Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.6% → 99.4%

Time: 33.3s

Alternatives: 16

Speedup: 5.1×

• 45.7% 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: 70.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

   3. Simplified 99.6%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around inf 0.0%

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

   6. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.7%

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

Alternative 2: 99.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around inf 0.0%

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

   6. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.6%

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

Alternative 3: 98.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ \mathbf{if}\;x1 \leq -4 \cdot 10^{+61} \lor \neg \left(x1 \leq 1.5 \cdot 10^{+71}\right):\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t\_2 \cdot 4 - 6\right)\right) + 3 \cdot t\_0\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (if (or (<= x1 -4e+61) (not (<= x1 1.5e+71)))
     (* 6.0 (pow x1 4.0))
     (+
      x1
      (+
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (*
           t_1
           (+
            (* (* (* x1 2.0) t_2) (- t_2 3.0))
            (* (* x1 x1) (- (* t_2 4.0) 6.0))))
          (* 3.0 t_0))))
       (* 3.0 (- (* x2 -2.0) x1)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -4e+61) || !(x1 <= 1.5e+71)) {
		tmp = 6.0 * pow(x1, 4.0);
	} else {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (3.0 * t_0)))) + (3.0 * ((x2 * -2.0) - x1)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    if ((x1 <= (-4d+61)) .or. (.not. (x1 <= 1.5d+71))) then
        tmp = 6.0d0 * (x1 ** 4.0d0)
    else
        tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * ((t_2 * 4.0d0) - 6.0d0)))) + (3.0d0 * t_0)))) + (3.0d0 * ((x2 * (-2.0d0)) - x1)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -4e+61) || !(x1 <= 1.5e+71)) {
		tmp = 6.0 * Math.pow(x1, 4.0);
	} else {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (3.0 * t_0)))) + (3.0 * ((x2 * -2.0) - x1)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1
	tmp = 0
	if (x1 <= -4e+61) or not (x1 <= 1.5e+71):
		tmp = 6.0 * math.pow(x1, 4.0)
	else:
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (3.0 * t_0)))) + (3.0 * ((x2 * -2.0) - x1)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if ((x1 <= -4e+61) || !(x1 <= 1.5e+71))
		tmp = Float64(6.0 * (x1 ^ 4.0));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)))) + Float64(3.0 * t_0)))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	tmp = 0.0;
	if ((x1 <= -4e+61) || ~((x1 <= 1.5e+71)))
		tmp = 6.0 * (x1 ^ 4.0);
	else
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (3.0 * t_0)))) + (3.0 * ((x2 * -2.0) - x1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[x1, -4e+61], N[Not[LessEqual[x1, 1.5e+71]], $MachinePrecision]], N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(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]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -3.9999999999999998e61 or 1.50000000000000006e71 < x1

   1. Initial program 25.4%

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

   3. Simplified 25.4%

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

   5. Taylor expanded in x1 around inf 25.4%

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

   6. Taylor expanded in x1 around inf 100.0%

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

   if -3.9999999999999998e61 < x1 < 1.50000000000000006e71

   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 98.2%

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

   4. Taylor expanded in x1 around 0 99.3%

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

      1. mul-1-neg 99.3%

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

      2. unsub-neg 99.3%

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

      3. *-commutative 99.3%

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

   6. Simplified 99.3%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+61} \lor \neg \left(x1 \leq 1.5 \cdot 10^{+71}\right):\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := \left(x1 \cdot 2\right) \cdot 3\\ t_2 := x1 \cdot \left(x1 \cdot x1\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := 3 \cdot \frac{\left(t\_3 - 2 \cdot x2\right) - x1}{t\_0}\\ t_5 := \frac{\left(t\_3 + 2 \cdot x2\right) - x1}{t\_0}\\ t_6 := \left(x1 \cdot x1\right) \cdot \left(t\_5 \cdot 4 - 6\right)\\ \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\\ \mathbf{elif}\;x1 \leq -40:\\ \;\;\;\;x1 + \left(t\_4 + \left(x1 + \left(t\_2 + \left(3 \cdot t\_3 + t\_0 \cdot \left(t\_6 + \left(t\_5 - 3\right) \cdot t\_1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.17:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(t\_4 + \left(x1 + \left(t\_2 + \left(t\_3 \cdot t\_5 + t\_0 \cdot \left(t\_6 + t\_1 \cdot 0\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* (* x1 2.0) 3.0))
        (t_2 (* x1 (* x1 x1)))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (* 3.0 (/ (- (- t_3 (* 2.0 x2)) x1) t_0)))
        (t_5 (/ (- (+ t_3 (* 2.0 x2)) x1) t_0))
        (t_6 (* (* x1 x1) (- (* t_5 4.0) 6.0))))
   (if (<= x1 -5.5e+102)
     (+ (* x2 -6.0) (* x1 (+ (* x1 (+ 9.0 (* x1 -19.0))) -1.0)))
     (if (<= x1 -40.0)
       (+
        x1
        (+
         t_4
         (+ x1 (+ t_2 (+ (* 3.0 t_3) (* t_0 (+ t_6 (* (- t_5 3.0) t_1))))))))
       (if (<= x1 0.17)
         (- (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0)) x1)
         (if (<= x1 5e+153)
           (+
            x1
            (+ t_4 (+ x1 (+ t_2 (+ (* t_3 t_5) (* t_0 (+ t_6 (* t_1 0.0))))))))
           (+ (* x2 -6.0) (* x1 (+ (* x1 9.0) -1.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = (x1 * 2.0) * 3.0;
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = 3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0);
	double t_5 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	double t_6 = (x1 * x1) * ((t_5 * 4.0) - 6.0);
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	} else if (x1 <= -40.0) {
		tmp = x1 + (t_4 + (x1 + (t_2 + ((3.0 * t_3) + (t_0 * (t_6 + ((t_5 - 3.0) * t_1)))))));
	} else if (x1 <= 0.17) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else if (x1 <= 5e+153) {
		tmp = x1 + (t_4 + (x1 + (t_2 + ((t_3 * t_5) + (t_0 * (t_6 + (t_1 * 0.0)))))));
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = (x1 * 2.0d0) * 3.0d0
    t_2 = x1 * (x1 * x1)
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = 3.0d0 * (((t_3 - (2.0d0 * x2)) - x1) / t_0)
    t_5 = ((t_3 + (2.0d0 * x2)) - x1) / t_0
    t_6 = (x1 * x1) * ((t_5 * 4.0d0) - 6.0d0)
    if (x1 <= (-5.5d+102)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * (9.0d0 + (x1 * (-19.0d0)))) + (-1.0d0)))
    else if (x1 <= (-40.0d0)) then
        tmp = x1 + (t_4 + (x1 + (t_2 + ((3.0d0 * t_3) + (t_0 * (t_6 + ((t_5 - 3.0d0) * t_1)))))))
    else if (x1 <= 0.17d0) then
        tmp = (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)) - x1
    else if (x1 <= 5d+153) then
        tmp = x1 + (t_4 + (x1 + (t_2 + ((t_3 * t_5) + (t_0 * (t_6 + (t_1 * 0.0d0)))))))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) + (-1.0d0)))
    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 * 2.0) * 3.0;
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = 3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0);
	double t_5 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	double t_6 = (x1 * x1) * ((t_5 * 4.0) - 6.0);
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	} else if (x1 <= -40.0) {
		tmp = x1 + (t_4 + (x1 + (t_2 + ((3.0 * t_3) + (t_0 * (t_6 + ((t_5 - 3.0) * t_1)))))));
	} else if (x1 <= 0.17) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else if (x1 <= 5e+153) {
		tmp = x1 + (t_4 + (x1 + (t_2 + ((t_3 * t_5) + (t_0 * (t_6 + (t_1 * 0.0)))))));
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = (x1 * 2.0) * 3.0
	t_2 = x1 * (x1 * x1)
	t_3 = x1 * (x1 * 3.0)
	t_4 = 3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0)
	t_5 = ((t_3 + (2.0 * x2)) - x1) / t_0
	t_6 = (x1 * x1) * ((t_5 * 4.0) - 6.0)
	tmp = 0
	if x1 <= -5.5e+102:
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0))
	elif x1 <= -40.0:
		tmp = x1 + (t_4 + (x1 + (t_2 + ((3.0 * t_3) + (t_0 * (t_6 + ((t_5 - 3.0) * t_1)))))))
	elif x1 <= 0.17:
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1
	elif x1 <= 5e+153:
		tmp = x1 + (t_4 + (x1 + (t_2 + ((t_3 * t_5) + (t_0 * (t_6 + (t_1 * 0.0)))))))
	else:
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(Float64(x1 * 2.0) * 3.0)
	t_2 = Float64(x1 * Float64(x1 * x1))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(3.0 * Float64(Float64(Float64(t_3 - Float64(2.0 * x2)) - x1) / t_0))
	t_5 = Float64(Float64(Float64(t_3 + Float64(2.0 * x2)) - x1) / t_0)
	t_6 = Float64(Float64(x1 * x1) * Float64(Float64(t_5 * 4.0) - 6.0))
	tmp = 0.0
	if (x1 <= -5.5e+102)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))) + -1.0)));
	elseif (x1 <= -40.0)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(t_2 + Float64(Float64(3.0 * t_3) + Float64(t_0 * Float64(t_6 + Float64(Float64(t_5 - 3.0) * t_1))))))));
	elseif (x1 <= 0.17)
		tmp = Float64(Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0)) - x1);
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(t_2 + Float64(Float64(t_3 * t_5) + Float64(t_0 * Float64(t_6 + Float64(t_1 * 0.0))))))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = (x1 * 2.0) * 3.0;
	t_2 = x1 * (x1 * x1);
	t_3 = x1 * (x1 * 3.0);
	t_4 = 3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0);
	t_5 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	t_6 = (x1 * x1) * ((t_5 * 4.0) - 6.0);
	tmp = 0.0;
	if (x1 <= -5.5e+102)
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	elseif (x1 <= -40.0)
		tmp = x1 + (t_4 + (x1 + (t_2 + ((3.0 * t_3) + (t_0 * (t_6 + ((t_5 - 3.0) * t_1)))))));
	elseif (x1 <= 0.17)
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	elseif (x1 <= 5e+153)
		tmp = x1 + (t_4 + (x1 + (t_2 + ((t_3 * t_5) + (t_0 * (t_6 + (t_1 * 0.0)))))));
	else
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	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[(N[(x1 * 2.0), $MachinePrecision] * 3.0), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(N[(N[(t$95$3 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$5 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.5e+102], 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, -40.0], N[(x1 + N[(t$95$4 + N[(x1 + N[(t$95$2 + N[(N[(3.0 * t$95$3), $MachinePrecision] + N[(t$95$0 * N[(t$95$6 + N[(N[(t$95$5 - 3.0), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.17], N[(N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 5e+153], N[(x1 + N[(t$95$4 + N[(x1 + N[(t$95$2 + N[(N[(t$95$3 * t$95$5), $MachinePrecision] + N[(t$95$0 * N[(t$95$6 + N[(t$95$1 * 0.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -5.49999999999999981e102

   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 70.3%

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

   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 -5.49999999999999981e102 < x1 < -40

   1. Initial program 99.0%

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

   3. Taylor expanded in x1 around inf 83.2%

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

   4. Taylor expanded in x1 around inf 83.4%

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

   if -40 < x1 < 0.170000000000000012

   1. Initial program 99.5%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x1 around 0 87.3%

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

   6. Taylor expanded in x2 around 0 98.9%

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

   if 0.170000000000000012 < x1 < 5.00000000000000018e153

   1. Initial program 99.1%

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

   3. Taylor expanded in x1 around inf 84.2%

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

   4. Taylor expanded in x1 around inf 84.2%

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

   if 5.00000000000000018e153 < x1

   1. Initial program 2.9%

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

   3. Simplified 2.9%

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

   5. Taylor expanded in x1 around inf 2.9%

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

   6. Taylor expanded in x1 around 0 73.5%

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

   7. Taylor expanded in x2 around 0 100.0%

      \[\leadsto -6 \cdot x2 + \color{blue}{x1 \cdot \left(9 \cdot x1 - 1\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\\ \mathbf{elif}\;x1 \leq -40:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.17:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot 3\right) \cdot 0\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \frac{\left(t\_2 + 2 \cdot x2\right) - x1}{t\_0}\\ t_4 := \left(x1 \cdot x1\right) \cdot \left(t\_3 \cdot 4 - 6\right)\\ t_5 := 3 \cdot \frac{\left(t\_2 - 2 \cdot x2\right) - x1}{t\_0}\\ t_6 := t\_2 \cdot t\_3\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+103}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\\ \mathbf{elif}\;x1 \leq -350:\\ \;\;\;\;x1 + \left(t\_5 + \left(x1 + \left(t\_1 + \left(t\_6 + t\_0 \cdot \left(t\_4 + -6\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.17:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(t\_5 + \left(x1 + \left(t\_1 + \left(t\_6 + t\_0 \cdot \left(t\_4 + \left(\left(x1 \cdot 2\right) \cdot 3\right) \cdot 0\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 x1)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (/ (- (+ t_2 (* 2.0 x2)) x1) t_0))
        (t_4 (* (* x1 x1) (- (* t_3 4.0) 6.0)))
        (t_5 (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_0)))
        (t_6 (* t_2 t_3)))
   (if (<= x1 -1e+103)
     (+ (* x2 -6.0) (* x1 (+ (* x1 (+ 9.0 (* x1 -19.0))) -1.0)))
     (if (<= x1 -350.0)
       (+ x1 (+ t_5 (+ x1 (+ t_1 (+ t_6 (* t_0 (+ t_4 -6.0)))))))
       (if (<= x1 0.17)
         (- (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0)) x1)
         (if (<= x1 5e+153)
           (+
            x1
            (+
             t_5
             (+
              x1
              (+ t_1 (+ t_6 (* t_0 (+ t_4 (* (* (* x1 2.0) 3.0) 0.0))))))))
           (+ (* x2 -6.0) (* x1 (+ (* x1 9.0) -1.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = ((t_2 + (2.0 * x2)) - x1) / t_0;
	double t_4 = (x1 * x1) * ((t_3 * 4.0) - 6.0);
	double t_5 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0);
	double t_6 = t_2 * t_3;
	double tmp;
	if (x1 <= -1e+103) {
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	} else if (x1 <= -350.0) {
		tmp = x1 + (t_5 + (x1 + (t_1 + (t_6 + (t_0 * (t_4 + -6.0))))));
	} else if (x1 <= 0.17) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else if (x1 <= 5e+153) {
		tmp = x1 + (t_5 + (x1 + (t_1 + (t_6 + (t_0 * (t_4 + (((x1 * 2.0) * 3.0) * 0.0)))))));
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * (x1 * x1)
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = ((t_2 + (2.0d0 * x2)) - x1) / t_0
    t_4 = (x1 * x1) * ((t_3 * 4.0d0) - 6.0d0)
    t_5 = 3.0d0 * (((t_2 - (2.0d0 * x2)) - x1) / t_0)
    t_6 = t_2 * t_3
    if (x1 <= (-1d+103)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * (9.0d0 + (x1 * (-19.0d0)))) + (-1.0d0)))
    else if (x1 <= (-350.0d0)) then
        tmp = x1 + (t_5 + (x1 + (t_1 + (t_6 + (t_0 * (t_4 + (-6.0d0)))))))
    else if (x1 <= 0.17d0) then
        tmp = (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)) - x1
    else if (x1 <= 5d+153) then
        tmp = x1 + (t_5 + (x1 + (t_1 + (t_6 + (t_0 * (t_4 + (((x1 * 2.0d0) * 3.0d0) * 0.0d0)))))))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) + (-1.0d0)))
    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 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = ((t_2 + (2.0 * x2)) - x1) / t_0;
	double t_4 = (x1 * x1) * ((t_3 * 4.0) - 6.0);
	double t_5 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0);
	double t_6 = t_2 * t_3;
	double tmp;
	if (x1 <= -1e+103) {
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	} else if (x1 <= -350.0) {
		tmp = x1 + (t_5 + (x1 + (t_1 + (t_6 + (t_0 * (t_4 + -6.0))))));
	} else if (x1 <= 0.17) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else if (x1 <= 5e+153) {
		tmp = x1 + (t_5 + (x1 + (t_1 + (t_6 + (t_0 * (t_4 + (((x1 * 2.0) * 3.0) * 0.0)))))));
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * x1)
	t_2 = x1 * (x1 * 3.0)
	t_3 = ((t_2 + (2.0 * x2)) - x1) / t_0
	t_4 = (x1 * x1) * ((t_3 * 4.0) - 6.0)
	t_5 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)
	t_6 = t_2 * t_3
	tmp = 0
	if x1 <= -1e+103:
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0))
	elif x1 <= -350.0:
		tmp = x1 + (t_5 + (x1 + (t_1 + (t_6 + (t_0 * (t_4 + -6.0))))))
	elif x1 <= 0.17:
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1
	elif x1 <= 5e+153:
		tmp = x1 + (t_5 + (x1 + (t_1 + (t_6 + (t_0 * (t_4 + (((x1 * 2.0) * 3.0) * 0.0)))))))
	else:
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * 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(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0))
	t_5 = Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_0))
	t_6 = Float64(t_2 * t_3)
	tmp = 0.0
	if (x1 <= -1e+103)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))) + -1.0)));
	elseif (x1 <= -350.0)
		tmp = Float64(x1 + Float64(t_5 + Float64(x1 + Float64(t_1 + Float64(t_6 + Float64(t_0 * Float64(t_4 + -6.0)))))));
	elseif (x1 <= 0.17)
		tmp = Float64(Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0)) - x1);
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + Float64(t_5 + Float64(x1 + Float64(t_1 + Float64(t_6 + Float64(t_0 * Float64(t_4 + Float64(Float64(Float64(x1 * 2.0) * 3.0) * 0.0))))))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * x1);
	t_2 = x1 * (x1 * 3.0);
	t_3 = ((t_2 + (2.0 * x2)) - x1) / t_0;
	t_4 = (x1 * x1) * ((t_3 * 4.0) - 6.0);
	t_5 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0);
	t_6 = t_2 * t_3;
	tmp = 0.0;
	if (x1 <= -1e+103)
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	elseif (x1 <= -350.0)
		tmp = x1 + (t_5 + (x1 + (t_1 + (t_6 + (t_0 * (t_4 + -6.0))))));
	elseif (x1 <= 0.17)
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	elseif (x1 <= 5e+153)
		tmp = x1 + (t_5 + (x1 + (t_1 + (t_6 + (t_0 * (t_4 + (((x1 * 2.0) * 3.0) * 0.0)))))));
	else
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 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[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$2 * t$95$3), $MachinePrecision]}, If[LessEqual[x1, -1e+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, -350.0], N[(x1 + N[(t$95$5 + N[(x1 + N[(t$95$1 + N[(t$95$6 + N[(t$95$0 * N[(t$95$4 + -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.17], N[(N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 5e+153], N[(x1 + N[(t$95$5 + N[(x1 + N[(t$95$1 + N[(t$95$6 + N[(t$95$0 * N[(t$95$4 + N[(N[(N[(x1 * 2.0), $MachinePrecision] * 3.0), $MachinePrecision] * 0.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -1e103

   1. Initial program 0.0%

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

   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 70.3%

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

   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 -1e103 < x1 < -350

   1. Initial program 99.0%

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

   3. Taylor expanded in x1 around inf 94.7%

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

      1. associate-*r/ 94.7%

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

      2. metadata-eval 94.7%

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

   5. Simplified 94.7%

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

   6. Taylor expanded in x1 around inf 82.6%

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

   if -350 < x1 < 0.170000000000000012

   1. Initial program 99.5%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x1 around 0 87.3%

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

   6. Taylor expanded in x2 around 0 98.9%

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

   if 0.170000000000000012 < x1 < 5.00000000000000018e153

   1. Initial program 99.1%

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

   3. Taylor expanded in x1 around inf 84.2%

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

   4. Taylor expanded in x1 around inf 84.2%

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

   if 5.00000000000000018e153 < x1

   1. Initial program 2.9%

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

   3. Simplified 2.9%

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

   5. Taylor expanded in x1 around inf 2.9%

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

   6. Taylor expanded in x1 around 0 73.5%

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

   7. Taylor expanded in x2 around 0 100.0%

      \[\leadsto -6 \cdot x2 + \color{blue}{x1 \cdot \left(9 \cdot x1 - 1\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+103}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\\ \mathbf{elif}\;x1 \leq -350:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + -6\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.17:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot 3\right) \cdot 0\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+103}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t\_2 \cdot 4 - 6\right)\right) + 3 \cdot t\_0\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \end{array} \]

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 -1e+103)
     (+ (* x2 -6.0) (* x1 (+ (* x1 (+ 9.0 (* x1 -19.0))) -1.0)))
     (if (<= x1 5e+153)
       (+
        x1
        (+
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (*
             t_1
             (+
              (* (* (* x1 2.0) t_2) (- t_2 3.0))
              (* (* x1 x1) (- (* t_2 4.0) 6.0))))
            (* 3.0 t_0))))
         (* 3.0 (- (* x2 -2.0) x1))))
       (+ (* x2 -6.0) (* x1 (+ (* x1 9.0) -1.0)))))))

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 <= -1e+103) {
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	} else if (x1 <= 5e+153) {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (3.0 * t_0)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	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 <= (-1d+103)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * (9.0d0 + (x1 * (-19.0d0)))) + (-1.0d0)))
    else if (x1 <= 5d+153) then
        tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * ((t_2 * 4.0d0) - 6.0d0)))) + (3.0d0 * t_0)))) + (3.0d0 * ((x2 * (-2.0d0)) - x1)))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) + (-1.0d0)))
    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 <= -1e+103) {
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	} else if (x1 <= 5e+153) {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (3.0 * t_0)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	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 <= -1e+103:
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0))
	elif x1 <= 5e+153:
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (3.0 * t_0)))) + (3.0 * ((x2 * -2.0) - x1)))
	else:
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0))
	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 <= -1e+103)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))) + -1.0)));
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)))) + Float64(3.0 * t_0)))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0)));
	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 <= -1e+103)
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	elseif (x1 <= 5e+153)
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (3.0 * t_0)))) + (3.0 * ((x2 * -2.0) - x1)));
	else
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	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, -1e+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, 5e+153], N[(x1 + N[(N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(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[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1e103

   1. Initial program 0.0%

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

   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 70.3%

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

   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 -1e103 < x1 < 5.00000000000000018e153

   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 98.4%

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

   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. mul-1-neg 99.4%

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

      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 5.00000000000000018e153 < x1

   1. Initial program 2.9%

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

   3. Simplified 2.9%

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

   5. Taylor expanded in x1 around inf 2.9%

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

   6. Taylor expanded in x1 around 0 73.5%

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

   7. Taylor expanded in x2 around 0 100.0%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+103}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\left(t\_1 + 2 \cdot x2\right) - x1}{t\_0}\\ t_3 := x1 + \left(3 \cdot \frac{\left(t\_1 - 2 \cdot x2\right) - x1}{t\_0} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_1 \cdot t\_2 + t\_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t\_2 \cdot 4 - 6\right) + -6\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\\ \mathbf{elif}\;x1 \leq -56:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x1 \leq 12600:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (/ (- (+ t_1 (* 2.0 x2)) x1) t_0))
        (t_3
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_0))
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* t_1 t_2)
              (* t_0 (+ (* (* x1 x1) (- (* t_2 4.0) 6.0)) -6.0)))))))))
   (if (<= x1 -5e+102)
     (+ (* x2 -6.0) (* x1 (+ (* x1 (+ 9.0 (* x1 -19.0))) -1.0)))
     (if (<= x1 -56.0)
       t_3
       (if (<= x1 12600.0)
         (- (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0)) x1)
         (if (<= x1 5e+153)
           t_3
           (+ (* x2 -6.0) (* x1 (+ (* x1 9.0) -1.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0;
	double t_3 = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_2) + (t_0 * (((x1 * x1) * ((t_2 * 4.0) - 6.0)) + -6.0))))));
	double tmp;
	if (x1 <= -5e+102) {
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	} else if (x1 <= -56.0) {
		tmp = t_3;
	} else if (x1 <= 12600.0) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else if (x1 <= 5e+153) {
		tmp = t_3;
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	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 * 3.0d0)
    t_2 = ((t_1 + (2.0d0 * x2)) - x1) / t_0
    t_3 = x1 + ((3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_2) + (t_0 * (((x1 * x1) * ((t_2 * 4.0d0) - 6.0d0)) + (-6.0d0)))))))
    if (x1 <= (-5d+102)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * (9.0d0 + (x1 * (-19.0d0)))) + (-1.0d0)))
    else if (x1 <= (-56.0d0)) then
        tmp = t_3
    else if (x1 <= 12600.0d0) then
        tmp = (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)) - x1
    else if (x1 <= 5d+153) then
        tmp = t_3
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0;
	double t_3 = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_2) + (t_0 * (((x1 * x1) * ((t_2 * 4.0) - 6.0)) + -6.0))))));
	double tmp;
	if (x1 <= -5e+102) {
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	} else if (x1 <= -56.0) {
		tmp = t_3;
	} else if (x1 <= 12600.0) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else if (x1 <= 5e+153) {
		tmp = t_3;
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0
	t_3 = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_2) + (t_0 * (((x1 * x1) * ((t_2 * 4.0) - 6.0)) + -6.0))))))
	tmp = 0
	if x1 <= -5e+102:
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0))
	elif x1 <= -56.0:
		tmp = t_3
	elif x1 <= 12600.0:
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1
	elif x1 <= 5e+153:
		tmp = t_3
	else:
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_0)
	t_3 = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * t_2) + Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)) + -6.0)))))))
	tmp = 0.0
	if (x1 <= -5e+102)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))) + -1.0)));
	elseif (x1 <= -56.0)
		tmp = t_3;
	elseif (x1 <= 12600.0)
		tmp = Float64(Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0)) - x1);
	elseif (x1 <= 5e+153)
		tmp = t_3;
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * 3.0);
	t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0;
	t_3 = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_2) + (t_0 * (((x1 * x1) * ((t_2 * 4.0) - 6.0)) + -6.0))))));
	tmp = 0.0;
	if (x1 <= -5e+102)
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	elseif (x1 <= -56.0)
		tmp = t_3;
	elseif (x1 <= 12600.0)
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	elseif (x1 <= 5e+153)
		tmp = t_3;
	else
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * t$95$2), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5e+102], 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, -56.0], t$95$3, If[LessEqual[x1, 12600.0], N[(N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 5e+153], t$95$3, N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5e102

   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 70.3%

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

   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 -5e102 < x1 < -56 or 12600 < x1 < 5.00000000000000018e153

   1. Initial program 99.2%

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

   3. Taylor expanded in x1 around inf 97.7%

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

      1. associate-*r/ 97.7%

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

      2. metadata-eval 97.7%

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

   5. Simplified 97.7%

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

   6. Taylor expanded in x1 around inf 85.1%

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

   if -56 < x1 < 12600

   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

   5. Taylor expanded in x1 around 0 86.8%

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

   6. Taylor expanded in x2 around 0 98.3%

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

   if 5.00000000000000018e153 < x1

   1. Initial program 2.9%

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

   3. Simplified 2.9%

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

   5. Taylor expanded in x1 around inf 2.9%

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

   6. Taylor expanded in x1 around 0 73.5%

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

   7. Taylor expanded in x2 around 0 100.0%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\\ \mathbf{elif}\;x1 \leq -56:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + -6\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 12600:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + -6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 96.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\left(t\_1 + 2 \cdot x2\right) - x1}{t\_0}\\ \mathbf{if}\;x1 \leq -3 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_1 - 2 \cdot x2\right) - x1}{t\_0} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_1 + t\_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (/ (- (+ t_1 (* 2.0 x2)) x1) t_0)))
   (if (<= x1 -3e+102)
     (+ (* x2 -6.0) (* x1 (+ (* x1 (+ 9.0 (* x1 -19.0))) -1.0)))
     (if (<= x1 5e+153)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_0))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* 3.0 t_1)
            (*
             t_0
             (+ (* (* (* x1 2.0) t_2) (- t_2 3.0)) (* (* x1 x1) 6.0))))))))
       (+ (* x2 -6.0) (* x1 (+ (* x1 9.0) -1.0)))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0;
	double tmp;
	if (x1 <= -3e+102) {
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	} else if (x1 <= 5e+153) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = ((t_1 + (2.0d0 * x2)) - x1) / t_0
    if (x1 <= (-3d+102)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * (9.0d0 + (x1 * (-19.0d0)))) + (-1.0d0)))
    else if (x1 <= 5d+153) then
        tmp = x1 + ((3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_1) + (t_0 * ((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * 6.0d0)))))))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0;
	double tmp;
	if (x1 <= -3e+102) {
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	} else if (x1 <= 5e+153) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0
	tmp = 0
	if x1 <= -3e+102:
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0))
	elif x1 <= 5e+153:
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))))
	else:
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_0)
	tmp = 0.0
	if (x1 <= -3e+102)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))) + -1.0)));
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_1) + Float64(t_0 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * 6.0))))))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * 3.0);
	t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0;
	tmp = 0.0;
	if (x1 <= -3e+102)
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	elseif (x1 <= 5e+153)
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	else
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[LessEqual[x1, -3e+102], 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, 5e+153], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$1), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.9999999999999998e102

   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 70.3%

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

   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 -2.9999999999999998e102 < x1 < 5.00000000000000018e153

   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 98.4%

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

   4. Taylor expanded in x1 around inf 96.7%

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

   if 5.00000000000000018e153 < x1

   1. Initial program 2.9%

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

   3. Simplified 2.9%

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

   5. Taylor expanded in x1 around inf 2.9%

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

   6. Taylor expanded in x1 around 0 73.5%

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

   7. Taylor expanded in x2 around 0 100.0%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.5% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{if}\;x1 \leq -3.8 \cdot 10^{+54}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\\ \mathbf{elif}\;x1 \leq -2.4 \cdot 10^{-107}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 6.2 \cdot 10^{-93}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ -1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))))))
   (if (<= x1 -3.8e+54)
     (+ (* x2 -6.0) (* x1 (+ (* x1 (+ 9.0 (* x1 -19.0))) -1.0)))
     (if (<= x1 -2.4e-107)
       t_0
       (if (<= x1 6.2e-93)
         (- (* x2 -6.0) x1)
         (if (<= x1 4.5e+153)
           t_0
           (+ (* x2 -6.0) (* x1 (+ (* x1 9.0) -1.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	double tmp;
	if (x1 <= -3.8e+54) {
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	} else if (x1 <= -2.4e-107) {
		tmp = t_0;
	} else if (x1 <= 6.2e-93) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 4.5e+153) {
		tmp = t_0;
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	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 * ((-1.0d0) + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))))
    if (x1 <= (-3.8d+54)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * (9.0d0 + (x1 * (-19.0d0)))) + (-1.0d0)))
    else if (x1 <= (-2.4d-107)) then
        tmp = t_0
    else if (x1 <= 6.2d-93) then
        tmp = (x2 * (-6.0d0)) - x1
    else if (x1 <= 4.5d+153) then
        tmp = t_0
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	double tmp;
	if (x1 <= -3.8e+54) {
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	} else if (x1 <= -2.4e-107) {
		tmp = t_0;
	} else if (x1 <= 6.2e-93) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 4.5e+153) {
		tmp = t_0;
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))))
	tmp = 0
	if x1 <= -3.8e+54:
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0))
	elif x1 <= -2.4e-107:
		tmp = t_0
	elif x1 <= 6.2e-93:
		tmp = (x2 * -6.0) - x1
	elif x1 <= 4.5e+153:
		tmp = t_0
	else:
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(-1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))))
	tmp = 0.0
	if (x1 <= -3.8e+54)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))) + -1.0)));
	elseif (x1 <= -2.4e-107)
		tmp = t_0;
	elseif (x1 <= 6.2e-93)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	elseif (x1 <= 4.5e+153)
		tmp = t_0;
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	tmp = 0.0;
	if (x1 <= -3.8e+54)
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	elseif (x1 <= -2.4e-107)
		tmp = t_0;
	elseif (x1 <= 6.2e-93)
		tmp = (x2 * -6.0) - x1;
	elseif (x1 <= 4.5e+153)
		tmp = t_0;
	else
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(-1.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3.8e+54], 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, -2.4e-107], t$95$0, If[LessEqual[x1, 6.2e-93], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 4.5e+153], t$95$0, N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -3.8000000000000002e54

   1. Initial program 15.7%

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

   3. Simplified 15.7%

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

   5. Taylor expanded in x1 around 0 60.2%

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

   6. Taylor expanded in x2 around 0 85.2%

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

      1. *-commutative 85.2%

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

   8. Simplified 85.2%

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

   if -3.8000000000000002e54 < x1 < -2.39999999999999994e-107 or 6.19999999999999999e-93 < x1 < 4.5000000000000001e153

   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 99.5%

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

   5. Taylor expanded in x1 around 0 59.4%

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

   6. Taylor expanded in x1 around inf 52.6%

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

   if -2.39999999999999994e-107 < x1 < 6.19999999999999999e-93

   1. Initial program 99.5%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x1 around 0 85.7%

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

   6. Taylor expanded in x2 around 0 87.5%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{-12 \cdot x2} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 87.5%

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

   8. Simplified 87.5%

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

   9. Taylor expanded in x2 around 0 87.5%

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

       1. mul-1-neg 87.5%

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

   11. Simplified 87.5%

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

   if 4.5000000000000001e153 < x1

   1. Initial program 2.9%

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

   3. Simplified 2.9%

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

   5. Taylor expanded in x1 around inf 2.9%

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

   6. Taylor expanded in x1 around 0 73.5%

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

   7. Taylor expanded in x2 around 0 100.0%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.8 \cdot 10^{+54}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\\ \mathbf{elif}\;x1 \leq -2.4 \cdot 10^{-107}:\\ \;\;\;\;x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6.2 \cdot 10^{-93}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 70.8% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ t_1 := x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \mathbf{if}\;x1 \leq -3.8 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -8.2 \cdot 10^{-107}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 5.8 \cdot 10^{-93}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ -1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))))
        (t_1 (+ (* x2 -6.0) (* x1 (+ (* x1 9.0) -1.0)))))
   (if (<= x1 -3.8e+54)
     t_1
     (if (<= x1 -8.2e-107)
       t_0
       (if (<= x1 5.8e-93)
         (- (* x2 -6.0) x1)
         (if (<= x1 4.5e+153) t_0 t_1))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	double t_1 = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	double tmp;
	if (x1 <= -3.8e+54) {
		tmp = t_1;
	} else if (x1 <= -8.2e-107) {
		tmp = t_0;
	} else if (x1 <= 5.8e-93) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 4.5e+153) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x1 * ((-1.0d0) + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))))
    t_1 = (x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) + (-1.0d0)))
    if (x1 <= (-3.8d+54)) then
        tmp = t_1
    else if (x1 <= (-8.2d-107)) then
        tmp = t_0
    else if (x1 <= 5.8d-93) then
        tmp = (x2 * (-6.0d0)) - x1
    else if (x1 <= 4.5d+153) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	double t_1 = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	double tmp;
	if (x1 <= -3.8e+54) {
		tmp = t_1;
	} else if (x1 <= -8.2e-107) {
		tmp = t_0;
	} else if (x1 <= 5.8e-93) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 4.5e+153) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))))
	t_1 = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0))
	tmp = 0
	if x1 <= -3.8e+54:
		tmp = t_1
	elif x1 <= -8.2e-107:
		tmp = t_0
	elif x1 <= 5.8e-93:
		tmp = (x2 * -6.0) - x1
	elif x1 <= 4.5e+153:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(-1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))))
	t_1 = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0)))
	tmp = 0.0
	if (x1 <= -3.8e+54)
		tmp = t_1;
	elseif (x1 <= -8.2e-107)
		tmp = t_0;
	elseif (x1 <= 5.8e-93)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	elseif (x1 <= 4.5e+153)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	t_1 = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	tmp = 0.0;
	if (x1 <= -3.8e+54)
		tmp = t_1;
	elseif (x1 <= -8.2e-107)
		tmp = t_0;
	elseif (x1 <= 5.8e-93)
		tmp = (x2 * -6.0) - x1;
	elseif (x1 <= 4.5e+153)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(-1.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3.8e+54], t$95$1, If[LessEqual[x1, -8.2e-107], t$95$0, If[LessEqual[x1, 5.8e-93], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 4.5e+153], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.8000000000000002e54 or 4.5000000000000001e153 < x1

   1. Initial program 10.2%

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

   3. Simplified 10.2%

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

   5. Taylor expanded in x1 around inf 10.2%

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

   6. Taylor expanded in x1 around 0 57.1%

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

   7. Taylor expanded in x2 around 0 83.1%

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

   if -3.8000000000000002e54 < x1 < -8.1999999999999998e-107 or 5.7999999999999997e-93 < x1 < 4.5000000000000001e153

   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 99.5%

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

   5. Taylor expanded in x1 around 0 59.4%

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

   6. Taylor expanded in x1 around inf 52.6%

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

   if -8.1999999999999998e-107 < x1 < 5.7999999999999997e-93

   1. Initial program 99.5%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x1 around 0 85.7%

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

   6. Taylor expanded in x2 around 0 87.5%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{-12 \cdot x2} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 87.5%

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

   8. Simplified 87.5%

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

   9. Taylor expanded in x2 around 0 87.5%

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

       1. mul-1-neg 87.5%

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

   11. Simplified 87.5%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.8 \cdot 10^{+54}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \mathbf{elif}\;x1 \leq -8.2 \cdot 10^{-107}:\\ \;\;\;\;x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5.8 \cdot 10^{-93}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 83.7% accurate, 5.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -3.8 \cdot 10^{+54}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+153}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -3.8e+54)
   (+ (* x2 -6.0) (* x1 (+ (* x1 (+ 9.0 (* x1 -19.0))) -1.0)))
   (if (<= x1 4e+153)
     (- (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0)) x1)
     (+ (* x2 -6.0) (* x1 (+ (* x1 9.0) -1.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3.8e+54) {
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	} else if (x1 <= 4e+153) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-3.8d+54)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * (9.0d0 + (x1 * (-19.0d0)))) + (-1.0d0)))
    else if (x1 <= 4d+153) then
        tmp = (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)) - x1
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3.8e+54) {
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	} else if (x1 <= 4e+153) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -3.8e+54:
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0))
	elif x1 <= 4e+153:
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1
	else:
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -3.8e+54)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))) + -1.0)));
	elseif (x1 <= 4e+153)
		tmp = Float64(Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0)) - x1);
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -3.8e+54)
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	elseif (x1 <= 4e+153)
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	else
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -3.8e+54], 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, 4e+153], N[(N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.8000000000000002e54

   1. Initial program 15.7%

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

   3. Simplified 15.7%

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

   5. Taylor expanded in x1 around 0 60.2%

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

   6. Taylor expanded in x2 around 0 85.2%

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

      1. *-commutative 85.2%

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

   8. Simplified 85.2%

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

   if -3.8000000000000002e54 < x1 < 4e153

   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 99.6%

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

   5. Taylor expanded in x1 around 0 72.4%

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

   6. Taylor expanded in x2 around 0 81.4%

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

   if 4e153 < x1

   1. Initial program 2.9%

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

   3. Simplified 2.9%

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

   5. Taylor expanded in x1 around inf 2.9%

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

   6. Taylor expanded in x1 around 0 73.5%

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

   7. Taylor expanded in x2 around 0 100.0%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.8 \cdot 10^{+54}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+153}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 77.6% accurate, 5.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.95 \cdot 10^{+54}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x2 \cdot \left(x2 \cdot 8 - 12\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -2.95e+54)
   (+ (* x2 -6.0) (* x1 (+ (* x1 (+ 9.0 (* x1 -19.0))) -1.0)))
   (if (<= x1 4.5e+153)
     (+ (* x2 -6.0) (* x1 (+ -1.0 (* x2 (- (* x2 8.0) 12.0)))))
     (+ (* x2 -6.0) (* x1 (+ (* x1 9.0) -1.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.95e+54) {
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	} else if (x1 <= 4.5e+153) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0))));
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-2.95d+54)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * (9.0d0 + (x1 * (-19.0d0)))) + (-1.0d0)))
    else if (x1 <= 4.5d+153) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x2 * ((x2 * 8.0d0) - 12.0d0))))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.95e+54) {
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	} else if (x1 <= 4.5e+153) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0))));
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -2.95e+54:
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0))
	elif x1 <= 4.5e+153:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0))))
	else:
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -2.95e+54)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))) + -1.0)));
	elseif (x1 <= 4.5e+153)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x2 * Float64(Float64(x2 * 8.0) - 12.0)))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -2.95e+54)
		tmp = (x2 * -6.0) + (x1 * ((x1 * (9.0 + (x1 * -19.0))) + -1.0));
	elseif (x1 <= 4.5e+153)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0))));
	else
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -2.95e+54], 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, 4.5e+153], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x2 * N[(N[(x2 * 8.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.9499999999999999e54

   1. Initial program 15.7%

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

   3. Simplified 15.7%

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

   5. Taylor expanded in x1 around 0 60.2%

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

   6. Taylor expanded in x2 around 0 85.2%

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

      1. *-commutative 85.2%

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

   8. Simplified 85.2%

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

   if -2.9499999999999999e54 < x1 < 4.5000000000000001e153

   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 99.6%

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

   5. Taylor expanded in x1 around 0 72.4%

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

   6. Taylor expanded in x2 around 0 72.4%

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

   if 4.5000000000000001e153 < x1

   1. Initial program 2.9%

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

   3. Simplified 2.9%

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

   5. Taylor expanded in x1 around inf 2.9%

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

   6. Taylor expanded in x1 around 0 73.5%

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

   7. Taylor expanded in x2 around 0 100.0%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.95 \cdot 10^{+54}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x2 \cdot \left(x2 \cdot 8 - 12\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 42.6% accurate, 10.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq 9.5 \cdot 10^{+26}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 9.5e+26) (- (* x2 -6.0) x1) (* x2 (- (* x1 -12.0) 6.0))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= 9.5e+26) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = x2 * ((x1 * -12.0) - 6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= 9.5d+26) then
        tmp = (x2 * (-6.0d0)) - x1
    else
        tmp = x2 * ((x1 * (-12.0d0)) - 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= 9.5e+26) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = x2 * ((x1 * -12.0) - 6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= 9.5e+26:
		tmp = (x2 * -6.0) - x1
	else:
		tmp = x2 * ((x1 * -12.0) - 6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= 9.5e+26)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	else
		tmp = Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= 9.5e+26)
		tmp = (x2 * -6.0) - x1;
	else
		tmp = x2 * ((x1 * -12.0) - 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, 9.5e+26], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < 9.50000000000000054e26

   1. Initial program 80.5%

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

   3. Simplified 80.7%

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

   5. Taylor expanded in x1 around 0 63.4%

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

   6. Taylor expanded in x2 around 0 52.3%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{-12 \cdot x2} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 52.3%

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

   8. Simplified 52.3%

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

   9. Taylor expanded in x2 around 0 50.8%

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

       1. mul-1-neg 50.8%

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

   11. Simplified 50.8%

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

   if 9.50000000000000054e26 < x1

   1. Initial program 45.6%

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

   3. Simplified 45.7%

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

   5. Taylor expanded in x1 around 0 35.1%

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

   6. Taylor expanded in x2 around 0 18.4%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{-12 \cdot x2} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 18.4%

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

   8. Simplified 18.4%

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

   9. Taylor expanded in x2 around inf 19.3%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq 9.5 \cdot 10^{+26}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 64.4% accurate, 11.5× speedup

Math

\[\begin{array}{l} \\ x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right) \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (+ (* x2 -6.0) (* x1 (+ (* x1 9.0) -1.0))))

C

double code(double x1, double x2) {
	return (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = (x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) + (-1.0d0)))
end function

Java

public static double code(double x1, double x2) {
	return (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
}

Python

def code(x1, x2):
	return (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0))

Julia

function code(x1, x2)
	return Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0)))
end

MATLAB

function tmp = code(x1, x2)
	tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
end

Wolfram

code[x1_, x2_] := N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 72.2%

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

3. Simplified 72.4%

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

5. Taylor expanded in x1 around inf 71.6%

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

6. Taylor expanded in x1 around 0 67.4%

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

7. Taylor expanded in x2 around 0 63.9%

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

8. Final simplification 63.9%

   \[\leadsto x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right) \]
9. Add Preprocessing

Alternative 15: 39.6% 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 72.2%

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

3. Simplified 72.4%

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

5. Taylor expanded in x1 around 0 56.7%

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

6. Taylor expanded in x2 around 0 44.2%

   \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{-12 \cdot x2} - 1\right) \]
7. Step-by-step derivation

   1. *-commutative 44.2%

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

8. Simplified 44.2%

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

9. Taylor expanded in x2 around 0 38.9%

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

    1. mul-1-neg 38.9%

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

11. Simplified 38.9%

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

12. Final simplification 38.9%

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

Alternative 16: 26.8% accurate, 42.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 72.2%

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

3. Simplified 72.4%

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

5. Taylor expanded in x1 around 0 28.1%

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

   1. *-commutative 28.1%

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

7. Simplified 28.1%

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

Reproduce

herbie shell --seed 2024133 
(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))))))