1)
     (if (<= x1 5.7e-73)
       (+ x1 (+ (+ x1 (* 4.0 (* x2 (* x1 t_0)))) (* 3.0 (- (* x2 -2.0) x1))))
       (+ x1 (+ (* x1 (- (* 4.0 (* x2 t_0)) 2.0)) (+ t_1 (* x2 -6.0))))))))

C

double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = x1 * (x1 * 9.0);
	double tmp;
	if (x1 <= -7.8e+135) {
		tmp = x1 + t_1;
	} else if (x1 <= 5.7e-73) {
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * t_0)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = x1 + ((x1 * ((4.0 * (x2 * t_0)) - 2.0)) + (t_1 + (x2 * -6.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (2.0d0 * x2) - 3.0d0
    t_1 = x1 * (x1 * 9.0d0)
    if (x1 <= (-7.8d+135)) then
        tmp = x1 + t_1
    else if (x1 <= 5.7d-73) then
        tmp = x1 + ((x1 + (4.0d0 * (x2 * (x1 * t_0)))) + (3.0d0 * ((x2 * (-2.0d0)) - x1)))
    else
        tmp = x1 + ((x1 * ((4.0d0 * (x2 * t_0)) - 2.0d0)) + (t_1 + (x2 * (-6.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = x1 * (x1 * 9.0);
	double tmp;
	if (x1 <= -7.8e+135) {
		tmp = x1 + t_1;
	} else if (x1 <= 5.7e-73) {
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * t_0)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = x1 + ((x1 * ((4.0 * (x2 * t_0)) - 2.0)) + (t_1 + (x2 * -6.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (2.0 * x2) - 3.0
	t_1 = x1 * (x1 * 9.0)
	tmp = 0
	if x1 <= -7.8e+135:
		tmp = x1 + t_1
	elif x1 <= 5.7e-73:
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * t_0)))) + (3.0 * ((x2 * -2.0) - x1)))
	else:
		tmp = x1 + ((x1 * ((4.0 * (x2 * t_0)) - 2.0)) + (t_1 + (x2 * -6.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(2.0 * x2) - 3.0)
	t_1 = Float64(x1 * Float64(x1 * 9.0))
	tmp = 0.0
	if (x1 <= -7.8e+135)
		tmp = Float64(x1 + t_1);
	elseif (x1 <= 5.7e-73)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * t_0)))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * t_0)) - 2.0)) + Float64(t_1 + Float64(x2 * -6.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (2.0 * x2) - 3.0;
	t_1 = x1 * (x1 * 9.0);
	tmp = 0.0;
	if (x1 <= -7.8e+135)
		tmp = x1 + t_1;
	elseif (x1 <= 5.7e-73)
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * t_0)))) + (3.0 * ((x2 * -2.0) - x1)));
	else
		tmp = x1 + ((x1 * ((4.0 * (x2 * t_0)) - 2.0)) + (t_1 + (x2 * -6.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -7.8e+135], N[(x1 + t$95$1), $MachinePrecision], If[LessEqual[x1, 5.7e-73], N[(x1 + N[(N[(x1 + N[(4.0 * N[(x2 * N[(x1 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 * N[(N[(4.0 * N[(x2 * t$95$0), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -7.80000000000000064e135

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 48.2%

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

   4. Taylor expanded in x2 around 0 48.2%

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

      1. *-commutative 48.2%

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

      2. unpow2 48.2%

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

   6. Simplified 48.2%

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

   7. Taylor expanded in x1 around inf 77.2%

      \[\leadsto x1 + \color{blue}{9 \cdot {x1}^{2}} \]
   8. Step-by-step derivation

      1. *-commutative 77.2%

         \[\leadsto x1 + \color{blue}{{x1}^{2} \cdot 9} \]

      2. unpow2 77.2%

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

      3. associate-*r* 77.2%

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

   9. Simplified 77.2%

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

   if -7.80000000000000064e135 < x1 < 5.6999999999999998e-73

   1. Initial program 95.8%

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

   2. Taylor expanded in x1 around 0 83.7%

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

   3. Taylor expanded in x1 around 0 84.1%

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

   if 5.6999999999999998e-73 < x1

   1. Initial program 53.9%

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

   2. Taylor expanded in x1 around 0 28.0%

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

   3. Taylor expanded in x1 around 0 53.5%

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

   4. Taylor expanded in x2 around 0 74.2%

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

      1. *-commutative 74.2%

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

      2. unpow2 74.2%

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

      3. associate-*l* 74.2%

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

   6. Simplified 74.2%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.8 \cdot 10^{+135}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq 5.7 \cdot 10^{-73}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + \left(x1 \cdot \left(x1 \cdot 9\right) + x2 \cdot -6\right)\right)\\ \end{array} \]

Alternative 14: 70.0% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;2 \cdot x2 \leq -5 \cdot 10^{+179} \lor \neg \left(2 \cdot x2 \leq 10^{+163}\right):\\ \;\;\;\;x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + \left(x2 \cdot -6 + 9 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= (* 2.0 x2) -5e+179) (not (<= (* 2.0 x2) 1e+163)))
   (+ x1 (* 8.0 (* x2 (* x1 x2))))
   (+ x1 (+ (* x1 -2.0) (+ (* x2 -6.0) (* 9.0 (* x1 x1)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (((2.0 * x2) <= -5e+179) || !((2.0 * x2) <= 1e+163)) {
		tmp = x1 + (8.0 * (x2 * (x1 * x2)));
	} else {
		tmp = x1 + ((x1 * -2.0) + ((x2 * -6.0) + (9.0 * (x1 * x1))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (((2.0d0 * x2) <= (-5d+179)) .or. (.not. ((2.0d0 * x2) <= 1d+163))) then
        tmp = x1 + (8.0d0 * (x2 * (x1 * x2)))
    else
        tmp = x1 + ((x1 * (-2.0d0)) + ((x2 * (-6.0d0)) + (9.0d0 * (x1 * x1))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (((2.0 * x2) <= -5e+179) || !((2.0 * x2) <= 1e+163)) {
		tmp = x1 + (8.0 * (x2 * (x1 * x2)));
	} else {
		tmp = x1 + ((x1 * -2.0) + ((x2 * -6.0) + (9.0 * (x1 * x1))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if ((2.0 * x2) <= -5e+179) or not ((2.0 * x2) <= 1e+163):
		tmp = x1 + (8.0 * (x2 * (x1 * x2)))
	else:
		tmp = x1 + ((x1 * -2.0) + ((x2 * -6.0) + (9.0 * (x1 * x1))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((Float64(2.0 * x2) <= -5e+179) || !(Float64(2.0 * x2) <= 1e+163))
		tmp = Float64(x1 + Float64(8.0 * Float64(x2 * Float64(x1 * x2))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 * -2.0) + Float64(Float64(x2 * -6.0) + Float64(9.0 * Float64(x1 * x1)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (((2.0 * x2) <= -5e+179) || ~(((2.0 * x2) <= 1e+163)))
		tmp = x1 + (8.0 * (x2 * (x1 * x2)));
	else
		tmp = x1 + ((x1 * -2.0) + ((x2 * -6.0) + (9.0 * (x1 * x1))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[N[(2.0 * x2), $MachinePrecision], -5e+179], N[Not[LessEqual[N[(2.0 * x2), $MachinePrecision], 1e+163]], $MachinePrecision]], N[(x1 + N[(8.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] + N[(N[(x2 * -6.0), $MachinePrecision] + N[(9.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 2 x2) < -5e179 or 9.9999999999999994e162 < (*.f64 2 x2)

   1. Initial program 74.0%

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

   2. Taylor expanded in x1 around 0 69.1%

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

   3. Taylor expanded in x1 around 0 48.5%

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

   4. Taylor expanded in x2 around 0 58.2%

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

      1. *-commutative 58.2%

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

      2. unpow2 58.2%

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

   6. Simplified 58.2%

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

   7. Taylor expanded in x2 around inf 58.2%

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

      1. unpow2 58.2%

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

      2. associate-*l* 72.3%

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

   9. Simplified 72.3%

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

   if -5e179 < (*.f64 2 x2) < 9.9999999999999994e162

   1. Initial program 67.1%

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

   2. Taylor expanded in x1 around 0 49.0%

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

   3. Taylor expanded in x1 around 0 64.8%

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

   4. Taylor expanded in x2 around 0 71.1%

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

      1. *-commutative 71.1%

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

      2. unpow2 71.1%

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

   6. Simplified 71.1%

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

   7. Taylor expanded in x2 around 0 72.1%

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

      1. *-commutative 72.1%

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

   9. Simplified 72.1%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;2 \cdot x2 \leq -5 \cdot 10^{+179} \lor \neg \left(2 \cdot x2 \leq 10^{+163}\right):\\ \;\;\;\;x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + \left(x2 \cdot -6 + 9 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \end{array} \]

Alternative 15: 60.3% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + x1 \cdot \left(x1 \cdot 9\right)\\ t_1 := x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\\ \mathbf{if}\;x1 \leq -4.1 \cdot 10^{+145}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq -1.42 \cdot 10^{+23}:\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.15 \cdot 10^{-135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq 2.85 \cdot 10^{-86}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 4.4 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* x1 (* x1 9.0)))) (t_1 (+ x1 (* 8.0 (* x2 (* x1 x2))))))
   (if (<= x1 -4.1e+145)
     t_0
     (if (<= x1 -1.42e+23)
       (+ x1 (* 3.0 (* x1 (* x1 (+ 3.0 (* 2.0 x2))))))
       (if (<= x1 -1.15e-135)
         t_1
         (if (<= x1 2.85e-86) (* x2 -6.0) (if (<= x1 4.4e+153) t_1 t_0)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 * (x1 * 9.0));
	double t_1 = x1 + (8.0 * (x2 * (x1 * x2)));
	double tmp;
	if (x1 <= -4.1e+145) {
		tmp = t_0;
	} else if (x1 <= -1.42e+23) {
		tmp = x1 + (3.0 * (x1 * (x1 * (3.0 + (2.0 * x2)))));
	} else if (x1 <= -1.15e-135) {
		tmp = t_1;
	} else if (x1 <= 2.85e-86) {
		tmp = x2 * -6.0;
	} else if (x1 <= 4.4e+153) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x1 + (x1 * (x1 * 9.0d0))
    t_1 = x1 + (8.0d0 * (x2 * (x1 * x2)))
    if (x1 <= (-4.1d+145)) then
        tmp = t_0
    else if (x1 <= (-1.42d+23)) then
        tmp = x1 + (3.0d0 * (x1 * (x1 * (3.0d0 + (2.0d0 * x2)))))
    else if (x1 <= (-1.15d-135)) then
        tmp = t_1
    else if (x1 <= 2.85d-86) then
        tmp = x2 * (-6.0d0)
    else if (x1 <= 4.4d+153) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 * (x1 * 9.0));
	double t_1 = x1 + (8.0 * (x2 * (x1 * x2)));
	double tmp;
	if (x1 <= -4.1e+145) {
		tmp = t_0;
	} else if (x1 <= -1.42e+23) {
		tmp = x1 + (3.0 * (x1 * (x1 * (3.0 + (2.0 * x2)))));
	} else if (x1 <= -1.15e-135) {
		tmp = t_1;
	} else if (x1 <= 2.85e-86) {
		tmp = x2 * -6.0;
	} else if (x1 <= 4.4e+153) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 * (x1 * 9.0))
	t_1 = x1 + (8.0 * (x2 * (x1 * x2)))
	tmp = 0
	if x1 <= -4.1e+145:
		tmp = t_0
	elif x1 <= -1.42e+23:
		tmp = x1 + (3.0 * (x1 * (x1 * (3.0 + (2.0 * x2)))))
	elif x1 <= -1.15e-135:
		tmp = t_1
	elif x1 <= 2.85e-86:
		tmp = x2 * -6.0
	elif x1 <= 4.4e+153:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 * Float64(x1 * 9.0)))
	t_1 = Float64(x1 + Float64(8.0 * Float64(x2 * Float64(x1 * x2))))
	tmp = 0.0
	if (x1 <= -4.1e+145)
		tmp = t_0;
	elseif (x1 <= -1.42e+23)
		tmp = Float64(x1 + Float64(3.0 * Float64(x1 * Float64(x1 * Float64(3.0 + Float64(2.0 * x2))))));
	elseif (x1 <= -1.15e-135)
		tmp = t_1;
	elseif (x1 <= 2.85e-86)
		tmp = Float64(x2 * -6.0);
	elseif (x1 <= 4.4e+153)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 * (x1 * 9.0));
	t_1 = x1 + (8.0 * (x2 * (x1 * x2)));
	tmp = 0.0;
	if (x1 <= -4.1e+145)
		tmp = t_0;
	elseif (x1 <= -1.42e+23)
		tmp = x1 + (3.0 * (x1 * (x1 * (3.0 + (2.0 * x2)))));
	elseif (x1 <= -1.15e-135)
		tmp = t_1;
	elseif (x1 <= 2.85e-86)
		tmp = x2 * -6.0;
	elseif (x1 <= 4.4e+153)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(8.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.1e+145], t$95$0, If[LessEqual[x1, -1.42e+23], N[(x1 + N[(3.0 * N[(x1 * N[(x1 * N[(3.0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.15e-135], t$95$1, If[LessEqual[x1, 2.85e-86], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x1, 4.4e+153], t$95$1, t$95$0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.1000000000000001e145 or 4.3999999999999999e153 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 60.6%

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

   4. Taylor expanded in x2 around 0 83.3%

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

      1. *-commutative 83.3%

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

      2. unpow2 83.3%

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

   6. Simplified 83.3%

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

   7. Taylor expanded in x1 around inf 98.6%

      \[\leadsto x1 + \color{blue}{9 \cdot {x1}^{2}} \]
   8. Step-by-step derivation

      1. *-commutative 98.6%

         \[\leadsto x1 + \color{blue}{{x1}^{2} \cdot 9} \]

      2. unpow2 98.6%

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

      3. associate-*r* 98.6%

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

   9. Simplified 98.6%

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

   if -4.1000000000000001e145 < x1 < -1.42000000000000004e23

   1. Initial program 54.8%

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

   2. Taylor expanded in x1 around 0 7.2%

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

   3. Taylor expanded in x1 around 0 10.7%

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

   4. Taylor expanded in x1 around inf 24.4%

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

      1. associate-*r* 24.4%

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

      2. *-commutative 24.4%

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

      3. associate-*r* 24.4%

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

      4. unpow2 24.4%

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

      5. associate-*l* 24.4%

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

      6. *-commutative 24.4%

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

      7. cancel-sign-sub-inv 24.4%

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

      8. metadata-eval 24.4%

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

   6. Simplified 24.4%

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

   if -1.42000000000000004e23 < x1 < -1.15e-135 or 2.8500000000000002e-86 < x1 < 4.3999999999999999e153

   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 66.5%

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

   3. Taylor expanded in x1 around 0 58.1%

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

   4. Taylor expanded in x2 around 0 62.3%

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

      1. *-commutative 62.3%

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

      2. unpow2 62.3%

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

   6. Simplified 62.3%

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

   7. Taylor expanded in x2 around inf 32.3%

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

      1. unpow2 32.3%

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

      2. associate-*l* 37.1%

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

   9. Simplified 37.1%

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

   if -1.15e-135 < x1 < 2.8500000000000002e-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 66.1%

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

      1. *-commutative 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in x1 around 0 66.4%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.1 \cdot 10^{+145}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -1.42 \cdot 10^{+23}:\\ \;\;\;\;x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.15 \cdot 10^{-135}:\\ \;\;\;\;x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq 2.85 \cdot 10^{-86}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \end{array} \]

Alternative 16: 59.5% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + x1 \cdot \left(x1 \cdot 9\right)\\ t_1 := x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\\ \mathbf{if}\;x1 \leq -1.6 \cdot 10^{+135}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq -7.8 \cdot 10^{-136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq 3.1 \cdot 10^{-86}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 4.4 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* x1 (* x1 9.0)))) (t_1 (+ x1 (* 8.0 (* x2 (* x1 x2))))))
   (if (<= x1 -1.6e+135)
     t_0
     (if (<= x1 -7.8e-136)
       t_1
       (if (<= x1 3.1e-86) (* x2 -6.0) (if (<= x1 4.4e+153) t_1 t_0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 * (x1 * 9.0));
	double t_1 = x1 + (8.0 * (x2 * (x1 * x2)));
	double tmp;
	if (x1 <= -1.6e+135) {
		tmp = t_0;
	} else if (x1 <= -7.8e-136) {
		tmp = t_1;
	} else if (x1 <= 3.1e-86) {
		tmp = x2 * -6.0;
	} else if (x1 <= 4.4e+153) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x1 + (x1 * (x1 * 9.0d0))
    t_1 = x1 + (8.0d0 * (x2 * (x1 * x2)))
    if (x1 <= (-1.6d+135)) then
        tmp = t_0
    else if (x1 <= (-7.8d-136)) then
        tmp = t_1
    else if (x1 <= 3.1d-86) then
        tmp = x2 * (-6.0d0)
    else if (x1 <= 4.4d+153) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 * (x1 * 9.0));
	double t_1 = x1 + (8.0 * (x2 * (x1 * x2)));
	double tmp;
	if (x1 <= -1.6e+135) {
		tmp = t_0;
	} else if (x1 <= -7.8e-136) {
		tmp = t_1;
	} else if (x1 <= 3.1e-86) {
		tmp = x2 * -6.0;
	} else if (x1 <= 4.4e+153) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 * (x1 * 9.0))
	t_1 = x1 + (8.0 * (x2 * (x1 * x2)))
	tmp = 0
	if x1 <= -1.6e+135:
		tmp = t_0
	elif x1 <= -7.8e-136:
		tmp = t_1
	elif x1 <= 3.1e-86:
		tmp = x2 * -6.0
	elif x1 <= 4.4e+153:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 * Float64(x1 * 9.0)))
	t_1 = Float64(x1 + Float64(8.0 * Float64(x2 * Float64(x1 * x2))))
	tmp = 0.0
	if (x1 <= -1.6e+135)
		tmp = t_0;
	elseif (x1 <= -7.8e-136)
		tmp = t_1;
	elseif (x1 <= 3.1e-86)
		tmp = Float64(x2 * -6.0);
	elseif (x1 <= 4.4e+153)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 * (x1 * 9.0));
	t_1 = x1 + (8.0 * (x2 * (x1 * x2)));
	tmp = 0.0;
	if (x1 <= -1.6e+135)
		tmp = t_0;
	elseif (x1 <= -7.8e-136)
		tmp = t_1;
	elseif (x1 <= 3.1e-86)
		tmp = x2 * -6.0;
	elseif (x1 <= 4.4e+153)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(8.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.6e+135], t$95$0, If[LessEqual[x1, -7.8e-136], t$95$1, If[LessEqual[x1, 3.1e-86], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x1, 4.4e+153], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.59999999999999987e135 or 4.3999999999999999e153 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 54.5%

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

   4. Taylor expanded in x2 around 0 74.8%

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

      1. *-commutative 74.8%

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

      2. unpow2 74.8%

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

   6. Simplified 74.8%

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

   7. Taylor expanded in x1 around inf 88.9%

      \[\leadsto x1 + \color{blue}{9 \cdot {x1}^{2}} \]
   8. Step-by-step derivation

      1. *-commutative 88.9%

         \[\leadsto x1 + \color{blue}{{x1}^{2} \cdot 9} \]

      2. unpow2 88.9%

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

      3. associate-*r* 88.9%

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

   9. Simplified 88.9%

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

   if -1.59999999999999987e135 < x1 < -7.79999999999999952e-136 or 3.09999999999999989e-86 < x1 < 4.3999999999999999e153

   1. Initial program 94.1%

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

   2. Taylor expanded in x1 around 0 54.0%

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

   3. Taylor expanded in x1 around 0 48.1%

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

   4. Taylor expanded in x2 around 0 51.5%

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

      1. *-commutative 51.5%

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

      2. unpow2 51.5%

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

   6. Simplified 51.5%

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

   7. Taylor expanded in x2 around inf 27.4%

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

      1. unpow2 27.4%

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

      2. associate-*l* 31.1%

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

   9. Simplified 31.1%

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

   if -7.79999999999999952e-136 < x1 < 3.09999999999999989e-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 66.1%

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

      1. *-commutative 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in x1 around 0 66.4%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.6 \cdot 10^{+135}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -7.8 \cdot 10^{-136}:\\ \;\;\;\;x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq 3.1 \cdot 10^{-86}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \end{array} \]

Alternative 17: 51.3% accurate, 11.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -3.4 \cdot 10^{-50} \lor \neg \left(x1 \leq 0.185\right):\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -3.4e-50) (not (<= x1 0.185)))
   (+ x1 (* x1 (* x1 9.0)))
   (* x2 -6.0)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -3.4e-50) || !(x1 <= 0.185)) {
		tmp = x1 + (x1 * (x1 * 9.0));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-3.4d-50)) .or. (.not. (x1 <= 0.185d0))) then
        tmp = x1 + (x1 * (x1 * 9.0d0))
    else
        tmp = x2 * (-6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -3.4e-50) || !(x1 <= 0.185)) {
		tmp = x1 + (x1 * (x1 * 9.0));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -3.4e-50) or not (x1 <= 0.185):
		tmp = x1 + (x1 * (x1 * 9.0))
	else:
		tmp = x2 * -6.0
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -3.4e-50) || !(x1 <= 0.185))
		tmp = Float64(x1 + Float64(x1 * Float64(x1 * 9.0)));
	else
		tmp = Float64(x2 * -6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -3.4e-50) || ~((x1 <= 0.185)))
		tmp = x1 + (x1 * (x1 * 9.0));
	else
		tmp = x2 * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -3.4e-50], N[Not[LessEqual[x1, 0.185]], $MachinePrecision]], N[(x1 + N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * -6.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -3.40000000000000014e-50 or 0.185 < x1

   1. Initial program 40.3%

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

   2. Taylor expanded in x1 around 0 11.7%

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

   3. Taylor expanded in x1 around 0 40.4%

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

   4. Taylor expanded in x2 around 0 54.1%

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

      1. *-commutative 54.1%

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

      2. unpow2 54.1%

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

   6. Simplified 54.1%

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

   7. Taylor expanded in x1 around inf 52.0%

      \[\leadsto x1 + \color{blue}{9 \cdot {x1}^{2}} \]
   8. Step-by-step derivation

      1. *-commutative 52.0%

         \[\leadsto x1 + \color{blue}{{x1}^{2} \cdot 9} \]

      2. unpow2 52.0%

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

      3. associate-*r* 52.0%

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

   9. Simplified 52.0%

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

   if -3.40000000000000014e-50 < x1 < 0.185

   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 54.0%

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

      1. *-commutative 54.0%

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

   5. Simplified 54.0%

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

   6. Taylor expanded in x1 around 0 54.6%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.4 \cdot 10^{-50} \lor \neg \left(x1 \leq 0.185\right):\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]

Alternative 18: 26.8% 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 68.7%

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

2. Taylor expanded in x1 around 0 53.9%

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

3. Taylor expanded in x1 around 0 27.7%

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

   1. *-commutative 27.7%

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

5. Simplified 27.7%

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

6. Final simplification 27.7%

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

Alternative 19: 26.6% accurate, 42.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.7%

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

2. Taylor expanded in x1 around 0 53.9%

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

3. Taylor expanded in x1 around 0 27.7%

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

   1. *-commutative 27.7%

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

5. Simplified 27.7%

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

6. Taylor expanded in x1 around 0 27.4%

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

7. Final simplification 27.4%

   \[\leadsto x2 \cdot -6 \]

Alternative 20: 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 68.7%

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

2. Taylor expanded in x1 around 0 53.9%

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

3. Taylor expanded in x1 around 0 27.7%

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

   1. *-commutative 27.7%

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

5. Simplified 27.7%

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

6. Taylor expanded in x1 around inf 3.6%

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

7. Final simplification 3.6%

   \[\leadsto x1 \]

Reproduce

herbie shell --seed 2023192 
(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))))))