Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 68.2% → 99.4%

Time: 1.4min

Alternatives: 30

Speedup: 3.3×

• 46.6% of points produce a very large (infinite) output. You may want to add a precondition.

• could not determine a ground truth

  1. x1 = 7.656252917002746e-268
  2. x2 = 3.0386166163201598e-229

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: 68.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(3 \cdot x1\right) \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_2 - 6\right)\right) \cdot t\_1 + t\_0 \cdot t\_2\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_1}\right) \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ t_3 := x1 + \left(\left(t\_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t\_2 \cdot 4 - 6\right)\right) + t\_0 \cdot t\_2\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\\ \mathbf{if}\;x1 + \left(t\_3 + 3 \cdot \frac{x1 - \left(t\_0 - 2 \cdot x2\right)}{-1 - x1 \cdot x1}\right) \leq \infty:\\ \;\;\;\;x1 + \left(t\_3 + 3 \cdot \left(\frac{\mathsf{fma}\left(3, {x1}^{2}, x2 \cdot -2\right)}{\mathsf{fma}\left(x1, x1, 1\right)} - \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + 6 \cdot {x1}^{4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1))
        (t_3
         (+
          x1
          (+
           (+
            (*
             t_1
             (+
              (* (* (* x1 2.0) t_2) (- t_2 3.0))
              (* (* x1 x1) (- (* t_2 4.0) 6.0))))
            (* t_0 t_2))
           (* x1 (* x1 x1))))))
   (if (<=
        (+ x1 (+ t_3 (* 3.0 (/ (- x1 (- t_0 (* 2.0 x2))) (- -1.0 (* x1 x1))))))
        INFINITY)
     (+
      x1
      (+
       t_3
       (*
        3.0
        (-
         (/ (fma 3.0 (pow x1 2.0) (* x2 -2.0)) (fma x1 x1 1.0))
         (expm1 (log1p (/ x1 (fma x1 x1 1.0))))))))
     (+ x1 (* 6.0 (pow x1 4.0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double t_3 = x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)));
	double tmp;
	if ((x1 + (t_3 + (3.0 * ((x1 - (t_0 - (2.0 * x2))) / (-1.0 - (x1 * x1)))))) <= ((double) INFINITY)) {
		tmp = x1 + (t_3 + (3.0 * ((fma(3.0, pow(x1, 2.0), (x2 * -2.0)) / fma(x1, x1, 1.0)) - expm1(log1p((x1 / fma(x1, x1, 1.0)))))));
	} else {
		tmp = x1 + (6.0 * pow(x1, 4.0));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	t_3 = Float64(x1 + Float64(Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)))) + Float64(t_0 * t_2)) + Float64(x1 * Float64(x1 * x1))))
	tmp = 0.0
	if (Float64(x1 + Float64(t_3 + Float64(3.0 * Float64(Float64(x1 - Float64(t_0 - Float64(2.0 * x2))) / Float64(-1.0 - Float64(x1 * x1)))))) <= Inf)
		tmp = Float64(x1 + Float64(t_3 + Float64(3.0 * Float64(Float64(fma(3.0, (x1 ^ 2.0), Float64(x2 * -2.0)) / fma(x1, x1, 1.0)) - expm1(log1p(Float64(x1 / fma(x1, x1, 1.0))))))));
	else
		tmp = Float64(x1 + Float64(6.0 * (x1 ^ 4.0)));
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 #s(literal 4 binary64) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) #s(literal 6 binary64)))) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 #s(literal 3 binary64) (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))))) < +inf.0

   1. Initial program 99.4%

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

      1. div-sub 99.4%

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

      2. cancel-sign-sub-inv 99.4%

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

      3. associate-*r* 99.4%

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

      4. fma-define 99.4%

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

      5. pow2 99.4%

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

      6. metadata-eval 99.4%

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

      7. fma-define 99.4%

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

      8. fma-define 99.4%

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

   4. Applied egg-rr 99.4%

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

      1. *-commutative 99.4%

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

   6. Simplified 99.4%

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

      1. expm1-log1p-u 99.4%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(\frac{\mathsf{fma}\left(3, {x1}^{2}, x2 \cdot -2\right)}{\mathsf{fma}\left(x1, x1, 1\right)} - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right)}\right)\right) \]

      2. expm1-undefine 77.8%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(\frac{\mathsf{fma}\left(3, {x1}^{2}, x2 \cdot -2\right)}{\mathsf{fma}\left(x1, x1, 1\right)} - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)} - 1\right)}\right)\right) \]

   8. Applied egg-rr 77.8%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(\frac{\mathsf{fma}\left(3, {x1}^{2}, x2 \cdot -2\right)}{\mathsf{fma}\left(x1, x1, 1\right)} - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)} - 1\right)}\right)\right) \]
   9. Step-by-step derivation

      1. expm1-define 99.4%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(\frac{\mathsf{fma}\left(3, {x1}^{2}, x2 \cdot -2\right)}{\mathsf{fma}\left(x1, x1, 1\right)} - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right)}\right)\right) \]

   10. Simplified 99.4%

       \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(\frac{\mathsf{fma}\left(3, {x1}^{2}, x2 \cdot -2\right)}{\mathsf{fma}\left(x1, x1, 1\right)} - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right)}\right)\right) \]

   if +inf.0 < (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 #s(literal 4 binary64) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) #s(literal 6 binary64)))) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 #s(literal 3 binary64) (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))))

   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. Add Preprocessing

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. metadata-eval 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1}\right) \leq \infty:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(\frac{\mathsf{fma}\left(3, {x1}^{2}, x2 \cdot -2\right)}{\mathsf{fma}\left(x1, x1, 1\right)} - \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + 6 \cdot {x1}^{4}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ t_3 := x1 + \left(\left(t\_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t\_2 \cdot 4 - 6\right)\right) + t\_0 \cdot t\_2\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\\ \mathbf{if}\;x1 + \left(t\_3 + 3 \cdot \frac{x1 - \left(t\_0 - 2 \cdot x2\right)}{-1 - x1 \cdot x1}\right) \leq \infty:\\ \;\;\;\;x1 + \left(t\_3 + 3 \cdot \left(\frac{\mathsf{fma}\left(3, {x1}^{2}, x2 \cdot -2\right)}{\mathsf{fma}\left(x1, x1, 1\right)} - \frac{x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + 6 \cdot {x1}^{4}\\ \end{array} \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 #s(literal 4 binary64) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) #s(literal 6 binary64)))) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 #s(literal 3 binary64) (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))))) < +inf.0

   1. Initial program 99.4%

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

      1. div-sub 99.4%

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

      2. cancel-sign-sub-inv 99.4%

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

      3. associate-*r* 99.4%

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

      4. fma-define 99.4%

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

      5. pow2 99.4%

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

      6. metadata-eval 99.4%

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

      7. fma-define 99.4%

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

      8. fma-define 99.4%

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

   4. Applied egg-rr 99.4%

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

      1. *-commutative 99.4%

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

   6. Simplified 99.4%

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

   if +inf.0 < (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 #s(literal 4 binary64) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) #s(literal 6 binary64)))) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 #s(literal 3 binary64) (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))))

   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. Add Preprocessing

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. metadata-eval 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.5%

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

Alternative 3: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ t_3 := x1 + \left(\left(x1 + \left(\left(t\_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t\_2 \cdot 4 - 6\right)\right) + t\_0 \cdot t\_2\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{x1 - \left(t\_0 - 2 \cdot x2\right)}{-1 - x1 \cdot x1}\right)\\ \mathbf{if}\;t\_3 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;x1 + 6 \cdot {x1}^{4}\\ \end{array} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	t_3 = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * ((x1 - (t_0 - (2.0 * x2))) / (-1.0 - (x1 * x1)))));
	tmp = 0.0;
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = x1 + (6.0 * (x1 ^ 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 #s(literal 4 binary64) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) #s(literal 6 binary64)))) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 #s(literal 3 binary64) (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))))) < +inf.0

   1. Initial program 99.4%

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

   if +inf.0 < (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 #s(literal 4 binary64) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) #s(literal 6 binary64)))) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 #s(literal 3 binary64) (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))))

   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. Add Preprocessing

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. metadata-eval 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.5%

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

Alternative 4: 96.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ \mathbf{if}\;x1 \leq -9 \cdot 10^{+55}:\\ \;\;\;\;x1 + {x1}^{4} \cdot \left(6 + \frac{\frac{9 + 4 \cdot \left(2 \cdot x2 - 3\right)}{x1} - 3}{x1}\right)\\ \mathbf{elif}\;x1 \leq 3.6 \cdot 10^{+48}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(t\_0 - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_0 \cdot t\_2 + t\_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - {x1}^{3} \cdot \left(3 - x1 \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (if (<= x1 -9e+55)
     (+
      x1
      (*
       (pow x1 4.0)
       (+ 6.0 (/ (- (/ (+ 9.0 (* 4.0 (- (* 2.0 x2) 3.0))) x1) 3.0) x1))))
     (if (<= x1 3.6e+48)
       (+
        x1
        (+
         (* 3.0 (/ (- x1 (- t_0 (* 2.0 x2))) (- -1.0 (* x1 x1))))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* t_0 t_2)
            (*
             t_1
             (+ (* (* (* x1 2.0) t_2) (- t_2 3.0)) (* (* x1 x1) 6.0))))))))
       (- x1 (* (pow x1 3.0) (- 3.0 (* x1 6.0))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if (x1 <= -9e+55) {
		tmp = x1 + (pow(x1, 4.0) * (6.0 + ((((9.0 + (4.0 * ((2.0 * x2) - 3.0))) / x1) - 3.0) / x1)));
	} else if (x1 <= 3.6e+48) {
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	} else {
		tmp = x1 - (pow(x1, 3.0) * (3.0 - (x1 * 6.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    if (x1 <= (-9d+55)) then
        tmp = x1 + ((x1 ** 4.0d0) * (6.0d0 + ((((9.0d0 + (4.0d0 * ((2.0d0 * x2) - 3.0d0))) / x1) - 3.0d0) / x1)))
    else if (x1 <= 3.6d+48) then
        tmp = x1 + ((3.0d0 * ((x1 - (t_0 - (2.0d0 * x2))) / ((-1.0d0) - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * 6.0d0)))))))
    else
        tmp = x1 - ((x1 ** 3.0d0) * (3.0d0 - (x1 * 6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if (x1 <= -9e+55) {
		tmp = x1 + (Math.pow(x1, 4.0) * (6.0 + ((((9.0 + (4.0 * ((2.0 * x2) - 3.0))) / x1) - 3.0) / x1)));
	} else if (x1 <= 3.6e+48) {
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	} else {
		tmp = x1 - (Math.pow(x1, 3.0) * (3.0 - (x1 * 6.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1
	tmp = 0
	if x1 <= -9e+55:
		tmp = x1 + (math.pow(x1, 4.0) * (6.0 + ((((9.0 + (4.0 * ((2.0 * x2) - 3.0))) / x1) - 3.0) / x1)))
	elif x1 <= 3.6e+48:
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))))
	else:
		tmp = x1 - (math.pow(x1, 3.0) * (3.0 - (x1 * 6.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if (x1 <= -9e+55)
		tmp = Float64(x1 + Float64((x1 ^ 4.0) * Float64(6.0 + Float64(Float64(Float64(Float64(9.0 + Float64(4.0 * Float64(Float64(2.0 * x2) - 3.0))) / x1) - 3.0) / x1))));
	elseif (x1 <= 3.6e+48)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 - Float64(t_0 - Float64(2.0 * x2))) / Float64(-1.0 - Float64(x1 * x1)))) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * t_2) + Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * 6.0))))))));
	else
		tmp = Float64(x1 - Float64((x1 ^ 3.0) * Float64(3.0 - Float64(x1 * 6.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	tmp = 0.0;
	if (x1 <= -9e+55)
		tmp = x1 + ((x1 ^ 4.0) * (6.0 + ((((9.0 + (4.0 * ((2.0 * x2) - 3.0))) / x1) - 3.0) / x1)));
	elseif (x1 <= 3.6e+48)
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	else
		tmp = x1 - ((x1 ^ 3.0) * (3.0 - (x1 * 6.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[x1, -9e+55], N[(x1 + N[(N[Power[x1, 4.0], $MachinePrecision] * N[(6.0 + N[(N[(N[(N[(9.0 + N[(4.0 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision] - 3.0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.6e+48], N[(x1 + N[(N[(3.0 * N[(N[(x1 - N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * t$95$2), $MachinePrecision] + N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 - N[(N[Power[x1, 3.0], $MachinePrecision] * N[(3.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -8.99999999999999996e55

   1. Initial program 22.4%

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

   3. Taylor expanded in x1 around -inf 44.9%

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

   4. Taylor expanded in x1 around -inf 99.9%

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

   if -8.99999999999999996e55 < x1 < 3.59999999999999983e48

   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. Add Preprocessing

   3. Taylor expanded in x1 around inf 97.4%

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

   if 3.59999999999999983e48 < x1

   1. Initial program 33.3%

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

   3. Taylor expanded in x1 around inf 33.3%

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

   4. Taylor expanded in x1 around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. metadata-eval 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x1 around 0 100.0%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9 \cdot 10^{+55}:\\ \;\;\;\;x1 + {x1}^{4} \cdot \left(6 + \frac{\frac{9 + 4 \cdot \left(2 \cdot x2 - 3\right)}{x1} - 3}{x1}\right)\\ \mathbf{elif}\;x1 \leq 3.6 \cdot 10^{+48}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - {x1}^{3} \cdot \left(3 - x1 \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ \mathbf{if}\;x1 \leq -1.2 \cdot 10^{+50} \lor \neg \left(x1 \leq 3.6 \cdot 10^{+48}\right):\\ \;\;\;\;x1 - {x1}^{3} \cdot \left(3 - x1 \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(3 \cdot \left(x1 - x2 \cdot -2\right) - \left(x1 - \left(\left(t\_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - t\_2 \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(3 - 2 \cdot x2\right)\right) - 3 \cdot t\_0\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (if (or (<= x1 -1.2e+50) (not (<= x1 3.6e+48)))
     (- x1 (* (pow x1 3.0) (- 3.0 (* x1 6.0))))
     (-
      x1
      (-
       (* 3.0 (- x1 (* x2 -2.0)))
       (-
        x1
        (-
         (-
          (*
           t_1
           (+
            (* (* x1 x1) (- 6.0 (* t_2 4.0)))
            (* (* (* x1 2.0) t_2) (- 3.0 (* 2.0 x2)))))
          (* 3.0 t_0))
         (* x1 (* x1 x1)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -1.2e+50) || !(x1 <= 3.6e+48)) {
		tmp = x1 - (pow(x1, 3.0) * (3.0 - (x1 * 6.0)));
	} else {
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) - (x1 - (((t_1 * (((x1 * x1) * (6.0 - (t_2 * 4.0))) + (((x1 * 2.0) * t_2) * (3.0 - (2.0 * x2))))) - (3.0 * t_0)) - (x1 * (x1 * x1)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    if ((x1 <= (-1.2d+50)) .or. (.not. (x1 <= 3.6d+48))) then
        tmp = x1 - ((x1 ** 3.0d0) * (3.0d0 - (x1 * 6.0d0)))
    else
        tmp = x1 - ((3.0d0 * (x1 - (x2 * (-2.0d0)))) - (x1 - (((t_1 * (((x1 * x1) * (6.0d0 - (t_2 * 4.0d0))) + (((x1 * 2.0d0) * t_2) * (3.0d0 - (2.0d0 * x2))))) - (3.0d0 * t_0)) - (x1 * (x1 * x1)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -1.2e+50) || !(x1 <= 3.6e+48)) {
		tmp = x1 - (Math.pow(x1, 3.0) * (3.0 - (x1 * 6.0)));
	} else {
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) - (x1 - (((t_1 * (((x1 * x1) * (6.0 - (t_2 * 4.0))) + (((x1 * 2.0) * t_2) * (3.0 - (2.0 * x2))))) - (3.0 * t_0)) - (x1 * (x1 * x1)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1
	tmp = 0
	if (x1 <= -1.2e+50) or not (x1 <= 3.6e+48):
		tmp = x1 - (math.pow(x1, 3.0) * (3.0 - (x1 * 6.0)))
	else:
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) - (x1 - (((t_1 * (((x1 * x1) * (6.0 - (t_2 * 4.0))) + (((x1 * 2.0) * t_2) * (3.0 - (2.0 * x2))))) - (3.0 * t_0)) - (x1 * (x1 * x1)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if ((x1 <= -1.2e+50) || !(x1 <= 3.6e+48))
		tmp = Float64(x1 - Float64((x1 ^ 3.0) * Float64(3.0 - Float64(x1 * 6.0))));
	else
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(x1 - Float64(x2 * -2.0))) - Float64(x1 - Float64(Float64(Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(t_2 * 4.0))) + Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(3.0 - Float64(2.0 * x2))))) - Float64(3.0 * t_0)) - Float64(x1 * Float64(x1 * x1))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	tmp = 0.0;
	if ((x1 <= -1.2e+50) || ~((x1 <= 3.6e+48)))
		tmp = x1 - ((x1 ^ 3.0) * (3.0 - (x1 * 6.0)));
	else
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) - (x1 - (((t_1 * (((x1 * x1) * (6.0 - (t_2 * 4.0))) + (((x1 * 2.0) * t_2) * (3.0 - (2.0 * x2))))) - (3.0 * t_0)) - (x1 * (x1 * x1)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[x1, -1.2e+50], N[Not[LessEqual[x1, 3.6e+48]], $MachinePrecision]], N[(x1 - N[(N[Power[x1, 3.0], $MachinePrecision] * N[(3.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 - N[(N[(3.0 * N[(x1 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 - N[(N[(N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(t$95$2 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.2000000000000001e50 or 3.59999999999999983e48 < x1

   1. Initial program 29.3%

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

   3. Taylor expanded in x1 around inf 29.3%

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

   4. Taylor expanded in x1 around inf 97.8%

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

      1. associate-*r/ 97.8%

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

      2. metadata-eval 97.8%

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

   6. Simplified 97.8%

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

   7. Taylor expanded in x1 around 0 97.8%

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

   if -1.2000000000000001e50 < x1 < 3.59999999999999983e48

   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. Add Preprocessing

   3. Taylor expanded in x1 around 0 96.4%

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

   4. Taylor expanded in x1 around inf 96.0%

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

   5. Taylor expanded in x1 around 0 96.4%

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

      1. mul-1-neg 96.4%

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

      2. unsub-neg 96.4%

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

      3. *-commutative 96.4%

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

   7. Simplified 96.4%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.2 \cdot 10^{+50} \lor \neg \left(x1 \leq 3.6 \cdot 10^{+48}\right):\\ \;\;\;\;x1 - {x1}^{3} \cdot \left(3 - x1 \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(3 \cdot \left(x1 - x2 \cdot -2\right) - \left(x1 - \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 - 2 \cdot x2\right)\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ \mathbf{if}\;x1 \leq -1.36 \cdot 10^{+57} \lor \neg \left(x1 \leq 3.6 \cdot 10^{+48}\right):\\ \;\;\;\;x1 - {x1}^{3} \cdot \left(3 - x1 \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(t\_0 - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_0 \cdot t\_2 + t\_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (if (or (<= x1 -1.36e+57) (not (<= x1 3.6e+48)))
     (- x1 (* (pow x1 3.0) (- 3.0 (* x1 6.0))))
     (+
      x1
      (+
       (* 3.0 (/ (- x1 (- t_0 (* 2.0 x2))) (- -1.0 (* x1 x1))))
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (* t_0 t_2)
          (*
           t_1
           (+ (* (* (* x1 2.0) t_2) (- t_2 3.0)) (* (* x1 x1) 6.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -1.36e+57) || !(x1 <= 3.6e+48)) {
		tmp = x1 - (pow(x1, 3.0) * (3.0 - (x1 * 6.0)));
	} else {
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    if ((x1 <= (-1.36d+57)) .or. (.not. (x1 <= 3.6d+48))) then
        tmp = x1 - ((x1 ** 3.0d0) * (3.0d0 - (x1 * 6.0d0)))
    else
        tmp = x1 + ((3.0d0 * ((x1 - (t_0 - (2.0d0 * x2))) / ((-1.0d0) - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * 6.0d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -1.36e+57) || !(x1 <= 3.6e+48)) {
		tmp = x1 - (Math.pow(x1, 3.0) * (3.0 - (x1 * 6.0)));
	} else {
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1
	tmp = 0
	if (x1 <= -1.36e+57) or not (x1 <= 3.6e+48):
		tmp = x1 - (math.pow(x1, 3.0) * (3.0 - (x1 * 6.0)))
	else:
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if ((x1 <= -1.36e+57) || !(x1 <= 3.6e+48))
		tmp = Float64(x1 - Float64((x1 ^ 3.0) * Float64(3.0 - Float64(x1 * 6.0))));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 - Float64(t_0 - Float64(2.0 * x2))) / Float64(-1.0 - Float64(x1 * x1)))) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * t_2) + Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * 6.0))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	tmp = 0.0;
	if ((x1 <= -1.36e+57) || ~((x1 <= 3.6e+48)))
		tmp = x1 - ((x1 ^ 3.0) * (3.0 - (x1 * 6.0)));
	else
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[x1, -1.36e+57], N[Not[LessEqual[x1, 3.6e+48]], $MachinePrecision]], N[(x1 - N[(N[Power[x1, 3.0], $MachinePrecision] * N[(3.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(x1 - N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * t$95$2), $MachinePrecision] + N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.36e57 or 3.59999999999999983e48 < x1

   1. Initial program 28.5%

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

   3. Taylor expanded in x1 around inf 28.5%

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

   4. Taylor expanded in x1 around inf 97.8%

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

      1. associate-*r/ 97.8%

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

      2. metadata-eval 97.8%

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

   6. Simplified 97.8%

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

   7. Taylor expanded in x1 around 0 97.8%

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

   if -1.36e57 < x1 < 3.59999999999999983e48

   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. Add Preprocessing

   3. Taylor expanded in x1 around inf 97.4%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.36 \cdot 10^{+57} \lor \neg \left(x1 \leq 3.6 \cdot 10^{+48}\right):\\ \;\;\;\;x1 - {x1}^{3} \cdot \left(3 - x1 \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 94.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ \mathbf{if}\;x1 \leq -7.8 \cdot 10^{+49} \lor \neg \left(x1 \leq 3.3 \cdot 10^{+48}\right):\\ \;\;\;\;x1 + 6 \cdot {x1}^{4}\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(3 \cdot \left(x1 - x2 \cdot -2\right) - \left(x1 - \left(\left(t\_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - t\_2 \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(3 - 2 \cdot x2\right)\right) - 3 \cdot t\_0\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (if (or (<= x1 -7.8e+49) (not (<= x1 3.3e+48)))
     (+ x1 (* 6.0 (pow x1 4.0)))
     (-
      x1
      (-
       (* 3.0 (- x1 (* x2 -2.0)))
       (-
        x1
        (-
         (-
          (*
           t_1
           (+
            (* (* x1 x1) (- 6.0 (* t_2 4.0)))
            (* (* (* x1 2.0) t_2) (- 3.0 (* 2.0 x2)))))
          (* 3.0 t_0))
         (* x1 (* x1 x1)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -7.8e+49) || !(x1 <= 3.3e+48)) {
		tmp = x1 + (6.0 * pow(x1, 4.0));
	} else {
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) - (x1 - (((t_1 * (((x1 * x1) * (6.0 - (t_2 * 4.0))) + (((x1 * 2.0) * t_2) * (3.0 - (2.0 * x2))))) - (3.0 * t_0)) - (x1 * (x1 * x1)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    if ((x1 <= (-7.8d+49)) .or. (.not. (x1 <= 3.3d+48))) then
        tmp = x1 + (6.0d0 * (x1 ** 4.0d0))
    else
        tmp = x1 - ((3.0d0 * (x1 - (x2 * (-2.0d0)))) - (x1 - (((t_1 * (((x1 * x1) * (6.0d0 - (t_2 * 4.0d0))) + (((x1 * 2.0d0) * t_2) * (3.0d0 - (2.0d0 * x2))))) - (3.0d0 * t_0)) - (x1 * (x1 * x1)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -7.8e+49) || !(x1 <= 3.3e+48)) {
		tmp = x1 + (6.0 * Math.pow(x1, 4.0));
	} else {
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) - (x1 - (((t_1 * (((x1 * x1) * (6.0 - (t_2 * 4.0))) + (((x1 * 2.0) * t_2) * (3.0 - (2.0 * x2))))) - (3.0 * t_0)) - (x1 * (x1 * x1)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1
	tmp = 0
	if (x1 <= -7.8e+49) or not (x1 <= 3.3e+48):
		tmp = x1 + (6.0 * math.pow(x1, 4.0))
	else:
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) - (x1 - (((t_1 * (((x1 * x1) * (6.0 - (t_2 * 4.0))) + (((x1 * 2.0) * t_2) * (3.0 - (2.0 * x2))))) - (3.0 * t_0)) - (x1 * (x1 * x1)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if ((x1 <= -7.8e+49) || !(x1 <= 3.3e+48))
		tmp = Float64(x1 + Float64(6.0 * (x1 ^ 4.0)));
	else
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(x1 - Float64(x2 * -2.0))) - Float64(x1 - Float64(Float64(Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(t_2 * 4.0))) + Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(3.0 - Float64(2.0 * x2))))) - Float64(3.0 * t_0)) - Float64(x1 * Float64(x1 * x1))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	tmp = 0.0;
	if ((x1 <= -7.8e+49) || ~((x1 <= 3.3e+48)))
		tmp = x1 + (6.0 * (x1 ^ 4.0));
	else
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) - (x1 - (((t_1 * (((x1 * x1) * (6.0 - (t_2 * 4.0))) + (((x1 * 2.0) * t_2) * (3.0 - (2.0 * x2))))) - (3.0 * t_0)) - (x1 * (x1 * x1)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[x1, -7.8e+49], N[Not[LessEqual[x1, 3.3e+48]], $MachinePrecision]], N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 - N[(N[(3.0 * N[(x1 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 - N[(N[(N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(t$95$2 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -7.8000000000000002e49 or 3.30000000000000023e48 < x1

   1. Initial program 29.3%

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

   3. Taylor expanded in x1 around inf 29.3%

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

   4. Taylor expanded in x1 around inf 97.8%

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

      1. associate-*r/ 97.8%

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

      2. metadata-eval 97.8%

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

   6. Simplified 97.8%

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

   7. Taylor expanded in x1 around inf 97.8%

      \[\leadsto x1 + {x1}^{4} \cdot \color{blue}{6} \]

   if -7.8000000000000002e49 < x1 < 3.30000000000000023e48

   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. Add Preprocessing

   3. Taylor expanded in x1 around 0 96.4%

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

   4. Taylor expanded in x1 around inf 96.0%

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

   5. Taylor expanded in x1 around 0 96.4%

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

      1. mul-1-neg 96.4%

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

      2. unsub-neg 96.4%

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

      3. *-commutative 96.4%

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

   7. Simplified 96.4%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.8 \cdot 10^{+49} \lor \neg \left(x1 \leq 3.3 \cdot 10^{+48}\right):\\ \;\;\;\;x1 + 6 \cdot {x1}^{4}\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(3 \cdot \left(x1 - x2 \cdot -2\right) - \left(x1 - \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 - 2 \cdot x2\right)\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 2 \cdot x2 - 3\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_2}\\ \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 6\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -2.8 \cdot 10^{+112}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(t\_0 - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 - \left(x1 \cdot \left(x1 \cdot \left(6 + \left(\left(\left(-2 \cdot t\_1 - \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - x2 \cdot -4\right) - x1 \cdot -6\right)\right) - 2\right) - x2 \cdot -4\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.2 \cdot 10^{+87}:\\ \;\;\;\;x1 - \left(3 \cdot \left(x1 - x2 \cdot -2\right) - \left(x1 - \left(\left(t\_2 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - t\_3 \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot t\_3\right) \cdot \left(3 - 2 \cdot x2\right)\right) - 3 \cdot t\_0\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot t\_1\right) + x2 \cdot \left(x1 \cdot 6 + \frac{x1 \cdot \left(x1 \cdot 3 + 9\right)}{x2}\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (- (* 2.0 x2) 3.0))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (/ (- (+ t_0 (* 2.0 x2)) x1) t_2)))
   (if (<= x1 -1.35e+154)
     (+
      x1
      (+
       (* x2 -6.0)
       (* x1 (- (+ (* x2 -12.0) (* x1 (+ 9.0 (* x2 6.0)))) 2.0))))
     (if (<= x1 -2.8e+112)
       (+
        x1
        (+
         (* 3.0 (/ (- x1 (- t_0 (* 2.0 x2))) (- -1.0 (* x1 x1))))
         (-
          x1
          (-
           (*
            x1
            (-
             (*
              x1
              (+
               6.0
               (-
                (- (- (* -2.0 t_1) (+ (* x2 6.0) (* x2 8.0))) (* x2 -4.0))
                (* x1 -6.0))))
             2.0))
           (* x2 -4.0)))))
       (if (<= x1 3.2e+87)
         (-
          x1
          (-
           (* 3.0 (- x1 (* x2 -2.0)))
           (-
            x1
            (-
             (-
              (*
               t_2
               (+
                (* (* x1 x1) (- 6.0 (* t_3 4.0)))
                (* (* (* x1 2.0) t_3) (- 3.0 (* 2.0 x2)))))
              (* 3.0 t_0))
             (* x1 (* x1 x1))))))
         (+
          x1
          (+
           (* x2 -6.0)
           (*
            x1
            (-
             (+
              (* 4.0 (* x2 t_1))
              (* x2 (+ (* x1 6.0) (/ (* x1 (+ (* x1 3.0) 9.0)) x2))))
             2.0)))))))))

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) + 1.0;
	double t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	double tmp;
	if (x1 <= -1.35e+154) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	} else if (x1 <= -2.8e+112) {
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 - ((x1 * ((x1 * (6.0 + ((((-2.0 * t_1) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))) - 2.0)) - (x2 * -4.0))));
	} else if (x1 <= 3.2e+87) {
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) - (x1 - (((t_2 * (((x1 * x1) * (6.0 - (t_3 * 4.0))) + (((x1 * 2.0) * t_3) * (3.0 - (2.0 * x2))))) - (3.0 * t_0)) - (x1 * (x1 * x1)))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_1)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (2.0d0 * x2) - 3.0d0
    t_2 = (x1 * x1) + 1.0d0
    t_3 = ((t_0 + (2.0d0 * x2)) - x1) / t_2
    if (x1 <= (-1.35d+154)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((x2 * (-12.0d0)) + (x1 * (9.0d0 + (x2 * 6.0d0)))) - 2.0d0)))
    else if (x1 <= (-2.8d+112)) then
        tmp = x1 + ((3.0d0 * ((x1 - (t_0 - (2.0d0 * x2))) / ((-1.0d0) - (x1 * x1)))) + (x1 - ((x1 * ((x1 * (6.0d0 + (((((-2.0d0) * t_1) - ((x2 * 6.0d0) + (x2 * 8.0d0))) - (x2 * (-4.0d0))) - (x1 * (-6.0d0))))) - 2.0d0)) - (x2 * (-4.0d0)))))
    else if (x1 <= 3.2d+87) then
        tmp = x1 - ((3.0d0 * (x1 - (x2 * (-2.0d0)))) - (x1 - (((t_2 * (((x1 * x1) * (6.0d0 - (t_3 * 4.0d0))) + (((x1 * 2.0d0) * t_3) * (3.0d0 - (2.0d0 * x2))))) - (3.0d0 * t_0)) - (x1 * (x1 * x1)))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((4.0d0 * (x2 * t_1)) + (x2 * ((x1 * 6.0d0) + ((x1 * ((x1 * 3.0d0) + 9.0d0)) / x2)))) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (2.0 * x2) - 3.0;
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	double tmp;
	if (x1 <= -1.35e+154) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	} else if (x1 <= -2.8e+112) {
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 - ((x1 * ((x1 * (6.0 + ((((-2.0 * t_1) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))) - 2.0)) - (x2 * -4.0))));
	} else if (x1 <= 3.2e+87) {
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) - (x1 - (((t_2 * (((x1 * x1) * (6.0 - (t_3 * 4.0))) + (((x1 * 2.0) * t_3) * (3.0 - (2.0 * x2))))) - (3.0 * t_0)) - (x1 * (x1 * x1)))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_1)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (2.0 * x2) - 3.0
	t_2 = (x1 * x1) + 1.0
	t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2
	tmp = 0
	if x1 <= -1.35e+154:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)))
	elif x1 <= -2.8e+112:
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 - ((x1 * ((x1 * (6.0 + ((((-2.0 * t_1) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))) - 2.0)) - (x2 * -4.0))))
	elif x1 <= 3.2e+87:
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) - (x1 - (((t_2 * (((x1 * x1) * (6.0 - (t_3 * 4.0))) + (((x1 * 2.0) * t_3) * (3.0 - (2.0 * x2))))) - (3.0 * t_0)) - (x1 * (x1 * x1)))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_1)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)))
	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(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_2)
	tmp = 0.0
	if (x1 <= -1.35e+154)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(x2 * -12.0) + Float64(x1 * Float64(9.0 + Float64(x2 * 6.0)))) - 2.0))));
	elseif (x1 <= -2.8e+112)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 - Float64(t_0 - Float64(2.0 * x2))) / Float64(-1.0 - Float64(x1 * x1)))) + Float64(x1 - Float64(Float64(x1 * Float64(Float64(x1 * Float64(6.0 + Float64(Float64(Float64(Float64(-2.0 * t_1) - Float64(Float64(x2 * 6.0) + Float64(x2 * 8.0))) - Float64(x2 * -4.0)) - Float64(x1 * -6.0)))) - 2.0)) - Float64(x2 * -4.0)))));
	elseif (x1 <= 3.2e+87)
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(x1 - Float64(x2 * -2.0))) - Float64(x1 - Float64(Float64(Float64(t_2 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(t_3 * 4.0))) + Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(3.0 - Float64(2.0 * x2))))) - Float64(3.0 * t_0)) - Float64(x1 * Float64(x1 * x1))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(4.0 * Float64(x2 * t_1)) + Float64(x2 * Float64(Float64(x1 * 6.0) + Float64(Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0)) / x2)))) - 2.0))));
	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) + 1.0;
	t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	tmp = 0.0;
	if (x1 <= -1.35e+154)
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	elseif (x1 <= -2.8e+112)
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 - ((x1 * ((x1 * (6.0 + ((((-2.0 * t_1) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))) - 2.0)) - (x2 * -4.0))));
	elseif (x1 <= 3.2e+87)
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) - (x1 - (((t_2 * (((x1 * x1) * (6.0 - (t_3 * 4.0))) + (((x1 * 2.0) * t_3) * (3.0 - (2.0 * x2))))) - (3.0 * t_0)) - (x1 * (x1 * x1)))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_1)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[x1, -1.35e+154], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(x2 * -12.0), $MachinePrecision] + N[(x1 * N[(9.0 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.8e+112], N[(x1 + N[(N[(3.0 * N[(N[(x1 - N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 - N[(N[(x1 * N[(N[(x1 * N[(6.0 + N[(N[(N[(N[(-2.0 * t$95$1), $MachinePrecision] - N[(N[(x2 * 6.0), $MachinePrecision] + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision] - N[(x1 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] - N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.2e+87], N[(x1 - N[(N[(3.0 * N[(x1 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 - N[(N[(N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(t$95$3 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(4.0 * N[(x2 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * 6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.35000000000000003e154

   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. Add Preprocessing

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x2 around 0 0.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x2 \cdot \left(6 \cdot x1 - 12\right)\right) + x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right)\right)}\right) \]

   6. Taylor expanded in x1 around 0 68.2%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{x1 \cdot \left(\left(-12 \cdot x2 + x1 \cdot \left(9 + 6 \cdot x2\right)\right) - 2\right)}\right) \]

   if -1.35000000000000003e154 < x1 < -2.8000000000000001e112

   1. Initial program 10.0%

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

   3. Taylor expanded in x1 around inf 10.0%

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

   4. Taylor expanded in x1 around 0 100.0%

      \[\leadsto x1 + \left(\left(\color{blue}{\left(-4 \cdot x2 + x1 \cdot \left(2 + x1 \cdot \left(\left(-6 \cdot x1 + \left(-4 \cdot x2 + \left(-2 \cdot \left(3 - 2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right)\right) - 6\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if -2.8000000000000001e112 < x1 < 3.2e87

   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. Add Preprocessing

   3. Taylor expanded in x1 around 0 95.5%

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

   4. Taylor expanded in x1 around inf 95.1%

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

   5. Taylor expanded in x1 around 0 95.5%

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

      1. mul-1-neg 95.5%

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

      2. unsub-neg 95.5%

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

      3. *-commutative 95.5%

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

   7. Simplified 95.5%

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

   if 3.2e87 < x1

   1. Initial program 27.7%

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

   3. Taylor expanded in x1 around 0 11.4%

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

   4. Taylor expanded in x1 around 0 89.4%

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

   5. Taylor expanded in x2 around inf 100.0%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 6\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -2.8 \cdot 10^{+112}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 - \left(x1 \cdot \left(x1 \cdot \left(6 + \left(\left(\left(-2 \cdot \left(2 \cdot x2 - 3\right) - \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - x2 \cdot -4\right) - x1 \cdot -6\right)\right) - 2\right) - x2 \cdot -4\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.2 \cdot 10^{+87}:\\ \;\;\;\;x1 - \left(3 \cdot \left(x1 - x2 \cdot -2\right) - \left(x1 - \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 - 2 \cdot x2\right)\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x2 \cdot \left(x1 \cdot 6 + \frac{x1 \cdot \left(x1 \cdot 3 + 9\right)}{x2}\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 2 \cdot x2 - 3\\ t_2 := x1 \cdot x1 + 1\\ t_3 := 3 \cdot \frac{x1 - \left(t\_0 - 2 \cdot x2\right)}{-1 - x1 \cdot x1}\\ \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 6\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -2.8 \cdot 10^{+112}:\\ \;\;\;\;x1 + \left(t\_3 + \left(x1 - \left(x1 \cdot \left(x1 \cdot \left(6 + \left(\left(\left(-2 \cdot t\_1 - \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - x2 \cdot -4\right) - x1 \cdot -6\right)\right) - 2\right) - x2 \cdot -4\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.2 \cdot 10^{+87}:\\ \;\;\;\;x1 + \left(t\_3 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_0 - t\_2 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_2}\right) \cdot \left(3 - 2 \cdot x2\right) - \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot t\_1\right) + x2 \cdot \left(x1 \cdot 6 + \frac{x1 \cdot \left(x1 \cdot 3 + 9\right)}{x2}\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (- (* 2.0 x2) 3.0))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* 3.0 (/ (- x1 (- t_0 (* 2.0 x2))) (- -1.0 (* x1 x1))))))
   (if (<= x1 -1.35e+154)
     (+
      x1
      (+
       (* x2 -6.0)
       (* x1 (- (+ (* x2 -12.0) (* x1 (+ 9.0 (* x2 6.0)))) 2.0))))
     (if (<= x1 -2.8e+112)
       (+
        x1
        (+
         t_3
         (-
          x1
          (-
           (*
            x1
            (-
             (*
              x1
              (+
               6.0
               (-
                (- (- (* -2.0 t_1) (+ (* x2 6.0) (* x2 8.0))) (* x2 -4.0))
                (* x1 -6.0))))
             2.0))
           (* x2 -4.0)))))
       (if (<= x1 3.2e+87)
         (+
          x1
          (+
           t_3
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (-
              (* 3.0 t_0)
              (*
               t_2
               (-
                (*
                 (* (* x1 2.0) (/ (- (+ t_0 (* 2.0 x2)) x1) t_2))
                 (- 3.0 (* 2.0 x2)))
                (* (* x1 x1) 6.0))))))))
         (+
          x1
          (+
           (* x2 -6.0)
           (*
            x1
            (-
             (+
              (* 4.0 (* x2 t_1))
              (* x2 (+ (* x1 6.0) (/ (* x1 (+ (* x1 3.0) 9.0)) x2))))
             2.0)))))))))

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) + 1.0;
	double t_3 = 3.0 * ((x1 - (t_0 - (2.0 * x2))) / (-1.0 - (x1 * x1)));
	double tmp;
	if (x1 <= -1.35e+154) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	} else if (x1 <= -2.8e+112) {
		tmp = x1 + (t_3 + (x1 - ((x1 * ((x1 * (6.0 + ((((-2.0 * t_1) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))) - 2.0)) - (x2 * -4.0))));
	} else if (x1 <= 3.2e+87) {
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) - (t_2 * ((((x1 * 2.0) * (((t_0 + (2.0 * x2)) - x1) / t_2)) * (3.0 - (2.0 * x2))) - ((x1 * x1) * 6.0)))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_1)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (2.0d0 * x2) - 3.0d0
    t_2 = (x1 * x1) + 1.0d0
    t_3 = 3.0d0 * ((x1 - (t_0 - (2.0d0 * x2))) / ((-1.0d0) - (x1 * x1)))
    if (x1 <= (-1.35d+154)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((x2 * (-12.0d0)) + (x1 * (9.0d0 + (x2 * 6.0d0)))) - 2.0d0)))
    else if (x1 <= (-2.8d+112)) then
        tmp = x1 + (t_3 + (x1 - ((x1 * ((x1 * (6.0d0 + (((((-2.0d0) * t_1) - ((x2 * 6.0d0) + (x2 * 8.0d0))) - (x2 * (-4.0d0))) - (x1 * (-6.0d0))))) - 2.0d0)) - (x2 * (-4.0d0)))))
    else if (x1 <= 3.2d+87) then
        tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_0) - (t_2 * ((((x1 * 2.0d0) * (((t_0 + (2.0d0 * x2)) - x1) / t_2)) * (3.0d0 - (2.0d0 * x2))) - ((x1 * x1) * 6.0d0)))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((4.0d0 * (x2 * t_1)) + (x2 * ((x1 * 6.0d0) + ((x1 * ((x1 * 3.0d0) + 9.0d0)) / x2)))) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (2.0 * x2) - 3.0;
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * ((x1 - (t_0 - (2.0 * x2))) / (-1.0 - (x1 * x1)));
	double tmp;
	if (x1 <= -1.35e+154) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	} else if (x1 <= -2.8e+112) {
		tmp = x1 + (t_3 + (x1 - ((x1 * ((x1 * (6.0 + ((((-2.0 * t_1) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))) - 2.0)) - (x2 * -4.0))));
	} else if (x1 <= 3.2e+87) {
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) - (t_2 * ((((x1 * 2.0) * (((t_0 + (2.0 * x2)) - x1) / t_2)) * (3.0 - (2.0 * x2))) - ((x1 * x1) * 6.0)))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_1)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (2.0 * x2) - 3.0
	t_2 = (x1 * x1) + 1.0
	t_3 = 3.0 * ((x1 - (t_0 - (2.0 * x2))) / (-1.0 - (x1 * x1)))
	tmp = 0
	if x1 <= -1.35e+154:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)))
	elif x1 <= -2.8e+112:
		tmp = x1 + (t_3 + (x1 - ((x1 * ((x1 * (6.0 + ((((-2.0 * t_1) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))) - 2.0)) - (x2 * -4.0))))
	elif x1 <= 3.2e+87:
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) - (t_2 * ((((x1 * 2.0) * (((t_0 + (2.0 * x2)) - x1) / t_2)) * (3.0 - (2.0 * x2))) - ((x1 * x1) * 6.0)))))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_1)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)))
	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(Float64(x1 * x1) + 1.0)
	t_3 = Float64(3.0 * Float64(Float64(x1 - Float64(t_0 - Float64(2.0 * x2))) / Float64(-1.0 - Float64(x1 * x1))))
	tmp = 0.0
	if (x1 <= -1.35e+154)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(x2 * -12.0) + Float64(x1 * Float64(9.0 + Float64(x2 * 6.0)))) - 2.0))));
	elseif (x1 <= -2.8e+112)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 - Float64(Float64(x1 * Float64(Float64(x1 * Float64(6.0 + Float64(Float64(Float64(Float64(-2.0 * t_1) - Float64(Float64(x2 * 6.0) + Float64(x2 * 8.0))) - Float64(x2 * -4.0)) - Float64(x1 * -6.0)))) - 2.0)) - Float64(x2 * -4.0)))));
	elseif (x1 <= 3.2e+87)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_0) - Float64(t_2 * Float64(Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_2)) * Float64(3.0 - Float64(2.0 * x2))) - Float64(Float64(x1 * x1) * 6.0))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(4.0 * Float64(x2 * t_1)) + Float64(x2 * Float64(Float64(x1 * 6.0) + Float64(Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0)) / x2)))) - 2.0))));
	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) + 1.0;
	t_3 = 3.0 * ((x1 - (t_0 - (2.0 * x2))) / (-1.0 - (x1 * x1)));
	tmp = 0.0;
	if (x1 <= -1.35e+154)
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	elseif (x1 <= -2.8e+112)
		tmp = x1 + (t_3 + (x1 - ((x1 * ((x1 * (6.0 + ((((-2.0 * t_1) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))) - 2.0)) - (x2 * -4.0))));
	elseif (x1 <= 3.2e+87)
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) - (t_2 * ((((x1 * 2.0) * (((t_0 + (2.0 * x2)) - x1) / t_2)) * (3.0 - (2.0 * x2))) - ((x1 * x1) * 6.0)))))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_1)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(x1 - N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.35e+154], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(x2 * -12.0), $MachinePrecision] + N[(x1 * N[(9.0 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.8e+112], N[(x1 + N[(t$95$3 + N[(x1 - N[(N[(x1 * N[(N[(x1 * N[(6.0 + N[(N[(N[(N[(-2.0 * t$95$1), $MachinePrecision] - N[(N[(x2 * 6.0), $MachinePrecision] + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision] - N[(x1 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] - N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.2e+87], N[(x1 + N[(t$95$3 + 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[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(4.0 * N[(x2 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * 6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.35000000000000003e154

   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. Add Preprocessing

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x2 around 0 0.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x2 \cdot \left(6 \cdot x1 - 12\right)\right) + x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right)\right)}\right) \]

   6. Taylor expanded in x1 around 0 68.2%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{x1 \cdot \left(\left(-12 \cdot x2 + x1 \cdot \left(9 + 6 \cdot x2\right)\right) - 2\right)}\right) \]

   if -1.35000000000000003e154 < x1 < -2.8000000000000001e112

   1. Initial program 10.0%

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

   3. Taylor expanded in x1 around inf 10.0%

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

   4. Taylor expanded in x1 around 0 100.0%

      \[\leadsto x1 + \left(\left(\color{blue}{\left(-4 \cdot x2 + x1 \cdot \left(2 + x1 \cdot \left(\left(-6 \cdot x1 + \left(-4 \cdot x2 + \left(-2 \cdot \left(3 - 2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right)\right) - 6\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if -2.8000000000000001e112 < x1 < 3.2e87

   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. Add Preprocessing

   3. Taylor expanded in x1 around 0 95.5%

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

   4. Taylor expanded in x1 around inf 95.1%

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

   5. Taylor expanded in x1 around inf 95.2%

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

   if 3.2e87 < x1

   1. Initial program 27.7%

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

   3. Taylor expanded in x1 around 0 11.4%

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

   4. Taylor expanded in x1 around 0 89.4%

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

   5. Taylor expanded in x2 around inf 100.0%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 6\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -2.8 \cdot 10^{+112}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 - \left(x1 \cdot \left(x1 \cdot \left(6 + \left(\left(\left(-2 \cdot \left(2 \cdot x2 - 3\right) - \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - x2 \cdot -4\right) - x1 \cdot -6\right)\right) - 2\right) - x2 \cdot -4\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.2 \cdot 10^{+87}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 - 2 \cdot x2\right) - \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x2 \cdot \left(x1 \cdot 6 + \frac{x1 \cdot \left(x1 \cdot 3 + 9\right)}{x2}\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 87.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 2 \cdot x2 - 3\\ t_2 := -1 - x1 \cdot x1\\ t_3 := x1 \cdot \left(x1 \cdot 3 + 9\right)\\ t_4 := x1 - \left(t\_0 - 2 \cdot x2\right)\\ t_5 := x1 - \left(3 \cdot \frac{t\_4}{x1 \cdot x1 + 1} - \left(x1 - \left(\left(\left(\left(x1 \cdot x1\right) \cdot 6 + t\_1 \cdot \left(\left(x1 \cdot 2\right) \cdot 3\right)\right) \cdot t\_2 - 3 \cdot t\_0\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 6\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -3.1 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{t\_4}{t\_2} + \left(x1 - \left(x1 \cdot \left(x1 \cdot \left(6 + \left(\left(\left(-2 \cdot t\_1 - \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - x2 \cdot -4\right) - x1 \cdot -6\right)\right) - 2\right) - x2 \cdot -4\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2.7 \cdot 10^{+28}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x1 \leq 0.43:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - \left(x1 \cdot \left(2 - t\_3\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.2 \cdot 10^{+87}:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot t\_1\right) + x2 \cdot \left(x1 \cdot 6 + \frac{t\_3}{x2}\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (- (* 2.0 x2) 3.0))
        (t_2 (- -1.0 (* x1 x1)))
        (t_3 (* x1 (+ (* x1 3.0) 9.0)))
        (t_4 (- x1 (- t_0 (* 2.0 x2))))
        (t_5
         (-
          x1
          (-
           (* 3.0 (/ t_4 (+ (* x1 x1) 1.0)))
           (-
            x1
            (-
             (-
              (* (+ (* (* x1 x1) 6.0) (* t_1 (* (* x1 2.0) 3.0))) t_2)
              (* 3.0 t_0))
             (* x1 (* x1 x1))))))))
   (if (<= x1 -1.35e+154)
     (+
      x1
      (+
       (* x2 -6.0)
       (* x1 (- (+ (* x2 -12.0) (* x1 (+ 9.0 (* x2 6.0)))) 2.0))))
     (if (<= x1 -3.1e+102)
       (+
        x1
        (+
         (* 3.0 (/ t_4 t_2))
         (-
          x1
          (-
           (*
            x1
            (-
             (*
              x1
              (+
               6.0
               (-
                (- (- (* -2.0 t_1) (+ (* x2 6.0) (* x2 8.0))) (* x2 -4.0))
                (* x1 -6.0))))
             2.0))
           (* x2 -4.0)))))
       (if (<= x1 -2.7e+28)
         t_5
         (if (<= x1 0.43)
           (+
            x1
            (-
             (* x2 -6.0)
             (+
              (* x1 (- 2.0 t_3))
              (* x2 (- (* x1 (- 12.0 (* x1 6.0))) (* 8.0 (* x1 x2)))))))
           (if (<= x1 3.2e+87)
             t_5
             (+
              x1
              (+
               (* x2 -6.0)
               (*
                x1
                (-
                 (+ (* 4.0 (* x2 t_1)) (* x2 (+ (* x1 6.0) (/ t_3 x2))))
                 2.0)))))))))))

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 = -1.0 - (x1 * x1);
	double t_3 = x1 * ((x1 * 3.0) + 9.0);
	double t_4 = x1 - (t_0 - (2.0 * x2));
	double t_5 = x1 - ((3.0 * (t_4 / ((x1 * x1) + 1.0))) - (x1 - ((((((x1 * x1) * 6.0) + (t_1 * ((x1 * 2.0) * 3.0))) * t_2) - (3.0 * t_0)) - (x1 * (x1 * x1)))));
	double tmp;
	if (x1 <= -1.35e+154) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	} else if (x1 <= -3.1e+102) {
		tmp = x1 + ((3.0 * (t_4 / t_2)) + (x1 - ((x1 * ((x1 * (6.0 + ((((-2.0 * t_1) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))) - 2.0)) - (x2 * -4.0))));
	} else if (x1 <= -2.7e+28) {
		tmp = t_5;
	} else if (x1 <= 0.43) {
		tmp = x1 + ((x2 * -6.0) - ((x1 * (2.0 - t_3)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	} else if (x1 <= 3.2e+87) {
		tmp = t_5;
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_1)) + (x2 * ((x1 * 6.0) + (t_3 / x2)))) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (2.0d0 * x2) - 3.0d0
    t_2 = (-1.0d0) - (x1 * x1)
    t_3 = x1 * ((x1 * 3.0d0) + 9.0d0)
    t_4 = x1 - (t_0 - (2.0d0 * x2))
    t_5 = x1 - ((3.0d0 * (t_4 / ((x1 * x1) + 1.0d0))) - (x1 - ((((((x1 * x1) * 6.0d0) + (t_1 * ((x1 * 2.0d0) * 3.0d0))) * t_2) - (3.0d0 * t_0)) - (x1 * (x1 * x1)))))
    if (x1 <= (-1.35d+154)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((x2 * (-12.0d0)) + (x1 * (9.0d0 + (x2 * 6.0d0)))) - 2.0d0)))
    else if (x1 <= (-3.1d+102)) then
        tmp = x1 + ((3.0d0 * (t_4 / t_2)) + (x1 - ((x1 * ((x1 * (6.0d0 + (((((-2.0d0) * t_1) - ((x2 * 6.0d0) + (x2 * 8.0d0))) - (x2 * (-4.0d0))) - (x1 * (-6.0d0))))) - 2.0d0)) - (x2 * (-4.0d0)))))
    else if (x1 <= (-2.7d+28)) then
        tmp = t_5
    else if (x1 <= 0.43d0) then
        tmp = x1 + ((x2 * (-6.0d0)) - ((x1 * (2.0d0 - t_3)) + (x2 * ((x1 * (12.0d0 - (x1 * 6.0d0))) - (8.0d0 * (x1 * x2))))))
    else if (x1 <= 3.2d+87) then
        tmp = t_5
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((4.0d0 * (x2 * t_1)) + (x2 * ((x1 * 6.0d0) + (t_3 / x2)))) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (2.0 * x2) - 3.0;
	double t_2 = -1.0 - (x1 * x1);
	double t_3 = x1 * ((x1 * 3.0) + 9.0);
	double t_4 = x1 - (t_0 - (2.0 * x2));
	double t_5 = x1 - ((3.0 * (t_4 / ((x1 * x1) + 1.0))) - (x1 - ((((((x1 * x1) * 6.0) + (t_1 * ((x1 * 2.0) * 3.0))) * t_2) - (3.0 * t_0)) - (x1 * (x1 * x1)))));
	double tmp;
	if (x1 <= -1.35e+154) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	} else if (x1 <= -3.1e+102) {
		tmp = x1 + ((3.0 * (t_4 / t_2)) + (x1 - ((x1 * ((x1 * (6.0 + ((((-2.0 * t_1) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))) - 2.0)) - (x2 * -4.0))));
	} else if (x1 <= -2.7e+28) {
		tmp = t_5;
	} else if (x1 <= 0.43) {
		tmp = x1 + ((x2 * -6.0) - ((x1 * (2.0 - t_3)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	} else if (x1 <= 3.2e+87) {
		tmp = t_5;
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_1)) + (x2 * ((x1 * 6.0) + (t_3 / x2)))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (2.0 * x2) - 3.0
	t_2 = -1.0 - (x1 * x1)
	t_3 = x1 * ((x1 * 3.0) + 9.0)
	t_4 = x1 - (t_0 - (2.0 * x2))
	t_5 = x1 - ((3.0 * (t_4 / ((x1 * x1) + 1.0))) - (x1 - ((((((x1 * x1) * 6.0) + (t_1 * ((x1 * 2.0) * 3.0))) * t_2) - (3.0 * t_0)) - (x1 * (x1 * x1)))))
	tmp = 0
	if x1 <= -1.35e+154:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)))
	elif x1 <= -3.1e+102:
		tmp = x1 + ((3.0 * (t_4 / t_2)) + (x1 - ((x1 * ((x1 * (6.0 + ((((-2.0 * t_1) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))) - 2.0)) - (x2 * -4.0))))
	elif x1 <= -2.7e+28:
		tmp = t_5
	elif x1 <= 0.43:
		tmp = x1 + ((x2 * -6.0) - ((x1 * (2.0 - t_3)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))))
	elif x1 <= 3.2e+87:
		tmp = t_5
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_1)) + (x2 * ((x1 * 6.0) + (t_3 / x2)))) - 2.0)))
	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(-1.0 - Float64(x1 * x1))
	t_3 = Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0))
	t_4 = Float64(x1 - Float64(t_0 - Float64(2.0 * x2)))
	t_5 = Float64(x1 - Float64(Float64(3.0 * Float64(t_4 / Float64(Float64(x1 * x1) + 1.0))) - Float64(x1 - Float64(Float64(Float64(Float64(Float64(Float64(x1 * x1) * 6.0) + Float64(t_1 * Float64(Float64(x1 * 2.0) * 3.0))) * t_2) - Float64(3.0 * t_0)) - Float64(x1 * Float64(x1 * x1))))))
	tmp = 0.0
	if (x1 <= -1.35e+154)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(x2 * -12.0) + Float64(x1 * Float64(9.0 + Float64(x2 * 6.0)))) - 2.0))));
	elseif (x1 <= -3.1e+102)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(t_4 / t_2)) + Float64(x1 - Float64(Float64(x1 * Float64(Float64(x1 * Float64(6.0 + Float64(Float64(Float64(Float64(-2.0 * t_1) - Float64(Float64(x2 * 6.0) + Float64(x2 * 8.0))) - Float64(x2 * -4.0)) - Float64(x1 * -6.0)))) - 2.0)) - Float64(x2 * -4.0)))));
	elseif (x1 <= -2.7e+28)
		tmp = t_5;
	elseif (x1 <= 0.43)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(Float64(x1 * Float64(2.0 - t_3)) + Float64(x2 * Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(8.0 * Float64(x1 * x2)))))));
	elseif (x1 <= 3.2e+87)
		tmp = t_5;
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(4.0 * Float64(x2 * t_1)) + Float64(x2 * Float64(Float64(x1 * 6.0) + Float64(t_3 / x2)))) - 2.0))));
	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 = -1.0 - (x1 * x1);
	t_3 = x1 * ((x1 * 3.0) + 9.0);
	t_4 = x1 - (t_0 - (2.0 * x2));
	t_5 = x1 - ((3.0 * (t_4 / ((x1 * x1) + 1.0))) - (x1 - ((((((x1 * x1) * 6.0) + (t_1 * ((x1 * 2.0) * 3.0))) * t_2) - (3.0 * t_0)) - (x1 * (x1 * x1)))));
	tmp = 0.0;
	if (x1 <= -1.35e+154)
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	elseif (x1 <= -3.1e+102)
		tmp = x1 + ((3.0 * (t_4 / t_2)) + (x1 - ((x1 * ((x1 * (6.0 + ((((-2.0 * t_1) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))) - 2.0)) - (x2 * -4.0))));
	elseif (x1 <= -2.7e+28)
		tmp = t_5;
	elseif (x1 <= 0.43)
		tmp = x1 + ((x2 * -6.0) - ((x1 * (2.0 - t_3)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	elseif (x1 <= 3.2e+87)
		tmp = t_5;
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_1)) + (x2 * ((x1 * 6.0) + (t_3 / x2)))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$2 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 - N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 - N[(N[(3.0 * N[(t$95$4 / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 - N[(N[(N[(N[(N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision] + N[(t$95$1 * N[(N[(x1 * 2.0), $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] - N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.35e+154], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(x2 * -12.0), $MachinePrecision] + N[(x1 * N[(9.0 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -3.1e+102], N[(x1 + N[(N[(3.0 * N[(t$95$4 / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 - N[(N[(x1 * N[(N[(x1 * N[(6.0 + N[(N[(N[(N[(-2.0 * t$95$1), $MachinePrecision] - N[(N[(x2 * 6.0), $MachinePrecision] + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision] - N[(x1 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] - N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.7e+28], t$95$5, If[LessEqual[x1, 0.43], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(N[(x1 * N[(2.0 - t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.2e+87], t$95$5, N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(4.0 * N[(x2 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * 6.0), $MachinePrecision] + N[(t$95$3 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -1.35000000000000003e154

   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. Add Preprocessing

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x2 around 0 0.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x2 \cdot \left(6 \cdot x1 - 12\right)\right) + x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right)\right)}\right) \]

   6. Taylor expanded in x1 around 0 68.2%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{x1 \cdot \left(\left(-12 \cdot x2 + x1 \cdot \left(9 + 6 \cdot x2\right)\right) - 2\right)}\right) \]

   if -1.35000000000000003e154 < x1 < -3.09999999999999987e102

   1. Initial program 18.2%

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

   3. Taylor expanded in x1 around inf 18.2%

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

   4. Taylor expanded in x1 around 0 100.0%

      \[\leadsto x1 + \left(\left(\color{blue}{\left(-4 \cdot x2 + x1 \cdot \left(2 + x1 \cdot \left(\left(-6 \cdot x1 + \left(-4 \cdot x2 + \left(-2 \cdot \left(3 - 2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right)\right) - 6\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if -3.09999999999999987e102 < x1 < -2.7000000000000002e28 or 0.429999999999999993 < x1 < 3.2e87

   1. Initial program 98.9%

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

   3. Taylor expanded in x1 around 0 83.3%

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

   4. Taylor expanded in x1 around inf 82.4%

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

   5. Taylor expanded in x1 around inf 78.8%

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

   6. Taylor expanded in x1 around inf 79.1%

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

   if -2.7000000000000002e28 < x1 < 0.429999999999999993

   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. Add Preprocessing

   3. Taylor expanded in x1 around 0 88.8%

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

   4. Taylor expanded in x1 around 0 89.2%

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

   5. Taylor expanded in x2 around 0 97.4%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right)\right)}\right) \]

   if 3.2e87 < x1

   1. Initial program 27.7%

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

   3. Taylor expanded in x1 around 0 11.4%

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

   4. Taylor expanded in x1 around 0 89.4%

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

   5. Taylor expanded in x2 around inf 100.0%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 6\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -3.1 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 - \left(x1 \cdot \left(x1 \cdot \left(6 + \left(\left(\left(-2 \cdot \left(2 \cdot x2 - 3\right) - \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - x2 \cdot -4\right) - x1 \cdot -6\right)\right) - 2\right) - x2 \cdot -4\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2.7 \cdot 10^{+28}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{x1 \cdot x1 + 1} - \left(x1 - \left(\left(\left(\left(x1 \cdot x1\right) \cdot 6 + \left(2 \cdot x2 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot 3\right)\right) \cdot \left(-1 - x1 \cdot x1\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.43:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - \left(x1 \cdot \left(2 - x1 \cdot \left(x1 \cdot 3 + 9\right)\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.2 \cdot 10^{+87}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{x1 \cdot x1 + 1} - \left(x1 - \left(\left(\left(\left(x1 \cdot x1\right) \cdot 6 + \left(2 \cdot x2 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot 3\right)\right) \cdot \left(-1 - x1 \cdot x1\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x2 \cdot \left(x1 \cdot 6 + \frac{x1 \cdot \left(x1 \cdot 3 + 9\right)}{x2}\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 87.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot x2 - 3\\ t_1 := x1 \cdot x1 + 1\\ t_2 := -1 - x1 \cdot x1\\ t_3 := \left(x1 \cdot 2\right) \cdot 3\\ t_4 := x1 \cdot \left(x1 \cdot 3 + 9\right)\\ t_5 := x1 \cdot \left(x1 \cdot x1\right)\\ t_6 := x1 \cdot \left(x1 \cdot 3\right)\\ t_7 := x1 - \left(t\_6 - 2 \cdot x2\right)\\ t_8 := 3 \cdot t\_6\\ \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 6\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -3.2 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{t\_7}{t\_2} + \left(x1 - \left(x1 \cdot \left(x1 \cdot \left(6 + \left(\left(\left(-2 \cdot t\_0 - \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - x2 \cdot -4\right) - x1 \cdot -6\right)\right) - 2\right) - x2 \cdot -4\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2.7 \cdot 10^{+28}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(t\_5 - \left(t\_1 \cdot \left(t\_3 \cdot \left(3 - 2 \cdot x2\right) - \left(x1 \cdot x1\right) \cdot \left(\frac{\left(t\_6 + 2 \cdot x2\right) - x1}{t\_1} \cdot 4 - 6\right)\right) - t\_8\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 0.43:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - \left(x1 \cdot \left(2 - t\_4\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.2 \cdot 10^{+87}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{t\_7}{t\_1} - \left(x1 - \left(\left(\left(\left(x1 \cdot x1\right) \cdot 6 + t\_0 \cdot t\_3\right) \cdot t\_2 - t\_8\right) - t\_5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot t\_0\right) + x2 \cdot \left(x1 \cdot 6 + \frac{t\_4}{x2}\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* 2.0 x2) 3.0))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (- -1.0 (* x1 x1)))
        (t_3 (* (* x1 2.0) 3.0))
        (t_4 (* x1 (+ (* x1 3.0) 9.0)))
        (t_5 (* x1 (* x1 x1)))
        (t_6 (* x1 (* x1 3.0)))
        (t_7 (- x1 (- t_6 (* 2.0 x2))))
        (t_8 (* 3.0 t_6)))
   (if (<= x1 -1.35e+154)
     (+
      x1
      (+
       (* x2 -6.0)
       (* x1 (- (+ (* x2 -12.0) (* x1 (+ 9.0 (* x2 6.0)))) 2.0))))
     (if (<= x1 -3.2e+102)
       (+
        x1
        (+
         (* 3.0 (/ t_7 t_2))
         (-
          x1
          (-
           (*
            x1
            (-
             (*
              x1
              (+
               6.0
               (-
                (- (- (* -2.0 t_0) (+ (* x2 6.0) (* x2 8.0))) (* x2 -4.0))
                (* x1 -6.0))))
             2.0))
           (* x2 -4.0)))))
       (if (<= x1 -2.7e+28)
         (+
          x1
          (+
           (+
            x1
            (-
             t_5
             (-
              (*
               t_1
               (-
                (* t_3 (- 3.0 (* 2.0 x2)))
                (*
                 (* x1 x1)
                 (- (* (/ (- (+ t_6 (* 2.0 x2)) x1) t_1) 4.0) 6.0))))
              t_8)))
           (* 3.0 (* x2 -2.0))))
         (if (<= x1 0.43)
           (+
            x1
            (-
             (* x2 -6.0)
             (+
              (* x1 (- 2.0 t_4))
              (* x2 (- (* x1 (- 12.0 (* x1 6.0))) (* 8.0 (* x1 x2)))))))
           (if (<= x1 3.2e+87)
             (-
              x1
              (-
               (* 3.0 (/ t_7 t_1))
               (-
                x1
                (- (- (* (+ (* (* x1 x1) 6.0) (* t_0 t_3)) t_2) t_8) t_5))))
             (+
              x1
              (+
               (* x2 -6.0)
               (*
                x1
                (-
                 (+ (* 4.0 (* x2 t_0)) (* x2 (+ (* x1 6.0) (/ t_4 x2))))
                 2.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = -1.0 - (x1 * x1);
	double t_3 = (x1 * 2.0) * 3.0;
	double t_4 = x1 * ((x1 * 3.0) + 9.0);
	double t_5 = x1 * (x1 * x1);
	double t_6 = x1 * (x1 * 3.0);
	double t_7 = x1 - (t_6 - (2.0 * x2));
	double t_8 = 3.0 * t_6;
	double tmp;
	if (x1 <= -1.35e+154) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	} else if (x1 <= -3.2e+102) {
		tmp = x1 + ((3.0 * (t_7 / t_2)) + (x1 - ((x1 * ((x1 * (6.0 + ((((-2.0 * t_0) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))) - 2.0)) - (x2 * -4.0))));
	} else if (x1 <= -2.7e+28) {
		tmp = x1 + ((x1 + (t_5 - ((t_1 * ((t_3 * (3.0 - (2.0 * x2))) - ((x1 * x1) * (((((t_6 + (2.0 * x2)) - x1) / t_1) * 4.0) - 6.0)))) - t_8))) + (3.0 * (x2 * -2.0)));
	} else if (x1 <= 0.43) {
		tmp = x1 + ((x2 * -6.0) - ((x1 * (2.0 - t_4)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	} else if (x1 <= 3.2e+87) {
		tmp = x1 - ((3.0 * (t_7 / t_1)) - (x1 - ((((((x1 * x1) * 6.0) + (t_0 * t_3)) * t_2) - t_8) - t_5)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_0)) + (x2 * ((x1 * 6.0) + (t_4 / x2)))) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: tmp
    t_0 = (2.0d0 * x2) - 3.0d0
    t_1 = (x1 * x1) + 1.0d0
    t_2 = (-1.0d0) - (x1 * x1)
    t_3 = (x1 * 2.0d0) * 3.0d0
    t_4 = x1 * ((x1 * 3.0d0) + 9.0d0)
    t_5 = x1 * (x1 * x1)
    t_6 = x1 * (x1 * 3.0d0)
    t_7 = x1 - (t_6 - (2.0d0 * x2))
    t_8 = 3.0d0 * t_6
    if (x1 <= (-1.35d+154)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((x2 * (-12.0d0)) + (x1 * (9.0d0 + (x2 * 6.0d0)))) - 2.0d0)))
    else if (x1 <= (-3.2d+102)) then
        tmp = x1 + ((3.0d0 * (t_7 / t_2)) + (x1 - ((x1 * ((x1 * (6.0d0 + (((((-2.0d0) * t_0) - ((x2 * 6.0d0) + (x2 * 8.0d0))) - (x2 * (-4.0d0))) - (x1 * (-6.0d0))))) - 2.0d0)) - (x2 * (-4.0d0)))))
    else if (x1 <= (-2.7d+28)) then
        tmp = x1 + ((x1 + (t_5 - ((t_1 * ((t_3 * (3.0d0 - (2.0d0 * x2))) - ((x1 * x1) * (((((t_6 + (2.0d0 * x2)) - x1) / t_1) * 4.0d0) - 6.0d0)))) - t_8))) + (3.0d0 * (x2 * (-2.0d0))))
    else if (x1 <= 0.43d0) then
        tmp = x1 + ((x2 * (-6.0d0)) - ((x1 * (2.0d0 - t_4)) + (x2 * ((x1 * (12.0d0 - (x1 * 6.0d0))) - (8.0d0 * (x1 * x2))))))
    else if (x1 <= 3.2d+87) then
        tmp = x1 - ((3.0d0 * (t_7 / t_1)) - (x1 - ((((((x1 * x1) * 6.0d0) + (t_0 * t_3)) * t_2) - t_8) - t_5)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((4.0d0 * (x2 * t_0)) + (x2 * ((x1 * 6.0d0) + (t_4 / x2)))) - 2.0d0)))
    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) + 1.0;
	double t_2 = -1.0 - (x1 * x1);
	double t_3 = (x1 * 2.0) * 3.0;
	double t_4 = x1 * ((x1 * 3.0) + 9.0);
	double t_5 = x1 * (x1 * x1);
	double t_6 = x1 * (x1 * 3.0);
	double t_7 = x1 - (t_6 - (2.0 * x2));
	double t_8 = 3.0 * t_6;
	double tmp;
	if (x1 <= -1.35e+154) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	} else if (x1 <= -3.2e+102) {
		tmp = x1 + ((3.0 * (t_7 / t_2)) + (x1 - ((x1 * ((x1 * (6.0 + ((((-2.0 * t_0) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))) - 2.0)) - (x2 * -4.0))));
	} else if (x1 <= -2.7e+28) {
		tmp = x1 + ((x1 + (t_5 - ((t_1 * ((t_3 * (3.0 - (2.0 * x2))) - ((x1 * x1) * (((((t_6 + (2.0 * x2)) - x1) / t_1) * 4.0) - 6.0)))) - t_8))) + (3.0 * (x2 * -2.0)));
	} else if (x1 <= 0.43) {
		tmp = x1 + ((x2 * -6.0) - ((x1 * (2.0 - t_4)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	} else if (x1 <= 3.2e+87) {
		tmp = x1 - ((3.0 * (t_7 / t_1)) - (x1 - ((((((x1 * x1) * 6.0) + (t_0 * t_3)) * t_2) - t_8) - t_5)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_0)) + (x2 * ((x1 * 6.0) + (t_4 / x2)))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (2.0 * x2) - 3.0
	t_1 = (x1 * x1) + 1.0
	t_2 = -1.0 - (x1 * x1)
	t_3 = (x1 * 2.0) * 3.0
	t_4 = x1 * ((x1 * 3.0) + 9.0)
	t_5 = x1 * (x1 * x1)
	t_6 = x1 * (x1 * 3.0)
	t_7 = x1 - (t_6 - (2.0 * x2))
	t_8 = 3.0 * t_6
	tmp = 0
	if x1 <= -1.35e+154:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)))
	elif x1 <= -3.2e+102:
		tmp = x1 + ((3.0 * (t_7 / t_2)) + (x1 - ((x1 * ((x1 * (6.0 + ((((-2.0 * t_0) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))) - 2.0)) - (x2 * -4.0))))
	elif x1 <= -2.7e+28:
		tmp = x1 + ((x1 + (t_5 - ((t_1 * ((t_3 * (3.0 - (2.0 * x2))) - ((x1 * x1) * (((((t_6 + (2.0 * x2)) - x1) / t_1) * 4.0) - 6.0)))) - t_8))) + (3.0 * (x2 * -2.0)))
	elif x1 <= 0.43:
		tmp = x1 + ((x2 * -6.0) - ((x1 * (2.0 - t_4)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))))
	elif x1 <= 3.2e+87:
		tmp = x1 - ((3.0 * (t_7 / t_1)) - (x1 - ((((((x1 * x1) * 6.0) + (t_0 * t_3)) * t_2) - t_8) - t_5)))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_0)) + (x2 * ((x1 * 6.0) + (t_4 / x2)))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(2.0 * x2) - 3.0)
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(-1.0 - Float64(x1 * x1))
	t_3 = Float64(Float64(x1 * 2.0) * 3.0)
	t_4 = Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0))
	t_5 = Float64(x1 * Float64(x1 * x1))
	t_6 = Float64(x1 * Float64(x1 * 3.0))
	t_7 = Float64(x1 - Float64(t_6 - Float64(2.0 * x2)))
	t_8 = Float64(3.0 * t_6)
	tmp = 0.0
	if (x1 <= -1.35e+154)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(x2 * -12.0) + Float64(x1 * Float64(9.0 + Float64(x2 * 6.0)))) - 2.0))));
	elseif (x1 <= -3.2e+102)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(t_7 / t_2)) + Float64(x1 - Float64(Float64(x1 * Float64(Float64(x1 * Float64(6.0 + Float64(Float64(Float64(Float64(-2.0 * t_0) - Float64(Float64(x2 * 6.0) + Float64(x2 * 8.0))) - Float64(x2 * -4.0)) - Float64(x1 * -6.0)))) - 2.0)) - Float64(x2 * -4.0)))));
	elseif (x1 <= -2.7e+28)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(t_5 - Float64(Float64(t_1 * Float64(Float64(t_3 * Float64(3.0 - Float64(2.0 * x2))) - Float64(Float64(x1 * x1) * Float64(Float64(Float64(Float64(Float64(t_6 + Float64(2.0 * x2)) - x1) / t_1) * 4.0) - 6.0)))) - t_8))) + Float64(3.0 * Float64(x2 * -2.0))));
	elseif (x1 <= 0.43)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(Float64(x1 * Float64(2.0 - t_4)) + Float64(x2 * Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(8.0 * Float64(x1 * x2)))))));
	elseif (x1 <= 3.2e+87)
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(t_7 / t_1)) - Float64(x1 - Float64(Float64(Float64(Float64(Float64(Float64(x1 * x1) * 6.0) + Float64(t_0 * t_3)) * t_2) - t_8) - t_5))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(4.0 * Float64(x2 * t_0)) + Float64(x2 * Float64(Float64(x1 * 6.0) + Float64(t_4 / x2)))) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (2.0 * x2) - 3.0;
	t_1 = (x1 * x1) + 1.0;
	t_2 = -1.0 - (x1 * x1);
	t_3 = (x1 * 2.0) * 3.0;
	t_4 = x1 * ((x1 * 3.0) + 9.0);
	t_5 = x1 * (x1 * x1);
	t_6 = x1 * (x1 * 3.0);
	t_7 = x1 - (t_6 - (2.0 * x2));
	t_8 = 3.0 * t_6;
	tmp = 0.0;
	if (x1 <= -1.35e+154)
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	elseif (x1 <= -3.2e+102)
		tmp = x1 + ((3.0 * (t_7 / t_2)) + (x1 - ((x1 * ((x1 * (6.0 + ((((-2.0 * t_0) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))) - 2.0)) - (x2 * -4.0))));
	elseif (x1 <= -2.7e+28)
		tmp = x1 + ((x1 + (t_5 - ((t_1 * ((t_3 * (3.0 - (2.0 * x2))) - ((x1 * x1) * (((((t_6 + (2.0 * x2)) - x1) / t_1) * 4.0) - 6.0)))) - t_8))) + (3.0 * (x2 * -2.0)));
	elseif (x1 <= 0.43)
		tmp = x1 + ((x2 * -6.0) - ((x1 * (2.0 - t_4)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	elseif (x1 <= 3.2e+87)
		tmp = x1 - ((3.0 * (t_7 / t_1)) - (x1 - ((((((x1 * x1) * 6.0) + (t_0 * t_3)) * t_2) - t_8) - t_5)));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_0)) + (x2 * ((x1 * 6.0) + (t_4 / x2)))) - 2.0)));
	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[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * 2.0), $MachinePrecision] * 3.0), $MachinePrecision]}, Block[{t$95$4 = N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(x1 - N[(t$95$6 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(3.0 * t$95$6), $MachinePrecision]}, If[LessEqual[x1, -1.35e+154], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(x2 * -12.0), $MachinePrecision] + N[(x1 * N[(9.0 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -3.2e+102], N[(x1 + N[(N[(3.0 * N[(t$95$7 / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 - N[(N[(x1 * N[(N[(x1 * N[(6.0 + N[(N[(N[(N[(-2.0 * t$95$0), $MachinePrecision] - N[(N[(x2 * 6.0), $MachinePrecision] + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision] - N[(x1 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] - N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.7e+28], N[(x1 + N[(N[(x1 + N[(t$95$5 - N[(N[(t$95$1 * N[(N[(t$95$3 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * N[(N[(N[(N[(N[(t$95$6 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision] * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.43], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(N[(x1 * N[(2.0 - t$95$4), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.2e+87], N[(x1 - N[(N[(3.0 * N[(t$95$7 / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(x1 - N[(N[(N[(N[(N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision] + N[(t$95$0 * t$95$3), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] - t$95$8), $MachinePrecision] - t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(4.0 * N[(x2 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * 6.0), $MachinePrecision] + N[(t$95$4 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x1 < -1.35000000000000003e154

   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. Add Preprocessing

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x2 around 0 0.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x2 \cdot \left(6 \cdot x1 - 12\right)\right) + x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right)\right)}\right) \]

   6. Taylor expanded in x1 around 0 68.2%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{x1 \cdot \left(\left(-12 \cdot x2 + x1 \cdot \left(9 + 6 \cdot x2\right)\right) - 2\right)}\right) \]

   if -1.35000000000000003e154 < x1 < -3.1999999999999999e102

   1. Initial program 18.2%

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

   3. Taylor expanded in x1 around inf 18.2%

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

   4. Taylor expanded in x1 around 0 100.0%

      \[\leadsto x1 + \left(\left(\color{blue}{\left(-4 \cdot x2 + x1 \cdot \left(2 + x1 \cdot \left(\left(-6 \cdot x1 + \left(-4 \cdot x2 + \left(-2 \cdot \left(3 - 2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right)\right) - 6\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if -3.1999999999999999e102 < x1 < -2.7000000000000002e28

   1. Initial program 99.2%

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

   3. Taylor expanded in x1 around 0 83.9%

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

   4. Taylor expanded in x1 around inf 83.9%

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

   5. Taylor expanded in x1 around inf 83.9%

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

   6. Taylor expanded in x1 around 0 83.9%

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

      1. *-commutative 83.9%

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

   8. Simplified 83.9%

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

   if -2.7000000000000002e28 < x1 < 0.429999999999999993

   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. Add Preprocessing

   3. Taylor expanded in x1 around 0 88.8%

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

   4. Taylor expanded in x1 around 0 89.2%

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

   5. Taylor expanded in x2 around 0 97.4%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right)\right)}\right) \]

   if 0.429999999999999993 < x1 < 3.2e87

   1. Initial program 98.6%

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

   3. Taylor expanded in x1 around 0 82.6%

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

   4. Taylor expanded in x1 around inf 80.8%

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

   5. Taylor expanded in x1 around inf 73.7%

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

   6. Taylor expanded in x1 around inf 74.4%

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

   if 3.2e87 < x1

   1. Initial program 27.7%

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

   3. Taylor expanded in x1 around 0 11.4%

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

   4. Taylor expanded in x1 around 0 89.4%

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

   5. Taylor expanded in x2 around inf 100.0%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 6\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -3.2 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 - \left(x1 \cdot \left(x1 \cdot \left(6 + \left(\left(\left(-2 \cdot \left(2 \cdot x2 - 3\right) - \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - x2 \cdot -4\right) - x1 \cdot -6\right)\right) - 2\right) - x2 \cdot -4\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2.7 \cdot 10^{+28}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot 3\right) \cdot \left(3 - 2 \cdot x2\right) - \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 0.43:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - \left(x1 \cdot \left(2 - x1 \cdot \left(x1 \cdot 3 + 9\right)\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.2 \cdot 10^{+87}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{x1 \cdot x1 + 1} - \left(x1 - \left(\left(\left(\left(x1 \cdot x1\right) \cdot 6 + \left(2 \cdot x2 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot 3\right)\right) \cdot \left(-1 - x1 \cdot x1\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x2 \cdot \left(x1 \cdot 6 + \frac{x1 \cdot \left(x1 \cdot 3 + 9\right)}{x2}\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 82.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3 + 9\right)\\ t_1 := 2 \cdot x2 - 3\\ \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 6\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -4.5 \cdot 10^{+45}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 - \left(x1 \cdot \left(x1 \cdot \left(6 + \left(\left(\left(-2 \cdot t\_1 - \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - x2 \cdot -4\right) - x1 \cdot -6\right)\right) - 2\right) - x2 \cdot -4\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7.5 \cdot 10^{+51}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - \left(x1 \cdot \left(2 - t\_0\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot t\_1\right) + x2 \cdot \left(x1 \cdot 6 + \frac{t\_0}{x2}\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ (* x1 3.0) 9.0))) (t_1 (- (* 2.0 x2) 3.0)))
   (if (<= x1 -9.5e+153)
     (+
      x1
      (+
       (* x2 -6.0)
       (* x1 (- (+ (* x2 -12.0) (* x1 (+ 9.0 (* x2 6.0)))) 2.0))))
     (if (<= x1 -4.5e+45)
       (+
        x1
        (+
         (* 3.0 (/ (- x1 (- (* x1 (* x1 3.0)) (* 2.0 x2))) (- -1.0 (* x1 x1))))
         (-
          x1
          (-
           (*
            x1
            (-
             (*
              x1
              (+
               6.0
               (-
                (- (- (* -2.0 t_1) (+ (* x2 6.0) (* x2 8.0))) (* x2 -4.0))
                (* x1 -6.0))))
             2.0))
           (* x2 -4.0)))))
       (if (<= x1 7.5e+51)
         (+
          x1
          (-
           (* x2 -6.0)
           (+
            (* x1 (- 2.0 t_0))
            (* x2 (- (* x1 (- 12.0 (* x1 6.0))) (* 8.0 (* x1 x2)))))))
         (+
          x1
          (+
           (* x2 -6.0)
           (*
            x1
            (-
             (+ (* 4.0 (* x2 t_1)) (* x2 (+ (* x1 6.0) (/ t_0 x2))))
             2.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 3.0) + 9.0);
	double t_1 = (2.0 * x2) - 3.0;
	double tmp;
	if (x1 <= -9.5e+153) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	} else if (x1 <= -4.5e+45) {
		tmp = x1 + ((3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 - ((x1 * ((x1 * (6.0 + ((((-2.0 * t_1) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))) - 2.0)) - (x2 * -4.0))));
	} else if (x1 <= 7.5e+51) {
		tmp = x1 + ((x2 * -6.0) - ((x1 * (2.0 - t_0)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_1)) + (x2 * ((x1 * 6.0) + (t_0 / x2)))) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x1 * ((x1 * 3.0d0) + 9.0d0)
    t_1 = (2.0d0 * x2) - 3.0d0
    if (x1 <= (-9.5d+153)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((x2 * (-12.0d0)) + (x1 * (9.0d0 + (x2 * 6.0d0)))) - 2.0d0)))
    else if (x1 <= (-4.5d+45)) then
        tmp = x1 + ((3.0d0 * ((x1 - ((x1 * (x1 * 3.0d0)) - (2.0d0 * x2))) / ((-1.0d0) - (x1 * x1)))) + (x1 - ((x1 * ((x1 * (6.0d0 + (((((-2.0d0) * t_1) - ((x2 * 6.0d0) + (x2 * 8.0d0))) - (x2 * (-4.0d0))) - (x1 * (-6.0d0))))) - 2.0d0)) - (x2 * (-4.0d0)))))
    else if (x1 <= 7.5d+51) then
        tmp = x1 + ((x2 * (-6.0d0)) - ((x1 * (2.0d0 - t_0)) + (x2 * ((x1 * (12.0d0 - (x1 * 6.0d0))) - (8.0d0 * (x1 * x2))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((4.0d0 * (x2 * t_1)) + (x2 * ((x1 * 6.0d0) + (t_0 / x2)))) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 3.0) + 9.0);
	double t_1 = (2.0 * x2) - 3.0;
	double tmp;
	if (x1 <= -9.5e+153) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	} else if (x1 <= -4.5e+45) {
		tmp = x1 + ((3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 - ((x1 * ((x1 * (6.0 + ((((-2.0 * t_1) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))) - 2.0)) - (x2 * -4.0))));
	} else if (x1 <= 7.5e+51) {
		tmp = x1 + ((x2 * -6.0) - ((x1 * (2.0 - t_0)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_1)) + (x2 * ((x1 * 6.0) + (t_0 / x2)))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((x1 * 3.0) + 9.0)
	t_1 = (2.0 * x2) - 3.0
	tmp = 0
	if x1 <= -9.5e+153:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)))
	elif x1 <= -4.5e+45:
		tmp = x1 + ((3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 - ((x1 * ((x1 * (6.0 + ((((-2.0 * t_1) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))) - 2.0)) - (x2 * -4.0))))
	elif x1 <= 7.5e+51:
		tmp = x1 + ((x2 * -6.0) - ((x1 * (2.0 - t_0)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_1)) + (x2 * ((x1 * 6.0) + (t_0 / x2)))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0))
	t_1 = Float64(Float64(2.0 * x2) - 3.0)
	tmp = 0.0
	if (x1 <= -9.5e+153)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(x2 * -12.0) + Float64(x1 * Float64(9.0 + Float64(x2 * 6.0)))) - 2.0))));
	elseif (x1 <= -4.5e+45)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 - Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2))) / Float64(-1.0 - Float64(x1 * x1)))) + Float64(x1 - Float64(Float64(x1 * Float64(Float64(x1 * Float64(6.0 + Float64(Float64(Float64(Float64(-2.0 * t_1) - Float64(Float64(x2 * 6.0) + Float64(x2 * 8.0))) - Float64(x2 * -4.0)) - Float64(x1 * -6.0)))) - 2.0)) - Float64(x2 * -4.0)))));
	elseif (x1 <= 7.5e+51)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(Float64(x1 * Float64(2.0 - t_0)) + Float64(x2 * Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(8.0 * Float64(x1 * x2)))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(4.0 * Float64(x2 * t_1)) + Float64(x2 * Float64(Float64(x1 * 6.0) + Float64(t_0 / x2)))) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((x1 * 3.0) + 9.0);
	t_1 = (2.0 * x2) - 3.0;
	tmp = 0.0;
	if (x1 <= -9.5e+153)
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	elseif (x1 <= -4.5e+45)
		tmp = x1 + ((3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 - ((x1 * ((x1 * (6.0 + ((((-2.0 * t_1) - ((x2 * 6.0) + (x2 * 8.0))) - (x2 * -4.0)) - (x1 * -6.0)))) - 2.0)) - (x2 * -4.0))));
	elseif (x1 <= 7.5e+51)
		tmp = x1 + ((x2 * -6.0) - ((x1 * (2.0 - t_0)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * t_1)) + (x2 * ((x1 * 6.0) + (t_0 / x2)))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, If[LessEqual[x1, -9.5e+153], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(x2 * -12.0), $MachinePrecision] + N[(x1 * N[(9.0 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -4.5e+45], N[(x1 + N[(N[(3.0 * N[(N[(x1 - N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 - N[(N[(x1 * N[(N[(x1 * N[(6.0 + N[(N[(N[(N[(-2.0 * t$95$1), $MachinePrecision] - N[(N[(x2 * 6.0), $MachinePrecision] + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision] - N[(x1 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] - N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7.5e+51], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(N[(x1 * N[(2.0 - t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(4.0 * N[(x2 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * 6.0), $MachinePrecision] + N[(t$95$0 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -9.4999999999999995e153

   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. Add Preprocessing

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x2 around 0 0.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x2 \cdot \left(6 \cdot x1 - 12\right)\right) + x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right)\right)}\right) \]

   6. Taylor expanded in x1 around 0 68.2%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{x1 \cdot \left(\left(-12 \cdot x2 + x1 \cdot \left(9 + 6 \cdot x2\right)\right) - 2\right)}\right) \]

   if -9.4999999999999995e153 < x1 < -4.4999999999999998e45

   1. Initial program 52.4%

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

   3. Taylor expanded in x1 around inf 52.4%

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

   4. Taylor expanded in x1 around 0 61.1%

      \[\leadsto x1 + \left(\left(\color{blue}{\left(-4 \cdot x2 + x1 \cdot \left(2 + x1 \cdot \left(\left(-6 \cdot x1 + \left(-4 \cdot x2 + \left(-2 \cdot \left(3 - 2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right)\right) - 6\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if -4.4999999999999998e45 < x1 < 7.4999999999999999e51

   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. Add Preprocessing

   3. Taylor expanded in x1 around 0 82.3%

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

   4. Taylor expanded in x1 around 0 82.8%

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

   5. Taylor expanded in x2 around 0 90.2%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right)\right)}\right) \]

   if 7.4999999999999999e51 < x1

   1. Initial program 32.0%

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

   3. Taylor expanded in x1 around 0 11.0%

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

   4. Taylor expanded in x1 around 0 84.4%

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

   5. Taylor expanded in x2 around inf 94.4%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 6\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -4.5 \cdot 10^{+45}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 - \left(x1 \cdot \left(x1 \cdot \left(6 + \left(\left(\left(-2 \cdot \left(2 \cdot x2 - 3\right) - \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - x2 \cdot -4\right) - x1 \cdot -6\right)\right) - 2\right) - x2 \cdot -4\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7.5 \cdot 10^{+51}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - \left(x1 \cdot \left(2 - x1 \cdot \left(x1 \cdot 3 + 9\right)\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x2 \cdot \left(x1 \cdot 6 + \frac{x1 \cdot \left(x1 \cdot 3 + 9\right)}{x2}\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 74.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3 + 9\right)\\ t_1 := x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - 3 \cdot \left(x1 \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -4.3 \cdot 10^{+49}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 6\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -4.8 \cdot 10^{-261}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq 6.5 \cdot 10^{-171}:\\ \;\;\;\;x1 + x2 \cdot \left(\left(x1 \cdot \left(x1 \cdot 6 - 12\right) + \frac{x1 \cdot \left(t\_0 - 2\right)}{x2}\right) - 6\right)\\ \mathbf{elif}\;x1 \leq 3.85 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - t\_0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ (* x1 3.0) 9.0)))
        (t_1
         (+
          x1
          (-
           (* x2 -6.0)
           (*
            x1
            (+
             2.0
             (-
              (* 4.0 (* x2 (- 3.0 (* 2.0 x2))))
              (* 3.0 (* x1 (- 3.0 (* x2 -2.0)))))))))))
   (if (<= x1 -4.3e+49)
     (+
      x1
      (+
       (* x2 -6.0)
       (* x1 (- (+ (* x2 -12.0) (* x1 (+ 9.0 (* x2 6.0)))) 2.0))))
     (if (<= x1 -4.8e-261)
       t_1
       (if (<= x1 6.5e-171)
         (+
          x1
          (*
           x2
           (- (+ (* x1 (- (* x1 6.0) 12.0)) (/ (* x1 (- t_0 2.0)) x2)) 6.0)))
         (if (<= x1 3.85e+102)
           t_1
           (+ x1 (- (* x2 -6.0) (* x1 (- 2.0 t_0))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 3.0) + 9.0);
	double t_1 = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (3.0 * (x1 * (3.0 - (x2 * -2.0))))))));
	double tmp;
	if (x1 <= -4.3e+49) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	} else if (x1 <= -4.8e-261) {
		tmp = t_1;
	} else if (x1 <= 6.5e-171) {
		tmp = x1 + (x2 * (((x1 * ((x1 * 6.0) - 12.0)) + ((x1 * (t_0 - 2.0)) / x2)) - 6.0));
	} else if (x1 <= 3.85e+102) {
		tmp = t_1;
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - t_0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x1 * ((x1 * 3.0d0) + 9.0d0)
    t_1 = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))) - (3.0d0 * (x1 * (3.0d0 - (x2 * (-2.0d0)))))))))
    if (x1 <= (-4.3d+49)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((x2 * (-12.0d0)) + (x1 * (9.0d0 + (x2 * 6.0d0)))) - 2.0d0)))
    else if (x1 <= (-4.8d-261)) then
        tmp = t_1
    else if (x1 <= 6.5d-171) then
        tmp = x1 + (x2 * (((x1 * ((x1 * 6.0d0) - 12.0d0)) + ((x1 * (t_0 - 2.0d0)) / x2)) - 6.0d0))
    else if (x1 <= 3.85d+102) then
        tmp = t_1
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 - t_0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 3.0) + 9.0);
	double t_1 = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (3.0 * (x1 * (3.0 - (x2 * -2.0))))))));
	double tmp;
	if (x1 <= -4.3e+49) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	} else if (x1 <= -4.8e-261) {
		tmp = t_1;
	} else if (x1 <= 6.5e-171) {
		tmp = x1 + (x2 * (((x1 * ((x1 * 6.0) - 12.0)) + ((x1 * (t_0 - 2.0)) / x2)) - 6.0));
	} else if (x1 <= 3.85e+102) {
		tmp = t_1;
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - t_0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((x1 * 3.0) + 9.0)
	t_1 = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (3.0 * (x1 * (3.0 - (x2 * -2.0))))))))
	tmp = 0
	if x1 <= -4.3e+49:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)))
	elif x1 <= -4.8e-261:
		tmp = t_1
	elif x1 <= 6.5e-171:
		tmp = x1 + (x2 * (((x1 * ((x1 * 6.0) - 12.0)) + ((x1 * (t_0 - 2.0)) / x2)) - 6.0))
	elif x1 <= 3.85e+102:
		tmp = t_1
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - t_0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0))
	t_1 = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))) - Float64(3.0 * Float64(x1 * Float64(3.0 - Float64(x2 * -2.0)))))))))
	tmp = 0.0
	if (x1 <= -4.3e+49)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(x2 * -12.0) + Float64(x1 * Float64(9.0 + Float64(x2 * 6.0)))) - 2.0))));
	elseif (x1 <= -4.8e-261)
		tmp = t_1;
	elseif (x1 <= 6.5e-171)
		tmp = Float64(x1 + Float64(x2 * Float64(Float64(Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)) + Float64(Float64(x1 * Float64(t_0 - 2.0)) / x2)) - 6.0)));
	elseif (x1 <= 3.85e+102)
		tmp = t_1;
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 - t_0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((x1 * 3.0) + 9.0);
	t_1 = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (3.0 * (x1 * (3.0 - (x2 * -2.0))))))));
	tmp = 0.0;
	if (x1 <= -4.3e+49)
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	elseif (x1 <= -4.8e-261)
		tmp = t_1;
	elseif (x1 <= 6.5e-171)
		tmp = x1 + (x2 * (((x1 * ((x1 * 6.0) - 12.0)) + ((x1 * (t_0 - 2.0)) / x2)) - 6.0));
	elseif (x1 <= 3.85e+102)
		tmp = t_1;
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - t_0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * N[(x1 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.3e+49], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(x2 * -12.0), $MachinePrecision] + N[(x1 * N[(9.0 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -4.8e-261], t$95$1, If[LessEqual[x1, 6.5e-171], N[(x1 + N[(x2 * N[(N[(N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(t$95$0 - 2.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.85e+102], t$95$1, N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.2999999999999999e49

   1. Initial program 24.3%

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

   3. Taylor expanded in x1 around 0 5.0%

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

   4. Taylor expanded in x1 around 0 4.9%

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

   5. Taylor expanded in x2 around 0 5.3%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x2 \cdot \left(6 \cdot x1 - 12\right)\right) + x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right)\right)}\right) \]

   6. Taylor expanded in x1 around 0 53.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{x1 \cdot \left(\left(-12 \cdot x2 + x1 \cdot \left(9 + 6 \cdot x2\right)\right) - 2\right)}\right) \]

   if -4.2999999999999999e49 < x1 < -4.80000000000000028e-261 or 6.5000000000000004e-171 < x1 < 3.85000000000000007e102

   1. Initial program 99.2%

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

   3. Taylor expanded in x1 around 0 81.4%

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

   4. Taylor expanded in x1 around 0 82.0%

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

   if -4.80000000000000028e-261 < x1 < 6.5000000000000004e-171

   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. Add Preprocessing

   3. Taylor expanded in x1 around 0 80.9%

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

   4. Taylor expanded in x1 around 0 81.1%

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

   5. Taylor expanded in x2 around 0 92.3%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x2 \cdot \left(6 \cdot x1 - 12\right)\right) + x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right)\right)}\right) \]

   6. Taylor expanded in x2 around inf 92.4%

      \[\leadsto x1 + \color{blue}{x2 \cdot \left(\left(x1 \cdot \left(6 \cdot x1 - 12\right) + \frac{x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right)}{x2}\right) - 6\right)} \]

   if 3.85000000000000007e102 < x1

   1. Initial program 22.7%

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

   3. Taylor expanded in x1 around 0 5.4%

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

   4. Taylor expanded in x1 around 0 88.6%

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

   5. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.3 \cdot 10^{+49}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 6\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -4.8 \cdot 10^{-261}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - 3 \cdot \left(x1 \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6.5 \cdot 10^{-171}:\\ \;\;\;\;x1 + x2 \cdot \left(\left(x1 \cdot \left(x1 \cdot 6 - 12\right) + \frac{x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 9\right) - 2\right)}{x2}\right) - 6\right)\\ \mathbf{elif}\;x1 \leq 3.85 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - 3 \cdot \left(x1 \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot \left(x1 \cdot 3 + 9\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 74.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3 + 9\right)\\ t_1 := 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\\ \mathbf{if}\;x1 \leq -7.5 \cdot 10^{+48}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 6\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -3.1 \cdot 10^{-266}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(t\_1 - 3 \cdot \left(x1 \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6.5 \cdot 10^{-171}:\\ \;\;\;\;x1 + x2 \cdot \left(\left(x1 \cdot \left(x1 \cdot 6 - 12\right) + \frac{x1 \cdot \left(t\_0 - 2\right)}{x2}\right) - 6\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+102}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 + \left(t\_1 - x1 \cdot \left(x1 \cdot 3 + x2 \cdot 6\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - t\_0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ (* x1 3.0) 9.0)))
        (t_1 (* 4.0 (* x2 (- 3.0 (* 2.0 x2))))))
   (if (<= x1 -7.5e+48)
     (+
      x1
      (+
       (* x2 -6.0)
       (* x1 (- (+ (* x2 -12.0) (* x1 (+ 9.0 (* x2 6.0)))) 2.0))))
     (if (<= x1 -3.1e-266)
       (+
        x1
        (-
         (* x2 -6.0)
         (* x1 (+ 2.0 (- t_1 (* 3.0 (* x1 (- 3.0 (* x2 -2.0)))))))))
       (if (<= x1 6.5e-171)
         (+
          x1
          (*
           x2
           (- (+ (* x1 (- (* x1 6.0) 12.0)) (/ (* x1 (- t_0 2.0)) x2)) 6.0)))
         (if (<= x1 5e+102)
           (-
            x1
            (-
             (* x1 (+ 2.0 (- t_1 (* x1 (+ (* x1 3.0) (* x2 6.0))))))
             (* x2 -6.0)))
           (+ x1 (- (* x2 -6.0) (* x1 (- 2.0 t_0))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 3.0) + 9.0);
	double t_1 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double tmp;
	if (x1 <= -7.5e+48) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	} else if (x1 <= -3.1e-266) {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + (t_1 - (3.0 * (x1 * (3.0 - (x2 * -2.0))))))));
	} else if (x1 <= 6.5e-171) {
		tmp = x1 + (x2 * (((x1 * ((x1 * 6.0) - 12.0)) + ((x1 * (t_0 - 2.0)) / x2)) - 6.0));
	} else if (x1 <= 5e+102) {
		tmp = x1 - ((x1 * (2.0 + (t_1 - (x1 * ((x1 * 3.0) + (x2 * 6.0)))))) - (x2 * -6.0));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - t_0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x1 * ((x1 * 3.0d0) + 9.0d0)
    t_1 = 4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))
    if (x1 <= (-7.5d+48)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((x2 * (-12.0d0)) + (x1 * (9.0d0 + (x2 * 6.0d0)))) - 2.0d0)))
    else if (x1 <= (-3.1d-266)) then
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + (t_1 - (3.0d0 * (x1 * (3.0d0 - (x2 * (-2.0d0)))))))))
    else if (x1 <= 6.5d-171) then
        tmp = x1 + (x2 * (((x1 * ((x1 * 6.0d0) - 12.0d0)) + ((x1 * (t_0 - 2.0d0)) / x2)) - 6.0d0))
    else if (x1 <= 5d+102) then
        tmp = x1 - ((x1 * (2.0d0 + (t_1 - (x1 * ((x1 * 3.0d0) + (x2 * 6.0d0)))))) - (x2 * (-6.0d0)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 - t_0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 3.0) + 9.0);
	double t_1 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double tmp;
	if (x1 <= -7.5e+48) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	} else if (x1 <= -3.1e-266) {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + (t_1 - (3.0 * (x1 * (3.0 - (x2 * -2.0))))))));
	} else if (x1 <= 6.5e-171) {
		tmp = x1 + (x2 * (((x1 * ((x1 * 6.0) - 12.0)) + ((x1 * (t_0 - 2.0)) / x2)) - 6.0));
	} else if (x1 <= 5e+102) {
		tmp = x1 - ((x1 * (2.0 + (t_1 - (x1 * ((x1 * 3.0) + (x2 * 6.0)))))) - (x2 * -6.0));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - t_0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((x1 * 3.0) + 9.0)
	t_1 = 4.0 * (x2 * (3.0 - (2.0 * x2)))
	tmp = 0
	if x1 <= -7.5e+48:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)))
	elif x1 <= -3.1e-266:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + (t_1 - (3.0 * (x1 * (3.0 - (x2 * -2.0))))))))
	elif x1 <= 6.5e-171:
		tmp = x1 + (x2 * (((x1 * ((x1 * 6.0) - 12.0)) + ((x1 * (t_0 - 2.0)) / x2)) - 6.0))
	elif x1 <= 5e+102:
		tmp = x1 - ((x1 * (2.0 + (t_1 - (x1 * ((x1 * 3.0) + (x2 * 6.0)))))) - (x2 * -6.0))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - t_0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0))
	t_1 = Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))
	tmp = 0.0
	if (x1 <= -7.5e+48)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(x2 * -12.0) + Float64(x1 * Float64(9.0 + Float64(x2 * 6.0)))) - 2.0))));
	elseif (x1 <= -3.1e-266)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(t_1 - Float64(3.0 * Float64(x1 * Float64(3.0 - Float64(x2 * -2.0)))))))));
	elseif (x1 <= 6.5e-171)
		tmp = Float64(x1 + Float64(x2 * Float64(Float64(Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)) + Float64(Float64(x1 * Float64(t_0 - 2.0)) / x2)) - 6.0)));
	elseif (x1 <= 5e+102)
		tmp = Float64(x1 - Float64(Float64(x1 * Float64(2.0 + Float64(t_1 - Float64(x1 * Float64(Float64(x1 * 3.0) + Float64(x2 * 6.0)))))) - Float64(x2 * -6.0)));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 - t_0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((x1 * 3.0) + 9.0);
	t_1 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	tmp = 0.0;
	if (x1 <= -7.5e+48)
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	elseif (x1 <= -3.1e-266)
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + (t_1 - (3.0 * (x1 * (3.0 - (x2 * -2.0))))))));
	elseif (x1 <= 6.5e-171)
		tmp = x1 + (x2 * (((x1 * ((x1 * 6.0) - 12.0)) + ((x1 * (t_0 - 2.0)) / x2)) - 6.0));
	elseif (x1 <= 5e+102)
		tmp = x1 - ((x1 * (2.0 + (t_1 - (x1 * ((x1 * 3.0) + (x2 * 6.0)))))) - (x2 * -6.0));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - t_0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -7.5e+48], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(x2 * -12.0), $MachinePrecision] + N[(x1 * N[(9.0 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -3.1e-266], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(t$95$1 - N[(3.0 * N[(x1 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6.5e-171], N[(x1 + N[(x2 * N[(N[(N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(t$95$0 - 2.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+102], N[(x1 - N[(N[(x1 * N[(2.0 + N[(t$95$1 - N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -7.5000000000000006e48

   1. Initial program 24.3%

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

   3. Taylor expanded in x1 around 0 5.0%

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

   4. Taylor expanded in x1 around 0 4.9%

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

   5. Taylor expanded in x2 around 0 5.3%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x2 \cdot \left(6 \cdot x1 - 12\right)\right) + x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right)\right)}\right) \]

   6. Taylor expanded in x1 around 0 53.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{x1 \cdot \left(\left(-12 \cdot x2 + x1 \cdot \left(9 + 6 \cdot x2\right)\right) - 2\right)}\right) \]

   if -7.5000000000000006e48 < x1 < -3.09999999999999995e-266

   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. Add Preprocessing

   3. Taylor expanded in x1 around 0 84.6%

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

   4. Taylor expanded in x1 around 0 85.2%

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

   if -3.09999999999999995e-266 < x1 < 6.5000000000000004e-171

   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. Add Preprocessing

   3. Taylor expanded in x1 around 0 80.9%

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

   4. Taylor expanded in x1 around 0 81.1%

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

   5. Taylor expanded in x2 around 0 92.3%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x2 \cdot \left(6 \cdot x1 - 12\right)\right) + x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right)\right)}\right) \]

   6. Taylor expanded in x2 around inf 92.4%

      \[\leadsto x1 + \color{blue}{x2 \cdot \left(\left(x1 \cdot \left(6 \cdot x1 - 12\right) + \frac{x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right)}{x2}\right) - 6\right)} \]

   if 6.5000000000000004e-171 < x1 < 5e102

   1. Initial program 99.2%

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

   3. Taylor expanded in x1 around 0 76.4%

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

   4. Taylor expanded in x1 around 0 77.3%

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

   5. Taylor expanded in x2 around inf 77.7%

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

      1. *-commutative 77.7%

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

   7. Simplified 77.7%

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

   if 5e102 < x1

   1. Initial program 22.7%

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

   3. Taylor expanded in x1 around 0 5.4%

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

   4. Taylor expanded in x1 around 0 88.6%

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

   5. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.5 \cdot 10^{+48}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 6\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -3.1 \cdot 10^{-266}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - 3 \cdot \left(x1 \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6.5 \cdot 10^{-171}:\\ \;\;\;\;x1 + x2 \cdot \left(\left(x1 \cdot \left(x1 \cdot 6 - 12\right) + \frac{x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 9\right) - 2\right)}{x2}\right) - 6\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+102}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - x1 \cdot \left(x1 \cdot 3 + x2 \cdot 6\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot \left(x1 \cdot 3 + 9\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 74.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -3 \cdot 10^{+50}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 6\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -1.48 \cdot 10^{-263}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{-170}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{+102}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - x2 \cdot \left(x1 \cdot 6\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot \left(x1 \cdot 3 + 9\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -3e+50)
   (+
    x1
    (+ (* x2 -6.0) (* x1 (- (+ (* x2 -12.0) (* x1 (+ 9.0 (* x2 6.0)))) 2.0))))
   (if (<= x1 -1.48e-263)
     (+ x1 (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0))))
     (if (<= x1 4.2e-170)
       (+ x1 (+ (* x2 -6.0) (* x1 -2.0)))
       (if (<= x1 3.9e+102)
         (-
          x1
          (-
           (*
            x1
            (+ 2.0 (- (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))) (* x2 (* x1 6.0)))))
           (* x2 -6.0)))
         (+ x1 (- (* x2 -6.0) (* x1 (- 2.0 (* x1 (+ (* x1 3.0) 9.0)))))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3e+50) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	} else if (x1 <= -1.48e-263) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	} else if (x1 <= 4.2e-170) {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	} else if (x1 <= 3.9e+102) {
		tmp = x1 - ((x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x2 * (x1 * 6.0))))) - (x2 * -6.0));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * ((x1 * 3.0) + 9.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-3d+50)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((x2 * (-12.0d0)) + (x1 * (9.0d0 + (x2 * 6.0d0)))) - 2.0d0)))
    else if (x1 <= (-1.48d-263)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)))
    else if (x1 <= 4.2d-170) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (-2.0d0)))
    else if (x1 <= 3.9d+102) then
        tmp = x1 - ((x1 * (2.0d0 + ((4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))) - (x2 * (x1 * 6.0d0))))) - (x2 * (-6.0d0)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 - (x1 * ((x1 * 3.0d0) + 9.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3e+50) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	} else if (x1 <= -1.48e-263) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	} else if (x1 <= 4.2e-170) {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	} else if (x1 <= 3.9e+102) {
		tmp = x1 - ((x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x2 * (x1 * 6.0))))) - (x2 * -6.0));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * ((x1 * 3.0) + 9.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -3e+50:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)))
	elif x1 <= -1.48e-263:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)))
	elif x1 <= 4.2e-170:
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0))
	elif x1 <= 3.9e+102:
		tmp = x1 - ((x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x2 * (x1 * 6.0))))) - (x2 * -6.0))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * ((x1 * 3.0) + 9.0)))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -3e+50)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(x2 * -12.0) + Float64(x1 * Float64(9.0 + Float64(x2 * 6.0)))) - 2.0))));
	elseif (x1 <= -1.48e-263)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0))));
	elseif (x1 <= 4.2e-170)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * -2.0)));
	elseif (x1 <= 3.9e+102)
		tmp = Float64(x1 - Float64(Float64(x1 * Float64(2.0 + Float64(Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))) - Float64(x2 * Float64(x1 * 6.0))))) - Float64(x2 * -6.0)));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 - Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -3e+50)
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	elseif (x1 <= -1.48e-263)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	elseif (x1 <= 4.2e-170)
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	elseif (x1 <= 3.9e+102)
		tmp = x1 - ((x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x2 * (x1 * 6.0))))) - (x2 * -6.0));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * ((x1 * 3.0) + 9.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -3e+50], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(x2 * -12.0), $MachinePrecision] + N[(x1 * N[(9.0 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.48e-263], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.2e-170], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.9e+102], N[(x1 - N[(N[(x1 * N[(2.0 + N[(N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 - N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -2.9999999999999998e50

   1. Initial program 24.3%

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

   3. Taylor expanded in x1 around 0 5.0%

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

   4. Taylor expanded in x1 around 0 4.9%

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

   5. Taylor expanded in x2 around 0 5.3%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x2 \cdot \left(6 \cdot x1 - 12\right)\right) + x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right)\right)}\right) \]

   6. Taylor expanded in x1 around 0 53.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{x1 \cdot \left(\left(-12 \cdot x2 + x1 \cdot \left(9 + 6 \cdot x2\right)\right) - 2\right)}\right) \]

   if -2.9999999999999998e50 < x1 < -1.47999999999999998e-263

   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. Add Preprocessing

   3. Taylor expanded in x1 around 0 84.6%

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

   4. Taylor expanded in x1 around 0 84.7%

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

   if -1.47999999999999998e-263 < x1 < 4.2000000000000001e-170

   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. Add Preprocessing

   3. Taylor expanded in x1 around -inf 0.0%

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

   4. Taylor expanded in x1 around 0 92.3%

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

   if 4.2000000000000001e-170 < x1 < 3.8999999999999998e102

   1. Initial program 99.2%

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

   3. Taylor expanded in x1 around 0 76.4%

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

   4. Taylor expanded in x1 around 0 77.3%

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

   5. Taylor expanded in x2 around inf 76.3%

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

      1. *-commutative 76.3%

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

      2. *-commutative 76.3%

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

      3. associate-*r* 76.3%

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

   7. Simplified 76.3%

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

   if 3.8999999999999998e102 < x1

   1. Initial program 22.7%

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

   3. Taylor expanded in x1 around 0 5.4%

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

   4. Taylor expanded in x1 around 0 88.6%

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

   5. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3 \cdot 10^{+50}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 6\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -1.48 \cdot 10^{-263}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{-170}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{+102}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - x2 \cdot \left(x1 \cdot 6\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot \left(x1 \cdot 3 + 9\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 74.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3 + 9\right)\\ \mathbf{if}\;x1 \leq -1.7 \cdot 10^{+47}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 6\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -2.5 \cdot 10^{-261}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 6.2 \cdot 10^{-171}:\\ \;\;\;\;x1 + x2 \cdot \left(\left(x1 \cdot \left(x1 \cdot 6 - 12\right) + \frac{x1 \cdot \left(t\_0 - 2\right)}{x2}\right) - 6\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{+100}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - x2 \cdot \left(x1 \cdot 6\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - t\_0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ (* x1 3.0) 9.0))))
   (if (<= x1 -1.7e+47)
     (+
      x1
      (+
       (* x2 -6.0)
       (* x1 (- (+ (* x2 -12.0) (* x1 (+ 9.0 (* x2 6.0)))) 2.0))))
     (if (<= x1 -2.5e-261)
       (+ x1 (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0))))
       (if (<= x1 6.2e-171)
         (+
          x1
          (*
           x2
           (- (+ (* x1 (- (* x1 6.0) 12.0)) (/ (* x1 (- t_0 2.0)) x2)) 6.0)))
         (if (<= x1 4.2e+100)
           (-
            x1
            (-
             (*
              x1
              (+ 2.0 (- (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))) (* x2 (* x1 6.0)))))
             (* x2 -6.0)))
           (+ x1 (- (* x2 -6.0) (* x1 (- 2.0 t_0))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 3.0) + 9.0);
	double tmp;
	if (x1 <= -1.7e+47) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	} else if (x1 <= -2.5e-261) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	} else if (x1 <= 6.2e-171) {
		tmp = x1 + (x2 * (((x1 * ((x1 * 6.0) - 12.0)) + ((x1 * (t_0 - 2.0)) / x2)) - 6.0));
	} else if (x1 <= 4.2e+100) {
		tmp = x1 - ((x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x2 * (x1 * 6.0))))) - (x2 * -6.0));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - t_0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 * ((x1 * 3.0d0) + 9.0d0)
    if (x1 <= (-1.7d+47)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((x2 * (-12.0d0)) + (x1 * (9.0d0 + (x2 * 6.0d0)))) - 2.0d0)))
    else if (x1 <= (-2.5d-261)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)))
    else if (x1 <= 6.2d-171) then
        tmp = x1 + (x2 * (((x1 * ((x1 * 6.0d0) - 12.0d0)) + ((x1 * (t_0 - 2.0d0)) / x2)) - 6.0d0))
    else if (x1 <= 4.2d+100) then
        tmp = x1 - ((x1 * (2.0d0 + ((4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))) - (x2 * (x1 * 6.0d0))))) - (x2 * (-6.0d0)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 - t_0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 3.0) + 9.0);
	double tmp;
	if (x1 <= -1.7e+47) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	} else if (x1 <= -2.5e-261) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	} else if (x1 <= 6.2e-171) {
		tmp = x1 + (x2 * (((x1 * ((x1 * 6.0) - 12.0)) + ((x1 * (t_0 - 2.0)) / x2)) - 6.0));
	} else if (x1 <= 4.2e+100) {
		tmp = x1 - ((x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x2 * (x1 * 6.0))))) - (x2 * -6.0));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - t_0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((x1 * 3.0) + 9.0)
	tmp = 0
	if x1 <= -1.7e+47:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)))
	elif x1 <= -2.5e-261:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)))
	elif x1 <= 6.2e-171:
		tmp = x1 + (x2 * (((x1 * ((x1 * 6.0) - 12.0)) + ((x1 * (t_0 - 2.0)) / x2)) - 6.0))
	elif x1 <= 4.2e+100:
		tmp = x1 - ((x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x2 * (x1 * 6.0))))) - (x2 * -6.0))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - t_0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0))
	tmp = 0.0
	if (x1 <= -1.7e+47)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(x2 * -12.0) + Float64(x1 * Float64(9.0 + Float64(x2 * 6.0)))) - 2.0))));
	elseif (x1 <= -2.5e-261)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0))));
	elseif (x1 <= 6.2e-171)
		tmp = Float64(x1 + Float64(x2 * Float64(Float64(Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)) + Float64(Float64(x1 * Float64(t_0 - 2.0)) / x2)) - 6.0)));
	elseif (x1 <= 4.2e+100)
		tmp = Float64(x1 - Float64(Float64(x1 * Float64(2.0 + Float64(Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))) - Float64(x2 * Float64(x1 * 6.0))))) - Float64(x2 * -6.0)));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 - t_0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((x1 * 3.0) + 9.0);
	tmp = 0.0;
	if (x1 <= -1.7e+47)
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	elseif (x1 <= -2.5e-261)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	elseif (x1 <= 6.2e-171)
		tmp = x1 + (x2 * (((x1 * ((x1 * 6.0) - 12.0)) + ((x1 * (t_0 - 2.0)) / x2)) - 6.0));
	elseif (x1 <= 4.2e+100)
		tmp = x1 - ((x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x2 * (x1 * 6.0))))) - (x2 * -6.0));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - t_0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.7e+47], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(x2 * -12.0), $MachinePrecision] + N[(x1 * N[(9.0 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.5e-261], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6.2e-171], N[(x1 + N[(x2 * N[(N[(N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(t$95$0 - 2.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.2e+100], N[(x1 - N[(N[(x1 * N[(2.0 + N[(N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -1.6999999999999999e47

   1. Initial program 24.3%

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

   3. Taylor expanded in x1 around 0 5.0%

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

   4. Taylor expanded in x1 around 0 4.9%

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

   5. Taylor expanded in x2 around 0 5.3%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x2 \cdot \left(6 \cdot x1 - 12\right)\right) + x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right)\right)}\right) \]

   6. Taylor expanded in x1 around 0 53.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{x1 \cdot \left(\left(-12 \cdot x2 + x1 \cdot \left(9 + 6 \cdot x2\right)\right) - 2\right)}\right) \]

   if -1.6999999999999999e47 < x1 < -2.4999999999999999e-261

   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. Add Preprocessing

   3. Taylor expanded in x1 around 0 84.6%

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

   4. Taylor expanded in x1 around 0 84.7%

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

   if -2.4999999999999999e-261 < x1 < 6.2000000000000001e-171

   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. Add Preprocessing

   3. Taylor expanded in x1 around 0 80.9%

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

   4. Taylor expanded in x1 around 0 81.1%

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

   5. Taylor expanded in x2 around 0 92.3%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x2 \cdot \left(6 \cdot x1 - 12\right)\right) + x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right)\right)}\right) \]

   6. Taylor expanded in x2 around inf 92.4%

      \[\leadsto x1 + \color{blue}{x2 \cdot \left(\left(x1 \cdot \left(6 \cdot x1 - 12\right) + \frac{x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right)}{x2}\right) - 6\right)} \]

   if 6.2000000000000001e-171 < x1 < 4.1999999999999997e100

   1. Initial program 99.2%

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

   3. Taylor expanded in x1 around 0 76.4%

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

   4. Taylor expanded in x1 around 0 77.3%

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

   5. Taylor expanded in x2 around inf 76.3%

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

      1. *-commutative 76.3%

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

      2. *-commutative 76.3%

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

      3. associate-*r* 76.3%

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

   7. Simplified 76.3%

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

   if 4.1999999999999997e100 < x1

   1. Initial program 22.7%

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

   3. Taylor expanded in x1 around 0 5.4%

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

   4. Taylor expanded in x1 around 0 88.6%

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

   5. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.7 \cdot 10^{+47}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 6\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -2.5 \cdot 10^{-261}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 6.2 \cdot 10^{-171}:\\ \;\;\;\;x1 + x2 \cdot \left(\left(x1 \cdot \left(x1 \cdot 6 - 12\right) + \frac{x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 9\right) - 2\right)}{x2}\right) - 6\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{+100}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - x2 \cdot \left(x1 \cdot 6\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot \left(x1 \cdot 3 + 9\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 79.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3 + 9\right)\\ \mathbf{if}\;x1 \leq -4.6 \cdot 10^{+49}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 6\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 3.1 \cdot 10^{+62}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - \left(x1 \cdot \left(2 - t\_0\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x2 \cdot \left(x1 \cdot 6 + \frac{t\_0}{x2}\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ (* x1 3.0) 9.0))))
   (if (<= x1 -4.6e+49)
     (+
      x1
      (+
       (* x2 -6.0)
       (* x1 (- (+ (* x2 -12.0) (* x1 (+ 9.0 (* x2 6.0)))) 2.0))))
     (if (<= x1 3.1e+62)
       (+
        x1
        (-
         (* x2 -6.0)
         (+
          (* x1 (- 2.0 t_0))
          (* x2 (- (* x1 (- 12.0 (* x1 6.0))) (* 8.0 (* x1 x2)))))))
       (+
        x1
        (+
         (* x2 -6.0)
         (*
          x1
          (-
           (+
            (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))
            (* x2 (+ (* x1 6.0) (/ t_0 x2))))
           2.0))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 3.0) + 9.0);
	double tmp;
	if (x1 <= -4.6e+49) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	} else if (x1 <= 3.1e+62) {
		tmp = x1 + ((x2 * -6.0) - ((x1 * (2.0 - t_0)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x2 * ((x1 * 6.0) + (t_0 / x2)))) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 * ((x1 * 3.0d0) + 9.0d0)
    if (x1 <= (-4.6d+49)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((x2 * (-12.0d0)) + (x1 * (9.0d0 + (x2 * 6.0d0)))) - 2.0d0)))
    else if (x1 <= 3.1d+62) then
        tmp = x1 + ((x2 * (-6.0d0)) - ((x1 * (2.0d0 - t_0)) + (x2 * ((x1 * (12.0d0 - (x1 * 6.0d0))) - (8.0d0 * (x1 * x2))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + (x2 * ((x1 * 6.0d0) + (t_0 / x2)))) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 3.0) + 9.0);
	double tmp;
	if (x1 <= -4.6e+49) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	} else if (x1 <= 3.1e+62) {
		tmp = x1 + ((x2 * -6.0) - ((x1 * (2.0 - t_0)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x2 * ((x1 * 6.0) + (t_0 / x2)))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((x1 * 3.0) + 9.0)
	tmp = 0
	if x1 <= -4.6e+49:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)))
	elif x1 <= 3.1e+62:
		tmp = x1 + ((x2 * -6.0) - ((x1 * (2.0 - t_0)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x2 * ((x1 * 6.0) + (t_0 / x2)))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0))
	tmp = 0.0
	if (x1 <= -4.6e+49)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(x2 * -12.0) + Float64(x1 * Float64(9.0 + Float64(x2 * 6.0)))) - 2.0))));
	elseif (x1 <= 3.1e+62)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(Float64(x1 * Float64(2.0 - t_0)) + Float64(x2 * Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(8.0 * Float64(x1 * x2)))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) + Float64(x2 * Float64(Float64(x1 * 6.0) + Float64(t_0 / x2)))) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((x1 * 3.0) + 9.0);
	tmp = 0.0;
	if (x1 <= -4.6e+49)
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	elseif (x1 <= 3.1e+62)
		tmp = x1 + ((x2 * -6.0) - ((x1 * (2.0 - t_0)) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x2 * ((x1 * 6.0) + (t_0 / x2)))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.6e+49], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(x2 * -12.0), $MachinePrecision] + N[(x1 * N[(9.0 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.1e+62], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(N[(x1 * N[(2.0 - t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * 6.0), $MachinePrecision] + N[(t$95$0 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4.60000000000000004e49

   1. Initial program 24.3%

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

   3. Taylor expanded in x1 around 0 5.0%

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

   4. Taylor expanded in x1 around 0 4.9%

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

   5. Taylor expanded in x2 around 0 5.3%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x2 \cdot \left(6 \cdot x1 - 12\right)\right) + x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right)\right)}\right) \]

   6. Taylor expanded in x1 around 0 53.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{x1 \cdot \left(\left(-12 \cdot x2 + x1 \cdot \left(9 + 6 \cdot x2\right)\right) - 2\right)}\right) \]

   if -4.60000000000000004e49 < x1 < 3.10000000000000014e62

   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. Add Preprocessing

   3. Taylor expanded in x1 around 0 81.8%

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

   4. Taylor expanded in x1 around 0 82.3%

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

   5. Taylor expanded in x2 around 0 89.7%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right)\right)}\right) \]

   if 3.10000000000000014e62 < x1

   1. Initial program 30.6%

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

   3. Taylor expanded in x1 around 0 11.1%

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

   4. Taylor expanded in x1 around 0 86.0%

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

   5. Taylor expanded in x2 around inf 96.2%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.6 \cdot 10^{+49}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 6\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 3.1 \cdot 10^{+62}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - \left(x1 \cdot \left(2 - x1 \cdot \left(x1 \cdot 3 + 9\right)\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x2 \cdot \left(x1 \cdot 6 + \frac{x1 \cdot \left(x1 \cdot 3 + 9\right)}{x2}\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 79.5% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(2 - x1 \cdot \left(x1 \cdot 3 + 9\right)\right)\\ \mathbf{if}\;x1 \leq -1.7 \cdot 10^{+49}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 6\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+100}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - \left(t\_0 + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (- 2.0 (* x1 (+ (* x1 3.0) 9.0))))))
   (if (<= x1 -1.7e+49)
     (+
      x1
      (+
       (* x2 -6.0)
       (* x1 (- (+ (* x2 -12.0) (* x1 (+ 9.0 (* x2 6.0)))) 2.0))))
     (if (<= x1 5e+100)
       (+
        x1
        (-
         (* x2 -6.0)
         (+ t_0 (* x2 (- (* x1 (- 12.0 (* x1 6.0))) (* 8.0 (* x1 x2)))))))
       (+ x1 (- (* x2 -6.0) t_0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (2.0 - (x1 * ((x1 * 3.0) + 9.0)));
	double tmp;
	if (x1 <= -1.7e+49) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	} else if (x1 <= 5e+100) {
		tmp = x1 + ((x2 * -6.0) - (t_0 + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	} else {
		tmp = x1 + ((x2 * -6.0) - t_0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 * (2.0d0 - (x1 * ((x1 * 3.0d0) + 9.0d0)))
    if (x1 <= (-1.7d+49)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((x2 * (-12.0d0)) + (x1 * (9.0d0 + (x2 * 6.0d0)))) - 2.0d0)))
    else if (x1 <= 5d+100) then
        tmp = x1 + ((x2 * (-6.0d0)) - (t_0 + (x2 * ((x1 * (12.0d0 - (x1 * 6.0d0))) - (8.0d0 * (x1 * x2))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - t_0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (2.0 - (x1 * ((x1 * 3.0) + 9.0)));
	double tmp;
	if (x1 <= -1.7e+49) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	} else if (x1 <= 5e+100) {
		tmp = x1 + ((x2 * -6.0) - (t_0 + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	} else {
		tmp = x1 + ((x2 * -6.0) - t_0);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (2.0 - (x1 * ((x1 * 3.0) + 9.0)))
	tmp = 0
	if x1 <= -1.7e+49:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)))
	elif x1 <= 5e+100:
		tmp = x1 + ((x2 * -6.0) - (t_0 + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))))
	else:
		tmp = x1 + ((x2 * -6.0) - t_0)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(2.0 - Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0))))
	tmp = 0.0
	if (x1 <= -1.7e+49)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(x2 * -12.0) + Float64(x1 * Float64(9.0 + Float64(x2 * 6.0)))) - 2.0))));
	elseif (x1 <= 5e+100)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(t_0 + Float64(x2 * Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(8.0 * Float64(x1 * x2)))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - t_0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (2.0 - (x1 * ((x1 * 3.0) + 9.0)));
	tmp = 0.0;
	if (x1 <= -1.7e+49)
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	elseif (x1 <= 5e+100)
		tmp = x1 + ((x2 * -6.0) - (t_0 + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	else
		tmp = x1 + ((x2 * -6.0) - t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(2.0 - N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.7e+49], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(x2 * -12.0), $MachinePrecision] + N[(x1 * N[(9.0 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+100], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(t$95$0 + N[(x2 * N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - t$95$0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.7e49

   1. Initial program 24.3%

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

   3. Taylor expanded in x1 around 0 5.0%

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

   4. Taylor expanded in x1 around 0 4.9%

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

   5. Taylor expanded in x2 around 0 5.3%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x2 \cdot \left(6 \cdot x1 - 12\right)\right) + x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right)\right)}\right) \]

   6. Taylor expanded in x1 around 0 53.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{x1 \cdot \left(\left(-12 \cdot x2 + x1 \cdot \left(9 + 6 \cdot x2\right)\right) - 2\right)}\right) \]

   if -1.7e49 < x1 < 4.9999999999999999e100

   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. Add Preprocessing

   3. Taylor expanded in x1 around 0 81.3%

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

   4. Taylor expanded in x1 around 0 81.7%

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

   5. Taylor expanded in x2 around 0 88.9%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right)\right)}\right) \]

   if 4.9999999999999999e100 < x1

   1. Initial program 22.7%

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

   3. Taylor expanded in x1 around 0 5.4%

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

   4. Taylor expanded in x1 around 0 88.6%

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

   5. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.7 \cdot 10^{+49}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 6\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+100}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - \left(x1 \cdot \left(2 - x1 \cdot \left(x1 \cdot 3 + 9\right)\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot \left(x1 \cdot 3 + 9\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 70.8% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{if}\;x1 \leq -8.2 \cdot 10^{+79}:\\ \;\;\;\;x1 + x2 \cdot \left(x1 \cdot \left(x1 \cdot 6 - 12\right) - 6\right)\\ \mathbf{elif}\;x1 \leq -7.1 \cdot 10^{-266}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 6.2 \cdot 10^{-171}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 3.8 \cdot 10^{+102}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot \left(x1 \cdot 3 + 9\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (+
          x1
          (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0))))))
   (if (<= x1 -8.2e+79)
     (+ x1 (* x2 (- (* x1 (- (* x1 6.0) 12.0)) 6.0)))
     (if (<= x1 -7.1e-266)
       t_0
       (if (<= x1 6.2e-171)
         (+ x1 (+ (* x2 -6.0) (* x1 -2.0)))
         (if (<= x1 3.8e+102)
           t_0
           (+
            x1
            (- (* x2 -6.0) (* x1 (- 2.0 (* x1 (+ (* x1 3.0) 9.0))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	double tmp;
	if (x1 <= -8.2e+79) {
		tmp = x1 + (x2 * ((x1 * ((x1 * 6.0) - 12.0)) - 6.0));
	} else if (x1 <= -7.1e-266) {
		tmp = t_0;
	} else if (x1 <= 6.2e-171) {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	} else if (x1 <= 3.8e+102) {
		tmp = t_0;
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * ((x1 * 3.0) + 9.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)))
    if (x1 <= (-8.2d+79)) then
        tmp = x1 + (x2 * ((x1 * ((x1 * 6.0d0) - 12.0d0)) - 6.0d0))
    else if (x1 <= (-7.1d-266)) then
        tmp = t_0
    else if (x1 <= 6.2d-171) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (-2.0d0)))
    else if (x1 <= 3.8d+102) then
        tmp = t_0
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 - (x1 * ((x1 * 3.0d0) + 9.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	double tmp;
	if (x1 <= -8.2e+79) {
		tmp = x1 + (x2 * ((x1 * ((x1 * 6.0) - 12.0)) - 6.0));
	} else if (x1 <= -7.1e-266) {
		tmp = t_0;
	} else if (x1 <= 6.2e-171) {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	} else if (x1 <= 3.8e+102) {
		tmp = t_0;
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * ((x1 * 3.0) + 9.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)))
	tmp = 0
	if x1 <= -8.2e+79:
		tmp = x1 + (x2 * ((x1 * ((x1 * 6.0) - 12.0)) - 6.0))
	elif x1 <= -7.1e-266:
		tmp = t_0
	elif x1 <= 6.2e-171:
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0))
	elif x1 <= 3.8e+102:
		tmp = t_0
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * ((x1 * 3.0) + 9.0)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0))))
	tmp = 0.0
	if (x1 <= -8.2e+79)
		tmp = Float64(x1 + Float64(x2 * Float64(Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)) - 6.0)));
	elseif (x1 <= -7.1e-266)
		tmp = t_0;
	elseif (x1 <= 6.2e-171)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * -2.0)));
	elseif (x1 <= 3.8e+102)
		tmp = t_0;
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 - Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	tmp = 0.0;
	if (x1 <= -8.2e+79)
		tmp = x1 + (x2 * ((x1 * ((x1 * 6.0) - 12.0)) - 6.0));
	elseif (x1 <= -7.1e-266)
		tmp = t_0;
	elseif (x1 <= 6.2e-171)
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	elseif (x1 <= 3.8e+102)
		tmp = t_0;
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * ((x1 * 3.0) + 9.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -8.2e+79], N[(x1 + N[(x2 * N[(N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -7.1e-266], t$95$0, If[LessEqual[x1, 6.2e-171], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.8e+102], t$95$0, N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 - N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -8.2e79

   1. Initial program 13.9%

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

   3. Taylor expanded in x1 around 0 5.6%

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

   4. Taylor expanded in x1 around 0 5.6%

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

   5. Taylor expanded in x2 around 0 5.8%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x2 \cdot \left(6 \cdot x1 - 12\right)\right) + x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right)\right)}\right) \]

   6. Taylor expanded in x2 around inf 39.4%

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

   if -8.2e79 < x1 < -7.09999999999999955e-266 or 6.2000000000000001e-171 < x1 < 3.79999999999999979e102

   1. Initial program 99.2%

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

   3. Taylor expanded in x1 around 0 78.5%

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

   4. Taylor expanded in x1 around 0 78.6%

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

   if -7.09999999999999955e-266 < x1 < 6.2000000000000001e-171

   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. Add Preprocessing

   3. Taylor expanded in x1 around -inf 0.0%

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

   4. Taylor expanded in x1 around 0 92.3%

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

   if 3.79999999999999979e102 < x1

   1. Initial program 22.7%

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

   3. Taylor expanded in x1 around 0 5.4%

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

   4. Taylor expanded in x1 around 0 88.6%

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

   5. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -8.2 \cdot 10^{+79}:\\ \;\;\;\;x1 + x2 \cdot \left(x1 \cdot \left(x1 \cdot 6 - 12\right) - 6\right)\\ \mathbf{elif}\;x1 \leq -7.1 \cdot 10^{-266}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 6.2 \cdot 10^{-171}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 3.8 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot \left(x1 \cdot 3 + 9\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 74.5% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{if}\;x1 \leq -3.1 \cdot 10^{+50}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 6\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -5.9 \cdot 10^{-266}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 9.6 \cdot 10^{-171}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{+102}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot \left(x1 \cdot 3 + 9\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (+
          x1
          (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0))))))
   (if (<= x1 -3.1e+50)
     (+
      x1
      (+
       (* x2 -6.0)
       (* x1 (- (+ (* x2 -12.0) (* x1 (+ 9.0 (* x2 6.0)))) 2.0))))
     (if (<= x1 -5.9e-266)
       t_0
       (if (<= x1 9.6e-171)
         (+ x1 (+ (* x2 -6.0) (* x1 -2.0)))
         (if (<= x1 3.9e+102)
           t_0
           (+
            x1
            (- (* x2 -6.0) (* x1 (- 2.0 (* x1 (+ (* x1 3.0) 9.0))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	double tmp;
	if (x1 <= -3.1e+50) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	} else if (x1 <= -5.9e-266) {
		tmp = t_0;
	} else if (x1 <= 9.6e-171) {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	} else if (x1 <= 3.9e+102) {
		tmp = t_0;
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * ((x1 * 3.0) + 9.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)))
    if (x1 <= (-3.1d+50)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((x2 * (-12.0d0)) + (x1 * (9.0d0 + (x2 * 6.0d0)))) - 2.0d0)))
    else if (x1 <= (-5.9d-266)) then
        tmp = t_0
    else if (x1 <= 9.6d-171) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (-2.0d0)))
    else if (x1 <= 3.9d+102) then
        tmp = t_0
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 - (x1 * ((x1 * 3.0d0) + 9.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	double tmp;
	if (x1 <= -3.1e+50) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	} else if (x1 <= -5.9e-266) {
		tmp = t_0;
	} else if (x1 <= 9.6e-171) {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	} else if (x1 <= 3.9e+102) {
		tmp = t_0;
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * ((x1 * 3.0) + 9.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)))
	tmp = 0
	if x1 <= -3.1e+50:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)))
	elif x1 <= -5.9e-266:
		tmp = t_0
	elif x1 <= 9.6e-171:
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0))
	elif x1 <= 3.9e+102:
		tmp = t_0
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * ((x1 * 3.0) + 9.0)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0))))
	tmp = 0.0
	if (x1 <= -3.1e+50)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(x2 * -12.0) + Float64(x1 * Float64(9.0 + Float64(x2 * 6.0)))) - 2.0))));
	elseif (x1 <= -5.9e-266)
		tmp = t_0;
	elseif (x1 <= 9.6e-171)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * -2.0)));
	elseif (x1 <= 3.9e+102)
		tmp = t_0;
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 - Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	tmp = 0.0;
	if (x1 <= -3.1e+50)
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * (9.0 + (x2 * 6.0)))) - 2.0)));
	elseif (x1 <= -5.9e-266)
		tmp = t_0;
	elseif (x1 <= 9.6e-171)
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	elseif (x1 <= 3.9e+102)
		tmp = t_0;
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * ((x1 * 3.0) + 9.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3.1e+50], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(x2 * -12.0), $MachinePrecision] + N[(x1 * N[(9.0 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5.9e-266], t$95$0, If[LessEqual[x1, 9.6e-171], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.9e+102], t$95$0, N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 - N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -3.10000000000000003e50

   1. Initial program 24.3%

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

   3. Taylor expanded in x1 around 0 5.0%

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

   4. Taylor expanded in x1 around 0 4.9%

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

   5. Taylor expanded in x2 around 0 5.3%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x2 \cdot \left(6 \cdot x1 - 12\right)\right) + x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right)\right)}\right) \]

   6. Taylor expanded in x1 around 0 53.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{x1 \cdot \left(\left(-12 \cdot x2 + x1 \cdot \left(9 + 6 \cdot x2\right)\right) - 2\right)}\right) \]

   if -3.10000000000000003e50 < x1 < -5.90000000000000025e-266 or 9.59999999999999947e-171 < x1 < 3.8999999999999998e102

   1. Initial program 99.2%

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

   3. Taylor expanded in x1 around 0 81.4%

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

   4. Taylor expanded in x1 around 0 81.4%

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

   if -5.90000000000000025e-266 < x1 < 9.59999999999999947e-171

   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. Add Preprocessing

   3. Taylor expanded in x1 around -inf 0.0%

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

   4. Taylor expanded in x1 around 0 92.3%

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

   if 3.8999999999999998e102 < x1

   1. Initial program 22.7%

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

   3. Taylor expanded in x1 around 0 5.4%

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

   4. Taylor expanded in x1 around 0 88.6%

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

   5. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.1 \cdot 10^{+50}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot -12 + x1 \cdot \left(9 + x2 \cdot 6\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -5.9 \cdot 10^{-266}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 9.6 \cdot 10^{-171}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot \left(x1 \cdot 3 + 9\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 52.9% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + 1\right)\\ \mathbf{if}\;x2 \leq -6.2 \cdot 10^{+121}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x2 \leq 1.05 \cdot 10^{-41}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 - 2\right)\right)\\ \mathbf{elif}\;x2 \leq 3.3 \cdot 10^{+177}:\\ \;\;\;\;x1 + x2 \cdot \left(x1 \cdot \left(x1 \cdot 6 - 12\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* x1 (+ (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 1.0)))))
   (if (<= x2 -6.2e+121)
     t_0
     (if (<= x2 1.05e-41)
       (+ x1 (+ (* x2 -6.0) (* x1 (- (* x2 -12.0) 2.0))))
       (if (<= x2 3.3e+177)
         (+ x1 (* x2 (- (* x1 (- (* x1 6.0) 12.0)) 6.0)))
         t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + 1.0));
	double tmp;
	if (x2 <= -6.2e+121) {
		tmp = t_0;
	} else if (x2 <= 1.05e-41) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x2 * -12.0) - 2.0)));
	} else if (x2 <= 3.3e+177) {
		tmp = x1 + (x2 * ((x1 * ((x1 * 6.0) - 12.0)) - 6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + 1.0d0))
    if (x2 <= (-6.2d+121)) then
        tmp = t_0
    else if (x2 <= 1.05d-41) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x2 * (-12.0d0)) - 2.0d0)))
    else if (x2 <= 3.3d+177) then
        tmp = x1 + (x2 * ((x1 * ((x1 * 6.0d0) - 12.0d0)) - 6.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + 1.0));
	double tmp;
	if (x2 <= -6.2e+121) {
		tmp = t_0;
	} else if (x2 <= 1.05e-41) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x2 * -12.0) - 2.0)));
	} else if (x2 <= 3.3e+177) {
		tmp = x1 + (x2 * ((x1 * ((x1 * 6.0) - 12.0)) - 6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + 1.0))
	tmp = 0
	if x2 <= -6.2e+121:
		tmp = t_0
	elif x2 <= 1.05e-41:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x2 * -12.0) - 2.0)))
	elif x2 <= 3.3e+177:
		tmp = x1 + (x2 * ((x1 * ((x1 * 6.0) - 12.0)) - 6.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) + 1.0)))
	tmp = 0.0
	if (x2 <= -6.2e+121)
		tmp = t_0;
	elseif (x2 <= 1.05e-41)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x2 * -12.0) - 2.0))));
	elseif (x2 <= 3.3e+177)
		tmp = Float64(x1 + Float64(x2 * Float64(Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)) - 6.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + 1.0));
	tmp = 0.0;
	if (x2 <= -6.2e+121)
		tmp = t_0;
	elseif (x2 <= 1.05e-41)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x2 * -12.0) - 2.0)));
	elseif (x2 <= 3.3e+177)
		tmp = x1 + (x2 * ((x1 * ((x1 * 6.0) - 12.0)) - 6.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x2, -6.2e+121], t$95$0, If[LessEqual[x2, 1.05e-41], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x2, 3.3e+177], N[(x1 + N[(x2 * N[(N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -6.20000000000000016e121 or 3.3000000000000001e177 < x2

   1. Initial program 72.2%

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

   3. Taylor expanded in x1 around 0 56.4%

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

   4. Taylor expanded in x1 around inf 71.8%

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

   if -6.20000000000000016e121 < x2 < 1.05000000000000006e-41

   1. Initial program 77.2%

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

   3. Taylor expanded in x1 around 0 57.6%

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

   4. Taylor expanded in x1 around 0 74.4%

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

   5. Taylor expanded in x2 around 0 67.7%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x2 \cdot \left(6 \cdot x1 - 12\right)\right) + x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right)\right)}\right) \]

   6. Taylor expanded in x1 around 0 57.0%

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

   if 1.05000000000000006e-41 < x2 < 3.3000000000000001e177

   1. Initial program 67.3%

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

   3. Taylor expanded in x1 around 0 50.4%

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

   4. Taylor expanded in x1 around 0 65.6%

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

   5. Taylor expanded in x2 around 0 56.2%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x2 \cdot \left(6 \cdot x1 - 12\right)\right) + x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right)\right)}\right) \]

   6. Taylor expanded in x2 around inf 71.7%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -6.2 \cdot 10^{+121}:\\ \;\;\;\;x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + 1\right)\\ \mathbf{elif}\;x2 \leq 1.05 \cdot 10^{-41}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 - 2\right)\right)\\ \mathbf{elif}\;x2 \leq 3.3 \cdot 10^{+177}:\\ \;\;\;\;x1 + x2 \cdot \left(x1 \cdot \left(x1 \cdot 6 - 12\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 62.3% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + 1\right)\\ \mathbf{if}\;x2 \leq -7.5 \cdot 10^{+121}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x2 \leq 1.55 \cdot 10^{-32}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot \left(x1 \cdot 3 + 9\right)\right)\right)\\ \mathbf{elif}\;x2 \leq 5.4 \cdot 10^{+175}:\\ \;\;\;\;x1 + x2 \cdot \left(x1 \cdot \left(x1 \cdot 6 - 12\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* x1 (+ (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 1.0)))))
   (if (<= x2 -7.5e+121)
     t_0
     (if (<= x2 1.55e-32)
       (+ x1 (- (* x2 -6.0) (* x1 (- 2.0 (* x1 (+ (* x1 3.0) 9.0))))))
       (if (<= x2 5.4e+175)
         (+ x1 (* x2 (- (* x1 (- (* x1 6.0) 12.0)) 6.0)))
         t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + 1.0));
	double tmp;
	if (x2 <= -7.5e+121) {
		tmp = t_0;
	} else if (x2 <= 1.55e-32) {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * ((x1 * 3.0) + 9.0)))));
	} else if (x2 <= 5.4e+175) {
		tmp = x1 + (x2 * ((x1 * ((x1 * 6.0) - 12.0)) - 6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + 1.0d0))
    if (x2 <= (-7.5d+121)) then
        tmp = t_0
    else if (x2 <= 1.55d-32) then
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 - (x1 * ((x1 * 3.0d0) + 9.0d0)))))
    else if (x2 <= 5.4d+175) then
        tmp = x1 + (x2 * ((x1 * ((x1 * 6.0d0) - 12.0d0)) - 6.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + 1.0));
	double tmp;
	if (x2 <= -7.5e+121) {
		tmp = t_0;
	} else if (x2 <= 1.55e-32) {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * ((x1 * 3.0) + 9.0)))));
	} else if (x2 <= 5.4e+175) {
		tmp = x1 + (x2 * ((x1 * ((x1 * 6.0) - 12.0)) - 6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + 1.0))
	tmp = 0
	if x2 <= -7.5e+121:
		tmp = t_0
	elif x2 <= 1.55e-32:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * ((x1 * 3.0) + 9.0)))))
	elif x2 <= 5.4e+175:
		tmp = x1 + (x2 * ((x1 * ((x1 * 6.0) - 12.0)) - 6.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) + 1.0)))
	tmp = 0.0
	if (x2 <= -7.5e+121)
		tmp = t_0;
	elseif (x2 <= 1.55e-32)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 - Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0))))));
	elseif (x2 <= 5.4e+175)
		tmp = Float64(x1 + Float64(x2 * Float64(Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)) - 6.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + 1.0));
	tmp = 0.0;
	if (x2 <= -7.5e+121)
		tmp = t_0;
	elseif (x2 <= 1.55e-32)
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * ((x1 * 3.0) + 9.0)))));
	elseif (x2 <= 5.4e+175)
		tmp = x1 + (x2 * ((x1 * ((x1 * 6.0) - 12.0)) - 6.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x2, -7.5e+121], t$95$0, If[LessEqual[x2, 1.55e-32], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 - N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x2, 5.4e+175], N[(x1 + N[(x2 * N[(N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -7.49999999999999965e121 or 5.4000000000000002e175 < x2

   1. Initial program 72.2%

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

   3. Taylor expanded in x1 around 0 56.4%

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

   4. Taylor expanded in x1 around inf 71.8%

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

   if -7.49999999999999965e121 < x2 < 1.55000000000000005e-32

   1. Initial program 77.3%

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

   3. Taylor expanded in x1 around 0 57.2%

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

   4. Taylor expanded in x1 around 0 74.6%

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

   5. Taylor expanded in x2 around 0 72.7%

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

      1. *-commutative 72.7%

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

   7. Simplified 72.7%

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

   if 1.55000000000000005e-32 < x2 < 5.4000000000000002e175

   1. Initial program 66.6%

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

   3. Taylor expanded in x1 around 0 51.4%

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

   4. Taylor expanded in x1 around 0 64.8%

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

   5. Taylor expanded in x2 around 0 55.2%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x2 \cdot \left(6 \cdot x1 - 12\right)\right) + x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right)\right)}\right) \]

   6. Taylor expanded in x2 around inf 73.2%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -7.5 \cdot 10^{+121}:\\ \;\;\;\;x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + 1\right)\\ \mathbf{elif}\;x2 \leq 1.55 \cdot 10^{-32}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot \left(x1 \cdot 3 + 9\right)\right)\right)\\ \mathbf{elif}\;x2 \leq 5.4 \cdot 10^{+175}:\\ \;\;\;\;x1 + x2 \cdot \left(x1 \cdot \left(x1 \cdot 6 - 12\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 51.1% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -3.7 \cdot 10^{+17} \lor \neg \left(x1 \leq 1.4\right):\\ \;\;\;\;x1 + x2 \cdot \left(x1 \cdot \left(x1 \cdot 6 - 12\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -3.7e+17) (not (<= x1 1.4)))
   (+ x1 (* x2 (- (* x1 (- (* x1 6.0) 12.0)) 6.0)))
   (+ x1 (+ (* x2 -6.0) (* x1 -2.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -3.7e+17) || !(x1 <= 1.4)) {
		tmp = x1 + (x2 * ((x1 * ((x1 * 6.0) - 12.0)) - 6.0));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-3.7d+17)) .or. (.not. (x1 <= 1.4d0))) then
        tmp = x1 + (x2 * ((x1 * ((x1 * 6.0d0) - 12.0d0)) - 6.0d0))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -3.7e+17) || !(x1 <= 1.4)) {
		tmp = x1 + (x2 * ((x1 * ((x1 * 6.0) - 12.0)) - 6.0));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -3.7e+17) or not (x1 <= 1.4):
		tmp = x1 + (x2 * ((x1 * ((x1 * 6.0) - 12.0)) - 6.0))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -3.7e+17) || !(x1 <= 1.4))
		tmp = Float64(x1 + Float64(x2 * Float64(Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)) - 6.0)));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -3.7e+17) || ~((x1 <= 1.4)))
		tmp = x1 + (x2 * ((x1 * ((x1 * 6.0) - 12.0)) - 6.0));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -3.7e+17], N[Not[LessEqual[x1, 1.4]], $MachinePrecision]], N[(x1 + N[(x2 * N[(N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -3.7e17 or 1.3999999999999999 < x1

   1. Initial program 39.0%

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

   3. Taylor expanded in x1 around 0 10.5%

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

   4. Taylor expanded in x1 around 0 44.9%

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

   5. Taylor expanded in x2 around 0 33.9%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x2 \cdot \left(6 \cdot x1 - 12\right)\right) + x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right)\right)}\right) \]

   6. Taylor expanded in x2 around inf 33.0%

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

   if -3.7e17 < x1 < 1.3999999999999999

   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. Add Preprocessing

   3. Taylor expanded in x1 around -inf 36.2%

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

   4. Taylor expanded in x1 around 0 69.1%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.7 \cdot 10^{+17} \lor \neg \left(x1 \leq 1.4\right):\\ \;\;\;\;x1 + x2 \cdot \left(x1 \cdot \left(x1 \cdot 6 - 12\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 48.4% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq 10^{-41}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot \left(x1 \cdot \left(x1 \cdot 6 - 12\right) - 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 1e-41)
   (+ x1 (+ (* x2 -6.0) (* x1 (- (* x2 -12.0) 2.0))))
   (+ x1 (* x2 (- (* x1 (- (* x1 6.0) 12.0)) 6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= 1e-41) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x2 * -12.0) - 2.0)));
	} else {
		tmp = x1 + (x2 * ((x1 * ((x1 * 6.0) - 12.0)) - 6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x2 <= 1d-41) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x2 * (-12.0d0)) - 2.0d0)))
    else
        tmp = x1 + (x2 * ((x1 * ((x1 * 6.0d0) - 12.0d0)) - 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x2 <= 1e-41) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x2 * -12.0) - 2.0)));
	} else {
		tmp = x1 + (x2 * ((x1 * ((x1 * 6.0) - 12.0)) - 6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= 1e-41:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x2 * -12.0) - 2.0)))
	else:
		tmp = x1 + (x2 * ((x1 * ((x1 * 6.0) - 12.0)) - 6.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= 1e-41)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x2 * -12.0) - 2.0))));
	else
		tmp = Float64(x1 + Float64(x2 * Float64(Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)) - 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= 1e-41)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x2 * -12.0) - 2.0)));
	else
		tmp = x1 + (x2 * ((x1 * ((x1 * 6.0) - 12.0)) - 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, 1e-41], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x2 * N[(N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < 1.00000000000000001e-41

   1. Initial program 76.1%

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

   3. Taylor expanded in x1 around 0 56.8%

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

   4. Taylor expanded in x1 around 0 70.9%

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

   5. Taylor expanded in x2 around 0 57.8%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x2 \cdot \left(6 \cdot x1 - 12\right)\right) + x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right)\right)}\right) \]

   6. Taylor expanded in x1 around 0 52.6%

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

   if 1.00000000000000001e-41 < x2

   1. Initial program 69.3%

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

   3. Taylor expanded in x1 around 0 54.0%

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

   4. Taylor expanded in x1 around 0 69.9%

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

   5. Taylor expanded in x2 around 0 46.3%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x2 \cdot \left(6 \cdot x1 - 12\right)\right) + x1 \cdot \left(x1 \cdot \left(9 + 3 \cdot x1\right) - 2\right)\right)}\right) \]

   6. Taylor expanded in x2 around inf 59.8%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq 10^{-41}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot \left(x1 \cdot \left(x1 \cdot 6 - 12\right) - 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 27.0% accurate, 9.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq 4 \cdot 10^{+253}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(\frac{x2 \cdot -6}{x1} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 4e+253)
   (* x2 (- (/ x1 x2) 6.0))
   (* x1 (+ (/ (* x2 -6.0) x1) 1.0))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= 4e+253) {
		tmp = x2 * ((x1 / x2) - 6.0);
	} else {
		tmp = x1 * (((x2 * -6.0) / x1) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x2 <= 4d+253) then
        tmp = x2 * ((x1 / x2) - 6.0d0)
    else
        tmp = x1 * (((x2 * (-6.0d0)) / x1) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x2 <= 4e+253) {
		tmp = x2 * ((x1 / x2) - 6.0);
	} else {
		tmp = x1 * (((x2 * -6.0) / x1) + 1.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= 4e+253:
		tmp = x2 * ((x1 / x2) - 6.0)
	else:
		tmp = x1 * (((x2 * -6.0) / x1) + 1.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= 4e+253)
		tmp = Float64(x2 * Float64(Float64(x1 / x2) - 6.0));
	else
		tmp = Float64(x1 * Float64(Float64(Float64(x2 * -6.0) / x1) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= 4e+253)
		tmp = x2 * ((x1 / x2) - 6.0);
	else
		tmp = x1 * (((x2 * -6.0) / x1) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, 4e+253], N[(x2 * N[(N[(x1 / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision], N[(x1 * N[(N[(N[(x2 * -6.0), $MachinePrecision] / x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < 3.9999999999999997e253

   1. Initial program 74.3%

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

   3. Taylor expanded in x1 around 0 55.8%

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

   4. Taylor expanded in x1 around 0 26.4%

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

      1. *-commutative 26.4%

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

   6. Simplified 26.4%

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

   7. Taylor expanded in x2 around inf 30.9%

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

   if 3.9999999999999997e253 < x2

   1. Initial program 70.0%

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

   3. Taylor expanded in x1 around 0 61.6%

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

   4. Taylor expanded in x1 around 0 6.6%

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

      1. *-commutative 6.6%

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

   6. Simplified 6.6%

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

   7. Taylor expanded in x1 around inf 50.8%

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

      1. associate-*r/ 50.8%

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

   9. Simplified 50.8%

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

4. Final simplification 31.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq 4 \cdot 10^{+253}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(\frac{x2 \cdot -6}{x1} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 41.2% accurate, 9.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq 1.4:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 1.4) (+ x1 (+ (* x2 -6.0) (* x1 -2.0))) (* x2 (- (/ x1 x2) 6.0))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= 1.4) {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	} else {
		tmp = x2 * ((x1 / x2) - 6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= 1.4d0) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (-2.0d0)))
    else
        tmp = x2 * ((x1 / x2) - 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= 1.4) {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	} else {
		tmp = x2 * ((x1 / x2) - 6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= 1.4:
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0))
	else:
		tmp = x2 * ((x1 / x2) - 6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= 1.4)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * -2.0)));
	else
		tmp = Float64(x2 * Float64(Float64(x1 / x2) - 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= 1.4)
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	else
		tmp = x2 * ((x1 / x2) - 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, 1.4], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * N[(N[(x1 / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < 1.3999999999999999

   1. Initial program 83.7%

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

   3. Taylor expanded in x1 around -inf 39.6%

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

   4. Taylor expanded in x1 around 0 53.4%

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

   if 1.3999999999999999 < x1

   1. Initial program 42.1%

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

   3. Taylor expanded in x1 around 0 11.9%

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

   4. Taylor expanded in x1 around 0 7.2%

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

      1. *-commutative 7.2%

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

   6. Simplified 7.2%

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

   7. Taylor expanded in x2 around inf 26.3%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq 1.4:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 26.6% accurate, 18.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 74.1%

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

3. Taylor expanded in x1 around 0 56.0%

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

4. Taylor expanded in x1 around 0 25.6%

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

   1. *-commutative 25.6%

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

6. Simplified 25.6%

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

7. Taylor expanded in x2 around inf 30.0%

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

8. Final simplification 30.0%

   \[\leadsto x2 \cdot \left(\frac{x1}{x2} - 6\right) \]
9. Add Preprocessing

Alternative 28: 20.9% 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 74.1%

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

3. Taylor expanded in x1 around 0 56.0%

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

4. Taylor expanded in x1 around 0 25.6%

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

   1. *-commutative 25.6%

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

6. Simplified 25.6%

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

7. Final simplification 25.6%

   \[\leadsto x1 + x2 \cdot -6 \]
8. Add Preprocessing

Alternative 29: 20.7% 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 74.1%

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

3. Taylor expanded in x1 around 0 56.0%

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

4. Taylor expanded in x1 around 0 25.6%

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

   1. *-commutative 25.6%

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

6. Simplified 25.6%

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

7. Taylor expanded in x1 around 0 25.6%

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

8. Final simplification 25.6%

   \[\leadsto x2 \cdot -6 \]
9. Add Preprocessing

Alternative 30: 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 74.1%

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

3. Taylor expanded in x1 around 0 56.0%

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

4. Taylor expanded in x1 around 0 25.6%

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

   1. *-commutative 25.6%

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

6. Simplified 25.6%

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

7. Taylor expanded in x1 around inf 3.5%

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

8. Final simplification 3.5%

   \[\leadsto x1 \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024079 
(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))))))