Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.5% → 99.6%

Time: 1.7min

Alternatives: 19

Speedup: 4.4×

• 46.6% 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: 70.5% 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: 99.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

   3. Simplified 99.7%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 9.7%

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

   4. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.8%

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

Alternative 2: 99.4% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 99.4%

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

   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%

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

   3. Taylor expanded in x1 around inf 9.7%

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

   4. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.6%

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

Alternative 3: 99.4% accurate, 0.5× speedup

Math

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

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_2
          (+
           (* (* t_3 (* x1 2.0)) (- t_3 3.0))
           (* (* x1 x1) (- (* t_3 4.0) 6.0))))))
   (if (<=
        (+
         x1
         (+
          (+ x1 (+ (+ t_4 (* t_1 t_3)) t_0))
          (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2))))
        INFINITY)
     (+ x1 (+ (+ x1 (+ t_0 (+ t_4 (* 3.0 t_1)))) (* 3.0 (- (* x2 -2.0) x1))))
     (+ x1 (* 6.0 (pow x1 4.0))))))

C

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

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 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_2 * (((t_3 * (x1 * 2.0)) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)));
	double tmp;
	if ((x1 + ((x1 + ((t_4 + (t_1 * t_3)) + t_0)) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)))) <= Double.POSITIVE_INFINITY) {
		tmp = x1 + ((x1 + (t_0 + (t_4 + (3.0 * t_1)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = x1 + (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_2 * (((t_3 * (x1 * 2.0)) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))
	tmp = 0
	if (x1 + ((x1 + ((t_4 + (t_1 * t_3)) + t_0)) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)))) <= math.inf:
		tmp = x1 + ((x1 + (t_0 + (t_4 + (3.0 * t_1)))) + (3.0 * ((x2 * -2.0) - x1)))
	else:
		tmp = x1 + (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_2 * Float64(Float64(Float64(t_3 * Float64(x1 * 2.0)) * Float64(t_3 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0))))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(t_4 + Float64(t_1 * t_3)) + t_0)) + Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2)))) <= Inf)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(t_0 + Float64(t_4 + Float64(3.0 * t_1)))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	else
		tmp = Float64(x1 + Float64(6.0 * (x1 ^ 4.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 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_2 * (((t_3 * (x1 * 2.0)) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)));
	tmp = 0.0;
	if ((x1 + ((x1 + ((t_4 + (t_1 * t_3)) + t_0)) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)))) <= Inf)
		tmp = x1 + ((x1 + (t_0 + (t_4 + (3.0 * t_1)))) + (3.0 * ((x2 * -2.0) - x1)));
	else
		tmp = x1 + (6.0 * (x1 ^ 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around inf 97.7%

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

   4. Taylor expanded in x1 around 0 99.4%

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

      1. neg-mul-1 99.4%

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

      2. unsub-neg 99.4%

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

      3. *-commutative 99.4%

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

   6. Simplified 99.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 9.7%

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

   4. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.6%

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

Alternative 4: 98.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+103}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\\ \mathbf{elif}\;x1 \leq 10^{+134}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_1 \cdot \left(\left(t\_2 \cdot \left(x1 \cdot 2\right)\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t\_2 \cdot 4 - 6\right)\right) + 3 \cdot t\_0\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 3 \cdot \left(3 - x2 \cdot -2\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

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 (<= x1 -1.5e+103)
     (+ (* x2 -6.0) (* x1 (+ (* x1 (+ 9.0 (* x1 -19.0))) -1.0)))
     (if (<= x1 1e+134)
       (+
        x1
        (+
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (*
             t_1
             (+
              (* (* t_2 (* x1 2.0)) (- t_2 3.0))
              (* (* x1 x1) (- (* t_2 4.0) 6.0))))
            (* 3.0 t_0))))
         (* 3.0 (- (* x2 -2.0) x1))))
       (+
        x1
        (+
         (* x2 -6.0)
         (* x1 (- (* x1 (+ (* x1 3.0) (* 3.0 (- 3.0 (* x2 -2.0))))) 2.0))))))))

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 <= -1.5e+103) {
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	} else if (x1 <= 1e+134) {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * (((t_2 * (x1 * 2.0)) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (3.0 * t_0)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + (3.0 * (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) :: 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 <= (-1.5d+103)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * (9.0d0 + (x1 * (-19.0d0)))) + (-1.0d0)))
    else if (x1 <= 1d+134) then
        tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * (((t_2 * (x1 * 2.0d0)) * (t_2 - 3.0d0)) + ((x1 * x1) * ((t_2 * 4.0d0) - 6.0d0)))) + (3.0d0 * t_0)))) + (3.0d0 * ((x2 * (-2.0d0)) - x1)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * ((x1 * 3.0d0) + (3.0d0 * (3.0d0 - (x2 * (-2.0d0)))))) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if (x1 <= -1.5e+103) {
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	} else if (x1 <= 1e+134) {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * (((t_2 * (x1 * 2.0)) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (3.0 * t_0)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0))))) - 2.0)));
	}
	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 <= -1.5e+103:
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0))
	elif x1 <= 1e+134:
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * (((t_2 * (x1 * 2.0)) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (3.0 * t_0)))) + (3.0 * ((x2 * -2.0) - x1)))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0))))) - 2.0)))
	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 <= -1.5e+103)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))) + -1.0)));
	elseif (x1 <= 1e+134)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * Float64(Float64(Float64(t_2 * Float64(x1 * 2.0)) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)))) + Float64(3.0 * t_0)))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x1 * 3.0) + Float64(3.0 * Float64(3.0 - Float64(x2 * -2.0))))) - 2.0))));
	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 <= -1.5e+103)
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	elseif (x1 <= 1e+134)
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * (((t_2 * (x1 * 2.0)) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (3.0 * t_0)))) + (3.0 * ((x2 * -2.0) - x1)));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0))))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(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, -1.5e+103], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1e+134], N[(x1 + N[(N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * N[(N[(N[(t$95$2 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + N[(3.0 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.5e103

   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 83.8%

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

   6. Taylor expanded in x2 around 0 100.0%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 1\right) \]

   8. Simplified 100.0%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 1\right) \]

   if -1.5e103 < x1 < 9.99999999999999921e133

   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 97.6%

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

   4. Taylor expanded in x1 around 0 99.4%

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

      1. neg-mul-1 99.4%

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

      2. unsub-neg 99.4%

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

      3. *-commutative 99.4%

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

   6. Simplified 99.4%

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

   if 9.99999999999999921e133 < x1

   1. Initial program 14.6%

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

   3. Taylor expanded in x1 around inf 14.6%

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

   4. Taylor expanded in x1 around 0 92.7%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+103}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\\ \mathbf{elif}\;x1 \leq 10^{+134}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 3 \cdot \left(3 - x2 \cdot -2\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := x1 + \left(3 \cdot \frac{\left(t\_2 - 2 \cdot x2\right) - x1}{t\_0} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_2 + t\_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(t\_2 + 2 \cdot x2\right) - x1}{t\_0} \cdot 4 - 6\right) + x1 \cdot 2\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+103}:\\ \;\;\;\;x2 \cdot -6 + t\_1\\ \mathbf{elif}\;x1 \leq -12000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x1 \leq 260:\\ \;\;\;\;x2 \cdot -6 + \left(t\_1 + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot \left(12 + x1 \cdot 24\right) - 12\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+132}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 3 \cdot \left(3 - x2 \cdot -2\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (+ (* x1 (+ 9.0 (* x1 -19.0))) -1.0)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_0))
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* 3.0 t_2)
              (*
               t_0
               (+
                (* (* x1 x1) (- (* (/ (- (+ t_2 (* 2.0 x2)) x1) t_0) 4.0) 6.0))
                (* x1 2.0))))))))))
   (if (<= x1 -1.5e+103)
     (+ (* x2 -6.0) t_1)
     (if (<= x1 -12000000000.0)
       t_3
       (if (<= x1 260.0)
         (+
          (* x2 -6.0)
          (+
           t_1
           (*
            x2
            (+
             (* 8.0 (* x1 x2))
             (* x1 (- (* x1 (+ 12.0 (* x1 24.0))) 12.0))))))
         (if (<= x1 2e+132)
           t_3
           (+
            x1
            (+
             (* x2 -6.0)
             (*
              x1
              (-
               (* x1 (+ (* x1 3.0) (* 3.0 (- 3.0 (* x2 -2.0)))))
               2.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_2) + (t_0 * (((x1 * x1) * (((((t_2 + (2.0 * x2)) - x1) / t_0) * 4.0) - 6.0)) + (x1 * 2.0)))))));
	double tmp;
	if (x1 <= -1.5e+103) {
		tmp = (x2 * -6.0) + t_1;
	} else if (x1 <= -12000000000.0) {
		tmp = t_3;
	} else if (x1 <= 260.0) {
		tmp = (x2 * -6.0) + (t_1 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * (12.0 + (x1 * 24.0))) - 12.0)))));
	} else if (x1 <= 2e+132) {
		tmp = t_3;
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + (3.0 * (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) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * ((x1 * (9.0d0 + (x1 * (-19.0d0)))) + (-1.0d0))
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = x1 + ((3.0d0 * (((t_2 - (2.0d0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_2) + (t_0 * (((x1 * x1) * (((((t_2 + (2.0d0 * x2)) - x1) / t_0) * 4.0d0) - 6.0d0)) + (x1 * 2.0d0)))))))
    if (x1 <= (-1.5d+103)) then
        tmp = (x2 * (-6.0d0)) + t_1
    else if (x1 <= (-12000000000.0d0)) then
        tmp = t_3
    else if (x1 <= 260.0d0) then
        tmp = (x2 * (-6.0d0)) + (t_1 + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * (12.0d0 + (x1 * 24.0d0))) - 12.0d0)))))
    else if (x1 <= 2d+132) then
        tmp = t_3
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * ((x1 * 3.0d0) + (3.0d0 * (3.0d0 - (x2 * (-2.0d0)))))) - 2.0d0)))
    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 * (9.0 + (x1 * -19.0))) + -1.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_2) + (t_0 * (((x1 * x1) * (((((t_2 + (2.0 * x2)) - x1) / t_0) * 4.0) - 6.0)) + (x1 * 2.0)))))));
	double tmp;
	if (x1 <= -1.5e+103) {
		tmp = (x2 * -6.0) + t_1;
	} else if (x1 <= -12000000000.0) {
		tmp = t_3;
	} else if (x1 <= 260.0) {
		tmp = (x2 * -6.0) + (t_1 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * (12.0 + (x1 * 24.0))) - 12.0)))));
	} else if (x1 <= 2e+132) {
		tmp = t_3;
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0))))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0)
	t_2 = x1 * (x1 * 3.0)
	t_3 = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_2) + (t_0 * (((x1 * x1) * (((((t_2 + (2.0 * x2)) - x1) / t_0) * 4.0) - 6.0)) + (x1 * 2.0)))))))
	tmp = 0
	if x1 <= -1.5e+103:
		tmp = (x2 * -6.0) + t_1
	elif x1 <= -12000000000.0:
		tmp = t_3
	elif x1 <= 260.0:
		tmp = (x2 * -6.0) + (t_1 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * (12.0 + (x1 * 24.0))) - 12.0)))))
	elif x1 <= 2e+132:
		tmp = t_3
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0))))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))) + -1.0))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_2) + Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(Float64(Float64(Float64(t_2 + Float64(2.0 * x2)) - x1) / t_0) * 4.0) - 6.0)) + Float64(x1 * 2.0))))))))
	tmp = 0.0
	if (x1 <= -1.5e+103)
		tmp = Float64(Float64(x2 * -6.0) + t_1);
	elseif (x1 <= -12000000000.0)
		tmp = t_3;
	elseif (x1 <= 260.0)
		tmp = Float64(Float64(x2 * -6.0) + Float64(t_1 + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * Float64(12.0 + Float64(x1 * 24.0))) - 12.0))))));
	elseif (x1 <= 2e+132)
		tmp = t_3;
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x1 * 3.0) + Float64(3.0 * Float64(3.0 - Float64(x2 * -2.0))))) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0);
	t_2 = x1 * (x1 * 3.0);
	t_3 = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_2) + (t_0 * (((x1 * x1) * (((((t_2 + (2.0 * x2)) - x1) / t_0) * 4.0) - 6.0)) + (x1 * 2.0)))))));
	tmp = 0.0;
	if (x1 <= -1.5e+103)
		tmp = (x2 * -6.0) + t_1;
	elseif (x1 <= -12000000000.0)
		tmp = t_3;
	elseif (x1 <= 260.0)
		tmp = (x2 * -6.0) + (t_1 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * (12.0 + (x1 * 24.0))) - 12.0)))));
	elseif (x1 <= 2e+132)
		tmp = t_3;
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0))))) - 2.0)));
	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[(N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$2), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(N[(N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision] * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.5e+103], N[(N[(x2 * -6.0), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x1, -12000000000.0], t$95$3, If[LessEqual[x1, 260.0], N[(N[(x2 * -6.0), $MachinePrecision] + N[(t$95$1 + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(12.0 + N[(x1 * 24.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+132], t$95$3, N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + N[(3.0 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.5e103

   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 83.8%

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

   6. Taylor expanded in x2 around 0 100.0%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 1\right) \]

   8. Simplified 100.0%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 1\right) \]

   if -1.5e103 < x1 < -1.2e10 or 260 < x1 < 1.99999999999999998e132

   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 99.6%

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

   4. Taylor expanded in x1 around 0 87.9%

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

      1. neg-mul-1 87.9%

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

      2. +-commutative 87.9%

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

      3. unsub-neg 87.9%

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

   6. Simplified 87.9%

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

   7. Taylor expanded in x1 around inf 97.1%

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

      1. *-commutative 97.1%

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

   9. Simplified 97.1%

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

   if -1.2e10 < x1 < 260

   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 99.7%

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

   5. Taylor expanded in x1 around 0 71.6%

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

   6. Taylor expanded in x2 around 0 86.3%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\color{blue}{\left(24 \cdot x2 - 16\right)} - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right) \]

   7. Taylor expanded in x2 around 0 96.9%

      \[\leadsto -6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right)\right)} \]

   if 1.99999999999999998e132 < x1

   1. Initial program 14.6%

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

   3. Taylor expanded in x1 around inf 14.6%

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

   4. Taylor expanded in x1 around 0 92.7%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+103}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\\ \mathbf{elif}\;x1 \leq -12000000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + x1 \cdot 2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 260:\\ \;\;\;\;x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot \left(12 + x1 \cdot 24\right) - 12\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+132}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + x1 \cdot 2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 3 \cdot \left(3 - x2 \cdot -2\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+103}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+130}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_0 + t\_1 \cdot \left(\left(t\_2 \cdot \left(x1 \cdot 2\right)\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 3 \cdot \left(3 - x2 \cdot -2\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

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 (<= x1 -1.5e+103)
     (+ (* x2 -6.0) (* x1 (+ (* x1 (+ 9.0 (* x1 -19.0))) -1.0)))
     (if (<= x1 2e+130)
       (+
        x1
        (+
         (* 3.0 (- (* x2 -2.0) x1))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* 3.0 t_0)
            (*
             t_1
             (+ (* (* t_2 (* x1 2.0)) (- t_2 3.0)) (* (* x1 x1) 6.0))))))))
       (+
        x1
        (+
         (* x2 -6.0)
         (* x1 (- (* x1 (+ (* x1 3.0) (* 3.0 (- 3.0 (* x2 -2.0))))) 2.0))))))))

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 <= -1.5e+103) {
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	} else if (x1 <= 2e+130) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * (((t_2 * (x1 * 2.0)) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + (3.0 * (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) :: 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 <= (-1.5d+103)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * (9.0d0 + (x1 * (-19.0d0)))) + (-1.0d0)))
    else if (x1 <= 2d+130) then
        tmp = x1 + ((3.0d0 * ((x2 * (-2.0d0)) - x1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_0) + (t_1 * (((t_2 * (x1 * 2.0d0)) * (t_2 - 3.0d0)) + ((x1 * x1) * 6.0d0)))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * ((x1 * 3.0d0) + (3.0d0 * (3.0d0 - (x2 * (-2.0d0)))))) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if (x1 <= -1.5e+103) {
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	} else if (x1 <= 2e+130) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * (((t_2 * (x1 * 2.0)) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0))))) - 2.0)));
	}
	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 <= -1.5e+103:
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0))
	elif x1 <= 2e+130:
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * (((t_2 * (x1 * 2.0)) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0))))) - 2.0)))
	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 <= -1.5e+103)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))) + -1.0)));
	elseif (x1 <= 2e+130)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - x1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_0) + Float64(t_1 * Float64(Float64(Float64(t_2 * Float64(x1 * 2.0)) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * 6.0))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x1 * 3.0) + Float64(3.0 * Float64(3.0 - Float64(x2 * -2.0))))) - 2.0))));
	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 <= -1.5e+103)
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	elseif (x1 <= 2e+130)
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * (((t_2 * (x1 * 2.0)) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0))))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(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, -1.5e+103], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+130], N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$0), $MachinePrecision] + N[(t$95$1 * N[(N[(N[(t$95$2 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + N[(3.0 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.5e103

   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 83.8%

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

   6. Taylor expanded in x2 around 0 100.0%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 1\right) \]

   8. Simplified 100.0%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 1\right) \]

   if -1.5e103 < x1 < 2.0000000000000001e130

   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 97.6%

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

   4. Taylor expanded in x1 around 0 99.4%

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

      1. neg-mul-1 99.4%

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

      2. unsub-neg 99.4%

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

      3. *-commutative 99.4%

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

   6. Simplified 99.4%

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

   7. Taylor expanded in x1 around inf 95.6%

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

   if 2.0000000000000001e130 < x1

   1. Initial program 14.6%

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

   3. Taylor expanded in x1 around inf 14.6%

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

   4. Taylor expanded in x1 around 0 92.7%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+103}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+130}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 3 \cdot \left(3 - x2 \cdot -2\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.8% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\\ \mathbf{if}\;x1 \leq -1.7 \cdot 10^{+100}:\\ \;\;\;\;x2 \cdot -6 + t\_0\\ \mathbf{elif}\;x1 \leq 3.8 \cdot 10^{+19}:\\ \;\;\;\;x2 \cdot -6 + \left(t\_0 + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot \left(12 + x1 \cdot 24\right) - 12\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 3 \cdot \left(3 - x2 \cdot -2\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ (* x1 (+ 9.0 (* x1 -19.0))) -1.0))))
   (if (<= x1 -1.7e+100)
     (+ (* x2 -6.0) t_0)
     (if (<= x1 3.8e+19)
       (+
        (* x2 -6.0)
        (+
         t_0
         (*
          x2
          (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 (+ 12.0 (* x1 24.0))) 12.0))))))
       (+
        x1
        (+
         (* x2 -6.0)
         (* x1 (- (* x1 (+ (* x1 3.0) (* 3.0 (- 3.0 (* x2 -2.0))))) 2.0))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0);
	double tmp;
	if (x1 <= -1.7e+100) {
		tmp = (x2 * -6.0) + t_0;
	} else if (x1 <= 3.8e+19) {
		tmp = (x2 * -6.0) + (t_0 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * (12.0 + (x1 * 24.0))) - 12.0)))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + (3.0 * (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) :: t_0
    real(8) :: tmp
    t_0 = x1 * ((x1 * (9.0d0 + (x1 * (-19.0d0)))) + (-1.0d0))
    if (x1 <= (-1.7d+100)) then
        tmp = (x2 * (-6.0d0)) + t_0
    else if (x1 <= 3.8d+19) then
        tmp = (x2 * (-6.0d0)) + (t_0 + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * (12.0d0 + (x1 * 24.0d0))) - 12.0d0)))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * ((x1 * 3.0d0) + (3.0d0 * (3.0d0 - (x2 * (-2.0d0)))))) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0);
	double tmp;
	if (x1 <= -1.7e+100) {
		tmp = (x2 * -6.0) + t_0;
	} else if (x1 <= 3.8e+19) {
		tmp = (x2 * -6.0) + (t_0 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * (12.0 + (x1 * 24.0))) - 12.0)))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0))))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0)
	tmp = 0
	if x1 <= -1.7e+100:
		tmp = (x2 * -6.0) + t_0
	elif x1 <= 3.8e+19:
		tmp = (x2 * -6.0) + (t_0 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * (12.0 + (x1 * 24.0))) - 12.0)))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0))))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))) + -1.0))
	tmp = 0.0
	if (x1 <= -1.7e+100)
		tmp = Float64(Float64(x2 * -6.0) + t_0);
	elseif (x1 <= 3.8e+19)
		tmp = Float64(Float64(x2 * -6.0) + Float64(t_0 + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * Float64(12.0 + Float64(x1 * 24.0))) - 12.0))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x1 * 3.0) + Float64(3.0 * Float64(3.0 - Float64(x2 * -2.0))))) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0);
	tmp = 0.0;
	if (x1 <= -1.7e+100)
		tmp = (x2 * -6.0) + t_0;
	elseif (x1 <= 3.8e+19)
		tmp = (x2 * -6.0) + (t_0 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * (12.0 + (x1 * 24.0))) - 12.0)))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0))))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.7e+100], N[(N[(x2 * -6.0), $MachinePrecision] + t$95$0), $MachinePrecision], If[LessEqual[x1, 3.8e+19], N[(N[(x2 * -6.0), $MachinePrecision] + N[(t$95$0 + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(12.0 + N[(x1 * 24.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + N[(3.0 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.69999999999999997e100

   1. Initial program 5.1%

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

   3. Simplified 5.1%

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

   5. Taylor expanded in x1 around 0 79.5%

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

   6. Taylor expanded in x2 around 0 95.2%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 95.2%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 1\right) \]

   8. Simplified 95.2%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 1\right) \]

   if -1.69999999999999997e100 < x1 < 3.8e19

   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 99.7%

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

   5. Taylor expanded in x1 around 0 64.5%

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

   6. Taylor expanded in x2 around 0 77.9%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\color{blue}{\left(24 \cdot x2 - 16\right)} - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right) \]

   7. Taylor expanded in x2 around 0 87.1%

      \[\leadsto -6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right)\right)} \]

   if 3.8e19 < x1

   1. Initial program 43.4%

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

   3. Taylor expanded in x1 around inf 41.9%

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

   4. Taylor expanded in x1 around 0 72.9%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.7 \cdot 10^{+100}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\\ \mathbf{elif}\;x1 \leq 3.8 \cdot 10^{+19}:\\ \;\;\;\;x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot \left(12 + x1 \cdot 24\right) - 12\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 3 \cdot \left(3 - x2 \cdot -2\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.5% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+103}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\\ \mathbf{elif}\;x1 \leq 1.3 \cdot 10^{-7}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot -12\right) - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 3 \cdot \left(3 - x2 \cdot -2\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.5e+103)
   (+ (* x2 -6.0) (* x1 (+ (* x1 (+ 9.0 (* x1 -19.0))) -1.0)))
   (if (<= x1 1.3e-7)
     (+ x1 (+ (* x1 -2.0) (* x2 (- (+ (* 8.0 (* x1 x2)) (* x1 -12.0)) 6.0))))
     (+
      x1
      (+
       (* x2 -6.0)
       (* x1 (- (* x1 (+ (* x1 3.0) (* 3.0 (- 3.0 (* x2 -2.0))))) 2.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.5e+103) {
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	} else if (x1 <= 1.3e-7) {
		tmp = x1 + ((x1 * -2.0) + (x2 * (((8.0 * (x1 * x2)) + (x1 * -12.0)) - 6.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + (3.0 * (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 (x1 <= (-1.5d+103)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * (9.0d0 + (x1 * (-19.0d0)))) + (-1.0d0)))
    else if (x1 <= 1.3d-7) then
        tmp = x1 + ((x1 * (-2.0d0)) + (x2 * (((8.0d0 * (x1 * x2)) + (x1 * (-12.0d0))) - 6.0d0)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * ((x1 * 3.0d0) + (3.0d0 * (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 (x1 <= -1.5e+103) {
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	} else if (x1 <= 1.3e-7) {
		tmp = x1 + ((x1 * -2.0) + (x2 * (((8.0 * (x1 * x2)) + (x1 * -12.0)) - 6.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0))))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.5e+103:
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0))
	elif x1 <= 1.3e-7:
		tmp = x1 + ((x1 * -2.0) + (x2 * (((8.0 * (x1 * x2)) + (x1 * -12.0)) - 6.0)))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0))))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.5e+103)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))) + -1.0)));
	elseif (x1 <= 1.3e-7)
		tmp = Float64(x1 + Float64(Float64(x1 * -2.0) + Float64(x2 * Float64(Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * -12.0)) - 6.0))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x1 * 3.0) + Float64(3.0 * Float64(3.0 - Float64(x2 * -2.0))))) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -1.5e+103)
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	elseif (x1 <= 1.3e-7)
		tmp = x1 + ((x1 * -2.0) + (x2 * (((8.0 * (x1 * x2)) + (x1 * -12.0)) - 6.0)));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0))))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.5e+103], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.3e-7], N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] + N[(x2 * N[(N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * -12.0), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + N[(3.0 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.5e103

   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 83.8%

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

   6. Taylor expanded in x2 around 0 100.0%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 1\right) \]

   8. Simplified 100.0%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 1\right) \]

   if -1.5e103 < x1 < 1.29999999999999999e-7

   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 99.7%

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

   5. Taylor expanded in x1 around 0 76.9%

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

   6. Taylor expanded in x2 around 0 85.6%

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

   if 1.29999999999999999e-7 < x1

   1. Initial program 47.5%

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

   3. Taylor expanded in x1 around inf 41.3%

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

   4. Taylor expanded in x1 around 0 69.9%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+103}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\\ \mathbf{elif}\;x1 \leq 1.3 \cdot 10^{-7}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot -12\right) - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 3 \cdot \left(3 - x2 \cdot -2\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.2% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+103}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\\ \mathbf{elif}\;x1 \leq -9.2 \cdot 10^{-248} \lor \neg \left(x1 \leq 8 \cdot 10^{-289}\right):\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.5e+103)
   (+ (* x2 -6.0) (* x1 (+ (* x1 (+ 9.0 (* x1 -19.0))) -1.0)))
   (if (or (<= x1 -9.2e-248) (not (<= x1 8e-289)))
     (+ (* x2 -6.0) (* x1 (+ (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) -1.0)))
     (- (* x2 -6.0) x1))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.5e+103) {
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	} else if ((x1 <= -9.2e-248) || !(x1 <= 8e-289)) {
		tmp = (x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0));
	} else {
		tmp = (x2 * -6.0) - x1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-1.5d+103)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * (9.0d0 + (x1 * (-19.0d0)))) + (-1.0d0)))
    else if ((x1 <= (-9.2d-248)) .or. (.not. (x1 <= 8d-289))) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + (-1.0d0)))
    else
        tmp = (x2 * (-6.0d0)) - x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.5e+103) {
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	} else if ((x1 <= -9.2e-248) || !(x1 <= 8e-289)) {
		tmp = (x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0));
	} else {
		tmp = (x2 * -6.0) - x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.5e+103:
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0))
	elif (x1 <= -9.2e-248) or not (x1 <= 8e-289):
		tmp = (x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0))
	else:
		tmp = (x2 * -6.0) - x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.5e+103)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))) + -1.0)));
	elseif ((x1 <= -9.2e-248) || !(x1 <= 8e-289))
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) + -1.0)));
	else
		tmp = Float64(Float64(x2 * -6.0) - x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -1.5e+103)
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	elseif ((x1 <= -9.2e-248) || ~((x1 <= 8e-289)))
		tmp = (x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0));
	else
		tmp = (x2 * -6.0) - x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.5e+103], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x1, -9.2e-248], N[Not[LessEqual[x1, 8e-289]], $MachinePrecision]], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.5e103

   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 83.8%

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

   6. Taylor expanded in x2 around 0 100.0%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 1\right) \]

   8. Simplified 100.0%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 1\right) \]

   if -1.5e103 < x1 < -9.2000000000000001e-248 or 8.0000000000000001e-289 < x1

   1. Initial program 81.6%

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

   3. Simplified 81.9%

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

   5. Taylor expanded in x1 around 0 62.1%

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

   if -9.2000000000000001e-248 < x1 < 8.0000000000000001e-289

   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 95.8%

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

   4. Taylor expanded in x1 around 0 95.8%

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

   5. Taylor expanded in x1 around 0 95.9%

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

      1. *-commutative 95.9%

         \[\leadsto \color{blue}{x2 \cdot -6} + -1 \cdot x1 \]

      2. neg-mul-1 95.9%

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

      3. unsub-neg 95.9%

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

   7. Simplified 95.9%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+103}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\\ \mathbf{elif}\;x1 \leq -9.2 \cdot 10^{-248} \lor \neg \left(x1 \leq 8 \cdot 10^{-289}\right):\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.0% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -1.5 \lor \neg \left(x2 \leq 6.1 \cdot 10^{+172}\right):\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot -12\right) - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(3 \cdot \left(x1 \cdot \left(3 - x2 \cdot -2\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -1.5) (not (<= x2 6.1e+172)))
   (+ x1 (+ (* x1 -2.0) (* x2 (- (+ (* 8.0 (* x1 x2)) (* x1 -12.0)) 6.0))))
   (+ x1 (+ (* x2 -6.0) (* x1 (- (* 3.0 (* x1 (- 3.0 (* x2 -2.0)))) 2.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.5) || !(x2 <= 6.1e+172)) {
		tmp = x1 + ((x1 * -2.0) + (x2 * (((8.0 * (x1 * x2)) + (x1 * -12.0)) - 6.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((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 ((x2 <= (-1.5d0)) .or. (.not. (x2 <= 6.1d+172))) then
        tmp = x1 + ((x1 * (-2.0d0)) + (x2 * (((8.0d0 * (x1 * x2)) + (x1 * (-12.0d0))) - 6.0d0)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((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 ((x2 <= -1.5) || !(x2 <= 6.1e+172)) {
		tmp = x1 + ((x1 * -2.0) + (x2 * (((8.0 * (x1 * x2)) + (x1 * -12.0)) - 6.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((3.0 * (x1 * (3.0 - (x2 * -2.0)))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -1.5) or not (x2 <= 6.1e+172):
		tmp = x1 + ((x1 * -2.0) + (x2 * (((8.0 * (x1 * x2)) + (x1 * -12.0)) - 6.0)))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((3.0 * (x1 * (3.0 - (x2 * -2.0)))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -1.5) || !(x2 <= 6.1e+172))
		tmp = Float64(x1 + Float64(Float64(x1 * -2.0) + Float64(x2 * Float64(Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * -12.0)) - 6.0))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(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 ((x2 <= -1.5) || ~((x2 <= 6.1e+172)))
		tmp = x1 + ((x1 * -2.0) + (x2 * (((8.0 * (x1 * x2)) + (x1 * -12.0)) - 6.0)));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((3.0 * (x1 * (3.0 - (x2 * -2.0)))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -1.5], N[Not[LessEqual[x2, 6.1e+172]], $MachinePrecision]], N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] + N[(x2 * N[(N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * -12.0), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(3.0 * N[(x1 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -1.5 or 6.0999999999999998e172 < x2

   1. Initial program 77.4%

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

   3. Simplified 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 65.0%

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

   6. Taylor expanded in x2 around 0 79.4%

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

   if -1.5 < x2 < 6.0999999999999998e172

   1. Initial program 68.4%

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

   3. Taylor expanded in x1 around inf 68.5%

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

   4. Taylor expanded in x1 around 0 77.4%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.5 \lor \neg \left(x2 \leq 6.1 \cdot 10^{+172}\right):\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot -12\right) - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(3 \cdot \left(x1 \cdot \left(3 - x2 \cdot -2\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.9% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -1.5 \lor \neg \left(x2 \leq 6.5 \cdot 10^{+220}\right):\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(3 \cdot \left(x1 \cdot \left(3 - x2 \cdot -2\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -1.5) (not (<= x2 6.5e+220)))
   (+ (* x2 -6.0) (* x1 (+ (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) -1.0)))
   (+ x1 (+ (* x2 -6.0) (* x1 (- (* 3.0 (* x1 (- 3.0 (* x2 -2.0)))) 2.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.5) || !(x2 <= 6.5e+220)) {
		tmp = (x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((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 ((x2 <= (-1.5d0)) .or. (.not. (x2 <= 6.5d+220))) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + (-1.0d0)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((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 ((x2 <= -1.5) || !(x2 <= 6.5e+220)) {
		tmp = (x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((3.0 * (x1 * (3.0 - (x2 * -2.0)))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -1.5) or not (x2 <= 6.5e+220):
		tmp = (x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((3.0 * (x1 * (3.0 - (x2 * -2.0)))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -1.5) || !(x2 <= 6.5e+220))
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) + -1.0)));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(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 ((x2 <= -1.5) || ~((x2 <= 6.5e+220)))
		tmp = (x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((3.0 * (x1 * (3.0 - (x2 * -2.0)))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -1.5], N[Not[LessEqual[x2, 6.5e+220]], $MachinePrecision]], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(3.0 * N[(x1 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -1.5 or 6.5000000000000001e220 < x2

   1. Initial program 79.5%

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

   3. Simplified 79.6%

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

   5. Taylor expanded in x1 around 0 67.1%

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

   if -1.5 < x2 < 6.5000000000000001e220

   1. Initial program 67.8%

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

   3. Taylor expanded in x1 around inf 66.7%

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

   4. Taylor expanded in x1 around 0 77.0%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.5 \lor \neg \left(x2 \leq 6.5 \cdot 10^{+220}\right):\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(3 \cdot \left(x1 \cdot \left(3 - x2 \cdot -2\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.8% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+103}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\\ \mathbf{elif}\;x1 \leq -6.8 \cdot 10^{-56} \lor \neg \left(x1 \leq 4.4 \cdot 10^{-131}\right):\\ \;\;\;\;x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.5e+103)
   (+ (* x2 -6.0) (* x1 (+ (* x1 (+ 9.0 (* x1 -19.0))) -1.0)))
   (if (or (<= x1 -6.8e-56) (not (<= x1 4.4e-131)))
     (* x1 (+ (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) -1.0))
     (- (* x2 -6.0) x1))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.5e+103) {
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	} else if ((x1 <= -6.8e-56) || !(x1 <= 4.4e-131)) {
		tmp = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0);
	} else {
		tmp = (x2 * -6.0) - x1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-1.5d+103)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * (9.0d0 + (x1 * (-19.0d0)))) + (-1.0d0)))
    else if ((x1 <= (-6.8d-56)) .or. (.not. (x1 <= 4.4d-131))) then
        tmp = x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + (-1.0d0))
    else
        tmp = (x2 * (-6.0d0)) - x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.5e+103) {
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	} else if ((x1 <= -6.8e-56) || !(x1 <= 4.4e-131)) {
		tmp = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0);
	} else {
		tmp = (x2 * -6.0) - x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.5e+103:
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0))
	elif (x1 <= -6.8e-56) or not (x1 <= 4.4e-131):
		tmp = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0)
	else:
		tmp = (x2 * -6.0) - x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.5e+103)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))) + -1.0)));
	elseif ((x1 <= -6.8e-56) || !(x1 <= 4.4e-131))
		tmp = Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) + -1.0));
	else
		tmp = Float64(Float64(x2 * -6.0) - x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -1.5e+103)
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	elseif ((x1 <= -6.8e-56) || ~((x1 <= 4.4e-131)))
		tmp = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0);
	else
		tmp = (x2 * -6.0) - x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.5e+103], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x1, -6.8e-56], N[Not[LessEqual[x1, 4.4e-131]], $MachinePrecision]], N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.5e103

   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 83.8%

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

   6. Taylor expanded in x2 around 0 100.0%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 1\right) \]

   8. Simplified 100.0%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 1\right) \]

   if -1.5e103 < x1 < -6.79999999999999964e-56 or 4.3999999999999999e-131 < x1

   1. Initial program 72.8%

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

   3. Simplified 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 48.5%

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

   6. Taylor expanded in x1 around inf 46.1%

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

   if -6.79999999999999964e-56 < x1 < 4.3999999999999999e-131

   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 84.1%

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

   4. Taylor expanded in x1 around 0 84.4%

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

   5. Taylor expanded in x1 around 0 84.4%

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

      1. *-commutative 84.4%

         \[\leadsto \color{blue}{x2 \cdot -6} + -1 \cdot x1 \]

      2. neg-mul-1 84.4%

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

      3. unsub-neg 84.4%

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

   7. Simplified 84.4%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+103}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\\ \mathbf{elif}\;x1 \leq -6.8 \cdot 10^{-56} \lor \neg \left(x1 \leq 4.4 \cdot 10^{-131}\right):\\ \;\;\;\;x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 55.8% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{if}\;x2 \leq -1.25 \cdot 10^{+67}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x2 \leq 1.9 \cdot 10^{-45}:\\ \;\;\;\;x2 \cdot \left(-6 - \frac{x1}{x2}\right)\\ \mathbf{elif}\;x2 \leq 6.6 \cdot 10^{+171}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) -1.0))))
   (if (<= x2 -1.25e+67)
     t_0
     (if (<= x2 1.9e-45)
       (* x2 (- -6.0 (/ x1 x2)))
       (if (<= x2 6.6e+171)
         (+ x1 (+ (* x2 -6.0) (* x1 (- (* x2 -12.0) 2.0))))
         t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0);
	double tmp;
	if (x2 <= -1.25e+67) {
		tmp = t_0;
	} else if (x2 <= 1.9e-45) {
		tmp = x2 * (-6.0 - (x1 / x2));
	} else if (x2 <= 6.6e+171) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x2 * -12.0) - 2.0)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + (-1.0d0))
    if (x2 <= (-1.25d+67)) then
        tmp = t_0
    else if (x2 <= 1.9d-45) then
        tmp = x2 * ((-6.0d0) - (x1 / x2))
    else if (x2 <= 6.6d+171) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x2 * (-12.0d0)) - 2.0d0)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0);
	double tmp;
	if (x2 <= -1.25e+67) {
		tmp = t_0;
	} else if (x2 <= 1.9e-45) {
		tmp = x2 * (-6.0 - (x1 / x2));
	} else if (x2 <= 6.6e+171) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x2 * -12.0) - 2.0)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0)
	tmp = 0
	if x2 <= -1.25e+67:
		tmp = t_0
	elif x2 <= 1.9e-45:
		tmp = x2 * (-6.0 - (x1 / x2))
	elif x2 <= 6.6e+171:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x2 * -12.0) - 2.0)))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) + -1.0))
	tmp = 0.0
	if (x2 <= -1.25e+67)
		tmp = t_0;
	elseif (x2 <= 1.9e-45)
		tmp = Float64(x2 * Float64(-6.0 - Float64(x1 / x2)));
	elseif (x2 <= 6.6e+171)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x2 * -12.0) - 2.0))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0);
	tmp = 0.0;
	if (x2 <= -1.25e+67)
		tmp = t_0;
	elseif (x2 <= 1.9e-45)
		tmp = x2 * (-6.0 - (x1 / x2));
	elseif (x2 <= 6.6e+171)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x2 * -12.0) - 2.0)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x2, -1.25e+67], t$95$0, If[LessEqual[x2, 1.9e-45], N[(x2 * N[(-6.0 - N[(x1 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x2, 6.6e+171], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -1.24999999999999994e67 or 6.59999999999999982e171 < x2

   1. Initial program 75.2%

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

   3. Simplified 75.2%

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

   5. Taylor expanded in x1 around 0 66.9%

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

   6. Taylor expanded in x1 around inf 62.5%

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

   if -1.24999999999999994e67 < x2 < 1.89999999999999999e-45

   1. Initial program 75.8%

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

   3. Taylor expanded in x1 around inf 76.4%

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

   4. Taylor expanded in x1 around 0 53.5%

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

   5. Taylor expanded in x2 around inf 52.7%

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

      1. sub-neg 52.7%

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

      2. distribute-lft1-in 64.5%

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

      3. metadata-eval 64.5%

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

      4. metadata-eval 64.5%

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

   7. Simplified 64.5%

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

   if 1.89999999999999999e-45 < x2 < 6.59999999999999982e171

   1. Initial program 49.9%

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

   3. Simplified 49.9%

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

   5. Taylor expanded in x1 around 0 41.3%

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

   6. Taylor expanded in x2 around 0 46.7%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{-12 \cdot x2} - 2\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative 46.7%

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

   8. Simplified 46.7%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.25 \cdot 10^{+67}:\\ \;\;\;\;x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{elif}\;x2 \leq 1.9 \cdot 10^{-45}:\\ \;\;\;\;x2 \cdot \left(-6 - \frac{x1}{x2}\right)\\ \mathbf{elif}\;x2 \leq 6.6 \cdot 10^{+171}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 55.0% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -1.82 \cdot 10^{+67} \lor \neg \left(x2 \leq 2.7 \cdot 10^{+89}\right):\\ \;\;\;\;x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(-6 - \frac{x1}{x2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -1.82e+67) (not (<= x2 2.7e+89)))
   (* x1 (+ (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) -1.0))
   (* x2 (- -6.0 (/ x1 x2)))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.82e+67) || !(x2 <= 2.7e+89)) {
		tmp = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0);
	} else {
		tmp = x2 * (-6.0 - (x1 / x2));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-1.82d+67)) .or. (.not. (x2 <= 2.7d+89))) then
        tmp = x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + (-1.0d0))
    else
        tmp = x2 * ((-6.0d0) - (x1 / x2))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.82e+67) || !(x2 <= 2.7e+89)) {
		tmp = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0);
	} else {
		tmp = x2 * (-6.0 - (x1 / x2));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -1.82e+67) or not (x2 <= 2.7e+89):
		tmp = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0)
	else:
		tmp = x2 * (-6.0 - (x1 / x2))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -1.82e+67) || !(x2 <= 2.7e+89))
		tmp = Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) + -1.0));
	else
		tmp = Float64(x2 * Float64(-6.0 - Float64(x1 / x2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -1.82e+67) || ~((x2 <= 2.7e+89)))
		tmp = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0);
	else
		tmp = x2 * (-6.0 - (x1 / x2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -1.82e+67], N[Not[LessEqual[x2, 2.7e+89]], $MachinePrecision]], N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(x2 * N[(-6.0 - N[(x1 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -1.81999999999999997e67 or 2.7e89 < x2

   1. Initial program 66.5%

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

   3. Simplified 66.6%

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

   5. Taylor expanded in x1 around 0 58.9%

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

   6. Taylor expanded in x1 around inf 54.4%

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

   if -1.81999999999999997e67 < x2 < 2.7e89

   1. Initial program 73.9%

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

   3. Taylor expanded in x1 around inf 74.5%

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

   4. Taylor expanded in x1 around 0 51.5%

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

   5. Taylor expanded in x2 around inf 50.8%

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

      1. sub-neg 50.8%

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

      2. distribute-lft1-in 60.9%

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

      3. metadata-eval 60.9%

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

      4. metadata-eval 60.9%

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

   7. Simplified 60.9%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.82 \cdot 10^{+67} \lor \neg \left(x2 \leq 2.7 \cdot 10^{+89}\right):\\ \;\;\;\;x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(-6 - \frac{x1}{x2}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 32.3% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -1.14 \cdot 10^{-163} \lor \neg \left(x2 \leq 1.02 \cdot 10^{-168}\right):\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -1.14e-163) (not (<= x2 1.02e-168)))
   (+ x1 (* x2 -6.0))
   (- x1)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.14e-163) || !(x2 <= 1.02e-168)) {
		tmp = x1 + (x2 * -6.0);
	} else {
		tmp = -x1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-1.14d-163)) .or. (.not. (x2 <= 1.02d-168))) then
        tmp = x1 + (x2 * (-6.0d0))
    else
        tmp = -x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.14e-163) || !(x2 <= 1.02e-168)) {
		tmp = x1 + (x2 * -6.0);
	} else {
		tmp = -x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -1.14e-163) or not (x2 <= 1.02e-168):
		tmp = x1 + (x2 * -6.0)
	else:
		tmp = -x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -1.14e-163) || !(x2 <= 1.02e-168))
		tmp = Float64(x1 + Float64(x2 * -6.0));
	else
		tmp = Float64(-x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -1.14e-163) || ~((x2 <= 1.02e-168)))
		tmp = x1 + (x2 * -6.0);
	else
		tmp = -x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -1.14e-163], N[Not[LessEqual[x2, 1.02e-168]], $MachinePrecision]], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision], (-x1)]

Derivation

1. Split input into 2 regimes

2. if x2 < -1.14000000000000005e-163 or 1.01999999999999999e-168 < x2

   1. Initial program 72.6%

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

   3. Taylor expanded in x1 around inf 53.4%

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

   4. Taylor expanded in x1 around 0 35.5%

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

   5. Taylor expanded in x2 around inf 31.7%

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

      1. *-commutative 31.7%

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

   7. Simplified 31.7%

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

   if -1.14000000000000005e-163 < x2 < 1.01999999999999999e-168

   1. Initial program 67.9%

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

   3. Taylor expanded in x1 around inf 70.6%

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

   4. Taylor expanded in x1 around 0 50.6%

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

   5. Taylor expanded in x1 around inf 43.1%

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

      1. neg-mul-1 43.1%

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

   7. Simplified 43.1%

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

4. Final simplification 34.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.14 \cdot 10^{-163} \lor \neg \left(x2 \leq 1.02 \cdot 10^{-168}\right):\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 32.1% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -3.3 \cdot 10^{-156} \lor \neg \left(x2 \leq 3 \cdot 10^{-168}\right):\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -3.3e-156) (not (<= x2 3e-168))) (* x2 -6.0) (- x1)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -3.3e-156) || !(x2 <= 3e-168)) {
		tmp = x2 * -6.0;
	} else {
		tmp = -x1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-3.3d-156)) .or. (.not. (x2 <= 3d-168))) then
        tmp = x2 * (-6.0d0)
    else
        tmp = -x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -3.3e-156) || !(x2 <= 3e-168)) {
		tmp = x2 * -6.0;
	} else {
		tmp = -x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -3.3e-156) or not (x2 <= 3e-168):
		tmp = x2 * -6.0
	else:
		tmp = -x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -3.3e-156) || !(x2 <= 3e-168))
		tmp = Float64(x2 * -6.0);
	else
		tmp = Float64(-x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -3.3e-156) || ~((x2 <= 3e-168)))
		tmp = x2 * -6.0;
	else
		tmp = -x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -3.3e-156], N[Not[LessEqual[x2, 3e-168]], $MachinePrecision]], N[(x2 * -6.0), $MachinePrecision], (-x1)]

Derivation

1. Split input into 2 regimes

2. if x2 < -3.2999999999999999e-156 or 2.99999999999999991e-168 < x2

   1. Initial program 72.6%

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

   3. Simplified 72.7%

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

   5. Taylor expanded in x1 around 0 31.2%

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

      1. *-commutative 31.2%

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

   7. Simplified 31.2%

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

   if -3.2999999999999999e-156 < x2 < 2.99999999999999991e-168

   1. Initial program 67.9%

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

   3. Taylor expanded in x1 around inf 70.6%

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

   4. Taylor expanded in x1 around 0 50.6%

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

   5. Taylor expanded in x1 around inf 43.1%

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

      1. neg-mul-1 43.1%

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

   7. Simplified 43.1%

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

4. Final simplification 34.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -3.3 \cdot 10^{-156} \lor \neg \left(x2 \leq 3 \cdot 10^{-168}\right):\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 44.3% accurate, 18.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.4%

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

3. Taylor expanded in x1 around inf 57.7%

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

4. Taylor expanded in x1 around 0 39.3%

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

5. Taylor expanded in x2 around inf 38.8%

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

   1. sub-neg 38.8%

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

   2. distribute-lft1-in 45.5%

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

   3. metadata-eval 45.5%

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

   4. metadata-eval 45.5%

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

7. Simplified 45.5%

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

8. Final simplification 45.5%

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

Alternative 18: 38.6% accurate, 25.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.4%

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

3. Taylor expanded in x1 around inf 57.7%

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

4. Taylor expanded in x1 around 0 39.3%

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

5. Taylor expanded in x1 around 0 39.3%

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

   1. *-commutative 39.3%

      \[\leadsto \color{blue}{x2 \cdot -6} + -1 \cdot x1 \]

   2. neg-mul-1 39.3%

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

   3. unsub-neg 39.3%

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

7. Simplified 39.3%

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

Alternative 19: 13.7% accurate, 63.5× speedup

Math

\[\begin{array}{l} \\ -x1 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x1, x2):
	return -x1

Julia

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

MATLAB

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

Wolfram

code[x1_, x2_] := (-x1)

Derivation

1. Initial program 71.4%

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

3. Taylor expanded in x1 around inf 57.7%

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

4. Taylor expanded in x1 around 0 39.3%

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

5. Taylor expanded in x1 around inf 15.3%

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

   1. neg-mul-1 15.3%

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

7. Simplified 15.3%

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

Reproduce

herbie shell --seed 2024110 
(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))))))