Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.9% → 99.5%

Time: 32.8s

Alternatives: 29

Speedup: 3.0×

• 46.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 70.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{x1 - t\_0}{\mathsf{fma}\left(x1, x1, 1\right)}\\ t_3 := 3 \cdot \left(x1 \cdot x1\right)\\ t_4 := x1 \cdot \left(x1 \cdot 3\right)\\ t_5 := \frac{\left(t\_4 + 2 \cdot x2\right) - x1}{t\_1}\\ t_6 := \frac{t\_0 - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\\ \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(t\_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_5\right) \cdot \left(t\_5 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t\_5 \cdot 4 - 6\right)\right) + t\_4 \cdot t\_5\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{x1 - \left(t\_4 - 2 \cdot x2\right)}{-1 - x1 \cdot x1}\right) \leq \infty:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{t\_3 - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 + \mathsf{fma}\left(\mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot \mathsf{fma}\left(t\_6, 4, -6\right), \left(x1 \cdot \left(2 \cdot t\_2\right)\right) \cdot \left(t\_2 - -3\right)\right), \mathsf{fma}\left(t\_3, t\_6, {x1}^{3}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \end{array} \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision] + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 - t$95$0), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(t$95$4 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$6 = N[(N[(t$95$0 - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$5), $MachinePrecision] * N[(t$95$5 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$5 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$4 * t$95$5), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x1 - N[(t$95$4 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(3.0 * N[(N[(t$95$3 - N[(2.0 * x2 + x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * x1 + 1.0), $MachinePrecision] * N[(x1 * N[(x1 * N[(t$95$6 * 4.0 + -6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(2.0 * t$95$2), $MachinePrecision]), $MachinePrecision] * N[(t$95$2 - -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 * t$95$6 + N[Power[x1, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[Power[x1, 4.0], $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 99.3%

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

   3. Simplified 99.6%

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

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.7%

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

Alternative 2: 99.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{\left(t\_1 + 2 \cdot x2\right) - x1}{t\_2}\\ t_4 := t\_1 \cdot t\_3\\ t_5 := \left(\left(x1 \cdot 2\right) \cdot t\_3\right) \cdot \left(t\_3 - 3\right)\\ t_6 := 3 \cdot \frac{x1 - \left(t\_1 - 2 \cdot x2\right)}{-1 - x1 \cdot x1}\\ \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(t\_2 \cdot \left(t\_5 + \left(x1 \cdot x1\right) \cdot \left(t\_3 \cdot 4 - 6\right)\right) + t\_4\right) + t\_0\right)\right) + t\_6\right) \leq \infty:\\ \;\;\;\;x1 + \left(t\_6 + \left(x1 + \left(t\_0 + \left(t\_4 + t\_2 \cdot \left(t\_5 - \left(x1 \cdot x1\right) \cdot \left(6 - 4 \cdot \frac{\left(2 \cdot x2 + 3 \cdot {x1}^{2}\right) - x1}{t\_2}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \end{array} \end{array} \]

FPCore

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

C

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

Java

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

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = x1 * (x1 * 3.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2
	t_4 = t_1 * t_3
	t_5 = ((x1 * 2.0) * t_3) * (t_3 - 3.0)
	t_6 = 3.0 * ((x1 - (t_1 - (2.0 * x2))) / (-1.0 - (x1 * x1)))
	tmp = 0
	if (x1 + ((x1 + (((t_2 * (t_5 + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + t_4) + t_0)) + t_6)) <= math.inf:
		tmp = x1 + (t_6 + (x1 + (t_0 + (t_4 + (t_2 * (t_5 - ((x1 * x1) * (6.0 - (4.0 * ((((2.0 * x2) + (3.0 * math.pow(x1, 2.0))) - x1) / t_2))))))))))
	else:
		tmp = 6.0 * math.pow(x1, 4.0)
	return tmp

Julia

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

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = x1 * (x1 * 3.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	t_4 = t_1 * t_3;
	t_5 = ((x1 * 2.0) * t_3) * (t_3 - 3.0);
	t_6 = 3.0 * ((x1 - (t_1 - (2.0 * x2))) / (-1.0 - (x1 * x1)));
	tmp = 0.0;
	if ((x1 + ((x1 + (((t_2 * (t_5 + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + t_4) + t_0)) + t_6)) <= Inf)
		tmp = x1 + (t_6 + (x1 + (t_0 + (t_4 + (t_2 * (t_5 - ((x1 * x1) * (6.0 - (4.0 * ((((2.0 * x2) + (3.0 * (x1 ^ 2.0))) - x1) / t_2))))))))));
	else
		tmp = 6.0 * (x1 ^ 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$1 * t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(3.0 * N[(N[(x1 - N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$2 * N[(t$95$5 + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(t$95$6 + N[(x1 + N[(t$95$0 + N[(t$95$4 + N[(t$95$2 * N[(t$95$5 - N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(4.0 * N[(N[(N[(N[(2.0 * x2), $MachinePrecision] + N[(3.0 * N[Power[x1, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[Power[x1, 4.0], $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 99.3%

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

   3. Taylor expanded in x1 around 0 99.4%

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

   if +inf.0 < (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 #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%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.5%

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

Alternative 3: 99.4% accurate, 0.5× speedup

Math

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

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 (* 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 = 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 = 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 = 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(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 = 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[(6.0 * N[Power[x1, 4.0], $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 99.3%

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

   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%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.5%

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

Alternative 4: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\left(t\_1 + 2 \cdot x2\right) - x1}{t\_0}\\ \mathbf{if}\;x1 \leq -5.2 \cdot 10^{+53}:\\ \;\;\;\;{x1}^{4} \cdot \left(6 + \frac{\frac{9 - 4 \cdot \left(3 - 2 \cdot x2\right)}{x1} - 3}{x1}\right)\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{+54}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(t\_1 - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t\_2 \cdot 4 - 6\right)\right) + 3 \cdot t\_1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (/ (- (+ t_1 (* 2.0 x2)) x1) t_0)))
   (if (<= x1 -5.2e+53)
     (*
      (pow x1 4.0)
      (+ 6.0 (/ (- (/ (- 9.0 (* 4.0 (- 3.0 (* 2.0 x2)))) x1) 3.0) x1)))
     (if (<= x1 2.1e+54)
       (+
        x1
        (+
         (* 3.0 (/ (- x1 (- t_1 (* 2.0 x2))) (- -1.0 (* x1 x1))))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (*
             t_0
             (+
              (* (* (* x1 2.0) t_2) (- t_2 3.0))
              (* (* x1 x1) (- (* t_2 4.0) 6.0))))
            (* 3.0 t_1))))))
       (* 6.0 (pow x1 4.0))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0;
	double tmp;
	if (x1 <= -5.2e+53) {
		tmp = pow(x1, 4.0) * (6.0 + ((((9.0 - (4.0 * (3.0 - (2.0 * x2)))) / x1) - 3.0) / x1));
	} else if (x1 <= 2.1e+54) {
		tmp = x1 + ((3.0 * ((x1 - (t_1 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (3.0 * t_1)))));
	} else {
		tmp = 6.0 * pow(x1, 4.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = ((t_1 + (2.0d0 * x2)) - x1) / t_0
    if (x1 <= (-5.2d+53)) then
        tmp = (x1 ** 4.0d0) * (6.0d0 + ((((9.0d0 - (4.0d0 * (3.0d0 - (2.0d0 * x2)))) / x1) - 3.0d0) / x1))
    else if (x1 <= 2.1d+54) then
        tmp = x1 + ((3.0d0 * ((x1 - (t_1 - (2.0d0 * x2))) / ((-1.0d0) - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * ((t_2 * 4.0d0) - 6.0d0)))) + (3.0d0 * t_1)))))
    else
        tmp = 6.0d0 * (x1 ** 4.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0;
	double tmp;
	if (x1 <= -5.2e+53) {
		tmp = Math.pow(x1, 4.0) * (6.0 + ((((9.0 - (4.0 * (3.0 - (2.0 * x2)))) / x1) - 3.0) / x1));
	} else if (x1 <= 2.1e+54) {
		tmp = x1 + ((3.0 * ((x1 - (t_1 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (3.0 * t_1)))));
	} else {
		tmp = 6.0 * Math.pow(x1, 4.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0
	tmp = 0
	if x1 <= -5.2e+53:
		tmp = math.pow(x1, 4.0) * (6.0 + ((((9.0 - (4.0 * (3.0 - (2.0 * x2)))) / x1) - 3.0) / x1))
	elif x1 <= 2.1e+54:
		tmp = x1 + ((3.0 * ((x1 - (t_1 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (3.0 * t_1)))))
	else:
		tmp = 6.0 * math.pow(x1, 4.0)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_0)
	tmp = 0.0
	if (x1 <= -5.2e+53)
		tmp = Float64((x1 ^ 4.0) * Float64(6.0 + Float64(Float64(Float64(Float64(9.0 - Float64(4.0 * Float64(3.0 - Float64(2.0 * x2)))) / x1) - 3.0) / x1)));
	elseif (x1 <= 2.1e+54)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 - Float64(t_1 - Float64(2.0 * x2))) / Float64(-1.0 - Float64(x1 * x1)))) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)))) + Float64(3.0 * t_1))))));
	else
		tmp = Float64(6.0 * (x1 ^ 4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * 3.0);
	t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0;
	tmp = 0.0;
	if (x1 <= -5.2e+53)
		tmp = (x1 ^ 4.0) * (6.0 + ((((9.0 - (4.0 * (3.0 - (2.0 * x2)))) / x1) - 3.0) / x1));
	elseif (x1 <= 2.1e+54)
		tmp = x1 + ((3.0 * ((x1 - (t_1 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (3.0 * t_1)))));
	else
		tmp = 6.0 * (x1 ^ 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[LessEqual[x1, -5.2e+53], N[(N[Power[x1, 4.0], $MachinePrecision] * N[(6.0 + N[(N[(N[(N[(9.0 - N[(4.0 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision] - 3.0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.1e+54], N[(x1 + N[(N[(3.0 * N[(N[(x1 - N[(t$95$1 - 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 * 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[(3.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.19999999999999996e53

   1. Initial program 23.9%

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

   3. Simplified 23.9%

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

   5. Taylor expanded in x1 around -inf 100.0%

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

   if -5.19999999999999996e53 < x1 < 2.09999999999999986e54

   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 97.8%

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

   if 2.09999999999999986e54 < x1

   1. Initial program 26.8%

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

   3. Simplified 26.8%

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

   5. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.2 \cdot 10^{+53}:\\ \;\;\;\;{x1}^{4} \cdot \left(6 + \frac{\frac{9 - 4 \cdot \left(3 - 2 \cdot x2\right)}{x1} - 3}{x1}\right)\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{+54}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x2 \cdot \left(3 - 2 \cdot x2\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := 3 \cdot \left(x2 \cdot -2 - 3\right)\\ t_4 := 3 + x2 \cdot -2\\ t_5 := x2 \cdot t\_4\\ t_6 := x1 \cdot x1 + 1\\ t_7 := \frac{\left(t\_2 + 2 \cdot x2\right) - x1}{t\_6}\\ t_8 := t\_2 \cdot t\_7\\ t_9 := -4 \cdot t\_5\\ t_10 := -1 - x1 \cdot x1\\ t_11 := \left(\left(x1 \cdot x1\right) \cdot \left(6 - t\_7 \cdot 4\right) + \left(t\_7 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right)\right) \cdot t\_10\\ t_12 := 3 \cdot \frac{x1 - \left(t\_2 - 2 \cdot x2\right)}{t\_10}\\ \mathbf{if}\;x1 \leq -5.7 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x1 \cdot \left(6 + \left(\left(t\_3 - \left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(t\_9 + 2 \cdot \left(\left(1 + \left(-3 \cdot t\_4 + 2 \cdot t\_1\right)\right) - -2 \cdot t\_5\right)\right) - 3\right)\right)\right)\right) - 2 \cdot \left(3 + x2 \cdot -4\right)\right)\right) - t\_9\right) - -1\right)\\ \mathbf{elif}\;x1 \leq -7.4 \cdot 10^{+31}:\\ \;\;\;\;x1 + \left(t\_12 + \left(x1 + \left(t\_0 + \left(3 \cdot t\_2 + t\_11\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7.5 \cdot 10^{+28}:\\ \;\;\;\;x1 + \left(t\_12 + \left(x1 + \left(t\_0 + \left(t\_8 + t\_6 \cdot \left(\left(x1 \cdot x1\right) \cdot 6 + \left(\left(x1 \cdot 2\right) \cdot t\_7\right) \cdot \left(\left(2 \cdot x2 - x1\right) - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+97}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(t\_0 + \left(t\_8 + t\_11\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(t\_3 - x1 \cdot 3\right) + 4 \cdot t\_1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (* x2 (- 3.0 (* 2.0 x2))))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (* 3.0 (- (* x2 -2.0) 3.0)))
        (t_4 (+ 3.0 (* x2 -2.0)))
        (t_5 (* x2 t_4))
        (t_6 (+ (* x1 x1) 1.0))
        (t_7 (/ (- (+ t_2 (* 2.0 x2)) x1) t_6))
        (t_8 (* t_2 t_7))
        (t_9 (* -4.0 t_5))
        (t_10 (- -1.0 (* x1 x1)))
        (t_11
         (*
          (+
           (* (* x1 x1) (- 6.0 (* t_7 4.0)))
           (* (- t_7 3.0) (* (* x1 2.0) (- (/ 1.0 x1) 3.0))))
          t_10))
        (t_12 (* 3.0 (/ (- x1 (- t_2 (* 2.0 x2))) t_10))))
   (if (<= x1 -5.7e+102)
     (-
      (* x2 -6.0)
      (*
       x1
       (-
        (-
         (*
          x1
          (+
           6.0
           (-
            (-
             t_3
             (+
              (* x2 6.0)
              (+
               (* x2 8.0)
               (*
                x1
                (-
                 (+
                  t_9
                  (*
                   2.0
                   (- (+ 1.0 (+ (* -3.0 t_4) (* 2.0 t_1))) (* -2.0 t_5))))
                 3.0)))))
            (* 2.0 (+ 3.0 (* x2 -4.0))))))
         t_9)
        -1.0)))
     (if (<= x1 -7.4e+31)
       (+ x1 (+ t_12 (+ x1 (+ t_0 (+ (* 3.0 t_2) t_11)))))
       (if (<= x1 7.5e+28)
         (+
          x1
          (+
           t_12
           (+
            x1
            (+
             t_0
             (+
              t_8
              (*
               t_6
               (+
                (* (* x1 x1) 6.0)
                (* (* (* x1 2.0) t_7) (- (- (* 2.0 x2) x1) 3.0)))))))))
         (if (<= x1 5e+97)
           (+ x1 (+ (+ x1 (+ t_0 (+ t_8 t_11))) (* 3.0 (* x2 -2.0))))
           (+
            x1
            (-
             (* x2 -6.0)
             (* x1 (+ 2.0 (+ (* x1 (- t_3 (* x1 3.0))) (* 4.0 t_1))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x2 * (3.0 - (2.0 * x2));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 3.0 * ((x2 * -2.0) - 3.0);
	double t_4 = 3.0 + (x2 * -2.0);
	double t_5 = x2 * t_4;
	double t_6 = (x1 * x1) + 1.0;
	double t_7 = ((t_2 + (2.0 * x2)) - x1) / t_6;
	double t_8 = t_2 * t_7;
	double t_9 = -4.0 * t_5;
	double t_10 = -1.0 - (x1 * x1);
	double t_11 = (((x1 * x1) * (6.0 - (t_7 * 4.0))) + ((t_7 - 3.0) * ((x1 * 2.0) * ((1.0 / x1) - 3.0)))) * t_10;
	double t_12 = 3.0 * ((x1 - (t_2 - (2.0 * x2))) / t_10);
	double tmp;
	if (x1 <= -5.7e+102) {
		tmp = (x2 * -6.0) - (x1 * (((x1 * (6.0 + ((t_3 - ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_9 + (2.0 * ((1.0 + ((-3.0 * t_4) + (2.0 * t_1))) - (-2.0 * t_5)))) - 3.0))))) - (2.0 * (3.0 + (x2 * -4.0)))))) - t_9) - -1.0));
	} else if (x1 <= -7.4e+31) {
		tmp = x1 + (t_12 + (x1 + (t_0 + ((3.0 * t_2) + t_11))));
	} else if (x1 <= 7.5e+28) {
		tmp = x1 + (t_12 + (x1 + (t_0 + (t_8 + (t_6 * (((x1 * x1) * 6.0) + (((x1 * 2.0) * t_7) * (((2.0 * x2) - x1) - 3.0))))))));
	} else if (x1 <= 5e+97) {
		tmp = x1 + ((x1 + (t_0 + (t_8 + t_11))) + (3.0 * (x2 * -2.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * (t_3 - (x1 * 3.0))) + (4.0 * t_1)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_0 = x1 * (x1 * x1)
    t_1 = x2 * (3.0d0 - (2.0d0 * x2))
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = 3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)
    t_4 = 3.0d0 + (x2 * (-2.0d0))
    t_5 = x2 * t_4
    t_6 = (x1 * x1) + 1.0d0
    t_7 = ((t_2 + (2.0d0 * x2)) - x1) / t_6
    t_8 = t_2 * t_7
    t_9 = (-4.0d0) * t_5
    t_10 = (-1.0d0) - (x1 * x1)
    t_11 = (((x1 * x1) * (6.0d0 - (t_7 * 4.0d0))) + ((t_7 - 3.0d0) * ((x1 * 2.0d0) * ((1.0d0 / x1) - 3.0d0)))) * t_10
    t_12 = 3.0d0 * ((x1 - (t_2 - (2.0d0 * x2))) / t_10)
    if (x1 <= (-5.7d+102)) then
        tmp = (x2 * (-6.0d0)) - (x1 * (((x1 * (6.0d0 + ((t_3 - ((x2 * 6.0d0) + ((x2 * 8.0d0) + (x1 * ((t_9 + (2.0d0 * ((1.0d0 + (((-3.0d0) * t_4) + (2.0d0 * t_1))) - ((-2.0d0) * t_5)))) - 3.0d0))))) - (2.0d0 * (3.0d0 + (x2 * (-4.0d0))))))) - t_9) - (-1.0d0)))
    else if (x1 <= (-7.4d+31)) then
        tmp = x1 + (t_12 + (x1 + (t_0 + ((3.0d0 * t_2) + t_11))))
    else if (x1 <= 7.5d+28) then
        tmp = x1 + (t_12 + (x1 + (t_0 + (t_8 + (t_6 * (((x1 * x1) * 6.0d0) + (((x1 * 2.0d0) * t_7) * (((2.0d0 * x2) - x1) - 3.0d0))))))))
    else if (x1 <= 5d+97) then
        tmp = x1 + ((x1 + (t_0 + (t_8 + t_11))) + (3.0d0 * (x2 * (-2.0d0))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((x1 * (t_3 - (x1 * 3.0d0))) + (4.0d0 * t_1)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x2 * (3.0 - (2.0 * x2));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 3.0 * ((x2 * -2.0) - 3.0);
	double t_4 = 3.0 + (x2 * -2.0);
	double t_5 = x2 * t_4;
	double t_6 = (x1 * x1) + 1.0;
	double t_7 = ((t_2 + (2.0 * x2)) - x1) / t_6;
	double t_8 = t_2 * t_7;
	double t_9 = -4.0 * t_5;
	double t_10 = -1.0 - (x1 * x1);
	double t_11 = (((x1 * x1) * (6.0 - (t_7 * 4.0))) + ((t_7 - 3.0) * ((x1 * 2.0) * ((1.0 / x1) - 3.0)))) * t_10;
	double t_12 = 3.0 * ((x1 - (t_2 - (2.0 * x2))) / t_10);
	double tmp;
	if (x1 <= -5.7e+102) {
		tmp = (x2 * -6.0) - (x1 * (((x1 * (6.0 + ((t_3 - ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_9 + (2.0 * ((1.0 + ((-3.0 * t_4) + (2.0 * t_1))) - (-2.0 * t_5)))) - 3.0))))) - (2.0 * (3.0 + (x2 * -4.0)))))) - t_9) - -1.0));
	} else if (x1 <= -7.4e+31) {
		tmp = x1 + (t_12 + (x1 + (t_0 + ((3.0 * t_2) + t_11))));
	} else if (x1 <= 7.5e+28) {
		tmp = x1 + (t_12 + (x1 + (t_0 + (t_8 + (t_6 * (((x1 * x1) * 6.0) + (((x1 * 2.0) * t_7) * (((2.0 * x2) - x1) - 3.0))))))));
	} else if (x1 <= 5e+97) {
		tmp = x1 + ((x1 + (t_0 + (t_8 + t_11))) + (3.0 * (x2 * -2.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * (t_3 - (x1 * 3.0))) + (4.0 * t_1)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = x2 * (3.0 - (2.0 * x2))
	t_2 = x1 * (x1 * 3.0)
	t_3 = 3.0 * ((x2 * -2.0) - 3.0)
	t_4 = 3.0 + (x2 * -2.0)
	t_5 = x2 * t_4
	t_6 = (x1 * x1) + 1.0
	t_7 = ((t_2 + (2.0 * x2)) - x1) / t_6
	t_8 = t_2 * t_7
	t_9 = -4.0 * t_5
	t_10 = -1.0 - (x1 * x1)
	t_11 = (((x1 * x1) * (6.0 - (t_7 * 4.0))) + ((t_7 - 3.0) * ((x1 * 2.0) * ((1.0 / x1) - 3.0)))) * t_10
	t_12 = 3.0 * ((x1 - (t_2 - (2.0 * x2))) / t_10)
	tmp = 0
	if x1 <= -5.7e+102:
		tmp = (x2 * -6.0) - (x1 * (((x1 * (6.0 + ((t_3 - ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_9 + (2.0 * ((1.0 + ((-3.0 * t_4) + (2.0 * t_1))) - (-2.0 * t_5)))) - 3.0))))) - (2.0 * (3.0 + (x2 * -4.0)))))) - t_9) - -1.0))
	elif x1 <= -7.4e+31:
		tmp = x1 + (t_12 + (x1 + (t_0 + ((3.0 * t_2) + t_11))))
	elif x1 <= 7.5e+28:
		tmp = x1 + (t_12 + (x1 + (t_0 + (t_8 + (t_6 * (((x1 * x1) * 6.0) + (((x1 * 2.0) * t_7) * (((2.0 * x2) - x1) - 3.0))))))))
	elif x1 <= 5e+97:
		tmp = x1 + ((x1 + (t_0 + (t_8 + t_11))) + (3.0 * (x2 * -2.0)))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * (t_3 - (x1 * 3.0))) + (4.0 * t_1)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0))
	t_4 = Float64(3.0 + Float64(x2 * -2.0))
	t_5 = Float64(x2 * t_4)
	t_6 = Float64(Float64(x1 * x1) + 1.0)
	t_7 = Float64(Float64(Float64(t_2 + Float64(2.0 * x2)) - x1) / t_6)
	t_8 = Float64(t_2 * t_7)
	t_9 = Float64(-4.0 * t_5)
	t_10 = Float64(-1.0 - Float64(x1 * x1))
	t_11 = Float64(Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(t_7 * 4.0))) + Float64(Float64(t_7 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(Float64(1.0 / x1) - 3.0)))) * t_10)
	t_12 = Float64(3.0 * Float64(Float64(x1 - Float64(t_2 - Float64(2.0 * x2))) / t_10))
	tmp = 0.0
	if (x1 <= -5.7e+102)
		tmp = Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(Float64(Float64(x1 * Float64(6.0 + Float64(Float64(t_3 - Float64(Float64(x2 * 6.0) + Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_9 + Float64(2.0 * Float64(Float64(1.0 + Float64(Float64(-3.0 * t_4) + Float64(2.0 * t_1))) - Float64(-2.0 * t_5)))) - 3.0))))) - Float64(2.0 * Float64(3.0 + Float64(x2 * -4.0)))))) - t_9) - -1.0)));
	elseif (x1 <= -7.4e+31)
		tmp = Float64(x1 + Float64(t_12 + Float64(x1 + Float64(t_0 + Float64(Float64(3.0 * t_2) + t_11)))));
	elseif (x1 <= 7.5e+28)
		tmp = Float64(x1 + Float64(t_12 + Float64(x1 + Float64(t_0 + Float64(t_8 + Float64(t_6 * Float64(Float64(Float64(x1 * x1) * 6.0) + Float64(Float64(Float64(x1 * 2.0) * t_7) * Float64(Float64(Float64(2.0 * x2) - x1) - 3.0)))))))));
	elseif (x1 <= 5e+97)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(t_0 + Float64(t_8 + t_11))) + Float64(3.0 * Float64(x2 * -2.0))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(x1 * Float64(t_3 - Float64(x1 * 3.0))) + Float64(4.0 * t_1))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = x2 * (3.0 - (2.0 * x2));
	t_2 = x1 * (x1 * 3.0);
	t_3 = 3.0 * ((x2 * -2.0) - 3.0);
	t_4 = 3.0 + (x2 * -2.0);
	t_5 = x2 * t_4;
	t_6 = (x1 * x1) + 1.0;
	t_7 = ((t_2 + (2.0 * x2)) - x1) / t_6;
	t_8 = t_2 * t_7;
	t_9 = -4.0 * t_5;
	t_10 = -1.0 - (x1 * x1);
	t_11 = (((x1 * x1) * (6.0 - (t_7 * 4.0))) + ((t_7 - 3.0) * ((x1 * 2.0) * ((1.0 / x1) - 3.0)))) * t_10;
	t_12 = 3.0 * ((x1 - (t_2 - (2.0 * x2))) / t_10);
	tmp = 0.0;
	if (x1 <= -5.7e+102)
		tmp = (x2 * -6.0) - (x1 * (((x1 * (6.0 + ((t_3 - ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_9 + (2.0 * ((1.0 + ((-3.0 * t_4) + (2.0 * t_1))) - (-2.0 * t_5)))) - 3.0))))) - (2.0 * (3.0 + (x2 * -4.0)))))) - t_9) - -1.0));
	elseif (x1 <= -7.4e+31)
		tmp = x1 + (t_12 + (x1 + (t_0 + ((3.0 * t_2) + t_11))));
	elseif (x1 <= 7.5e+28)
		tmp = x1 + (t_12 + (x1 + (t_0 + (t_8 + (t_6 * (((x1 * x1) * 6.0) + (((x1 * 2.0) * t_7) * (((2.0 * x2) - x1) - 3.0))))))));
	elseif (x1 <= 5e+97)
		tmp = x1 + ((x1 + (t_0 + (t_8 + t_11))) + (3.0 * (x2 * -2.0)));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * (t_3 - (x1 * 3.0))) + (4.0 * t_1)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x2 * t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$7 = N[(N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$6), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$2 * t$95$7), $MachinePrecision]}, Block[{t$95$9 = N[(-4.0 * t$95$5), $MachinePrecision]}, Block[{t$95$10 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$11 = N[(N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(t$95$7 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$7 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(1.0 / x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$10), $MachinePrecision]}, Block[{t$95$12 = N[(3.0 * N[(N[(x1 - N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$10), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.7e+102], N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(N[(N[(x1 * N[(6.0 + N[(N[(t$95$3 - N[(N[(x2 * 6.0), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$9 + N[(2.0 * N[(N[(1.0 + N[(N[(-3.0 * t$95$4), $MachinePrecision] + N[(2.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-2.0 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(2.0 * N[(3.0 + N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$9), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -7.4e+31], N[(x1 + N[(t$95$12 + N[(x1 + N[(t$95$0 + N[(N[(3.0 * t$95$2), $MachinePrecision] + t$95$11), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7.5e+28], N[(x1 + N[(t$95$12 + N[(x1 + N[(t$95$0 + N[(t$95$8 + N[(t$95$6 * N[(N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$7), $MachinePrecision] * N[(N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+97], N[(x1 + N[(N[(x1 + N[(t$95$0 + N[(t$95$8 + t$95$11), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(N[(x1 * N[(t$95$3 - N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(4.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -5.6999999999999999e102

   1. Initial program 0.0%

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

   3. Simplified 22.0%

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

   5. Taylor expanded in x1 around 0 70.7%

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

   if -5.6999999999999999e102 < x1 < -7.3999999999999996e31

   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 99.3%

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

   4. Taylor expanded in x1 around inf 99.3%

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

   if -7.3999999999999996e31 < x1 < 7.4999999999999998e28

   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 92.1%

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

   4. Taylor expanded in x1 around inf 91.7%

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

   if 7.4999999999999998e28 < x1 < 4.99999999999999999e97

   1. Initial program 99.6%

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

   3. Taylor expanded in x1 around inf 82.9%

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

   4. Taylor expanded in x1 around 0 82.9%

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

      1. *-commutative 82.9%

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

   6. Simplified 82.9%

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

   if 4.99999999999999999e97 < x1

   1. Initial program 14.3%

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

   3. Simplified 14.3%

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

   5. Taylor expanded in x1 around 0 6.1%

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

      1. associate-*r* 6.1%

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

      2. fmm-def 6.1%

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

      3. metadata-eval 6.1%

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

   7. Simplified 6.1%

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

   8. Taylor expanded in x1 around 0 97.1%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.7 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x1 \cdot \left(6 + \left(\left(3 \cdot \left(x2 \cdot -2 - 3\right) - \left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + 2 \cdot \left(\left(1 + \left(-3 \cdot \left(3 + x2 \cdot -2\right) + 2 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) - -2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right)\right) - 3\right)\right)\right)\right) - 2 \cdot \left(3 + x2 \cdot -4\right)\right)\right) - -4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq -7.4 \cdot 10^{+31}:\\ \;\;\;\;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(\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(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right)\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7.5 \cdot 10^{+28}:\\ \;\;\;\;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(x1 \cdot x1\right) \cdot 6 + \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(\left(2 \cdot x2 - x1\right) - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+97}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \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(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right)\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot \left(3 + x2 \cdot -4\right)\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := x2 \cdot \left(3 - 2 \cdot x2\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := \frac{\left(t\_3 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\\ t_5 := 3 \cdot \left(x2 \cdot -2 - 3\right)\\ t_6 := 3 + x2 \cdot -2\\ t_7 := x2 \cdot t\_6\\ t_8 := -4 \cdot t\_7\\ t_9 := -1 - x1 \cdot x1\\ t_10 := \left(\left(x1 \cdot x1\right) \cdot \left(6 - t\_4 \cdot 4\right) + \left(t\_4 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right)\right) \cdot t\_9\\ \mathbf{if}\;x1 \leq -5.7 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x1 \cdot \left(6 + \left(\left(t\_5 - \left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(t\_8 + 2 \cdot \left(\left(1 + \left(-3 \cdot t\_6 + 2 \cdot t\_2\right)\right) - -2 \cdot t\_7\right)\right) - 3\right)\right)\right)\right) - t\_0\right)\right) - t\_8\right) - -1\right)\\ \mathbf{elif}\;x1 \leq -7.4 \cdot 10^{+31}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(t\_3 - 2 \cdot x2\right)}{t\_9} + \left(x1 + \left(t\_1 + \left(3 \cdot t\_3 + t\_10\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7.5 \cdot 10^{+28}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(t\_8 + x1 \cdot \left(\left(t\_0 - \left(t\_5 - \left(x2 \cdot 6 + x2 \cdot 8\right)\right)\right) - 6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+97}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(t\_1 + \left(t\_3 \cdot t\_4 + t\_10\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(t\_5 - x1 \cdot 3\right) + 4 \cdot t\_2\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 2.0 (+ 3.0 (* x2 -4.0))))
        (t_1 (* x1 (* x1 x1)))
        (t_2 (* x2 (- 3.0 (* 2.0 x2))))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (/ (- (+ t_3 (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
        (t_5 (* 3.0 (- (* x2 -2.0) 3.0)))
        (t_6 (+ 3.0 (* x2 -2.0)))
        (t_7 (* x2 t_6))
        (t_8 (* -4.0 t_7))
        (t_9 (- -1.0 (* x1 x1)))
        (t_10
         (*
          (+
           (* (* x1 x1) (- 6.0 (* t_4 4.0)))
           (* (- t_4 3.0) (* (* x1 2.0) (- (/ 1.0 x1) 3.0))))
          t_9)))
   (if (<= x1 -5.7e+102)
     (-
      (* x2 -6.0)
      (*
       x1
       (-
        (-
         (*
          x1
          (+
           6.0
           (-
            (-
             t_5
             (+
              (* x2 6.0)
              (+
               (* x2 8.0)
               (*
                x1
                (-
                 (+
                  t_8
                  (*
                   2.0
                   (- (+ 1.0 (+ (* -3.0 t_6) (* 2.0 t_2))) (* -2.0 t_7))))
                 3.0)))))
            t_0)))
         t_8)
        -1.0)))
     (if (<= x1 -7.4e+31)
       (+
        x1
        (+
         (* 3.0 (/ (- x1 (- t_3 (* 2.0 x2))) t_9))
         (+ x1 (+ t_1 (+ (* 3.0 t_3) t_10)))))
       (if (<= x1 7.5e+28)
         (+
          (* x2 -6.0)
          (*
           x1
           (+
            -1.0
            (+ t_8 (* x1 (- (- t_0 (- t_5 (+ (* x2 6.0) (* x2 8.0)))) 6.0))))))
         (if (<= x1 5e+97)
           (+ x1 (+ (+ x1 (+ t_1 (+ (* t_3 t_4) t_10))) (* 3.0 (* x2 -2.0))))
           (+
            x1
            (-
             (* x2 -6.0)
             (* x1 (+ 2.0 (+ (* x1 (- t_5 (* x1 3.0))) (* 4.0 t_2))))))))))))

C

double code(double x1, double x2) {
	double t_0 = 2.0 * (3.0 + (x2 * -4.0));
	double t_1 = x1 * (x1 * x1);
	double t_2 = x2 * (3.0 - (2.0 * x2));
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = ((t_3 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0);
	double t_5 = 3.0 * ((x2 * -2.0) - 3.0);
	double t_6 = 3.0 + (x2 * -2.0);
	double t_7 = x2 * t_6;
	double t_8 = -4.0 * t_7;
	double t_9 = -1.0 - (x1 * x1);
	double t_10 = (((x1 * x1) * (6.0 - (t_4 * 4.0))) + ((t_4 - 3.0) * ((x1 * 2.0) * ((1.0 / x1) - 3.0)))) * t_9;
	double tmp;
	if (x1 <= -5.7e+102) {
		tmp = (x2 * -6.0) - (x1 * (((x1 * (6.0 + ((t_5 - ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_8 + (2.0 * ((1.0 + ((-3.0 * t_6) + (2.0 * t_2))) - (-2.0 * t_7)))) - 3.0))))) - t_0))) - t_8) - -1.0));
	} else if (x1 <= -7.4e+31) {
		tmp = x1 + ((3.0 * ((x1 - (t_3 - (2.0 * x2))) / t_9)) + (x1 + (t_1 + ((3.0 * t_3) + t_10))));
	} else if (x1 <= 7.5e+28) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (t_8 + (x1 * ((t_0 - (t_5 - ((x2 * 6.0) + (x2 * 8.0)))) - 6.0)))));
	} else if (x1 <= 5e+97) {
		tmp = x1 + ((x1 + (t_1 + ((t_3 * t_4) + t_10))) + (3.0 * (x2 * -2.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * (t_5 - (x1 * 3.0))) + (4.0 * t_2)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_0 = 2.0d0 * (3.0d0 + (x2 * (-4.0d0)))
    t_1 = x1 * (x1 * x1)
    t_2 = x2 * (3.0d0 - (2.0d0 * x2))
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = ((t_3 + (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0)
    t_5 = 3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)
    t_6 = 3.0d0 + (x2 * (-2.0d0))
    t_7 = x2 * t_6
    t_8 = (-4.0d0) * t_7
    t_9 = (-1.0d0) - (x1 * x1)
    t_10 = (((x1 * x1) * (6.0d0 - (t_4 * 4.0d0))) + ((t_4 - 3.0d0) * ((x1 * 2.0d0) * ((1.0d0 / x1) - 3.0d0)))) * t_9
    if (x1 <= (-5.7d+102)) then
        tmp = (x2 * (-6.0d0)) - (x1 * (((x1 * (6.0d0 + ((t_5 - ((x2 * 6.0d0) + ((x2 * 8.0d0) + (x1 * ((t_8 + (2.0d0 * ((1.0d0 + (((-3.0d0) * t_6) + (2.0d0 * t_2))) - ((-2.0d0) * t_7)))) - 3.0d0))))) - t_0))) - t_8) - (-1.0d0)))
    else if (x1 <= (-7.4d+31)) then
        tmp = x1 + ((3.0d0 * ((x1 - (t_3 - (2.0d0 * x2))) / t_9)) + (x1 + (t_1 + ((3.0d0 * t_3) + t_10))))
    else if (x1 <= 7.5d+28) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (t_8 + (x1 * ((t_0 - (t_5 - ((x2 * 6.0d0) + (x2 * 8.0d0)))) - 6.0d0)))))
    else if (x1 <= 5d+97) then
        tmp = x1 + ((x1 + (t_1 + ((t_3 * t_4) + t_10))) + (3.0d0 * (x2 * (-2.0d0))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((x1 * (t_5 - (x1 * 3.0d0))) + (4.0d0 * t_2)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 2.0 * (3.0 + (x2 * -4.0));
	double t_1 = x1 * (x1 * x1);
	double t_2 = x2 * (3.0 - (2.0 * x2));
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = ((t_3 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0);
	double t_5 = 3.0 * ((x2 * -2.0) - 3.0);
	double t_6 = 3.0 + (x2 * -2.0);
	double t_7 = x2 * t_6;
	double t_8 = -4.0 * t_7;
	double t_9 = -1.0 - (x1 * x1);
	double t_10 = (((x1 * x1) * (6.0 - (t_4 * 4.0))) + ((t_4 - 3.0) * ((x1 * 2.0) * ((1.0 / x1) - 3.0)))) * t_9;
	double tmp;
	if (x1 <= -5.7e+102) {
		tmp = (x2 * -6.0) - (x1 * (((x1 * (6.0 + ((t_5 - ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_8 + (2.0 * ((1.0 + ((-3.0 * t_6) + (2.0 * t_2))) - (-2.0 * t_7)))) - 3.0))))) - t_0))) - t_8) - -1.0));
	} else if (x1 <= -7.4e+31) {
		tmp = x1 + ((3.0 * ((x1 - (t_3 - (2.0 * x2))) / t_9)) + (x1 + (t_1 + ((3.0 * t_3) + t_10))));
	} else if (x1 <= 7.5e+28) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (t_8 + (x1 * ((t_0 - (t_5 - ((x2 * 6.0) + (x2 * 8.0)))) - 6.0)))));
	} else if (x1 <= 5e+97) {
		tmp = x1 + ((x1 + (t_1 + ((t_3 * t_4) + t_10))) + (3.0 * (x2 * -2.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * (t_5 - (x1 * 3.0))) + (4.0 * t_2)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 2.0 * (3.0 + (x2 * -4.0))
	t_1 = x1 * (x1 * x1)
	t_2 = x2 * (3.0 - (2.0 * x2))
	t_3 = x1 * (x1 * 3.0)
	t_4 = ((t_3 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0)
	t_5 = 3.0 * ((x2 * -2.0) - 3.0)
	t_6 = 3.0 + (x2 * -2.0)
	t_7 = x2 * t_6
	t_8 = -4.0 * t_7
	t_9 = -1.0 - (x1 * x1)
	t_10 = (((x1 * x1) * (6.0 - (t_4 * 4.0))) + ((t_4 - 3.0) * ((x1 * 2.0) * ((1.0 / x1) - 3.0)))) * t_9
	tmp = 0
	if x1 <= -5.7e+102:
		tmp = (x2 * -6.0) - (x1 * (((x1 * (6.0 + ((t_5 - ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_8 + (2.0 * ((1.0 + ((-3.0 * t_6) + (2.0 * t_2))) - (-2.0 * t_7)))) - 3.0))))) - t_0))) - t_8) - -1.0))
	elif x1 <= -7.4e+31:
		tmp = x1 + ((3.0 * ((x1 - (t_3 - (2.0 * x2))) / t_9)) + (x1 + (t_1 + ((3.0 * t_3) + t_10))))
	elif x1 <= 7.5e+28:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (t_8 + (x1 * ((t_0 - (t_5 - ((x2 * 6.0) + (x2 * 8.0)))) - 6.0)))))
	elif x1 <= 5e+97:
		tmp = x1 + ((x1 + (t_1 + ((t_3 * t_4) + t_10))) + (3.0 * (x2 * -2.0)))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * (t_5 - (x1 * 3.0))) + (4.0 * t_2)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(2.0 * Float64(3.0 + Float64(x2 * -4.0)))
	t_1 = Float64(x1 * Float64(x1 * x1))
	t_2 = Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(Float64(Float64(t_3 + Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))
	t_5 = Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0))
	t_6 = Float64(3.0 + Float64(x2 * -2.0))
	t_7 = Float64(x2 * t_6)
	t_8 = Float64(-4.0 * t_7)
	t_9 = Float64(-1.0 - Float64(x1 * x1))
	t_10 = Float64(Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(t_4 * 4.0))) + Float64(Float64(t_4 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(Float64(1.0 / x1) - 3.0)))) * t_9)
	tmp = 0.0
	if (x1 <= -5.7e+102)
		tmp = Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(Float64(Float64(x1 * Float64(6.0 + Float64(Float64(t_5 - Float64(Float64(x2 * 6.0) + Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_8 + Float64(2.0 * Float64(Float64(1.0 + Float64(Float64(-3.0 * t_6) + Float64(2.0 * t_2))) - Float64(-2.0 * t_7)))) - 3.0))))) - t_0))) - t_8) - -1.0)));
	elseif (x1 <= -7.4e+31)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 - Float64(t_3 - Float64(2.0 * x2))) / t_9)) + Float64(x1 + Float64(t_1 + Float64(Float64(3.0 * t_3) + t_10)))));
	elseif (x1 <= 7.5e+28)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(t_8 + Float64(x1 * Float64(Float64(t_0 - Float64(t_5 - Float64(Float64(x2 * 6.0) + Float64(x2 * 8.0)))) - 6.0))))));
	elseif (x1 <= 5e+97)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(t_1 + Float64(Float64(t_3 * t_4) + t_10))) + Float64(3.0 * Float64(x2 * -2.0))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(x1 * Float64(t_5 - Float64(x1 * 3.0))) + Float64(4.0 * t_2))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 2.0 * (3.0 + (x2 * -4.0));
	t_1 = x1 * (x1 * x1);
	t_2 = x2 * (3.0 - (2.0 * x2));
	t_3 = x1 * (x1 * 3.0);
	t_4 = ((t_3 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0);
	t_5 = 3.0 * ((x2 * -2.0) - 3.0);
	t_6 = 3.0 + (x2 * -2.0);
	t_7 = x2 * t_6;
	t_8 = -4.0 * t_7;
	t_9 = -1.0 - (x1 * x1);
	t_10 = (((x1 * x1) * (6.0 - (t_4 * 4.0))) + ((t_4 - 3.0) * ((x1 * 2.0) * ((1.0 / x1) - 3.0)))) * t_9;
	tmp = 0.0;
	if (x1 <= -5.7e+102)
		tmp = (x2 * -6.0) - (x1 * (((x1 * (6.0 + ((t_5 - ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_8 + (2.0 * ((1.0 + ((-3.0 * t_6) + (2.0 * t_2))) - (-2.0 * t_7)))) - 3.0))))) - t_0))) - t_8) - -1.0));
	elseif (x1 <= -7.4e+31)
		tmp = x1 + ((3.0 * ((x1 - (t_3 - (2.0 * x2))) / t_9)) + (x1 + (t_1 + ((3.0 * t_3) + t_10))));
	elseif (x1 <= 7.5e+28)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (t_8 + (x1 * ((t_0 - (t_5 - ((x2 * 6.0) + (x2 * 8.0)))) - 6.0)))));
	elseif (x1 <= 5e+97)
		tmp = x1 + ((x1 + (t_1 + ((t_3 * t_4) + t_10))) + (3.0 * (x2 * -2.0)));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * (t_5 - (x1 * 3.0))) + (4.0 * t_2)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(2.0 * N[(3.0 + N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(x2 * t$95$6), $MachinePrecision]}, Block[{t$95$8 = N[(-4.0 * t$95$7), $MachinePrecision]}, Block[{t$95$9 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(t$95$4 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$4 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(1.0 / x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$9), $MachinePrecision]}, If[LessEqual[x1, -5.7e+102], N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(N[(N[(x1 * N[(6.0 + N[(N[(t$95$5 - N[(N[(x2 * 6.0), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$8 + N[(2.0 * N[(N[(1.0 + N[(N[(-3.0 * t$95$6), $MachinePrecision] + N[(2.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-2.0 * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$8), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -7.4e+31], N[(x1 + N[(N[(3.0 * N[(N[(x1 - N[(t$95$3 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$9), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$1 + N[(N[(3.0 * t$95$3), $MachinePrecision] + t$95$10), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7.5e+28], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(t$95$8 + N[(x1 * N[(N[(t$95$0 - N[(t$95$5 - N[(N[(x2 * 6.0), $MachinePrecision] + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+97], N[(x1 + N[(N[(x1 + N[(t$95$1 + N[(N[(t$95$3 * t$95$4), $MachinePrecision] + t$95$10), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(N[(x1 * N[(t$95$5 - N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(4.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -5.6999999999999999e102

   1. Initial program 0.0%

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

   3. Simplified 22.0%

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

   5. Taylor expanded in x1 around 0 70.7%

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

   if -5.6999999999999999e102 < x1 < -7.3999999999999996e31

   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 99.3%

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

   4. Taylor expanded in x1 around inf 99.3%

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

   if -7.3999999999999996e31 < x1 < 7.4999999999999998e28

   1. Initial program 99.3%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in x1 around 0 82.8%

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

   if 7.4999999999999998e28 < x1 < 4.99999999999999999e97

   1. Initial program 99.6%

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

   3. Taylor expanded in x1 around inf 82.9%

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

   4. Taylor expanded in x1 around 0 82.9%

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

      1. *-commutative 82.9%

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

   6. Simplified 82.9%

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

   if 4.99999999999999999e97 < x1

   1. Initial program 14.3%

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

   3. Simplified 14.3%

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

   5. Taylor expanded in x1 around 0 6.1%

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

      1. associate-*r* 6.1%

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

      2. fmm-def 6.1%

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

      3. metadata-eval 6.1%

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

   7. Simplified 6.1%

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

   8. Taylor expanded in x1 around 0 97.1%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.7 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x1 \cdot \left(6 + \left(\left(3 \cdot \left(x2 \cdot -2 - 3\right) - \left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + 2 \cdot \left(\left(1 + \left(-3 \cdot \left(3 + x2 \cdot -2\right) + 2 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) - -2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right)\right) - 3\right)\right)\right)\right) - 2 \cdot \left(3 + x2 \cdot -4\right)\right)\right) - -4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq -7.4 \cdot 10^{+31}:\\ \;\;\;\;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(\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(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right)\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7.5 \cdot 10^{+28}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(-4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + x2 \cdot -4\right) - \left(3 \cdot \left(x2 \cdot -2 - 3\right) - \left(x2 \cdot 6 + x2 \cdot 8\right)\right)\right) - 6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+97}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \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(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right)\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\left(t\_1 + 2 \cdot x2\right) - x1}{t\_0}\\ \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102} \lor \neg \left(x1 \leq 2.1 \cdot 10^{+54}\right):\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(t\_1 - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t\_2 \cdot 4 - 6\right)\right) + 3 \cdot t\_1\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (/ (- (+ t_1 (* 2.0 x2)) x1) t_0)))
   (if (or (<= x1 -5.5e+102) (not (<= x1 2.1e+54)))
     (* 6.0 (pow x1 4.0))
     (+
      x1
      (+
       (* 3.0 (/ (- x1 (- t_1 (* 2.0 x2))) (- -1.0 (* x1 x1))))
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (*
           t_0
           (+
            (* (* (* x1 2.0) t_2) (- t_2 3.0))
            (* (* x1 x1) (- (* t_2 4.0) 6.0))))
          (* 3.0 t_1)))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0;
	double tmp;
	if ((x1 <= -5.5e+102) || !(x1 <= 2.1e+54)) {
		tmp = 6.0 * pow(x1, 4.0);
	} else {
		tmp = x1 + ((3.0 * ((x1 - (t_1 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (3.0 * t_1)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = ((t_1 + (2.0d0 * x2)) - x1) / t_0
    if ((x1 <= (-5.5d+102)) .or. (.not. (x1 <= 2.1d+54))) then
        tmp = 6.0d0 * (x1 ** 4.0d0)
    else
        tmp = x1 + ((3.0d0 * ((x1 - (t_1 - (2.0d0 * x2))) / ((-1.0d0) - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * ((t_2 * 4.0d0) - 6.0d0)))) + (3.0d0 * t_1)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0;
	double tmp;
	if ((x1 <= -5.5e+102) || !(x1 <= 2.1e+54)) {
		tmp = 6.0 * Math.pow(x1, 4.0);
	} else {
		tmp = x1 + ((3.0 * ((x1 - (t_1 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (3.0 * t_1)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0
	tmp = 0
	if (x1 <= -5.5e+102) or not (x1 <= 2.1e+54):
		tmp = 6.0 * math.pow(x1, 4.0)
	else:
		tmp = x1 + ((3.0 * ((x1 - (t_1 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (3.0 * t_1)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_0)
	tmp = 0.0
	if ((x1 <= -5.5e+102) || !(x1 <= 2.1e+54))
		tmp = Float64(6.0 * (x1 ^ 4.0));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 - Float64(t_1 - Float64(2.0 * x2))) / Float64(-1.0 - Float64(x1 * x1)))) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)))) + Float64(3.0 * t_1))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * 3.0);
	t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0;
	tmp = 0.0;
	if ((x1 <= -5.5e+102) || ~((x1 <= 2.1e+54)))
		tmp = 6.0 * (x1 ^ 4.0);
	else
		tmp = x1 + ((3.0 * ((x1 - (t_1 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (3.0 * t_1)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[Or[LessEqual[x1, -5.5e+102], N[Not[LessEqual[x1, 2.1e+54]], $MachinePrecision]], N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(x1 - N[(t$95$1 - 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 * 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[(3.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -5.49999999999999981e102 or 2.09999999999999986e54 < x1

   1. Initial program 13.4%

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

   3. Simplified 13.4%

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

   5. Taylor expanded in x1 around inf 100.0%

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

   if -5.49999999999999981e102 < x1 < 2.09999999999999986e54

   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 97.9%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102} \lor \neg \left(x1 \leq 2.1 \cdot 10^{+54}\right):\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot \left(3 + x2 \cdot -4\right)\\ t_1 := x2 \cdot \left(3 - 2 \cdot x2\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \frac{\left(t\_2 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\\ t_4 := 3 \cdot \left(x2 \cdot -2 - 3\right)\\ t_5 := 3 + x2 \cdot -2\\ t_6 := x2 \cdot t\_5\\ t_7 := -4 \cdot t\_6\\ t_8 := -1 - x1 \cdot x1\\ t_9 := x1 + \left(3 \cdot \frac{x1 - \left(t\_2 - 2 \cdot x2\right)}{t\_8} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_2 + \left(\left(x1 \cdot x1\right) \cdot \left(6 - t\_3 \cdot 4\right) + \left(t\_3 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right)\right) \cdot t\_8\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5.7 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x1 \cdot \left(6 + \left(\left(t\_4 - \left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(t\_7 + 2 \cdot \left(\left(1 + \left(-3 \cdot t\_5 + 2 \cdot t\_1\right)\right) - -2 \cdot t\_6\right)\right) - 3\right)\right)\right)\right) - t\_0\right)\right) - t\_7\right) - -1\right)\\ \mathbf{elif}\;x1 \leq -7.4 \cdot 10^{+31}:\\ \;\;\;\;t\_9\\ \mathbf{elif}\;x1 \leq 7.5 \cdot 10^{+28}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(t\_7 + x1 \cdot \left(\left(t\_0 - \left(t\_4 - \left(x2 \cdot 6 + x2 \cdot 8\right)\right)\right) - 6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+97}:\\ \;\;\;\;t\_9\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(t\_4 - x1 \cdot 3\right) + 4 \cdot t\_1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 2.0 (+ 3.0 (* x2 -4.0))))
        (t_1 (* x2 (- 3.0 (* 2.0 x2))))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (/ (- (+ t_2 (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
        (t_4 (* 3.0 (- (* x2 -2.0) 3.0)))
        (t_5 (+ 3.0 (* x2 -2.0)))
        (t_6 (* x2 t_5))
        (t_7 (* -4.0 t_6))
        (t_8 (- -1.0 (* x1 x1)))
        (t_9
         (+
          x1
          (+
           (* 3.0 (/ (- x1 (- t_2 (* 2.0 x2))) t_8))
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* 3.0 t_2)
              (*
               (+
                (* (* x1 x1) (- 6.0 (* t_3 4.0)))
                (* (- t_3 3.0) (* (* x1 2.0) (- (/ 1.0 x1) 3.0))))
               t_8))))))))
   (if (<= x1 -5.7e+102)
     (-
      (* x2 -6.0)
      (*
       x1
       (-
        (-
         (*
          x1
          (+
           6.0
           (-
            (-
             t_4
             (+
              (* x2 6.0)
              (+
               (* x2 8.0)
               (*
                x1
                (-
                 (+
                  t_7
                  (*
                   2.0
                   (- (+ 1.0 (+ (* -3.0 t_5) (* 2.0 t_1))) (* -2.0 t_6))))
                 3.0)))))
            t_0)))
         t_7)
        -1.0)))
     (if (<= x1 -7.4e+31)
       t_9
       (if (<= x1 7.5e+28)
         (+
          (* x2 -6.0)
          (*
           x1
           (+
            -1.0
            (+ t_7 (* x1 (- (- t_0 (- t_4 (+ (* x2 6.0) (* x2 8.0)))) 6.0))))))
         (if (<= x1 5e+97)
           t_9
           (+
            x1
            (-
             (* x2 -6.0)
             (* x1 (+ 2.0 (+ (* x1 (- t_4 (* x1 3.0))) (* 4.0 t_1))))))))))))

C

double code(double x1, double x2) {
	double t_0 = 2.0 * (3.0 + (x2 * -4.0));
	double t_1 = x2 * (3.0 - (2.0 * x2));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = ((t_2 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0);
	double t_4 = 3.0 * ((x2 * -2.0) - 3.0);
	double t_5 = 3.0 + (x2 * -2.0);
	double t_6 = x2 * t_5;
	double t_7 = -4.0 * t_6;
	double t_8 = -1.0 - (x1 * x1);
	double t_9 = x1 + ((3.0 * ((x1 - (t_2 - (2.0 * x2))) / t_8)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_2) + ((((x1 * x1) * (6.0 - (t_3 * 4.0))) + ((t_3 - 3.0) * ((x1 * 2.0) * ((1.0 / x1) - 3.0)))) * t_8)))));
	double tmp;
	if (x1 <= -5.7e+102) {
		tmp = (x2 * -6.0) - (x1 * (((x1 * (6.0 + ((t_4 - ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_7 + (2.0 * ((1.0 + ((-3.0 * t_5) + (2.0 * t_1))) - (-2.0 * t_6)))) - 3.0))))) - t_0))) - t_7) - -1.0));
	} else if (x1 <= -7.4e+31) {
		tmp = t_9;
	} else if (x1 <= 7.5e+28) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (t_7 + (x1 * ((t_0 - (t_4 - ((x2 * 6.0) + (x2 * 8.0)))) - 6.0)))));
	} else if (x1 <= 5e+97) {
		tmp = t_9;
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * (t_4 - (x1 * 3.0))) + (4.0 * t_1)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_0 = 2.0d0 * (3.0d0 + (x2 * (-4.0d0)))
    t_1 = x2 * (3.0d0 - (2.0d0 * x2))
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = ((t_2 + (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0)
    t_4 = 3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)
    t_5 = 3.0d0 + (x2 * (-2.0d0))
    t_6 = x2 * t_5
    t_7 = (-4.0d0) * t_6
    t_8 = (-1.0d0) - (x1 * x1)
    t_9 = x1 + ((3.0d0 * ((x1 - (t_2 - (2.0d0 * x2))) / t_8)) + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_2) + ((((x1 * x1) * (6.0d0 - (t_3 * 4.0d0))) + ((t_3 - 3.0d0) * ((x1 * 2.0d0) * ((1.0d0 / x1) - 3.0d0)))) * t_8)))))
    if (x1 <= (-5.7d+102)) then
        tmp = (x2 * (-6.0d0)) - (x1 * (((x1 * (6.0d0 + ((t_4 - ((x2 * 6.0d0) + ((x2 * 8.0d0) + (x1 * ((t_7 + (2.0d0 * ((1.0d0 + (((-3.0d0) * t_5) + (2.0d0 * t_1))) - ((-2.0d0) * t_6)))) - 3.0d0))))) - t_0))) - t_7) - (-1.0d0)))
    else if (x1 <= (-7.4d+31)) then
        tmp = t_9
    else if (x1 <= 7.5d+28) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (t_7 + (x1 * ((t_0 - (t_4 - ((x2 * 6.0d0) + (x2 * 8.0d0)))) - 6.0d0)))))
    else if (x1 <= 5d+97) then
        tmp = t_9
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((x1 * (t_4 - (x1 * 3.0d0))) + (4.0d0 * t_1)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 2.0 * (3.0 + (x2 * -4.0));
	double t_1 = x2 * (3.0 - (2.0 * x2));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = ((t_2 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0);
	double t_4 = 3.0 * ((x2 * -2.0) - 3.0);
	double t_5 = 3.0 + (x2 * -2.0);
	double t_6 = x2 * t_5;
	double t_7 = -4.0 * t_6;
	double t_8 = -1.0 - (x1 * x1);
	double t_9 = x1 + ((3.0 * ((x1 - (t_2 - (2.0 * x2))) / t_8)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_2) + ((((x1 * x1) * (6.0 - (t_3 * 4.0))) + ((t_3 - 3.0) * ((x1 * 2.0) * ((1.0 / x1) - 3.0)))) * t_8)))));
	double tmp;
	if (x1 <= -5.7e+102) {
		tmp = (x2 * -6.0) - (x1 * (((x1 * (6.0 + ((t_4 - ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_7 + (2.0 * ((1.0 + ((-3.0 * t_5) + (2.0 * t_1))) - (-2.0 * t_6)))) - 3.0))))) - t_0))) - t_7) - -1.0));
	} else if (x1 <= -7.4e+31) {
		tmp = t_9;
	} else if (x1 <= 7.5e+28) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (t_7 + (x1 * ((t_0 - (t_4 - ((x2 * 6.0) + (x2 * 8.0)))) - 6.0)))));
	} else if (x1 <= 5e+97) {
		tmp = t_9;
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * (t_4 - (x1 * 3.0))) + (4.0 * t_1)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 2.0 * (3.0 + (x2 * -4.0))
	t_1 = x2 * (3.0 - (2.0 * x2))
	t_2 = x1 * (x1 * 3.0)
	t_3 = ((t_2 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0)
	t_4 = 3.0 * ((x2 * -2.0) - 3.0)
	t_5 = 3.0 + (x2 * -2.0)
	t_6 = x2 * t_5
	t_7 = -4.0 * t_6
	t_8 = -1.0 - (x1 * x1)
	t_9 = x1 + ((3.0 * ((x1 - (t_2 - (2.0 * x2))) / t_8)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_2) + ((((x1 * x1) * (6.0 - (t_3 * 4.0))) + ((t_3 - 3.0) * ((x1 * 2.0) * ((1.0 / x1) - 3.0)))) * t_8)))))
	tmp = 0
	if x1 <= -5.7e+102:
		tmp = (x2 * -6.0) - (x1 * (((x1 * (6.0 + ((t_4 - ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_7 + (2.0 * ((1.0 + ((-3.0 * t_5) + (2.0 * t_1))) - (-2.0 * t_6)))) - 3.0))))) - t_0))) - t_7) - -1.0))
	elif x1 <= -7.4e+31:
		tmp = t_9
	elif x1 <= 7.5e+28:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (t_7 + (x1 * ((t_0 - (t_4 - ((x2 * 6.0) + (x2 * 8.0)))) - 6.0)))))
	elif x1 <= 5e+97:
		tmp = t_9
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * (t_4 - (x1 * 3.0))) + (4.0 * t_1)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(2.0 * Float64(3.0 + Float64(x2 * -4.0)))
	t_1 = Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(Float64(t_2 + Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))
	t_4 = Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0))
	t_5 = Float64(3.0 + Float64(x2 * -2.0))
	t_6 = Float64(x2 * t_5)
	t_7 = Float64(-4.0 * t_6)
	t_8 = Float64(-1.0 - Float64(x1 * x1))
	t_9 = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 - Float64(t_2 - Float64(2.0 * x2))) / t_8)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_2) + Float64(Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(t_3 * 4.0))) + Float64(Float64(t_3 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(Float64(1.0 / x1) - 3.0)))) * t_8))))))
	tmp = 0.0
	if (x1 <= -5.7e+102)
		tmp = Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(Float64(Float64(x1 * Float64(6.0 + Float64(Float64(t_4 - Float64(Float64(x2 * 6.0) + Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_7 + Float64(2.0 * Float64(Float64(1.0 + Float64(Float64(-3.0 * t_5) + Float64(2.0 * t_1))) - Float64(-2.0 * t_6)))) - 3.0))))) - t_0))) - t_7) - -1.0)));
	elseif (x1 <= -7.4e+31)
		tmp = t_9;
	elseif (x1 <= 7.5e+28)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(t_7 + Float64(x1 * Float64(Float64(t_0 - Float64(t_4 - Float64(Float64(x2 * 6.0) + Float64(x2 * 8.0)))) - 6.0))))));
	elseif (x1 <= 5e+97)
		tmp = t_9;
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(x1 * Float64(t_4 - Float64(x1 * 3.0))) + Float64(4.0 * t_1))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 2.0 * (3.0 + (x2 * -4.0));
	t_1 = x2 * (3.0 - (2.0 * x2));
	t_2 = x1 * (x1 * 3.0);
	t_3 = ((t_2 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0);
	t_4 = 3.0 * ((x2 * -2.0) - 3.0);
	t_5 = 3.0 + (x2 * -2.0);
	t_6 = x2 * t_5;
	t_7 = -4.0 * t_6;
	t_8 = -1.0 - (x1 * x1);
	t_9 = x1 + ((3.0 * ((x1 - (t_2 - (2.0 * x2))) / t_8)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_2) + ((((x1 * x1) * (6.0 - (t_3 * 4.0))) + ((t_3 - 3.0) * ((x1 * 2.0) * ((1.0 / x1) - 3.0)))) * t_8)))));
	tmp = 0.0;
	if (x1 <= -5.7e+102)
		tmp = (x2 * -6.0) - (x1 * (((x1 * (6.0 + ((t_4 - ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_7 + (2.0 * ((1.0 + ((-3.0 * t_5) + (2.0 * t_1))) - (-2.0 * t_6)))) - 3.0))))) - t_0))) - t_7) - -1.0));
	elseif (x1 <= -7.4e+31)
		tmp = t_9;
	elseif (x1 <= 7.5e+28)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (t_7 + (x1 * ((t_0 - (t_4 - ((x2 * 6.0) + (x2 * 8.0)))) - 6.0)))));
	elseif (x1 <= 5e+97)
		tmp = t_9;
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * (t_4 - (x1 * 3.0))) + (4.0 * t_1)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(2.0 * N[(3.0 + N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(x2 * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(-4.0 * t$95$6), $MachinePrecision]}, Block[{t$95$8 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(x1 + N[(N[(3.0 * N[(N[(x1 - N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$8), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$2), $MachinePrecision] + N[(N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(t$95$3 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$3 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(1.0 / x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.7e+102], N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(N[(N[(x1 * N[(6.0 + N[(N[(t$95$4 - N[(N[(x2 * 6.0), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$7 + N[(2.0 * N[(N[(1.0 + N[(N[(-3.0 * t$95$5), $MachinePrecision] + N[(2.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-2.0 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$7), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -7.4e+31], t$95$9, If[LessEqual[x1, 7.5e+28], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(t$95$7 + N[(x1 * N[(N[(t$95$0 - N[(t$95$4 - N[(N[(x2 * 6.0), $MachinePrecision] + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+97], t$95$9, N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(N[(x1 * N[(t$95$4 - N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(4.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.6999999999999999e102

   1. Initial program 0.0%

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

   3. Simplified 22.0%

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

   5. Taylor expanded in x1 around 0 70.7%

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

   if -5.6999999999999999e102 < x1 < -7.3999999999999996e31 or 7.4999999999999998e28 < x1 < 4.99999999999999999e97

   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 inf 91.7%

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

   4. Taylor expanded in x1 around inf 91.7%

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

   if -7.3999999999999996e31 < x1 < 7.4999999999999998e28

   1. Initial program 99.3%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in x1 around 0 82.8%

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

   if 4.99999999999999999e97 < x1

   1. Initial program 14.3%

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

   3. Simplified 14.3%

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

   5. Taylor expanded in x1 around 0 6.1%

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

      1. associate-*r* 6.1%

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

      2. fmm-def 6.1%

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

      3. metadata-eval 6.1%

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

   7. Simplified 6.1%

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

   8. Taylor expanded in x1 around 0 97.1%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.7 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x1 \cdot \left(6 + \left(\left(3 \cdot \left(x2 \cdot -2 - 3\right) - \left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + 2 \cdot \left(\left(1 + \left(-3 \cdot \left(3 + x2 \cdot -2\right) + 2 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) - -2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right)\right) - 3\right)\right)\right)\right) - 2 \cdot \left(3 + x2 \cdot -4\right)\right)\right) - -4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq -7.4 \cdot 10^{+31}:\\ \;\;\;\;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(\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(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right)\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7.5 \cdot 10^{+28}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(-4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + x2 \cdot -4\right) - \left(3 \cdot \left(x2 \cdot -2 - 3\right) - \left(x2 \cdot 6 + x2 \cdot 8\right)\right)\right) - 6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+97}:\\ \;\;\;\;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(\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(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right)\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 96.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ \mathbf{if}\;x1 \leq -8 \cdot 10^{+59}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq 7 \cdot 10^{+44}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_0 \cdot t\_2 + t\_1 \cdot \left(\left(x1 \cdot x1\right) \cdot 6 - \left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(3 - t\_2\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{x1}^{3} \cdot \left(x1 \cdot 6 - 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (if (<= x1 -8e+59)
     (* 6.0 (pow x1 4.0))
     (if (<= x1 7e+44)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* t_0 t_2)
            (*
             t_1
             (- (* (* x1 x1) 6.0) (* (* (* x1 2.0) t_2) (- 3.0 t_2)))))))))
       (* (pow x1 3.0) (- (* x1 6.0) 3.0))))))

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 <= -8e+59) {
		tmp = 6.0 * pow(x1, 4.0);
	} else if (x1 <= 7e+44) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((x1 * x1) * 6.0) - (((x1 * 2.0) * t_2) * (3.0 - t_2))))))));
	} else {
		tmp = pow(x1, 3.0) * ((x1 * 6.0) - 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: 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 <= (-8d+59)) then
        tmp = 6.0d0 * (x1 ** 4.0d0)
    else if (x1 <= 7d+44) then
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((x1 * x1) * 6.0d0) - (((x1 * 2.0d0) * t_2) * (3.0d0 - t_2))))))))
    else
        tmp = (x1 ** 3.0d0) * ((x1 * 6.0d0) - 3.0d0)
    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 <= -8e+59) {
		tmp = 6.0 * Math.pow(x1, 4.0);
	} else if (x1 <= 7e+44) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((x1 * x1) * 6.0) - (((x1 * 2.0) * t_2) * (3.0 - t_2))))))));
	} else {
		tmp = Math.pow(x1, 3.0) * ((x1 * 6.0) - 3.0);
	}
	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 <= -8e+59:
		tmp = 6.0 * math.pow(x1, 4.0)
	elif x1 <= 7e+44:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((x1 * x1) * 6.0) - (((x1 * 2.0) * t_2) * (3.0 - t_2))))))))
	else:
		tmp = math.pow(x1, 3.0) * ((x1 * 6.0) - 3.0)
	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 <= -8e+59)
		tmp = Float64(6.0 * (x1 ^ 4.0));
	elseif (x1 <= 7e+44)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * t_2) + Float64(t_1 * Float64(Float64(Float64(x1 * x1) * 6.0) - Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(3.0 - t_2)))))))));
	else
		tmp = Float64((x1 ^ 3.0) * Float64(Float64(x1 * 6.0) - 3.0));
	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 <= -8e+59)
		tmp = 6.0 * (x1 ^ 4.0);
	elseif (x1 <= 7e+44)
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((x1 * x1) * 6.0) - (((x1 * 2.0) * t_2) * (3.0 - t_2))))))));
	else
		tmp = (x1 ^ 3.0) * ((x1 * 6.0) - 3.0);
	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, -8e+59], N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7e+44], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * t$95$2), $MachinePrecision] + N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision] - N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(3.0 - t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Power[x1, 3.0], $MachinePrecision] * N[(N[(x1 * 6.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -7.99999999999999977e59

   1. Initial program 22.5%

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

   3. Simplified 22.5%

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

   5. Taylor expanded in x1 around inf 98.1%

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

   if -7.99999999999999977e59 < x1 < 6.9999999999999998e44

   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 95.1%

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

   if 6.9999999999999998e44 < x1

   1. Initial program 31.7%

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

   3. Simplified 31.7%

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

   5. Taylor expanded in x1 around inf 97.7%

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

      1. associate-*r/ 97.7%

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

      2. metadata-eval 97.7%

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

   7. Simplified 97.7%

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

   8. Taylor expanded in x1 around 0 97.7%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -8 \cdot 10^{+59}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq 7 \cdot 10^{+44}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6 - \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{x1}^{3} \cdot \left(x1 \cdot 6 - 3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 94.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+51}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq 3 \cdot 10^{+44}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(t\_0 - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_0 \cdot t\_2 + t\_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t\_2 \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2\right)\right) \cdot \left(\left(2 \cdot x2 - x1\right) - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{x1}^{3} \cdot \left(x1 \cdot 6 - 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (if (<= x1 -1.35e+51)
     (* 6.0 (pow x1 4.0))
     (if (<= x1 3e+44)
       (+
        x1
        (+
         (* 3.0 (/ (- x1 (- t_0 (* 2.0 x2))) (- -1.0 (* x1 x1))))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* t_0 t_2)
            (*
             t_1
             (+
              (* (* x1 x1) (- (* t_2 4.0) 6.0))
              (* (* (* x1 2.0) (* 2.0 x2)) (- (- (* 2.0 x2) x1) 3.0)))))))))
       (* (pow x1 3.0) (- (* x1 6.0) 3.0))))))

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 <= -1.35e+51) {
		tmp = 6.0 * pow(x1, 4.0);
	} else if (x1 <= 3e+44) {
		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 * x1) * ((t_2 * 4.0) - 6.0)) + (((x1 * 2.0) * (2.0 * x2)) * (((2.0 * x2) - x1) - 3.0))))))));
	} else {
		tmp = pow(x1, 3.0) * ((x1 * 6.0) - 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: 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 <= (-1.35d+51)) then
        tmp = 6.0d0 * (x1 ** 4.0d0)
    else if (x1 <= 3d+44) 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 * x1) * ((t_2 * 4.0d0) - 6.0d0)) + (((x1 * 2.0d0) * (2.0d0 * x2)) * (((2.0d0 * x2) - x1) - 3.0d0))))))))
    else
        tmp = (x1 ** 3.0d0) * ((x1 * 6.0d0) - 3.0d0)
    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 <= -1.35e+51) {
		tmp = 6.0 * Math.pow(x1, 4.0);
	} else if (x1 <= 3e+44) {
		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 * x1) * ((t_2 * 4.0) - 6.0)) + (((x1 * 2.0) * (2.0 * x2)) * (((2.0 * x2) - x1) - 3.0))))))));
	} else {
		tmp = Math.pow(x1, 3.0) * ((x1 * 6.0) - 3.0);
	}
	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 <= -1.35e+51:
		tmp = 6.0 * math.pow(x1, 4.0)
	elif x1 <= 3e+44:
		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 * x1) * ((t_2 * 4.0) - 6.0)) + (((x1 * 2.0) * (2.0 * x2)) * (((2.0 * x2) - x1) - 3.0))))))))
	else:
		tmp = math.pow(x1, 3.0) * ((x1 * 6.0) - 3.0)
	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 <= -1.35e+51)
		tmp = Float64(6.0 * (x1 ^ 4.0));
	elseif (x1 <= 3e+44)
		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(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)) + Float64(Float64(Float64(x1 * 2.0) * Float64(2.0 * x2)) * Float64(Float64(Float64(2.0 * x2) - x1) - 3.0)))))))));
	else
		tmp = Float64((x1 ^ 3.0) * Float64(Float64(x1 * 6.0) - 3.0));
	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 <= -1.35e+51)
		tmp = 6.0 * (x1 ^ 4.0);
	elseif (x1 <= 3e+44)
		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 * x1) * ((t_2 * 4.0) - 6.0)) + (((x1 * 2.0) * (2.0 * x2)) * (((2.0 * x2) - x1) - 3.0))))))));
	else
		tmp = (x1 ^ 3.0) * ((x1 * 6.0) - 3.0);
	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, -1.35e+51], N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3e+44], 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[(x1 * x1), $MachinePrecision] * N[(N[(t$95$2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Power[x1, 3.0], $MachinePrecision] * N[(N[(x1 * 6.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.34999999999999996e51

   1. Initial program 23.9%

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

   3. Simplified 23.9%

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

   5. Taylor expanded in x1 around inf 98.1%

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

   if -1.34999999999999996e51 < x1 < 2.99999999999999987e44

   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 90.5%

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

   4. Taylor expanded in x1 around 0 92.8%

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

   if 2.99999999999999987e44 < x1

   1. Initial program 31.7%

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

   3. Simplified 31.7%

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

   5. Taylor expanded in x1 around inf 97.7%

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

      1. associate-*r/ 97.7%

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

      2. metadata-eval 97.7%

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

   7. Simplified 97.7%

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

   8. Taylor expanded in x1 around 0 97.7%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+51}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq 3 \cdot 10^{+44}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2\right)\right) \cdot \left(\left(2 \cdot x2 - x1\right) - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{x1}^{3} \cdot \left(x1 \cdot 6 - 3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 94.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ \mathbf{if}\;x1 \leq -2.3 \cdot 10^{+49}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq 6.5 \cdot 10^{+42}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(t\_0 - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_0 \cdot t\_2 + t\_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t\_2 \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2\right)\right) \cdot \left(\left(2 \cdot x2 - x1\right) - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{x1}^{3} \cdot \left(x1 \cdot 6\right)\\ \end{array} \end{array} \]

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 -2.3e+49)
     (* 6.0 (pow x1 4.0))
     (if (<= x1 6.5e+42)
       (+
        x1
        (+
         (* 3.0 (/ (- x1 (- t_0 (* 2.0 x2))) (- -1.0 (* x1 x1))))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* t_0 t_2)
            (*
             t_1
             (+
              (* (* x1 x1) (- (* t_2 4.0) 6.0))
              (* (* (* x1 2.0) (* 2.0 x2)) (- (- (* 2.0 x2) x1) 3.0)))))))))
       (* (pow x1 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 <= -2.3e+49) {
		tmp = 6.0 * pow(x1, 4.0);
	} else if (x1 <= 6.5e+42) {
		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 * x1) * ((t_2 * 4.0) - 6.0)) + (((x1 * 2.0) * (2.0 * x2)) * (((2.0 * x2) - x1) - 3.0))))))));
	} else {
		tmp = pow(x1, 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 <= (-2.3d+49)) then
        tmp = 6.0d0 * (x1 ** 4.0d0)
    else if (x1 <= 6.5d+42) 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 * x1) * ((t_2 * 4.0d0) - 6.0d0)) + (((x1 * 2.0d0) * (2.0d0 * x2)) * (((2.0d0 * x2) - x1) - 3.0d0))))))))
    else
        tmp = (x1 ** 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 <= -2.3e+49) {
		tmp = 6.0 * Math.pow(x1, 4.0);
	} else if (x1 <= 6.5e+42) {
		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 * x1) * ((t_2 * 4.0) - 6.0)) + (((x1 * 2.0) * (2.0 * x2)) * (((2.0 * x2) - x1) - 3.0))))))));
	} else {
		tmp = Math.pow(x1, 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 <= -2.3e+49:
		tmp = 6.0 * math.pow(x1, 4.0)
	elif x1 <= 6.5e+42:
		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 * x1) * ((t_2 * 4.0) - 6.0)) + (((x1 * 2.0) * (2.0 * x2)) * (((2.0 * x2) - x1) - 3.0))))))))
	else:
		tmp = math.pow(x1, 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 <= -2.3e+49)
		tmp = Float64(6.0 * (x1 ^ 4.0));
	elseif (x1 <= 6.5e+42)
		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(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)) + Float64(Float64(Float64(x1 * 2.0) * Float64(2.0 * x2)) * Float64(Float64(Float64(2.0 * x2) - x1) - 3.0)))))))));
	else
		tmp = Float64((x1 ^ 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 <= -2.3e+49)
		tmp = 6.0 * (x1 ^ 4.0);
	elseif (x1 <= 6.5e+42)
		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 * x1) * ((t_2 * 4.0) - 6.0)) + (((x1 * 2.0) * (2.0 * x2)) * (((2.0 * x2) - x1) - 3.0))))))));
	else
		tmp = (x1 ^ 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, -2.3e+49], N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6.5e+42], 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[(x1 * x1), $MachinePrecision] * N[(N[(t$95$2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Power[x1, 3.0], $MachinePrecision] * N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.30000000000000002e49

   1. Initial program 23.9%

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

   3. Simplified 23.9%

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

   5. Taylor expanded in x1 around inf 98.1%

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

   if -2.30000000000000002e49 < x1 < 6.50000000000000052e42

   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 90.5%

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

   4. Taylor expanded in x1 around 0 92.8%

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

   if 6.50000000000000052e42 < x1

   1. Initial program 31.7%

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

   3. Simplified 31.7%

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

   5. Taylor expanded in x1 around inf 97.7%

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

      1. associate-*r/ 97.7%

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

      2. metadata-eval 97.7%

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

   7. Simplified 97.7%

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

   8. Taylor expanded in x1 around 0 97.7%

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

   9. Taylor expanded in x1 around inf 97.7%

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

       1. *-commutative 97.7%

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

   11. Simplified 97.7%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.3 \cdot 10^{+49}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq 6.5 \cdot 10^{+42}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2\right)\right) \cdot \left(\left(2 \cdot x2 - x1\right) - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{x1}^{3} \cdot \left(x1 \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 94.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ \mathbf{if}\;x1 \leq -3.1 \cdot 10^{+50} \lor \neg \left(x1 \leq 2.8 \cdot 10^{+53}\right):\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(t\_0 - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_0 \cdot t\_2 + t\_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t\_2 \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2\right)\right) \cdot \left(\left(2 \cdot x2 - x1\right) - 3\right)\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

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 -3.1e+50) (not (<= x1 2.8e+53)))
     (* 6.0 (pow x1 4.0))
     (+
      x1
      (+
       (* 3.0 (/ (- x1 (- t_0 (* 2.0 x2))) (- -1.0 (* x1 x1))))
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (* t_0 t_2)
          (*
           t_1
           (+
            (* (* x1 x1) (- (* t_2 4.0) 6.0))
            (* (* (* x1 2.0) (* 2.0 x2)) (- (- (* 2.0 x2) x1) 3.0))))))))))))

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 <= -3.1e+50) || !(x1 <= 2.8e+53)) {
		tmp = 6.0 * pow(x1, 4.0);
	} 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 * x1) * ((t_2 * 4.0) - 6.0)) + (((x1 * 2.0) * (2.0 * x2)) * (((2.0 * x2) - x1) - 3.0))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: 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 <= (-3.1d+50)) .or. (.not. (x1 <= 2.8d+53))) then
        tmp = 6.0d0 * (x1 ** 4.0d0)
    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 * x1) * ((t_2 * 4.0d0) - 6.0d0)) + (((x1 * 2.0d0) * (2.0d0 * x2)) * (((2.0d0 * x2) - x1) - 3.0d0))))))))
    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 <= -3.1e+50) || !(x1 <= 2.8e+53)) {
		tmp = 6.0 * Math.pow(x1, 4.0);
	} 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 * x1) * ((t_2 * 4.0) - 6.0)) + (((x1 * 2.0) * (2.0 * x2)) * (((2.0 * x2) - x1) - 3.0))))))));
	}
	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 <= -3.1e+50) or not (x1 <= 2.8e+53):
		tmp = 6.0 * math.pow(x1, 4.0)
	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 * x1) * ((t_2 * 4.0) - 6.0)) + (((x1 * 2.0) * (2.0 * x2)) * (((2.0 * x2) - x1) - 3.0))))))))
	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 <= -3.1e+50) || !(x1 <= 2.8e+53))
		tmp = Float64(6.0 * (x1 ^ 4.0));
	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(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)) + Float64(Float64(Float64(x1 * 2.0) * Float64(2.0 * x2)) * Float64(Float64(Float64(2.0 * x2) - x1) - 3.0)))))))));
	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 <= -3.1e+50) || ~((x1 <= 2.8e+53)))
		tmp = 6.0 * (x1 ^ 4.0);
	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 * x1) * ((t_2 * 4.0) - 6.0)) + (((x1 * 2.0) * (2.0 * x2)) * (((2.0 * x2) - x1) - 3.0))))))));
	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, -3.1e+50], N[Not[LessEqual[x1, 2.8e+53]], $MachinePrecision]], N[(6.0 * N[Power[x1, 4.0], $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[(x1 * x1), $MachinePrecision] * N[(N[(t$95$2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -3.10000000000000003e50 or 2.8e53 < x1

   1. Initial program 25.1%

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

   3. Simplified 25.1%

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

   5. Taylor expanded in x1 around inf 98.9%

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

   if -3.10000000000000003e50 < x1 < 2.8e53

   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 88.9%

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

   4. Taylor expanded in x1 around 0 92.3%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.1 \cdot 10^{+50} \lor \neg \left(x1 \leq 2.8 \cdot 10^{+53}\right):\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2\right)\right) \cdot \left(\left(2 \cdot x2 - x1\right) - 3\right)\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 88.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x2 \cdot \left(3 - 2 \cdot x2\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \frac{\left(t\_2 + 2 \cdot x2\right) - x1}{t\_0}\\ t_4 := 3 \cdot \left(x2 \cdot -2 - 3\right)\\ t_5 := 3 + x2 \cdot -2\\ t_6 := x2 \cdot t\_5\\ t_7 := -4 \cdot t\_6\\ \mathbf{if}\;x1 \leq -4.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x1 \cdot \left(6 + \left(\left(t\_4 - \left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(t\_7 + 2 \cdot \left(\left(1 + \left(-3 \cdot t\_5 + 2 \cdot t\_1\right)\right) - -2 \cdot t\_6\right)\right) - 3\right)\right)\right)\right) - 2 \cdot \left(3 + x2 \cdot -4\right)\right)\right) - t\_7\right) - -1\right)\\ \mathbf{elif}\;x1 \leq 5.6 \cdot 10^{+94}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(t\_2 - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_2 \cdot t\_3 + t\_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t\_3 \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2\right)\right) \cdot \left(\left(2 \cdot x2 - x1\right) - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(t\_4 - x1 \cdot 3\right) + 4 \cdot t\_1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x2 (- 3.0 (* 2.0 x2))))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (/ (- (+ t_2 (* 2.0 x2)) x1) t_0))
        (t_4 (* 3.0 (- (* x2 -2.0) 3.0)))
        (t_5 (+ 3.0 (* x2 -2.0)))
        (t_6 (* x2 t_5))
        (t_7 (* -4.0 t_6)))
   (if (<= x1 -4.6e+102)
     (-
      (* x2 -6.0)
      (*
       x1
       (-
        (-
         (*
          x1
          (+
           6.0
           (-
            (-
             t_4
             (+
              (* x2 6.0)
              (+
               (* x2 8.0)
               (*
                x1
                (-
                 (+
                  t_7
                  (*
                   2.0
                   (- (+ 1.0 (+ (* -3.0 t_5) (* 2.0 t_1))) (* -2.0 t_6))))
                 3.0)))))
            (* 2.0 (+ 3.0 (* x2 -4.0))))))
         t_7)
        -1.0)))
     (if (<= x1 5.6e+94)
       (+
        x1
        (+
         (* 3.0 (/ (- x1 (- t_2 (* 2.0 x2))) (- -1.0 (* x1 x1))))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* t_2 t_3)
            (*
             t_0
             (+
              (* (* x1 x1) (- (* t_3 4.0) 6.0))
              (* (* (* x1 2.0) (* 2.0 x2)) (- (- (* 2.0 x2) x1) 3.0)))))))))
       (+
        x1
        (-
         (* x2 -6.0)
         (* x1 (+ 2.0 (+ (* x1 (- t_4 (* x1 3.0))) (* 4.0 t_1))))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x2 * (3.0 - (2.0 * x2));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = ((t_2 + (2.0 * x2)) - x1) / t_0;
	double t_4 = 3.0 * ((x2 * -2.0) - 3.0);
	double t_5 = 3.0 + (x2 * -2.0);
	double t_6 = x2 * t_5;
	double t_7 = -4.0 * t_6;
	double tmp;
	if (x1 <= -4.6e+102) {
		tmp = (x2 * -6.0) - (x1 * (((x1 * (6.0 + ((t_4 - ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_7 + (2.0 * ((1.0 + ((-3.0 * t_5) + (2.0 * t_1))) - (-2.0 * t_6)))) - 3.0))))) - (2.0 * (3.0 + (x2 * -4.0)))))) - t_7) - -1.0));
	} else if (x1 <= 5.6e+94) {
		tmp = x1 + ((3.0 * ((x1 - (t_2 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_3) + (t_0 * (((x1 * x1) * ((t_3 * 4.0) - 6.0)) + (((x1 * 2.0) * (2.0 * x2)) * (((2.0 * x2) - x1) - 3.0))))))));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * (t_4 - (x1 * 3.0))) + (4.0 * t_1)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x2 * (3.0d0 - (2.0d0 * x2))
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = ((t_2 + (2.0d0 * x2)) - x1) / t_0
    t_4 = 3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)
    t_5 = 3.0d0 + (x2 * (-2.0d0))
    t_6 = x2 * t_5
    t_7 = (-4.0d0) * t_6
    if (x1 <= (-4.6d+102)) then
        tmp = (x2 * (-6.0d0)) - (x1 * (((x1 * (6.0d0 + ((t_4 - ((x2 * 6.0d0) + ((x2 * 8.0d0) + (x1 * ((t_7 + (2.0d0 * ((1.0d0 + (((-3.0d0) * t_5) + (2.0d0 * t_1))) - ((-2.0d0) * t_6)))) - 3.0d0))))) - (2.0d0 * (3.0d0 + (x2 * (-4.0d0))))))) - t_7) - (-1.0d0)))
    else if (x1 <= 5.6d+94) then
        tmp = x1 + ((3.0d0 * ((x1 - (t_2 - (2.0d0 * x2))) / ((-1.0d0) - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_3) + (t_0 * (((x1 * x1) * ((t_3 * 4.0d0) - 6.0d0)) + (((x1 * 2.0d0) * (2.0d0 * x2)) * (((2.0d0 * x2) - x1) - 3.0d0))))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((x1 * (t_4 - (x1 * 3.0d0))) + (4.0d0 * t_1)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x2 * (3.0 - (2.0 * x2));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = ((t_2 + (2.0 * x2)) - x1) / t_0;
	double t_4 = 3.0 * ((x2 * -2.0) - 3.0);
	double t_5 = 3.0 + (x2 * -2.0);
	double t_6 = x2 * t_5;
	double t_7 = -4.0 * t_6;
	double tmp;
	if (x1 <= -4.6e+102) {
		tmp = (x2 * -6.0) - (x1 * (((x1 * (6.0 + ((t_4 - ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_7 + (2.0 * ((1.0 + ((-3.0 * t_5) + (2.0 * t_1))) - (-2.0 * t_6)))) - 3.0))))) - (2.0 * (3.0 + (x2 * -4.0)))))) - t_7) - -1.0));
	} else if (x1 <= 5.6e+94) {
		tmp = x1 + ((3.0 * ((x1 - (t_2 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_3) + (t_0 * (((x1 * x1) * ((t_3 * 4.0) - 6.0)) + (((x1 * 2.0) * (2.0 * x2)) * (((2.0 * x2) - x1) - 3.0))))))));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * (t_4 - (x1 * 3.0))) + (4.0 * t_1)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x2 * (3.0 - (2.0 * x2))
	t_2 = x1 * (x1 * 3.0)
	t_3 = ((t_2 + (2.0 * x2)) - x1) / t_0
	t_4 = 3.0 * ((x2 * -2.0) - 3.0)
	t_5 = 3.0 + (x2 * -2.0)
	t_6 = x2 * t_5
	t_7 = -4.0 * t_6
	tmp = 0
	if x1 <= -4.6e+102:
		tmp = (x2 * -6.0) - (x1 * (((x1 * (6.0 + ((t_4 - ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_7 + (2.0 * ((1.0 + ((-3.0 * t_5) + (2.0 * t_1))) - (-2.0 * t_6)))) - 3.0))))) - (2.0 * (3.0 + (x2 * -4.0)))))) - t_7) - -1.0))
	elif x1 <= 5.6e+94:
		tmp = x1 + ((3.0 * ((x1 - (t_2 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_3) + (t_0 * (((x1 * x1) * ((t_3 * 4.0) - 6.0)) + (((x1 * 2.0) * (2.0 * x2)) * (((2.0 * x2) - x1) - 3.0))))))))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * (t_4 - (x1 * 3.0))) + (4.0 * t_1)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(Float64(t_2 + Float64(2.0 * x2)) - x1) / t_0)
	t_4 = Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0))
	t_5 = Float64(3.0 + Float64(x2 * -2.0))
	t_6 = Float64(x2 * t_5)
	t_7 = Float64(-4.0 * t_6)
	tmp = 0.0
	if (x1 <= -4.6e+102)
		tmp = Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(Float64(Float64(x1 * Float64(6.0 + Float64(Float64(t_4 - Float64(Float64(x2 * 6.0) + Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_7 + Float64(2.0 * Float64(Float64(1.0 + Float64(Float64(-3.0 * t_5) + Float64(2.0 * t_1))) - Float64(-2.0 * t_6)))) - 3.0))))) - Float64(2.0 * Float64(3.0 + Float64(x2 * -4.0)))))) - t_7) - -1.0)));
	elseif (x1 <= 5.6e+94)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 - Float64(t_2 - Float64(2.0 * x2))) / Float64(-1.0 - Float64(x1 * x1)))) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_2 * t_3) + Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0)) + Float64(Float64(Float64(x1 * 2.0) * Float64(2.0 * x2)) * Float64(Float64(Float64(2.0 * x2) - x1) - 3.0)))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(x1 * Float64(t_4 - Float64(x1 * 3.0))) + Float64(4.0 * t_1))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x2 * (3.0 - (2.0 * x2));
	t_2 = x1 * (x1 * 3.0);
	t_3 = ((t_2 + (2.0 * x2)) - x1) / t_0;
	t_4 = 3.0 * ((x2 * -2.0) - 3.0);
	t_5 = 3.0 + (x2 * -2.0);
	t_6 = x2 * t_5;
	t_7 = -4.0 * t_6;
	tmp = 0.0;
	if (x1 <= -4.6e+102)
		tmp = (x2 * -6.0) - (x1 * (((x1 * (6.0 + ((t_4 - ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_7 + (2.0 * ((1.0 + ((-3.0 * t_5) + (2.0 * t_1))) - (-2.0 * t_6)))) - 3.0))))) - (2.0 * (3.0 + (x2 * -4.0)))))) - t_7) - -1.0));
	elseif (x1 <= 5.6e+94)
		tmp = x1 + ((3.0 * ((x1 - (t_2 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_3) + (t_0 * (((x1 * x1) * ((t_3 * 4.0) - 6.0)) + (((x1 * 2.0) * (2.0 * x2)) * (((2.0 * x2) - x1) - 3.0))))))));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * (t_4 - (x1 * 3.0))) + (4.0 * t_1)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(x2 * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(-4.0 * t$95$6), $MachinePrecision]}, If[LessEqual[x1, -4.6e+102], N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(N[(N[(x1 * N[(6.0 + N[(N[(t$95$4 - N[(N[(x2 * 6.0), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$7 + N[(2.0 * N[(N[(1.0 + N[(N[(-3.0 * t$95$5), $MachinePrecision] + N[(2.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-2.0 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(2.0 * N[(3.0 + N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$7), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.6e+94], N[(x1 + N[(N[(3.0 * N[(N[(x1 - N[(t$95$2 - 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$2 * t$95$3), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(N[(x1 * N[(t$95$4 - N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(4.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4.5999999999999998e102

   1. Initial program 2.4%

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

   3. Simplified 23.8%

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

   5. Taylor expanded in x1 around 0 71.4%

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

   if -4.5999999999999998e102 < x1 < 5.59999999999999997e94

   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 82.1%

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

   4. Taylor expanded in x1 around 0 91.6%

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

   if 5.59999999999999997e94 < x1

   1. Initial program 18.9%

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

   3. Simplified 18.9%

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

   5. Taylor expanded in x1 around 0 6.1%

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

      1. associate-*r* 6.1%

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

      2. fmm-def 6.1%

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

      3. metadata-eval 6.1%

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

   7. Simplified 6.1%

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

   8. Taylor expanded in x1 around 0 92.4%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x1 \cdot \left(6 + \left(\left(3 \cdot \left(x2 \cdot -2 - 3\right) - \left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + 2 \cdot \left(\left(1 + \left(-3 \cdot \left(3 + x2 \cdot -2\right) + 2 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) - -2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right)\right) - 3\right)\right)\right)\right) - 2 \cdot \left(3 + x2 \cdot -4\right)\right)\right) - -4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right) - -1\right)\\ \mathbf{elif}\;x1 \leq 5.6 \cdot 10^{+94}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2\right)\right) \cdot \left(\left(2 \cdot x2 - x1\right) - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 79.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 + x2 \cdot -2\\ t_1 := x2 \cdot t\_0\\ t_2 := -4 \cdot t\_1\\ t_3 := x1 \cdot x1 + 1\\ t_4 := 3 \cdot \left(3 - x2 \cdot -2\right)\\ t_5 := x1 \cdot \left(x1 \cdot 3\right)\\ t_6 := \frac{\left(t\_5 + 2 \cdot x2\right) - x1}{t\_3}\\ \mathbf{if}\;x1 \leq -5.7 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(t\_2 + x1 \cdot \left(\left(2 \cdot \left(3 + x2 \cdot -4\right) + \left(t\_4 + \left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(t\_2 + 2 \cdot \left(\left(1 + \left(-3 \cdot t\_0 + 2 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) - -2 \cdot t\_1\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -8 \cdot 10^{+24}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_5 - 2 \cdot x2\right) - x1}{t\_3} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_5 \cdot t\_6 + t\_3 \cdot \left(\left(x1 \cdot x1\right) \cdot 6 - \left(\left(x1 \cdot 2\right) \cdot \left(3 + \frac{-1}{x1}\right)\right) \cdot \left(3 - t\_6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(x1 \cdot 3 + t\_4\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ 3.0 (* x2 -2.0)))
        (t_1 (* x2 t_0))
        (t_2 (* -4.0 t_1))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (* 3.0 (- 3.0 (* x2 -2.0))))
        (t_5 (* x1 (* x1 3.0)))
        (t_6 (/ (- (+ t_5 (* 2.0 x2)) x1) t_3)))
   (if (<= x1 -5.7e+102)
     (+
      (* x2 -6.0)
      (*
       x1
       (+
        -1.0
        (+
         t_2
         (*
          x1
          (-
           (+
            (* 2.0 (+ 3.0 (* x2 -4.0)))
            (+
             t_4
             (+
              (* x2 6.0)
              (+
               (* x2 8.0)
               (*
                x1
                (-
                 (+
                  t_2
                  (*
                   2.0
                   (-
                    (+ 1.0 (+ (* -3.0 t_0) (* 2.0 (* x2 (- 3.0 (* 2.0 x2))))))
                    (* -2.0 t_1))))
                 3.0))))))
           6.0))))))
     (if (<= x1 -8e+24)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_5 (* 2.0 x2)) x1) t_3))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* t_5 t_6)
            (*
             t_3
             (-
              (* (* x1 x1) 6.0)
              (* (* (* x1 2.0) (+ 3.0 (/ -1.0 x1))) (- 3.0 t_6)))))))))
       (+
        x1
        (+
         (* x2 -6.0)
         (*
          x1
          (-
           (+ (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) (* x1 (+ (* x1 3.0) t_4)))
           2.0))))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 + (x2 * -2.0);
	double t_1 = x2 * t_0;
	double t_2 = -4.0 * t_1;
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = 3.0 * (3.0 - (x2 * -2.0));
	double t_5 = x1 * (x1 * 3.0);
	double t_6 = ((t_5 + (2.0 * x2)) - x1) / t_3;
	double tmp;
	if (x1 <= -5.7e+102) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (t_2 + (x1 * (((2.0 * (3.0 + (x2 * -4.0))) + (t_4 + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_2 + (2.0 * ((1.0 + ((-3.0 * t_0) + (2.0 * (x2 * (3.0 - (2.0 * x2)))))) - (-2.0 * t_1)))) - 3.0)))))) - 6.0)))));
	} else if (x1 <= -8e+24) {
		tmp = x1 + ((3.0 * (((t_5 - (2.0 * x2)) - x1) / t_3)) + (x1 + ((x1 * (x1 * x1)) + ((t_5 * t_6) + (t_3 * (((x1 * x1) * 6.0) - (((x1 * 2.0) * (3.0 + (-1.0 / x1))) * (3.0 - t_6))))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * ((x1 * 3.0) + t_4))) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = 3.0d0 + (x2 * (-2.0d0))
    t_1 = x2 * t_0
    t_2 = (-4.0d0) * t_1
    t_3 = (x1 * x1) + 1.0d0
    t_4 = 3.0d0 * (3.0d0 - (x2 * (-2.0d0)))
    t_5 = x1 * (x1 * 3.0d0)
    t_6 = ((t_5 + (2.0d0 * x2)) - x1) / t_3
    if (x1 <= (-5.7d+102)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (t_2 + (x1 * (((2.0d0 * (3.0d0 + (x2 * (-4.0d0)))) + (t_4 + ((x2 * 6.0d0) + ((x2 * 8.0d0) + (x1 * ((t_2 + (2.0d0 * ((1.0d0 + (((-3.0d0) * t_0) + (2.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))))) - ((-2.0d0) * t_1)))) - 3.0d0)))))) - 6.0d0)))))
    else if (x1 <= (-8d+24)) then
        tmp = x1 + ((3.0d0 * (((t_5 - (2.0d0 * x2)) - x1) / t_3)) + (x1 + ((x1 * (x1 * x1)) + ((t_5 * t_6) + (t_3 * (((x1 * x1) * 6.0d0) - (((x1 * 2.0d0) * (3.0d0 + ((-1.0d0) / x1))) * (3.0d0 - t_6))))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + (x1 * ((x1 * 3.0d0) + t_4))) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 + (x2 * -2.0);
	double t_1 = x2 * t_0;
	double t_2 = -4.0 * t_1;
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = 3.0 * (3.0 - (x2 * -2.0));
	double t_5 = x1 * (x1 * 3.0);
	double t_6 = ((t_5 + (2.0 * x2)) - x1) / t_3;
	double tmp;
	if (x1 <= -5.7e+102) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (t_2 + (x1 * (((2.0 * (3.0 + (x2 * -4.0))) + (t_4 + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_2 + (2.0 * ((1.0 + ((-3.0 * t_0) + (2.0 * (x2 * (3.0 - (2.0 * x2)))))) - (-2.0 * t_1)))) - 3.0)))))) - 6.0)))));
	} else if (x1 <= -8e+24) {
		tmp = x1 + ((3.0 * (((t_5 - (2.0 * x2)) - x1) / t_3)) + (x1 + ((x1 * (x1 * x1)) + ((t_5 * t_6) + (t_3 * (((x1 * x1) * 6.0) - (((x1 * 2.0) * (3.0 + (-1.0 / x1))) * (3.0 - t_6))))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * ((x1 * 3.0) + t_4))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 + (x2 * -2.0)
	t_1 = x2 * t_0
	t_2 = -4.0 * t_1
	t_3 = (x1 * x1) + 1.0
	t_4 = 3.0 * (3.0 - (x2 * -2.0))
	t_5 = x1 * (x1 * 3.0)
	t_6 = ((t_5 + (2.0 * x2)) - x1) / t_3
	tmp = 0
	if x1 <= -5.7e+102:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (t_2 + (x1 * (((2.0 * (3.0 + (x2 * -4.0))) + (t_4 + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_2 + (2.0 * ((1.0 + ((-3.0 * t_0) + (2.0 * (x2 * (3.0 - (2.0 * x2)))))) - (-2.0 * t_1)))) - 3.0)))))) - 6.0)))))
	elif x1 <= -8e+24:
		tmp = x1 + ((3.0 * (((t_5 - (2.0 * x2)) - x1) / t_3)) + (x1 + ((x1 * (x1 * x1)) + ((t_5 * t_6) + (t_3 * (((x1 * x1) * 6.0) - (((x1 * 2.0) * (3.0 + (-1.0 / x1))) * (3.0 - t_6))))))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * ((x1 * 3.0) + t_4))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 + Float64(x2 * -2.0))
	t_1 = Float64(x2 * t_0)
	t_2 = Float64(-4.0 * t_1)
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(3.0 * Float64(3.0 - Float64(x2 * -2.0)))
	t_5 = Float64(x1 * Float64(x1 * 3.0))
	t_6 = Float64(Float64(Float64(t_5 + Float64(2.0 * x2)) - x1) / t_3)
	tmp = 0.0
	if (x1 <= -5.7e+102)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(t_2 + Float64(x1 * Float64(Float64(Float64(2.0 * Float64(3.0 + Float64(x2 * -4.0))) + Float64(t_4 + Float64(Float64(x2 * 6.0) + Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_2 + Float64(2.0 * Float64(Float64(1.0 + Float64(Float64(-3.0 * t_0) + Float64(2.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))) - Float64(-2.0 * t_1)))) - 3.0)))))) - 6.0))))));
	elseif (x1 <= -8e+24)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_5 - Float64(2.0 * x2)) - x1) / t_3)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_5 * t_6) + Float64(t_3 * Float64(Float64(Float64(x1 * x1) * 6.0) - Float64(Float64(Float64(x1 * 2.0) * Float64(3.0 + Float64(-1.0 / x1))) * Float64(3.0 - t_6)))))))));
	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(x1 * Float64(Float64(x1 * 3.0) + t_4))) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 + (x2 * -2.0);
	t_1 = x2 * t_0;
	t_2 = -4.0 * t_1;
	t_3 = (x1 * x1) + 1.0;
	t_4 = 3.0 * (3.0 - (x2 * -2.0));
	t_5 = x1 * (x1 * 3.0);
	t_6 = ((t_5 + (2.0 * x2)) - x1) / t_3;
	tmp = 0.0;
	if (x1 <= -5.7e+102)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (t_2 + (x1 * (((2.0 * (3.0 + (x2 * -4.0))) + (t_4 + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_2 + (2.0 * ((1.0 + ((-3.0 * t_0) + (2.0 * (x2 * (3.0 - (2.0 * x2)))))) - (-2.0 * t_1)))) - 3.0)))))) - 6.0)))));
	elseif (x1 <= -8e+24)
		tmp = x1 + ((3.0 * (((t_5 - (2.0 * x2)) - x1) / t_3)) + (x1 + ((x1 * (x1 * x1)) + ((t_5 * t_6) + (t_3 * (((x1 * x1) * 6.0) - (((x1 * 2.0) * (3.0 + (-1.0 / x1))) * (3.0 - t_6))))))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * ((x1 * 3.0) + t_4))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x2 * t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$5 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, If[LessEqual[x1, -5.7e+102], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(t$95$2 + N[(x1 * N[(N[(N[(2.0 * N[(3.0 + N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$4 + N[(N[(x2 * 6.0), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$2 + N[(2.0 * N[(N[(1.0 + N[(N[(-3.0 * t$95$0), $MachinePrecision] + N[(2.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-2.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -8e+24], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$5 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$5 * t$95$6), $MachinePrecision] + N[(t$95$3 * N[(N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision] - N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(3.0 + N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(3.0 - t$95$6), $MachinePrecision]), $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 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.6999999999999999e102

   1. Initial program 0.0%

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

   3. Simplified 22.0%

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

   5. Taylor expanded in x1 around 0 70.7%

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

   if -5.6999999999999999e102 < x1 < -7.9999999999999999e24

   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 inf 93.0%

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

   4. Taylor expanded in x1 around inf 87.9%

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

   if -7.9999999999999999e24 < x1

   1. Initial program 84.4%

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

   3. Simplified 84.6%

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

   5. Taylor expanded in x1 around 0 65.8%

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

      1. associate-*r* 73.3%

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

      2. fmm-def 73.3%

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

      3. metadata-eval 73.3%

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

   7. Simplified 73.3%

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

   8. Taylor expanded in x1 around 0 80.9%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.7 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(-4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + x2 \cdot -4\right) + \left(3 \cdot \left(3 - x2 \cdot -2\right) + \left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + 2 \cdot \left(\left(1 + \left(-3 \cdot \left(3 + x2 \cdot -2\right) + 2 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) - -2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -8 \cdot 10^{+24}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6 - \left(\left(x1 \cdot 2\right) \cdot \left(3 + \frac{-1}{x1}\right)\right) \cdot \left(3 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(x1 \cdot 3 + 3 \cdot \left(3 - x2 \cdot -2\right)\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 75.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x2 \cdot \left(3 - 2 \cdot x2\right)\\ t_1 := 3 \cdot \left(x2 \cdot -2 - 3\right)\\ t_2 := 3 + x2 \cdot -2\\ t_3 := x2 \cdot t\_2\\ t_4 := -4 \cdot t\_3\\ \mathbf{if}\;x1 \leq -1.05 \cdot 10^{+35}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x1 \cdot \left(6 + \left(\left(t\_1 - \left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(t\_4 + 2 \cdot \left(\left(1 + \left(-3 \cdot t\_2 + 2 \cdot t\_0\right)\right) - -2 \cdot t\_3\right)\right) - 3\right)\right)\right)\right) - 2 \cdot \left(3 + x2 \cdot -4\right)\right)\right) - t\_4\right) - -1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(t\_1 - x1 \cdot 3\right) + 4 \cdot t\_0\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x2 (- 3.0 (* 2.0 x2))))
        (t_1 (* 3.0 (- (* x2 -2.0) 3.0)))
        (t_2 (+ 3.0 (* x2 -2.0)))
        (t_3 (* x2 t_2))
        (t_4 (* -4.0 t_3)))
   (if (<= x1 -1.05e+35)
     (-
      (* x2 -6.0)
      (*
       x1
       (-
        (-
         (*
          x1
          (+
           6.0
           (-
            (-
             t_1
             (+
              (* x2 6.0)
              (+
               (* x2 8.0)
               (*
                x1
                (-
                 (+
                  t_4
                  (*
                   2.0
                   (- (+ 1.0 (+ (* -3.0 t_2) (* 2.0 t_0))) (* -2.0 t_3))))
                 3.0)))))
            (* 2.0 (+ 3.0 (* x2 -4.0))))))
         t_4)
        -1.0)))
     (+
      x1
      (-
       (* x2 -6.0)
       (* x1 (+ 2.0 (+ (* x1 (- t_1 (* x1 3.0))) (* 4.0 t_0)))))))))

C

double code(double x1, double x2) {
	double t_0 = x2 * (3.0 - (2.0 * x2));
	double t_1 = 3.0 * ((x2 * -2.0) - 3.0);
	double t_2 = 3.0 + (x2 * -2.0);
	double t_3 = x2 * t_2;
	double t_4 = -4.0 * t_3;
	double tmp;
	if (x1 <= -1.05e+35) {
		tmp = (x2 * -6.0) - (x1 * (((x1 * (6.0 + ((t_1 - ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_4 + (2.0 * ((1.0 + ((-3.0 * t_2) + (2.0 * t_0))) - (-2.0 * t_3)))) - 3.0))))) - (2.0 * (3.0 + (x2 * -4.0)))))) - t_4) - -1.0));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * (t_1 - (x1 * 3.0))) + (4.0 * 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) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = x2 * (3.0d0 - (2.0d0 * x2))
    t_1 = 3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)
    t_2 = 3.0d0 + (x2 * (-2.0d0))
    t_3 = x2 * t_2
    t_4 = (-4.0d0) * t_3
    if (x1 <= (-1.05d+35)) then
        tmp = (x2 * (-6.0d0)) - (x1 * (((x1 * (6.0d0 + ((t_1 - ((x2 * 6.0d0) + ((x2 * 8.0d0) + (x1 * ((t_4 + (2.0d0 * ((1.0d0 + (((-3.0d0) * t_2) + (2.0d0 * t_0))) - ((-2.0d0) * t_3)))) - 3.0d0))))) - (2.0d0 * (3.0d0 + (x2 * (-4.0d0))))))) - t_4) - (-1.0d0)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((x1 * (t_1 - (x1 * 3.0d0))) + (4.0d0 * t_0)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x2 * (3.0 - (2.0 * x2));
	double t_1 = 3.0 * ((x2 * -2.0) - 3.0);
	double t_2 = 3.0 + (x2 * -2.0);
	double t_3 = x2 * t_2;
	double t_4 = -4.0 * t_3;
	double tmp;
	if (x1 <= -1.05e+35) {
		tmp = (x2 * -6.0) - (x1 * (((x1 * (6.0 + ((t_1 - ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_4 + (2.0 * ((1.0 + ((-3.0 * t_2) + (2.0 * t_0))) - (-2.0 * t_3)))) - 3.0))))) - (2.0 * (3.0 + (x2 * -4.0)))))) - t_4) - -1.0));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * (t_1 - (x1 * 3.0))) + (4.0 * t_0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x2 * (3.0 - (2.0 * x2))
	t_1 = 3.0 * ((x2 * -2.0) - 3.0)
	t_2 = 3.0 + (x2 * -2.0)
	t_3 = x2 * t_2
	t_4 = -4.0 * t_3
	tmp = 0
	if x1 <= -1.05e+35:
		tmp = (x2 * -6.0) - (x1 * (((x1 * (6.0 + ((t_1 - ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_4 + (2.0 * ((1.0 + ((-3.0 * t_2) + (2.0 * t_0))) - (-2.0 * t_3)))) - 3.0))))) - (2.0 * (3.0 + (x2 * -4.0)))))) - t_4) - -1.0))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * (t_1 - (x1 * 3.0))) + (4.0 * t_0)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))
	t_1 = Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0))
	t_2 = Float64(3.0 + Float64(x2 * -2.0))
	t_3 = Float64(x2 * t_2)
	t_4 = Float64(-4.0 * t_3)
	tmp = 0.0
	if (x1 <= -1.05e+35)
		tmp = Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(Float64(Float64(x1 * Float64(6.0 + Float64(Float64(t_1 - Float64(Float64(x2 * 6.0) + Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_4 + Float64(2.0 * Float64(Float64(1.0 + Float64(Float64(-3.0 * t_2) + Float64(2.0 * t_0))) - Float64(-2.0 * t_3)))) - 3.0))))) - Float64(2.0 * Float64(3.0 + Float64(x2 * -4.0)))))) - t_4) - -1.0)));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(x1 * Float64(t_1 - Float64(x1 * 3.0))) + Float64(4.0 * t_0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x2 * (3.0 - (2.0 * x2));
	t_1 = 3.0 * ((x2 * -2.0) - 3.0);
	t_2 = 3.0 + (x2 * -2.0);
	t_3 = x2 * t_2;
	t_4 = -4.0 * t_3;
	tmp = 0.0;
	if (x1 <= -1.05e+35)
		tmp = (x2 * -6.0) - (x1 * (((x1 * (6.0 + ((t_1 - ((x2 * 6.0) + ((x2 * 8.0) + (x1 * ((t_4 + (2.0 * ((1.0 + ((-3.0 * t_2) + (2.0 * t_0))) - (-2.0 * t_3)))) - 3.0))))) - (2.0 * (3.0 + (x2 * -4.0)))))) - t_4) - -1.0));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * (t_1 - (x1 * 3.0))) + (4.0 * t_0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x2 * t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(-4.0 * t$95$3), $MachinePrecision]}, If[LessEqual[x1, -1.05e+35], N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(N[(N[(x1 * N[(6.0 + N[(N[(t$95$1 - N[(N[(x2 * 6.0), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$4 + N[(2.0 * N[(N[(1.0 + N[(N[(-3.0 * t$95$2), $MachinePrecision] + N[(2.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-2.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(2.0 * N[(3.0 + N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$4), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(N[(x1 * N[(t$95$1 - N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(4.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.0499999999999999e35

   1. Initial program 25.3%

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

   3. Simplified 41.7%

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

   5. Taylor expanded in x1 around 0 57.7%

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

   if -1.0499999999999999e35 < x1

   1. Initial program 84.5%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in x1 around 0 65.6%

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

      1. associate-*r* 73.1%

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

      2. fmm-def 73.1%

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

      3. metadata-eval 73.1%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in x1 around 0 80.6%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.05 \cdot 10^{+35}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x1 \cdot \left(6 + \left(\left(3 \cdot \left(x2 \cdot -2 - 3\right) - \left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + 2 \cdot \left(\left(1 + \left(-3 \cdot \left(3 + x2 \cdot -2\right) + 2 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) - -2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right)\right) - 3\right)\right)\right)\right) - 2 \cdot \left(3 + x2 \cdot -4\right)\right)\right) - -4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right) - -1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 74.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot x2 - 3\\ t_1 := 3 - x2 \cdot -2\\ t_2 := 3 - 2 \cdot x2\\ t_3 := 4 \cdot \left(x2 \cdot t\_0\right)\\ \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(t\_3 + 3 \cdot \left(x1 \cdot t\_1\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -3.05 \cdot 10^{+25}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + x1 \cdot \left(\left(2 \cdot \left(1 + 3 \cdot t\_0\right) + x1 \cdot \left(x2 \cdot 6 + x1 \cdot \left(\left(3 \cdot \left(x1 \cdot t\_2\right) - 2 \cdot \left(-1 + 3 \cdot t\_2\right)\right) - 6\right)\right)\right) - 4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(t\_3 + x1 \cdot \left(x1 \cdot 3 + 3 \cdot t\_1\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* 2.0 x2) 3.0))
        (t_1 (- 3.0 (* x2 -2.0)))
        (t_2 (- 3.0 (* 2.0 x2)))
        (t_3 (* 4.0 (* x2 t_0))))
   (if (<= x1 -1.35e+154)
     (+ x1 (+ (* x2 -6.0) (* x1 (- (+ t_3 (* 3.0 (* x1 t_1))) 2.0))))
     (if (<= x1 -3.05e+25)
       (+
        x1
        (+
         (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
         (+
          x1
          (*
           x1
           (-
            (+
             (* 2.0 (+ 1.0 (* 3.0 t_0)))
             (*
              x1
              (+
               (* x2 6.0)
               (*
                x1
                (- (- (* 3.0 (* x1 t_2)) (* 2.0 (+ -1.0 (* 3.0 t_2)))) 6.0)))))
            4.0)))))
       (+
        x1
        (+
         (* x2 -6.0)
         (* x1 (- (+ t_3 (* x1 (+ (* x1 3.0) (* 3.0 t_1)))) 2.0))))))))

C

double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = 3.0 - (x2 * -2.0);
	double t_2 = 3.0 - (2.0 * x2);
	double t_3 = 4.0 * (x2 * t_0);
	double tmp;
	if (x1 <= -1.35e+154) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((t_3 + (3.0 * (x1 * t_1))) - 2.0)));
	} else if (x1 <= -3.05e+25) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (x1 * (((2.0 * (1.0 + (3.0 * t_0))) + (x1 * ((x2 * 6.0) + (x1 * (((3.0 * (x1 * t_2)) - (2.0 * (-1.0 + (3.0 * t_2)))) - 6.0))))) - 4.0))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((t_3 + (x1 * ((x1 * 3.0) + (3.0 * t_1)))) - 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 = (2.0d0 * x2) - 3.0d0
    t_1 = 3.0d0 - (x2 * (-2.0d0))
    t_2 = 3.0d0 - (2.0d0 * x2)
    t_3 = 4.0d0 * (x2 * t_0)
    if (x1 <= (-1.35d+154)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((t_3 + (3.0d0 * (x1 * t_1))) - 2.0d0)))
    else if (x1 <= (-3.05d+25)) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0))) + (x1 + (x1 * (((2.0d0 * (1.0d0 + (3.0d0 * t_0))) + (x1 * ((x2 * 6.0d0) + (x1 * (((3.0d0 * (x1 * t_2)) - (2.0d0 * ((-1.0d0) + (3.0d0 * t_2)))) - 6.0d0))))) - 4.0d0))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((t_3 + (x1 * ((x1 * 3.0d0) + (3.0d0 * t_1)))) - 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 = 3.0 - (x2 * -2.0);
	double t_2 = 3.0 - (2.0 * x2);
	double t_3 = 4.0 * (x2 * t_0);
	double tmp;
	if (x1 <= -1.35e+154) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((t_3 + (3.0 * (x1 * t_1))) - 2.0)));
	} else if (x1 <= -3.05e+25) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (x1 * (((2.0 * (1.0 + (3.0 * t_0))) + (x1 * ((x2 * 6.0) + (x1 * (((3.0 * (x1 * t_2)) - (2.0 * (-1.0 + (3.0 * t_2)))) - 6.0))))) - 4.0))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((t_3 + (x1 * ((x1 * 3.0) + (3.0 * t_1)))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (2.0 * x2) - 3.0
	t_1 = 3.0 - (x2 * -2.0)
	t_2 = 3.0 - (2.0 * x2)
	t_3 = 4.0 * (x2 * t_0)
	tmp = 0
	if x1 <= -1.35e+154:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((t_3 + (3.0 * (x1 * t_1))) - 2.0)))
	elif x1 <= -3.05e+25:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (x1 * (((2.0 * (1.0 + (3.0 * t_0))) + (x1 * ((x2 * 6.0) + (x1 * (((3.0 * (x1 * t_2)) - (2.0 * (-1.0 + (3.0 * t_2)))) - 6.0))))) - 4.0))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((t_3 + (x1 * ((x1 * 3.0) + (3.0 * t_1)))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(2.0 * x2) - 3.0)
	t_1 = Float64(3.0 - Float64(x2 * -2.0))
	t_2 = Float64(3.0 - Float64(2.0 * x2))
	t_3 = Float64(4.0 * Float64(x2 * t_0))
	tmp = 0.0
	if (x1 <= -1.35e+154)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(t_3 + Float64(3.0 * Float64(x1 * t_1))) - 2.0))));
	elseif (x1 <= -3.05e+25)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))) + Float64(x1 + Float64(x1 * Float64(Float64(Float64(2.0 * Float64(1.0 + Float64(3.0 * t_0))) + Float64(x1 * Float64(Float64(x2 * 6.0) + Float64(x1 * Float64(Float64(Float64(3.0 * Float64(x1 * t_2)) - Float64(2.0 * Float64(-1.0 + Float64(3.0 * t_2)))) - 6.0))))) - 4.0)))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(t_3 + Float64(x1 * Float64(Float64(x1 * 3.0) + Float64(3.0 * t_1)))) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (2.0 * x2) - 3.0;
	t_1 = 3.0 - (x2 * -2.0);
	t_2 = 3.0 - (2.0 * x2);
	t_3 = 4.0 * (x2 * t_0);
	tmp = 0.0;
	if (x1 <= -1.35e+154)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((t_3 + (3.0 * (x1 * t_1))) - 2.0)));
	elseif (x1 <= -3.05e+25)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (x1 * (((2.0 * (1.0 + (3.0 * t_0))) + (x1 * ((x2 * 6.0) + (x1 * (((3.0 * (x1 * t_2)) - (2.0 * (-1.0 + (3.0 * t_2)))) - 6.0))))) - 4.0))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((t_3 + (x1 * ((x1 * 3.0) + (3.0 * t_1)))) - 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[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(4.0 * N[(x2 * t$95$0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.35e+154], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$3 + N[(3.0 * N[(x1 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -3.05e+25], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x1 * N[(N[(N[(2.0 * N[(1.0 + N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x2 * 6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(3.0 * N[(x1 * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(2.0 * N[(-1.0 + N[(3.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$3 + N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + N[(3.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.35000000000000003e154

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 0.0%

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

      1. associate-*r* 0.0%

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

      2. fmm-def 0.0%

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

      3. metadata-eval 0.0%

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

   7. Simplified 0.0%

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

   8. Taylor expanded in x1 around 0 65.6%

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

   if -1.35000000000000003e154 < x1 < -3.0500000000000001e25

   1. Initial program 63.5%

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

   3. Taylor expanded in x1 around 0 12.5%

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

   4. Taylor expanded in x1 around inf 15.4%

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

   5. Taylor expanded in x1 around 0 53.9%

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

   if -3.0500000000000001e25 < x1

   1. Initial program 84.4%

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

   3. Simplified 84.6%

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

   5. Taylor expanded in x1 around 0 65.8%

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

      1. associate-*r* 73.3%

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

      2. fmm-def 73.3%

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

      3. metadata-eval 73.3%

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

   7. Simplified 73.3%

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

   8. Taylor expanded in x1 around 0 80.9%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + 3 \cdot \left(x1 \cdot \left(3 - x2 \cdot -2\right)\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -3.05 \cdot 10^{+25}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + x1 \cdot \left(\left(2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(x2 \cdot 6 + x1 \cdot \left(\left(3 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right) - 2 \cdot \left(-1 + 3 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - 6\right)\right)\right) - 4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(x1 \cdot 3 + 3 \cdot \left(3 - x2 \cdot -2\right)\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 74.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x2 \cdot -2 - 3\\ t_1 := 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\\ t_2 := 3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1}\\ \mathbf{if}\;x1 \leq -1.22 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(3 \cdot \left(x1 \cdot t\_0\right) + t\_1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -4.5 \cdot 10^{-238}:\\ \;\;\;\;x1 + \left(t\_2 + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(x1 \cdot -22 + x2 \cdot \left(6 + x1 \cdot 12\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.2 \cdot 10^{-187}:\\ \;\;\;\;x1 + \left(t\_2 + \left(x1 + 12 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot t\_0 - x1 \cdot 3\right) + t\_1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* x2 -2.0) 3.0))
        (t_1 (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))
        (t_2
         (*
          3.0
          (/ (- x1 (- (* x1 (* x1 3.0)) (* 2.0 x2))) (- -1.0 (* x1 x1))))))
   (if (<= x1 -1.22e+154)
     (+ x1 (- (* x2 -6.0) (* x1 (+ 2.0 (+ (* 3.0 (* x1 t_0)) t_1)))))
     (if (<= x1 -4.5e-238)
       (+
        x1
        (+
         t_2
         (+
          x1
          (*
           x1
           (+
            (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))
            (* x1 (+ (* x1 -22.0) (* x2 (+ 6.0 (* x1 12.0))))))))))
       (if (<= x1 2.2e-187)
         (+ x1 (+ t_2 (+ x1 (* 12.0 (* x1 x2)))))
         (+
          x1
          (-
           (* x2 -6.0)
           (* x1 (+ 2.0 (+ (* x1 (- (* 3.0 t_0) (* x1 3.0))) t_1))))))))))

C

double code(double x1, double x2) {
	double t_0 = (x2 * -2.0) - 3.0;
	double t_1 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double t_2 = 3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / (-1.0 - (x1 * x1)));
	double tmp;
	if (x1 <= -1.22e+154) {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((3.0 * (x1 * t_0)) + t_1))));
	} else if (x1 <= -4.5e-238) {
		tmp = x1 + (t_2 + (x1 + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * ((x1 * -22.0) + (x2 * (6.0 + (x1 * 12.0)))))))));
	} else if (x1 <= 2.2e-187) {
		tmp = x1 + (t_2 + (x1 + (12.0 * (x1 * x2))));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * t_0) - (x1 * 3.0))) + t_1))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (x2 * (-2.0d0)) - 3.0d0
    t_1 = 4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))
    t_2 = 3.0d0 * ((x1 - ((x1 * (x1 * 3.0d0)) - (2.0d0 * x2))) / ((-1.0d0) - (x1 * x1)))
    if (x1 <= (-1.22d+154)) then
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((3.0d0 * (x1 * t_0)) + t_1))))
    else if (x1 <= (-4.5d-238)) then
        tmp = x1 + (t_2 + (x1 + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + (x1 * ((x1 * (-22.0d0)) + (x2 * (6.0d0 + (x1 * 12.0d0)))))))))
    else if (x1 <= 2.2d-187) then
        tmp = x1 + (t_2 + (x1 + (12.0d0 * (x1 * x2))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((x1 * ((3.0d0 * t_0) - (x1 * 3.0d0))) + t_1))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x2 * -2.0) - 3.0;
	double t_1 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double t_2 = 3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / (-1.0 - (x1 * x1)));
	double tmp;
	if (x1 <= -1.22e+154) {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((3.0 * (x1 * t_0)) + t_1))));
	} else if (x1 <= -4.5e-238) {
		tmp = x1 + (t_2 + (x1 + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * ((x1 * -22.0) + (x2 * (6.0 + (x1 * 12.0)))))))));
	} else if (x1 <= 2.2e-187) {
		tmp = x1 + (t_2 + (x1 + (12.0 * (x1 * x2))));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * t_0) - (x1 * 3.0))) + t_1))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x2 * -2.0) - 3.0
	t_1 = 4.0 * (x2 * (3.0 - (2.0 * x2)))
	t_2 = 3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / (-1.0 - (x1 * x1)))
	tmp = 0
	if x1 <= -1.22e+154:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((3.0 * (x1 * t_0)) + t_1))))
	elif x1 <= -4.5e-238:
		tmp = x1 + (t_2 + (x1 + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * ((x1 * -22.0) + (x2 * (6.0 + (x1 * 12.0)))))))))
	elif x1 <= 2.2e-187:
		tmp = x1 + (t_2 + (x1 + (12.0 * (x1 * x2))))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * t_0) - (x1 * 3.0))) + t_1))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x2 * -2.0) - 3.0)
	t_1 = Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))
	t_2 = Float64(3.0 * Float64(Float64(x1 - Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2))) / Float64(-1.0 - Float64(x1 * x1))))
	tmp = 0.0
	if (x1 <= -1.22e+154)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(3.0 * Float64(x1 * t_0)) + t_1)))));
	elseif (x1 <= -4.5e-238)
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) + Float64(x1 * Float64(Float64(x1 * -22.0) + Float64(x2 * Float64(6.0 + Float64(x1 * 12.0))))))))));
	elseif (x1 <= 2.2e-187)
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(12.0 * Float64(x1 * x2)))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(x1 * Float64(Float64(3.0 * t_0) - Float64(x1 * 3.0))) + t_1)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x2 * -2.0) - 3.0;
	t_1 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	t_2 = 3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / (-1.0 - (x1 * x1)));
	tmp = 0.0;
	if (x1 <= -1.22e+154)
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((3.0 * (x1 * t_0)) + t_1))));
	elseif (x1 <= -4.5e-238)
		tmp = x1 + (t_2 + (x1 + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * ((x1 * -22.0) + (x2 * (6.0 + (x1 * 12.0)))))))));
	elseif (x1 <= 2.2e-187)
		tmp = x1 + (t_2 + (x1 + (12.0 * (x1 * x2))));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * t_0) - (x1 * 3.0))) + t_1))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$1 = N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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]}, If[LessEqual[x1, -1.22e+154], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(N[(3.0 * N[(x1 * t$95$0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -4.5e-238], N[(x1 + N[(t$95$2 + N[(x1 + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * -22.0), $MachinePrecision] + N[(x2 * N[(6.0 + N[(x1 * 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.2e-187], N[(x1 + N[(t$95$2 + N[(x1 + N[(12.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(N[(x1 * N[(N[(3.0 * t$95$0), $MachinePrecision] - N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.22e154

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 0.0%

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

      1. associate-*r* 0.0%

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

      2. fmm-def 0.0%

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

      3. metadata-eval 0.0%

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

   7. Simplified 0.0%

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

   8. Taylor expanded in x1 around 0 65.6%

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

   if -1.22e154 < x1 < -4.49999999999999996e-238

   1. Initial program 86.7%

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

   3. Taylor expanded in x1 around 0 65.2%

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

   4. Taylor expanded in x1 around 0 52.2%

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

   5. Taylor expanded in x2 around 0 65.5%

      \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(-22 \cdot x1 + x2 \cdot \left(6 + 12 \cdot x1\right)\right)}\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if -4.49999999999999996e-238 < x1 < 2.20000000000000008e-187

   1. Initial program 99.6%

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

   3. Taylor expanded in x1 around 0 99.6%

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

   4. Taylor expanded in x1 around inf 87.7%

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

   5. Taylor expanded in x1 around 0 87.7%

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

   6. Taylor expanded in x2 around inf 96.6%

      \[\leadsto x1 + \left(\left(\color{blue}{12 \cdot \left(x1 \cdot x2\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   7. Step-by-step derivation

      1. *-commutative 96.6%

         \[\leadsto x1 + \left(\left(12 \cdot \color{blue}{\left(x2 \cdot x1\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   8. Simplified 96.6%

      \[\leadsto x1 + \left(\left(\color{blue}{12 \cdot \left(x2 \cdot x1\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if 2.20000000000000008e-187 < x1

   1. Initial program 68.5%

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

   3. Simplified 68.8%

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

   5. Taylor expanded in x1 around 0 46.6%

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

      1. associate-*r* 48.4%

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

      2. fmm-def 48.4%

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

      3. metadata-eval 48.4%

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

   7. Simplified 48.4%

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

   8. Taylor expanded in x1 around 0 77.7%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.22 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(3 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right)\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -4.5 \cdot 10^{-238}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(x1 \cdot -22 + x2 \cdot \left(6 + x1 \cdot 12\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.2 \cdot 10^{-187}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + 12 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 73.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x2 \cdot -2 - 3\\ t_1 := 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\\ \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(3 \cdot \left(x1 \cdot t\_0\right) + t\_1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7 \cdot 10^{+89}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -22\right) - t\_1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot t\_0 - x1 \cdot 3\right) + t\_1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* x2 -2.0) 3.0)) (t_1 (* 4.0 (* x2 (- 3.0 (* 2.0 x2))))))
   (if (<= x1 -1.35e+154)
     (+ x1 (- (* x2 -6.0) (* x1 (+ 2.0 (+ (* 3.0 (* x1 t_0)) t_1)))))
     (if (<= x1 7e+89)
       (+
        x1
        (+
         (* 3.0 (/ (- x1 (- (* x1 (* x1 3.0)) (* 2.0 x2))) (- -1.0 (* x1 x1))))
         (+ x1 (* x1 (- (* x1 (* x1 -22.0)) t_1)))))
       (+
        x1
        (-
         (* x2 -6.0)
         (* x1 (+ 2.0 (+ (* x1 (- (* 3.0 t_0) (* x1 3.0))) t_1)))))))))

C

double code(double x1, double x2) {
	double t_0 = (x2 * -2.0) - 3.0;
	double t_1 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double tmp;
	if (x1 <= -1.35e+154) {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((3.0 * (x1 * t_0)) + t_1))));
	} else if (x1 <= 7e+89) {
		tmp = x1 + ((3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + (x1 * ((x1 * (x1 * -22.0)) - t_1))));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * t_0) - (x1 * 3.0))) + t_1))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (x2 * (-2.0d0)) - 3.0d0
    t_1 = 4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))
    if (x1 <= (-1.35d+154)) then
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((3.0d0 * (x1 * t_0)) + t_1))))
    else if (x1 <= 7d+89) then
        tmp = x1 + ((3.0d0 * ((x1 - ((x1 * (x1 * 3.0d0)) - (2.0d0 * x2))) / ((-1.0d0) - (x1 * x1)))) + (x1 + (x1 * ((x1 * (x1 * (-22.0d0))) - t_1))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((x1 * ((3.0d0 * t_0) - (x1 * 3.0d0))) + t_1))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x2 * -2.0) - 3.0;
	double t_1 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double tmp;
	if (x1 <= -1.35e+154) {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((3.0 * (x1 * t_0)) + t_1))));
	} else if (x1 <= 7e+89) {
		tmp = x1 + ((3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + (x1 * ((x1 * (x1 * -22.0)) - t_1))));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * t_0) - (x1 * 3.0))) + t_1))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x2 * -2.0) - 3.0
	t_1 = 4.0 * (x2 * (3.0 - (2.0 * x2)))
	tmp = 0
	if x1 <= -1.35e+154:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((3.0 * (x1 * t_0)) + t_1))))
	elif x1 <= 7e+89:
		tmp = x1 + ((3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + (x1 * ((x1 * (x1 * -22.0)) - t_1))))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * t_0) - (x1 * 3.0))) + t_1))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x2 * -2.0) - 3.0)
	t_1 = Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))
	tmp = 0.0
	if (x1 <= -1.35e+154)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(3.0 * Float64(x1 * t_0)) + t_1)))));
	elseif (x1 <= 7e+89)
		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(x1 * Float64(Float64(x1 * Float64(x1 * -22.0)) - t_1)))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(x1 * Float64(Float64(3.0 * t_0) - Float64(x1 * 3.0))) + t_1)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x2 * -2.0) - 3.0;
	t_1 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	tmp = 0.0;
	if (x1 <= -1.35e+154)
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((3.0 * (x1 * t_0)) + t_1))));
	elseif (x1 <= 7e+89)
		tmp = x1 + ((3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + (x1 * ((x1 * (x1 * -22.0)) - t_1))));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * t_0) - (x1 * 3.0))) + t_1))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$1 = N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.35e+154], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(N[(3.0 * N[(x1 * t$95$0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7e+89], 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[(x1 * N[(N[(x1 * N[(x1 * -22.0), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(N[(x1 * N[(N[(3.0 * t$95$0), $MachinePrecision] - N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.35000000000000003e154

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 0.0%

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

      1. associate-*r* 0.0%

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

      2. fmm-def 0.0%

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

      3. metadata-eval 0.0%

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

   7. Simplified 0.0%

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

   8. Taylor expanded in x1 around 0 65.6%

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

   if -1.35000000000000003e154 < x1 < 7.0000000000000001e89

   1. Initial program 94.5%

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

   3. Taylor expanded in x1 around 0 78.3%

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

   4. Taylor expanded in x1 around 0 61.4%

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

   5. Taylor expanded in x2 around 0 73.2%

      \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(-22 \cdot x1\right)}\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   6. Step-by-step derivation

      1. *-commutative 73.2%

         \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(x1 \cdot -22\right)}\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   7. Simplified 73.2%

      \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(x1 \cdot -22\right)}\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if 7.0000000000000001e89 < x1

   1. Initial program 18.9%

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

   3. Simplified 18.9%

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

   5. Taylor expanded in x1 around 0 6.1%

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

      1. associate-*r* 6.1%

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

      2. fmm-def 6.1%

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

      3. metadata-eval 6.1%

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

   7. Simplified 6.1%

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

   8. Taylor expanded in x1 around 0 92.4%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(3 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right)\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7 \cdot 10^{+89}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -22\right) - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 72.4% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x2 \cdot -2 - 3\\ t_1 := 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\\ \mathbf{if}\;x1 \leq -4.9 \cdot 10^{-238}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(3 \cdot \left(x1 \cdot t\_0\right) + t\_1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.4 \cdot 10^{-187}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + 12 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot t\_0 - x1 \cdot 3\right) + t\_1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* x2 -2.0) 3.0)) (t_1 (* 4.0 (* x2 (- 3.0 (* 2.0 x2))))))
   (if (<= x1 -4.9e-238)
     (+ x1 (- (* x2 -6.0) (* x1 (+ 2.0 (+ (* 3.0 (* x1 t_0)) t_1)))))
     (if (<= x1 2.4e-187)
       (+
        x1
        (+
         (* 3.0 (/ (- x1 (- (* x1 (* x1 3.0)) (* 2.0 x2))) (- -1.0 (* x1 x1))))
         (+ x1 (* 12.0 (* x1 x2)))))
       (+
        x1
        (-
         (* x2 -6.0)
         (* x1 (+ 2.0 (+ (* x1 (- (* 3.0 t_0) (* x1 3.0))) t_1)))))))))

C

double code(double x1, double x2) {
	double t_0 = (x2 * -2.0) - 3.0;
	double t_1 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double tmp;
	if (x1 <= -4.9e-238) {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((3.0 * (x1 * t_0)) + t_1))));
	} else if (x1 <= 2.4e-187) {
		tmp = x1 + ((3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + (12.0 * (x1 * x2))));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * t_0) - (x1 * 3.0))) + t_1))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (x2 * (-2.0d0)) - 3.0d0
    t_1 = 4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))
    if (x1 <= (-4.9d-238)) then
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((3.0d0 * (x1 * t_0)) + t_1))))
    else if (x1 <= 2.4d-187) then
        tmp = x1 + ((3.0d0 * ((x1 - ((x1 * (x1 * 3.0d0)) - (2.0d0 * x2))) / ((-1.0d0) - (x1 * x1)))) + (x1 + (12.0d0 * (x1 * x2))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((x1 * ((3.0d0 * t_0) - (x1 * 3.0d0))) + t_1))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x2 * -2.0) - 3.0;
	double t_1 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double tmp;
	if (x1 <= -4.9e-238) {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((3.0 * (x1 * t_0)) + t_1))));
	} else if (x1 <= 2.4e-187) {
		tmp = x1 + ((3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + (12.0 * (x1 * x2))));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * t_0) - (x1 * 3.0))) + t_1))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x2 * -2.0) - 3.0
	t_1 = 4.0 * (x2 * (3.0 - (2.0 * x2)))
	tmp = 0
	if x1 <= -4.9e-238:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((3.0 * (x1 * t_0)) + t_1))))
	elif x1 <= 2.4e-187:
		tmp = x1 + ((3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + (12.0 * (x1 * x2))))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * t_0) - (x1 * 3.0))) + t_1))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x2 * -2.0) - 3.0)
	t_1 = Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))
	tmp = 0.0
	if (x1 <= -4.9e-238)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(3.0 * Float64(x1 * t_0)) + t_1)))));
	elseif (x1 <= 2.4e-187)
		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(12.0 * Float64(x1 * x2)))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(x1 * Float64(Float64(3.0 * t_0) - Float64(x1 * 3.0))) + t_1)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x2 * -2.0) - 3.0;
	t_1 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	tmp = 0.0;
	if (x1 <= -4.9e-238)
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((3.0 * (x1 * t_0)) + t_1))));
	elseif (x1 <= 2.4e-187)
		tmp = x1 + ((3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + (12.0 * (x1 * x2))));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * t_0) - (x1 * 3.0))) + t_1))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$1 = N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.9e-238], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(N[(3.0 * N[(x1 * t$95$0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.4e-187], 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[(12.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(N[(x1 * N[(N[(3.0 * t$95$0), $MachinePrecision] - N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4.8999999999999998e-238

   1. Initial program 59.8%

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

   3. Simplified 60.0%

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

   5. Taylor expanded in x1 around 0 37.5%

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

      1. associate-*r* 43.8%

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

      2. fmm-def 43.8%

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

      3. metadata-eval 43.8%

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

   7. Simplified 43.8%

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

   8. Taylor expanded in x1 around 0 58.6%

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

   if -4.8999999999999998e-238 < x1 < 2.40000000000000013e-187

   1. Initial program 99.6%

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

   3. Taylor expanded in x1 around 0 99.6%

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

   4. Taylor expanded in x1 around inf 87.7%

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

   5. Taylor expanded in x1 around 0 87.7%

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

   6. Taylor expanded in x2 around inf 96.6%

      \[\leadsto x1 + \left(\left(\color{blue}{12 \cdot \left(x1 \cdot x2\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   7. Step-by-step derivation

      1. *-commutative 96.6%

         \[\leadsto x1 + \left(\left(12 \cdot \color{blue}{\left(x2 \cdot x1\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   8. Simplified 96.6%

      \[\leadsto x1 + \left(\left(\color{blue}{12 \cdot \left(x2 \cdot x1\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if 2.40000000000000013e-187 < x1

   1. Initial program 68.5%

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

   3. Simplified 68.8%

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

   5. Taylor expanded in x1 around 0 46.6%

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

      1. associate-*r* 48.4%

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

      2. fmm-def 48.4%

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

      3. metadata-eval 48.4%

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

   7. Simplified 48.4%

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

   8. Taylor expanded in x1 around 0 77.7%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.9 \cdot 10^{-238}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(3 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right)\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.4 \cdot 10^{-187}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + 12 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 69.9% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 - 2 \cdot x2\\ \mathbf{if}\;x1 \leq -8.5 \cdot 10^{+98}:\\ \;\;\;\;x1 + \left(\left(x1 - x1 \cdot \left(4 + 2 \cdot \left(-1 + 3 \cdot t\_0\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 + x1 \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 4 \cdot \left(x2 \cdot t\_0\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- 3.0 (* 2.0 x2))))
   (if (<= x1 -8.5e+98)
     (+
      x1
      (+
       (- x1 (* x1 (+ 4.0 (* 2.0 (+ -1.0 (* 3.0 t_0))))))
       (* 3.0 (+ (* x2 -2.0) (* x1 (+ -1.0 (* x1 (- 3.0 (* x2 -2.0)))))))))
     (+
      x1
      (-
       (* x2 -6.0)
       (*
        x1
        (+
         2.0
         (+
          (* x1 (- (* 3.0 (- (* x2 -2.0) 3.0)) (* x1 3.0)))
          (* 4.0 (* x2 t_0))))))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 - (2.0 * x2);
	double tmp;
	if (x1 <= -8.5e+98) {
		tmp = x1 + ((x1 - (x1 * (4.0 + (2.0 * (-1.0 + (3.0 * t_0)))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * (3.0 - (x2 * -2.0))))))));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (4.0 * (x2 * 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 = 3.0d0 - (2.0d0 * x2)
    if (x1 <= (-8.5d+98)) then
        tmp = x1 + ((x1 - (x1 * (4.0d0 + (2.0d0 * ((-1.0d0) + (3.0d0 * t_0)))))) + (3.0d0 * ((x2 * (-2.0d0)) + (x1 * ((-1.0d0) + (x1 * (3.0d0 - (x2 * (-2.0d0)))))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((x1 * ((3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)) - (x1 * 3.0d0))) + (4.0d0 * (x2 * t_0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 - (2.0 * x2);
	double tmp;
	if (x1 <= -8.5e+98) {
		tmp = x1 + ((x1 - (x1 * (4.0 + (2.0 * (-1.0 + (3.0 * t_0)))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * (3.0 - (x2 * -2.0))))))));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (4.0 * (x2 * t_0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 - (2.0 * x2)
	tmp = 0
	if x1 <= -8.5e+98:
		tmp = x1 + ((x1 - (x1 * (4.0 + (2.0 * (-1.0 + (3.0 * t_0)))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * (3.0 - (x2 * -2.0))))))))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (4.0 * (x2 * t_0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 - Float64(2.0 * x2))
	tmp = 0.0
	if (x1 <= -8.5e+98)
		tmp = Float64(x1 + Float64(Float64(x1 - Float64(x1 * Float64(4.0 + Float64(2.0 * Float64(-1.0 + Float64(3.0 * t_0)))))) + Float64(3.0 * Float64(Float64(x2 * -2.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(3.0 - Float64(x2 * -2.0)))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(x1 * Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)) - Float64(x1 * 3.0))) + Float64(4.0 * Float64(x2 * t_0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 - (2.0 * x2);
	tmp = 0.0;
	if (x1 <= -8.5e+98)
		tmp = x1 + ((x1 - (x1 * (4.0 + (2.0 * (-1.0 + (3.0 * t_0)))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * (3.0 - (x2 * -2.0))))))));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (4.0 * (x2 * t_0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -8.5e+98], N[(x1 + N[(N[(x1 - N[(x1 * N[(4.0 + N[(2.0 * N[(-1.0 + N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(N[(x1 * N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x2 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -8.4999999999999996e98

   1. Initial program 4.7%

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

   3. Taylor expanded in x1 around 0 2.3%

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

   4. Taylor expanded in x1 around inf 2.3%

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

   5. Taylor expanded in x1 around 0 0.8%

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

   6. Taylor expanded in x1 around 0 54.3%

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

   if -8.4999999999999996e98 < x1

   1. Initial program 85.4%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in x1 around 0 62.4%

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

      1. associate-*r* 69.4%

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

      2. fmm-def 69.4%

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

      3. metadata-eval 69.4%

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

   7. Simplified 69.4%

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

   8. Taylor expanded in x1 around 0 76.6%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -8.5 \cdot 10^{+98}:\\ \;\;\;\;x1 + \left(\left(x1 - x1 \cdot \left(4 + 2 \cdot \left(-1 + 3 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 + x1 \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 69.4% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;2 \cdot x2 \leq -10000:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + 3 \cdot \left(x1 \cdot \left(3 - x2 \cdot -2\right)\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= (* 2.0 x2) -10000.0)
   (+ (* x2 -6.0) (* x1 (- -1.0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))))
   (+
    x1
    (+
     (* x2 -6.0)
     (*
      x1
      (-
       (+ (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) (* 3.0 (* x1 (- 3.0 (* x2 -2.0)))))
       2.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((2.0 * x2) <= -10000.0) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (3.0 * (x1 * (3.0 - (x2 * -2.0))))) - 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 ((2.0d0 * x2) <= (-10000.0d0)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) - (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + (3.0d0 * (x1 * (3.0d0 - (x2 * (-2.0d0)))))) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((2.0 * x2) <= -10000.0) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (3.0 * (x1 * (3.0 - (x2 * -2.0))))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (2.0 * x2) <= -10000.0:
		tmp = (x2 * -6.0) + (x1 * (-1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (3.0 * (x1 * (3.0 - (x2 * -2.0))))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (Float64(2.0 * x2) <= -10000.0)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 - Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * 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(3.0 * Float64(x1 * Float64(3.0 - Float64(x2 * -2.0))))) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((2.0 * x2) <= -10000.0)
		tmp = (x2 * -6.0) + (x1 * (-1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (3.0 * (x1 * (3.0 - (x2 * -2.0))))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[N[(2.0 * x2), $MachinePrecision], -10000.0], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 - N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * 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[(3.0 * N[(x1 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 #s(literal 2 binary64) x2) < -1e4

   1. Initial program 77.5%

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

   3. Simplified 77.5%

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

   5. Taylor expanded in x1 around 0 54.8%

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

   if -1e4 < (*.f64 #s(literal 2 binary64) x2)

   1. Initial program 70.3%

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

   3. Simplified 70.5%

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

   5. Taylor expanded in x1 around 0 52.7%

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

      1. associate-*r* 56.4%

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

      2. fmm-def 56.4%

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

      3. metadata-eval 56.4%

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

   7. Simplified 56.4%

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

   8. Taylor expanded in x1 around 0 76.9%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;2 \cdot x2 \leq -10000:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + 3 \cdot \left(x1 \cdot \left(3 - x2 \cdot -2\right)\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 57.7% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.8 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + x1 \cdot \left(2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right) - 4\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 1.92 \cdot 10^{+198}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.8e+102)
   (+
    x1
    (+
     (+ x1 (* x1 (- (* 2.0 (+ 1.0 (* 3.0 (- (* 2.0 x2) 3.0)))) 4.0)))
     (* 3.0 (- (* x2 -2.0) x1))))
   (if (<= x1 1.92e+198)
     (+ (* x2 -6.0) (* x1 (- -1.0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))))
     (* x2 (- (/ x1 x2) 6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.8e+102) {
		tmp = x1 + ((x1 + (x1 * ((2.0 * (1.0 + (3.0 * ((2.0 * x2) - 3.0)))) - 4.0))) + (3.0 * ((x2 * -2.0) - x1)));
	} else if (x1 <= 1.92e+198) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	} 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 <= (-1.8d+102)) then
        tmp = x1 + ((x1 + (x1 * ((2.0d0 * (1.0d0 + (3.0d0 * ((2.0d0 * x2) - 3.0d0)))) - 4.0d0))) + (3.0d0 * ((x2 * (-2.0d0)) - x1)))
    else if (x1 <= 1.92d+198) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) - (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2))))))
    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 <= -1.8e+102) {
		tmp = x1 + ((x1 + (x1 * ((2.0 * (1.0 + (3.0 * ((2.0 * x2) - 3.0)))) - 4.0))) + (3.0 * ((x2 * -2.0) - x1)));
	} else if (x1 <= 1.92e+198) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	} else {
		tmp = x2 * ((x1 / x2) - 6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.8e+102:
		tmp = x1 + ((x1 + (x1 * ((2.0 * (1.0 + (3.0 * ((2.0 * x2) - 3.0)))) - 4.0))) + (3.0 * ((x2 * -2.0) - x1)))
	elif x1 <= 1.92e+198:
		tmp = (x2 * -6.0) + (x1 * (-1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))))
	else:
		tmp = x2 * ((x1 / x2) - 6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.8e+102)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(x1 * Float64(Float64(2.0 * Float64(1.0 + Float64(3.0 * Float64(Float64(2.0 * x2) - 3.0)))) - 4.0))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	elseif (x1 <= 1.92e+198)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 - Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))));
	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 <= -1.8e+102)
		tmp = x1 + ((x1 + (x1 * ((2.0 * (1.0 + (3.0 * ((2.0 * x2) - 3.0)))) - 4.0))) + (3.0 * ((x2 * -2.0) - x1)));
	elseif (x1 <= 1.92e+198)
		tmp = (x2 * -6.0) + (x1 * (-1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	else
		tmp = x2 * ((x1 / x2) - 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.8e+102], N[(x1 + N[(N[(x1 + N[(x1 * N[(N[(2.0 * N[(1.0 + N[(3.0 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.92e+198], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 - N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * N[(N[(x1 / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.8000000000000001e102

   1. Initial program 4.7%

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

   3. Taylor expanded in x1 around 0 2.3%

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

   4. Taylor expanded in x1 around inf 2.3%

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

   5. Taylor expanded in x1 around 0 0.8%

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

   6. Taylor expanded in x1 around 0 18.1%

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

      1. mul-1-neg 18.1%

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

      2. unsub-neg 18.1%

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

      3. *-commutative 18.1%

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

   8. Simplified 18.1%

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

   if -1.8000000000000001e102 < x1 < 1.9199999999999999e198

   1. Initial program 94.2%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in x1 around 0 70.7%

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

   if 1.9199999999999999e198 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 0.0%

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

      1. associate-*r* 0.0%

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

      2. fmm-def 0.0%

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

      3. metadata-eval 0.0%

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

   7. Simplified 0.0%

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

   8. Taylor expanded in x1 around 0 8.5%

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

      1. *-commutative 8.5%

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

   10. Simplified 8.5%

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

   11. Taylor expanded in x2 around inf 63.1%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.8 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + x1 \cdot \left(2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right) - 4\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 1.92 \cdot 10^{+198}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 57.7% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -4.1 \cdot 10^{+101}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + x1 \cdot \left(2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right) - 4\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+199}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -4.1e+101)
   (+
    x1
    (+
     (* 3.0 (* x2 -2.0))
     (+ x1 (* x1 (- (* 2.0 (+ 1.0 (* 3.0 (- (* 2.0 x2) 3.0)))) 4.0)))))
   (if (<= x1 1.8e+199)
     (+ (* x2 -6.0) (* x1 (- -1.0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))))
     (* x2 (- (/ x1 x2) 6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -4.1e+101) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (x1 * ((2.0 * (1.0 + (3.0 * ((2.0 * x2) - 3.0)))) - 4.0))));
	} else if (x1 <= 1.8e+199) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	} 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 <= (-4.1d+101)) then
        tmp = x1 + ((3.0d0 * (x2 * (-2.0d0))) + (x1 + (x1 * ((2.0d0 * (1.0d0 + (3.0d0 * ((2.0d0 * x2) - 3.0d0)))) - 4.0d0))))
    else if (x1 <= 1.8d+199) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) - (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2))))))
    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 <= -4.1e+101) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (x1 * ((2.0 * (1.0 + (3.0 * ((2.0 * x2) - 3.0)))) - 4.0))));
	} else if (x1 <= 1.8e+199) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	} else {
		tmp = x2 * ((x1 / x2) - 6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -4.1e+101:
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (x1 * ((2.0 * (1.0 + (3.0 * ((2.0 * x2) - 3.0)))) - 4.0))))
	elif x1 <= 1.8e+199:
		tmp = (x2 * -6.0) + (x1 * (-1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))))
	else:
		tmp = x2 * ((x1 / x2) - 6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -4.1e+101)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(x2 * -2.0)) + Float64(x1 + Float64(x1 * Float64(Float64(2.0 * Float64(1.0 + Float64(3.0 * Float64(Float64(2.0 * x2) - 3.0)))) - 4.0)))));
	elseif (x1 <= 1.8e+199)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 - Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))));
	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 <= -4.1e+101)
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (x1 * ((2.0 * (1.0 + (3.0 * ((2.0 * x2) - 3.0)))) - 4.0))));
	elseif (x1 <= 1.8e+199)
		tmp = (x2 * -6.0) + (x1 * (-1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	else
		tmp = x2 * ((x1 / x2) - 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -4.1e+101], N[(x1 + N[(N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x1 * N[(N[(2.0 * N[(1.0 + N[(3.0 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.8e+199], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 - N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * N[(N[(x1 / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4.1e101

   1. Initial program 4.7%

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

   3. Taylor expanded in x1 around 0 2.3%

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

   4. Taylor expanded in x1 around inf 2.3%

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

   5. Taylor expanded in x1 around 0 0.8%

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

   6. Taylor expanded in x1 around 0 18.1%

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

      1. *-commutative 4.7%

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

   8. Simplified 18.1%

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

   if -4.1e101 < x1 < 1.80000000000000001e199

   1. Initial program 94.2%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in x1 around 0 70.7%

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

   if 1.80000000000000001e199 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 0.0%

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

      1. associate-*r* 0.0%

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

      2. fmm-def 0.0%

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

      3. metadata-eval 0.0%

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

   7. Simplified 0.0%

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

   8. Taylor expanded in x1 around 0 8.5%

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

      1. *-commutative 8.5%

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

   10. Simplified 8.5%

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

   11. Taylor expanded in x2 around inf 63.1%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.1 \cdot 10^{+101}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + x1 \cdot \left(2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right) - 4\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{+199}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 42.7% accurate, 5.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -2.3 \cdot 10^{+136} \lor \neg \left(x2 \leq 5.4 \cdot 10^{+149}\right):\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -2.3e+136) (not (<= x2 5.4e+149)))
   (+ x1 (* x1 (- 1.0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))))
   (* x2 (- (/ x1 x2) 6.0))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -2.3e+136) || !(x2 <= 5.4e+149)) {
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	} 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 ((x2 <= (-2.3d+136)) .or. (.not. (x2 <= 5.4d+149))) then
        tmp = x1 + (x1 * (1.0d0 - (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2))))))
    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 ((x2 <= -2.3e+136) || !(x2 <= 5.4e+149)) {
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	} else {
		tmp = x2 * ((x1 / x2) - 6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -2.3e+136) or not (x2 <= 5.4e+149):
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))))
	else:
		tmp = x2 * ((x1 / x2) - 6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -2.3e+136) || !(x2 <= 5.4e+149))
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 - Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))));
	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 ((x2 <= -2.3e+136) || ~((x2 <= 5.4e+149)))
		tmp = x1 + (x1 * (1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	else
		tmp = x2 * ((x1 / x2) - 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -2.3e+136], N[Not[LessEqual[x2, 5.4e+149]], $MachinePrecision]], N[(x1 + N[(x1 * N[(1.0 - N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * N[(N[(x1 / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -2.3e136 or 5.4000000000000002e149 < x2

   1. Initial program 69.1%

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

   3. Simplified 69.1%

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

   5. Taylor expanded in x1 around 0 40.3%

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

      1. associate-*r* 63.2%

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

      2. fmm-def 63.2%

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

      3. metadata-eval 63.2%

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

   7. Simplified 63.2%

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

   8. Taylor expanded in x1 around inf 52.6%

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

   if -2.3e136 < x2 < 5.4000000000000002e149

   1. Initial program 72.7%

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

   3. Simplified 73.0%

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

   5. Taylor expanded in x1 around 0 55.9%

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

      1. associate-*r* 55.9%

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

      2. fmm-def 55.9%

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

      3. metadata-eval 55.9%

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

   7. Simplified 55.9%

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

   8. Taylor expanded in x1 around 0 36.0%

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

      1. *-commutative 36.0%

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

   10. Simplified 36.0%

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

   11. Taylor expanded in x2 around inf 43.2%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -2.3 \cdot 10^{+136} \lor \neg \left(x2 \leq 5.4 \cdot 10^{+149}\right):\\ \;\;\;\;x1 + x1 \cdot \left(1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 55.1% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq 3.15 \cdot 10^{+196}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 3.15e+196)
   (+ (* x2 -6.0) (* x1 (- -1.0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))))
   (* x2 (- (/ x1 x2) 6.0))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= 3.15e+196) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	} 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 <= 3.15d+196) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) - (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2))))))
    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 <= 3.15e+196) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	} else {
		tmp = x2 * ((x1 / x2) - 6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= 3.15e+196:
		tmp = (x2 * -6.0) + (x1 * (-1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))))
	else:
		tmp = x2 * ((x1 / x2) - 6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= 3.15e+196)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 - Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))));
	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 <= 3.15e+196)
		tmp = (x2 * -6.0) + (x1 * (-1.0 - (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	else
		tmp = x2 * ((x1 / x2) - 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, 3.15e+196], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 - N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * N[(N[(x1 / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < 3.15000000000000001e196

   1. Initial program 77.9%

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

   3. Simplified 78.1%

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

   5. Taylor expanded in x1 around 0 58.4%

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

   if 3.15000000000000001e196 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 0.0%

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

      1. associate-*r* 0.0%

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

      2. fmm-def 0.0%

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

      3. metadata-eval 0.0%

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

   7. Simplified 0.0%

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

   8. Taylor expanded in x1 around 0 8.5%

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

      1. *-commutative 8.5%

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

   10. Simplified 8.5%

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

   11. Taylor expanded in x2 around inf 63.1%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq 3.15 \cdot 10^{+196}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 31.6% 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 71.8%

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

3. Simplified 72.0%

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

5. Taylor expanded in x1 around 0 52.0%

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

   1. associate-*r* 57.8%

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

   2. fmm-def 57.8%

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

   3. metadata-eval 57.8%

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

7. Simplified 57.8%

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

8. Taylor expanded in x1 around 0 30.5%

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

   1. *-commutative 30.5%

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

10. Simplified 30.5%

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

11. Taylor expanded in x2 around inf 35.9%

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

Alternative 27: 26.3% 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 71.8%

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

3. Simplified 72.0%

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

5. Taylor expanded in x1 around 0 52.0%

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

   1. associate-*r* 57.8%

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

   2. fmm-def 57.8%

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

   3. metadata-eval 57.8%

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

7. Simplified 57.8%

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

8. Taylor expanded in x1 around 0 30.5%

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

   1. *-commutative 30.5%

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

10. Simplified 30.5%

    \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
11. Add Preprocessing

Alternative 28: 26.2% 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 71.8%

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

3. Simplified 72.0%

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

5. Taylor expanded in x1 around 0 30.4%

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

6. Final simplification 30.4%

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

Alternative 29: 3.2% 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 71.8%

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

3. Simplified 72.0%

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

5. Taylor expanded in x1 around 0 52.0%

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

   1. associate-*r* 57.8%

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

   2. fmm-def 57.8%

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

   3. metadata-eval 57.8%

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

7. Simplified 57.8%

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

8. Taylor expanded in x1 around 0 30.5%

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

   1. *-commutative 30.5%

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

10. Simplified 30.5%

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

11. Taylor expanded in x1 around inf 3.4%

    \[\leadsto \color{blue}{x1} \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024170 
(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))))))