Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.3% → 99.6%

Time: 32.1s

Alternatives: 27

Speedup: 5.1×

• 46.3% 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: 70.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := \mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right)\\ t_2 := -1 - x1 \cdot x1\\ t_3 := \frac{x1 - t\_1}{\mathsf{fma}\left(x1, x1, 1\right)}\\ t_4 := 3 \cdot \left(x1 \cdot x1\right)\\ t_5 := x1 \cdot \left(x1 \cdot 3\right)\\ t_6 := \left(t\_5 + 2 \cdot x2\right) - x1\\ t_7 := \frac{t\_6}{t\_0}\\ t_8 := \frac{t\_6}{t\_2}\\ t_9 := \frac{t\_1 - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\\ \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(t\_2 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_8\right) + \left(\left(x1 \cdot 2\right) \cdot t\_7\right) \cdot \left(3 + t\_8\right)\right) + t\_5 \cdot t\_7\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(t\_5 - 2 \cdot x2\right) - x1}{t\_0}\right) \leq \infty:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{t\_4 - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 + \mathsf{fma}\left(\mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot \mathsf{fma}\left(t\_9, 4, -6\right), \left(x1 \cdot \left(2 \cdot t\_3\right)\right) \cdot \left(t\_3 - -3\right)\right), \mathsf{fma}\left(t\_4, t\_9, {x1}^{3}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{x1}^{4} \cdot \left(6 + \frac{\frac{9 + \left(\frac{-1 + -2 \cdot \left(-1 + 3 \cdot \left(3 - 2 \cdot x2\right)\right)}{x1} + 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1} - 3}{x1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (fma x1 (* x1 3.0) (* 2.0 x2)))
        (t_2 (- -1.0 (* x1 x1)))
        (t_3 (/ (- x1 t_1) (fma x1 x1 1.0)))
        (t_4 (* 3.0 (* x1 x1)))
        (t_5 (* x1 (* x1 3.0)))
        (t_6 (- (+ t_5 (* 2.0 x2)) x1))
        (t_7 (/ t_6 t_0))
        (t_8 (/ t_6 t_2))
        (t_9 (/ (- t_1 x1) (fma x1 x1 1.0))))
   (if (<=
        (+
         x1
         (+
          (+
           x1
           (+
            (+
             (*
              t_2
              (+
               (* (* x1 x1) (+ 6.0 (* 4.0 t_8)))
               (* (* (* x1 2.0) t_7) (+ 3.0 t_8))))
             (* t_5 t_7))
            (* x1 (* x1 x1))))
          (* 3.0 (/ (- (- t_5 (* 2.0 x2)) x1) t_0))))
        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_9 4.0 -6.0)) (* (* x1 (* 2.0 t_3)) (- t_3 -3.0)))
         (fma t_4 t_9 (pow x1 3.0))))))
     (*
      (pow x1 4.0)
      (+
       6.0
       (/
        (-
         (/
          (+
           9.0
           (+
            (/ (+ -1.0 (* -2.0 (+ -1.0 (* 3.0 (- 3.0 (* 2.0 x2)))))) x1)
            (* 4.0 (- (* 2.0 x2) 3.0))))
          x1)
         3.0)
        x1))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = fma(x1, (x1 * 3.0), (2.0 * x2));
	double t_2 = -1.0 - (x1 * x1);
	double t_3 = (x1 - t_1) / fma(x1, x1, 1.0);
	double t_4 = 3.0 * (x1 * x1);
	double t_5 = x1 * (x1 * 3.0);
	double t_6 = (t_5 + (2.0 * x2)) - x1;
	double t_7 = t_6 / t_0;
	double t_8 = t_6 / t_2;
	double t_9 = (t_1 - x1) / fma(x1, x1, 1.0);
	double tmp;
	if ((x1 + ((x1 + (((t_2 * (((x1 * x1) * (6.0 + (4.0 * t_8))) + (((x1 * 2.0) * t_7) * (3.0 + t_8)))) + (t_5 * t_7)) + (x1 * (x1 * x1)))) + (3.0 * (((t_5 - (2.0 * x2)) - x1) / t_0)))) <= ((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_9, 4.0, -6.0)), ((x1 * (2.0 * t_3)) * (t_3 - -3.0))), fma(t_4, t_9, pow(x1, 3.0)))));
	} else {
		tmp = pow(x1, 4.0) * (6.0 + ((((9.0 + (((-1.0 + (-2.0 * (-1.0 + (3.0 * (3.0 - (2.0 * x2)))))) / x1) + (4.0 * ((2.0 * x2) - 3.0)))) / x1) - 3.0) / x1));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = fma(x1, Float64(x1 * 3.0), Float64(2.0 * x2))
	t_2 = Float64(-1.0 - Float64(x1 * x1))
	t_3 = Float64(Float64(x1 - t_1) / fma(x1, x1, 1.0))
	t_4 = Float64(3.0 * Float64(x1 * x1))
	t_5 = Float64(x1 * Float64(x1 * 3.0))
	t_6 = Float64(Float64(t_5 + Float64(2.0 * x2)) - x1)
	t_7 = Float64(t_6 / t_0)
	t_8 = Float64(t_6 / t_2)
	t_9 = Float64(Float64(t_1 - x1) / fma(x1, x1, 1.0))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_2 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_8))) + Float64(Float64(Float64(x1 * 2.0) * t_7) * Float64(3.0 + t_8)))) + Float64(t_5 * t_7)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(Float64(t_5 - Float64(2.0 * x2)) - x1) / t_0)))) <= 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_9, 4.0, -6.0)), Float64(Float64(x1 * Float64(2.0 * t_3)) * Float64(t_3 - -3.0))), fma(t_4, t_9, (x1 ^ 3.0))))));
	else
		tmp = Float64((x1 ^ 4.0) * Float64(6.0 + Float64(Float64(Float64(Float64(9.0 + Float64(Float64(Float64(-1.0 + Float64(-2.0 * Float64(-1.0 + Float64(3.0 * Float64(3.0 - Float64(2.0 * x2)))))) / x1) + Float64(4.0 * Float64(Float64(2.0 * x2) - 3.0)))) / x1) - 3.0) / x1)));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision] + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 - t$95$1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(t$95$5 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$6 / t$95$0), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$6 / t$95$2), $MachinePrecision]}, Block[{t$95$9 = N[(N[(t$95$1 - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$7), $MachinePrecision] * N[(3.0 + t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$5 * t$95$7), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$5 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(3.0 * N[(N[(t$95$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$9 * 4.0 + -6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(2.0 * t$95$3), $MachinePrecision]), $MachinePrecision] * N[(t$95$3 - -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$4 * t$95$9 + N[Power[x1, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Power[x1, 4.0], $MachinePrecision] * N[(6.0 + N[(N[(N[(N[(9.0 + N[(N[(N[(-1.0 + N[(-2.0 * N[(-1.0 + N[(3.0 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision] + N[(4.0 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision] - 3.0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

   3. Simplified 99.6%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around -inf 100.0%

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

4. Final simplification 99.7%

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

Alternative 2: 99.5% accurate, 0.5× speedup

Math

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

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_3 (/ t_2 t_0))
        (t_4 (- -1.0 (* x1 x1)))
        (t_5 (/ t_2 t_4))
        (t_6
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               t_4
               (+
                (* (* x1 x1) (+ 6.0 (* 4.0 t_5)))
                (* (* (* x1 2.0) t_3) (+ 3.0 t_5))))
              (* t_1 t_3))
             (* x1 (* x1 x1))))
           (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_0))))))
   (if (<= t_6 INFINITY)
     t_6
     (*
      (pow x1 4.0)
      (+
       6.0
       (/
        (-
         (/
          (+
           9.0
           (+
            (/ (+ -1.0 (* -2.0 (+ -1.0 (* 3.0 (- 3.0 (* 2.0 x2)))))) x1)
            (* 4.0 (- (* 2.0 x2) 3.0))))
          x1)
         3.0)
        x1))))))

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;
	double t_3 = t_2 / t_0;
	double t_4 = -1.0 - (x1 * x1);
	double t_5 = t_2 / t_4;
	double t_6 = x1 + ((x1 + (((t_4 * (((x1 * x1) * (6.0 + (4.0 * t_5))) + (((x1 * 2.0) * t_3) * (3.0 + t_5)))) + (t_1 * t_3)) + (x1 * (x1 * x1)))) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)));
	double tmp;
	if (t_6 <= ((double) INFINITY)) {
		tmp = t_6;
	} else {
		tmp = pow(x1, 4.0) * (6.0 + ((((9.0 + (((-1.0 + (-2.0 * (-1.0 + (3.0 * (3.0 - (2.0 * x2)))))) / x1) + (4.0 * ((2.0 * x2) - 3.0)))) / x1) - 3.0) / x1));
	}
	return tmp;
}

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;
	double t_3 = t_2 / t_0;
	double t_4 = -1.0 - (x1 * x1);
	double t_5 = t_2 / t_4;
	double t_6 = x1 + ((x1 + (((t_4 * (((x1 * x1) * (6.0 + (4.0 * t_5))) + (((x1 * 2.0) * t_3) * (3.0 + t_5)))) + (t_1 * t_3)) + (x1 * (x1 * x1)))) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)));
	double tmp;
	if (t_6 <= Double.POSITIVE_INFINITY) {
		tmp = t_6;
	} else {
		tmp = Math.pow(x1, 4.0) * (6.0 + ((((9.0 + (((-1.0 + (-2.0 * (-1.0 + (3.0 * (3.0 - (2.0 * x2)))))) / x1) + (4.0 * ((2.0 * x2) - 3.0)))) / x1) - 3.0) / x1));
	}
	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_3 = t_2 / t_0
	t_4 = -1.0 - (x1 * x1)
	t_5 = t_2 / t_4
	t_6 = x1 + ((x1 + (((t_4 * (((x1 * x1) * (6.0 + (4.0 * t_5))) + (((x1 * 2.0) * t_3) * (3.0 + t_5)))) + (t_1 * t_3)) + (x1 * (x1 * x1)))) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)))
	tmp = 0
	if t_6 <= math.inf:
		tmp = t_6
	else:
		tmp = math.pow(x1, 4.0) * (6.0 + ((((9.0 + (((-1.0 + (-2.0 * (-1.0 + (3.0 * (3.0 - (2.0 * x2)))))) / x1) + (4.0 * ((2.0 * x2) - 3.0)))) / x1) - 3.0) / x1))
	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(t_1 + Float64(2.0 * x2)) - x1)
	t_3 = Float64(t_2 / t_0)
	t_4 = Float64(-1.0 - Float64(x1 * x1))
	t_5 = Float64(t_2 / t_4)
	t_6 = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_4 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_5))) + Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(3.0 + t_5)))) + Float64(t_1 * t_3)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_0))))
	tmp = 0.0
	if (t_6 <= Inf)
		tmp = t_6;
	else
		tmp = Float64((x1 ^ 4.0) * Float64(6.0 + Float64(Float64(Float64(Float64(9.0 + Float64(Float64(Float64(-1.0 + Float64(-2.0 * Float64(-1.0 + Float64(3.0 * Float64(3.0 - Float64(2.0 * x2)))))) / x1) + Float64(4.0 * Float64(Float64(2.0 * x2) - 3.0)))) / x1) - 3.0) / x1)));
	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_3 = t_2 / t_0;
	t_4 = -1.0 - (x1 * x1);
	t_5 = t_2 / t_4;
	t_6 = x1 + ((x1 + (((t_4 * (((x1 * x1) * (6.0 + (4.0 * t_5))) + (((x1 * 2.0) * t_3) * (3.0 + t_5)))) + (t_1 * t_3)) + (x1 * (x1 * x1)))) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)));
	tmp = 0.0;
	if (t_6 <= Inf)
		tmp = t_6;
	else
		tmp = (x1 ^ 4.0) * (6.0 + ((((9.0 + (((-1.0 + (-2.0 * (-1.0 + (3.0 * (3.0 - (2.0 * x2)))))) / x1) + (4.0 * ((2.0 * x2) - 3.0)))) / x1) - 3.0) / x1));
	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[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / t$95$0), $MachinePrecision]}, Block[{t$95$4 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$2 / t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$4 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(3.0 + t$95$5), $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$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$6, Infinity], t$95$6, N[(N[Power[x1, 4.0], $MachinePrecision] * N[(6.0 + N[(N[(N[(N[(9.0 + N[(N[(N[(-1.0 + N[(-2.0 * N[(-1.0 + N[(3.0 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision] + N[(4.0 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision] - 3.0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around -inf 100.0%

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

4. Final simplification 99.6%

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

Alternative 3: 95.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \left(t\_1 + 2 \cdot x2\right) - x1\\ t_3 := \frac{t\_2}{t\_0}\\ t_4 := -1 - x1 \cdot x1\\ t_5 := \frac{t\_2}{t\_4}\\ t_6 := x1 + \left(\left(x1 + \left(\left(t\_4 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_5\right) + \left(\left(x1 \cdot 2\right) \cdot t\_3\right) \cdot \left(3 + t\_5\right)\right) + t\_1 \cdot t\_3\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(t\_1 - 2 \cdot x2\right) - x1}{t\_0}\right)\\ \mathbf{if}\;t\_6 \leq \infty:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (- (+ t_1 (* 2.0 x2)) x1))
        (t_3 (/ t_2 t_0))
        (t_4 (- -1.0 (* x1 x1)))
        (t_5 (/ t_2 t_4))
        (t_6
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               t_4
               (+
                (* (* x1 x1) (+ 6.0 (* 4.0 t_5)))
                (* (* (* x1 2.0) t_3) (+ 3.0 t_5))))
              (* t_1 t_3))
             (* x1 (* x1 x1))))
           (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_0))))))
   (if (<= t_6 INFINITY)
     t_6
     (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 9.0) 2.0)))))))

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;
	double t_3 = t_2 / t_0;
	double t_4 = -1.0 - (x1 * x1);
	double t_5 = t_2 / t_4;
	double t_6 = x1 + ((x1 + (((t_4 * (((x1 * x1) * (6.0 + (4.0 * t_5))) + (((x1 * 2.0) * t_3) * (3.0 + t_5)))) + (t_1 * t_3)) + (x1 * (x1 * x1)))) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)));
	double tmp;
	if (t_6 <= ((double) INFINITY)) {
		tmp = t_6;
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	}
	return tmp;
}

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;
	double t_3 = t_2 / t_0;
	double t_4 = -1.0 - (x1 * x1);
	double t_5 = t_2 / t_4;
	double t_6 = x1 + ((x1 + (((t_4 * (((x1 * x1) * (6.0 + (4.0 * t_5))) + (((x1 * 2.0) * t_3) * (3.0 + t_5)))) + (t_1 * t_3)) + (x1 * (x1 * x1)))) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)));
	double tmp;
	if (t_6 <= Double.POSITIVE_INFINITY) {
		tmp = t_6;
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	}
	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_3 = t_2 / t_0
	t_4 = -1.0 - (x1 * x1)
	t_5 = t_2 / t_4
	t_6 = x1 + ((x1 + (((t_4 * (((x1 * x1) * (6.0 + (4.0 * t_5))) + (((x1 * 2.0) * t_3) * (3.0 + t_5)))) + (t_1 * t_3)) + (x1 * (x1 * x1)))) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)))
	tmp = 0
	if t_6 <= math.inf:
		tmp = t_6
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)))
	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(t_1 + Float64(2.0 * x2)) - x1)
	t_3 = Float64(t_2 / t_0)
	t_4 = Float64(-1.0 - Float64(x1 * x1))
	t_5 = Float64(t_2 / t_4)
	t_6 = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_4 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_5))) + Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(3.0 + t_5)))) + Float64(t_1 * t_3)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_0))))
	tmp = 0.0
	if (t_6 <= Inf)
		tmp = t_6;
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))));
	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_3 = t_2 / t_0;
	t_4 = -1.0 - (x1 * x1);
	t_5 = t_2 / t_4;
	t_6 = x1 + ((x1 + (((t_4 * (((x1 * x1) * (6.0 + (4.0 * t_5))) + (((x1 * 2.0) * t_3) * (3.0 + t_5)))) + (t_1 * t_3)) + (x1 * (x1 * x1)))) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)));
	tmp = 0.0;
	if (t_6 <= Inf)
		tmp = t_6;
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

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

   1. Initial program 0.0%

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

   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 64.2%

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

   6. Taylor expanded in x2 around 0 94.0%

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

      1. *-commutative 94.0%

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

   8. Simplified 94.0%

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

4. Final simplification 98.1%

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

Alternative 4: 94.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{2 \cdot x2 - 3}{x1}\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := \left(t\_3 + 2 \cdot x2\right) - x1\\ t_5 := \frac{t\_4}{t\_2}\\ t_6 := x1 \cdot \left(x1 \cdot 9 - 2\right)\\ t_7 := x1 + \left(x2 \cdot -6 + t\_6\right)\\ t_8 := -1 - x1 \cdot x1\\ t_9 := \frac{t\_4}{t\_8}\\ t_10 := \left(x1 \cdot 2\right) \cdot t\_5\\ \mathbf{if}\;x1 \leq -4.6 \cdot 10^{+113}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x1 \leq -1.15 \cdot 10^{-5}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(t\_1 + \left(t\_8 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_9\right) + t\_10 \cdot \left(3 + t\_9\right)\right) + t\_3 \cdot \left(3 + \frac{-1 + t\_0}{x1}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.9 \cdot 10^{-22}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(t\_6 + x2 \cdot \left(x2 \cdot \left(x1 \cdot 8\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(t\_1 + \left(t\_3 \cdot t\_5 - t\_2 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \left(\frac{1 - t\_0}{x1} - 3\right)\right) - t\_10 \cdot \left(t\_5 - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_7\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (/ (- (* 2.0 x2) 3.0) x1))
        (t_1 (* x1 (* x1 x1)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (- (+ t_3 (* 2.0 x2)) x1))
        (t_5 (/ t_4 t_2))
        (t_6 (* x1 (- (* x1 9.0) 2.0)))
        (t_7 (+ x1 (+ (* x2 -6.0) t_6)))
        (t_8 (- -1.0 (* x1 x1)))
        (t_9 (/ t_4 t_8))
        (t_10 (* (* x1 2.0) t_5)))
   (if (<= x1 -4.6e+113)
     t_7
     (if (<= x1 -1.15e-5)
       (+
        x1
        (+
         9.0
         (+
          x1
          (+
           t_1
           (+
            (* t_8 (+ (* (* x1 x1) (+ 6.0 (* 4.0 t_9))) (* t_10 (+ 3.0 t_9))))
            (* t_3 (+ 3.0 (/ (+ -1.0 t_0) x1))))))))
       (if (<= x1 1.9e-22)
         (+ x1 (+ (* x2 -6.0) (+ t_6 (* x2 (* x2 (* x1 8.0))))))
         (if (<= x1 5e+153)
           (+
            x1
            (+
             9.0
             (+
              x1
              (+
               t_1
               (-
                (* t_3 t_5)
                (*
                 t_2
                 (-
                  (* (* x1 x1) (+ 6.0 (* 4.0 (- (/ (- 1.0 t_0) x1) 3.0))))
                  (* t_10 (- t_5 3.0)))))))))
           t_7))))))

C

double code(double x1, double x2) {
	double t_0 = ((2.0 * x2) - 3.0) / x1;
	double t_1 = x1 * (x1 * x1);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = (t_3 + (2.0 * x2)) - x1;
	double t_5 = t_4 / t_2;
	double t_6 = x1 * ((x1 * 9.0) - 2.0);
	double t_7 = x1 + ((x2 * -6.0) + t_6);
	double t_8 = -1.0 - (x1 * x1);
	double t_9 = t_4 / t_8;
	double t_10 = (x1 * 2.0) * t_5;
	double tmp;
	if (x1 <= -4.6e+113) {
		tmp = t_7;
	} else if (x1 <= -1.15e-5) {
		tmp = x1 + (9.0 + (x1 + (t_1 + ((t_8 * (((x1 * x1) * (6.0 + (4.0 * t_9))) + (t_10 * (3.0 + t_9)))) + (t_3 * (3.0 + ((-1.0 + t_0) / x1)))))));
	} else if (x1 <= 1.9e-22) {
		tmp = x1 + ((x2 * -6.0) + (t_6 + (x2 * (x2 * (x1 * 8.0)))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + (9.0 + (x1 + (t_1 + ((t_3 * t_5) - (t_2 * (((x1 * x1) * (6.0 + (4.0 * (((1.0 - t_0) / x1) - 3.0)))) - (t_10 * (t_5 - 3.0))))))));
	} else {
		tmp = t_7;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_0 = ((2.0d0 * x2) - 3.0d0) / x1
    t_1 = x1 * (x1 * x1)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = (t_3 + (2.0d0 * x2)) - x1
    t_5 = t_4 / t_2
    t_6 = x1 * ((x1 * 9.0d0) - 2.0d0)
    t_7 = x1 + ((x2 * (-6.0d0)) + t_6)
    t_8 = (-1.0d0) - (x1 * x1)
    t_9 = t_4 / t_8
    t_10 = (x1 * 2.0d0) * t_5
    if (x1 <= (-4.6d+113)) then
        tmp = t_7
    else if (x1 <= (-1.15d-5)) then
        tmp = x1 + (9.0d0 + (x1 + (t_1 + ((t_8 * (((x1 * x1) * (6.0d0 + (4.0d0 * t_9))) + (t_10 * (3.0d0 + t_9)))) + (t_3 * (3.0d0 + (((-1.0d0) + t_0) / x1)))))))
    else if (x1 <= 1.9d-22) then
        tmp = x1 + ((x2 * (-6.0d0)) + (t_6 + (x2 * (x2 * (x1 * 8.0d0)))))
    else if (x1 <= 5d+153) then
        tmp = x1 + (9.0d0 + (x1 + (t_1 + ((t_3 * t_5) - (t_2 * (((x1 * x1) * (6.0d0 + (4.0d0 * (((1.0d0 - t_0) / x1) - 3.0d0)))) - (t_10 * (t_5 - 3.0d0))))))))
    else
        tmp = t_7
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = ((2.0 * x2) - 3.0) / x1;
	double t_1 = x1 * (x1 * x1);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = (t_3 + (2.0 * x2)) - x1;
	double t_5 = t_4 / t_2;
	double t_6 = x1 * ((x1 * 9.0) - 2.0);
	double t_7 = x1 + ((x2 * -6.0) + t_6);
	double t_8 = -1.0 - (x1 * x1);
	double t_9 = t_4 / t_8;
	double t_10 = (x1 * 2.0) * t_5;
	double tmp;
	if (x1 <= -4.6e+113) {
		tmp = t_7;
	} else if (x1 <= -1.15e-5) {
		tmp = x1 + (9.0 + (x1 + (t_1 + ((t_8 * (((x1 * x1) * (6.0 + (4.0 * t_9))) + (t_10 * (3.0 + t_9)))) + (t_3 * (3.0 + ((-1.0 + t_0) / x1)))))));
	} else if (x1 <= 1.9e-22) {
		tmp = x1 + ((x2 * -6.0) + (t_6 + (x2 * (x2 * (x1 * 8.0)))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + (9.0 + (x1 + (t_1 + ((t_3 * t_5) - (t_2 * (((x1 * x1) * (6.0 + (4.0 * (((1.0 - t_0) / x1) - 3.0)))) - (t_10 * (t_5 - 3.0))))))));
	} else {
		tmp = t_7;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = ((2.0 * x2) - 3.0) / x1
	t_1 = x1 * (x1 * x1)
	t_2 = (x1 * x1) + 1.0
	t_3 = x1 * (x1 * 3.0)
	t_4 = (t_3 + (2.0 * x2)) - x1
	t_5 = t_4 / t_2
	t_6 = x1 * ((x1 * 9.0) - 2.0)
	t_7 = x1 + ((x2 * -6.0) + t_6)
	t_8 = -1.0 - (x1 * x1)
	t_9 = t_4 / t_8
	t_10 = (x1 * 2.0) * t_5
	tmp = 0
	if x1 <= -4.6e+113:
		tmp = t_7
	elif x1 <= -1.15e-5:
		tmp = x1 + (9.0 + (x1 + (t_1 + ((t_8 * (((x1 * x1) * (6.0 + (4.0 * t_9))) + (t_10 * (3.0 + t_9)))) + (t_3 * (3.0 + ((-1.0 + t_0) / x1)))))))
	elif x1 <= 1.9e-22:
		tmp = x1 + ((x2 * -6.0) + (t_6 + (x2 * (x2 * (x1 * 8.0)))))
	elif x1 <= 5e+153:
		tmp = x1 + (9.0 + (x1 + (t_1 + ((t_3 * t_5) - (t_2 * (((x1 * x1) * (6.0 + (4.0 * (((1.0 - t_0) / x1) - 3.0)))) - (t_10 * (t_5 - 3.0))))))))
	else:
		tmp = t_7
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(Float64(2.0 * x2) - 3.0) / x1)
	t_1 = Float64(x1 * Float64(x1 * x1))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(Float64(t_3 + Float64(2.0 * x2)) - x1)
	t_5 = Float64(t_4 / t_2)
	t_6 = Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))
	t_7 = Float64(x1 + Float64(Float64(x2 * -6.0) + t_6))
	t_8 = Float64(-1.0 - Float64(x1 * x1))
	t_9 = Float64(t_4 / t_8)
	t_10 = Float64(Float64(x1 * 2.0) * t_5)
	tmp = 0.0
	if (x1 <= -4.6e+113)
		tmp = t_7;
	elseif (x1 <= -1.15e-5)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_1 + Float64(Float64(t_8 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_9))) + Float64(t_10 * Float64(3.0 + t_9)))) + Float64(t_3 * Float64(3.0 + Float64(Float64(-1.0 + t_0) / x1))))))));
	elseif (x1 <= 1.9e-22)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(t_6 + Float64(x2 * Float64(x2 * Float64(x1 * 8.0))))));
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_1 + Float64(Float64(t_3 * t_5) - Float64(t_2 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * Float64(Float64(Float64(1.0 - t_0) / x1) - 3.0)))) - Float64(t_10 * Float64(t_5 - 3.0)))))))));
	else
		tmp = t_7;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = ((2.0 * x2) - 3.0) / x1;
	t_1 = x1 * (x1 * x1);
	t_2 = (x1 * x1) + 1.0;
	t_3 = x1 * (x1 * 3.0);
	t_4 = (t_3 + (2.0 * x2)) - x1;
	t_5 = t_4 / t_2;
	t_6 = x1 * ((x1 * 9.0) - 2.0);
	t_7 = x1 + ((x2 * -6.0) + t_6);
	t_8 = -1.0 - (x1 * x1);
	t_9 = t_4 / t_8;
	t_10 = (x1 * 2.0) * t_5;
	tmp = 0.0;
	if (x1 <= -4.6e+113)
		tmp = t_7;
	elseif (x1 <= -1.15e-5)
		tmp = x1 + (9.0 + (x1 + (t_1 + ((t_8 * (((x1 * x1) * (6.0 + (4.0 * t_9))) + (t_10 * (3.0 + t_9)))) + (t_3 * (3.0 + ((-1.0 + t_0) / x1)))))));
	elseif (x1 <= 1.9e-22)
		tmp = x1 + ((x2 * -6.0) + (t_6 + (x2 * (x2 * (x1 * 8.0)))));
	elseif (x1 <= 5e+153)
		tmp = x1 + (9.0 + (x1 + (t_1 + ((t_3 * t_5) - (t_2 * (((x1 * x1) * (6.0 + (4.0 * (((1.0 - t_0) / x1) - 3.0)))) - (t_10 * (t_5 - 3.0))))))));
	else
		tmp = t_7;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision] / x1), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / t$95$2), $MachinePrecision]}, Block[{t$95$6 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(t$95$4 / t$95$8), $MachinePrecision]}, Block[{t$95$10 = N[(N[(x1 * 2.0), $MachinePrecision] * t$95$5), $MachinePrecision]}, If[LessEqual[x1, -4.6e+113], t$95$7, If[LessEqual[x1, -1.15e-5], N[(x1 + N[(9.0 + N[(x1 + N[(t$95$1 + N[(N[(t$95$8 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$9), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$10 * N[(3.0 + t$95$9), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 * N[(3.0 + N[(N[(-1.0 + t$95$0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.9e-22], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(t$95$6 + N[(x2 * N[(x2 * N[(x1 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], N[(x1 + N[(9.0 + N[(x1 + N[(t$95$1 + N[(N[(t$95$3 * t$95$5), $MachinePrecision] - N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * N[(N[(N[(1.0 - t$95$0), $MachinePrecision] / x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$10 * N[(t$95$5 - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$7]]]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.59999999999999993e113 or 5.00000000000000018e153 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 64.2%

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

   6. Taylor expanded in x2 around 0 94.0%

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

      1. *-commutative 94.0%

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

   8. Simplified 94.0%

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

   if -4.59999999999999993e113 < x1 < -1.15e-5

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around inf 98.2%

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

   4. Taylor expanded in x1 around -inf 99.4%

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

   if -1.15e-5 < x1 < 1.90000000000000012e-22

   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 87.3%

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

   6. Taylor expanded in x2 around 0 87.3%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\color{blue}{15} - 6\right)\right) - 2\right)\right) \]

   7. Taylor expanded in x2 around 0 99.6%

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

   8. Taylor expanded in x2 around inf 99.6%

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

      1. associate-*r* 99.6%

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

      2. *-commutative 99.6%

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

      3. *-commutative 99.6%

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

   10. Simplified 99.6%

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

   if 1.90000000000000012e-22 < x1 < 5.00000000000000018e153

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around inf 99.5%

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

   4. Taylor expanded in x1 around -inf 99.7%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.6 \cdot 10^{+113}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -1.15 \cdot 10^{-5}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(-1 - x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 + \frac{-1 + \frac{2 \cdot x2 - 3}{x1}}{x1}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.9 \cdot 10^{-22}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(x2 \cdot \left(x1 \cdot 8\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \left(\frac{1 - \frac{2 \cdot x2 - 3}{x1}}{x1} - 3\right)\right) - \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 9 - 2\right)\\ t_2 := x1 + \left(x2 \cdot -6 + t\_1\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := \frac{\left(t\_3 + 2 \cdot x2\right) - x1}{t\_0}\\ t_5 := x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_3 \cdot t\_4 - t\_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \left(\frac{1 - \frac{2 \cdot x2 - 3}{x1}}{x1} - 3\right)\right) - \left(\left(x1 \cdot 2\right) \cdot t\_4\right) \cdot \left(t\_4 - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -3.6 \cdot 10^{+113}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq -0.029:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x1 \leq 1.9 \cdot 10^{-22}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(t\_1 + x2 \cdot \left(x2 \cdot \left(x1 \cdot 8\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (- (* x1 9.0) 2.0)))
        (t_2 (+ x1 (+ (* x2 -6.0) t_1)))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (/ (- (+ t_3 (* 2.0 x2)) x1) t_0))
        (t_5
         (+
          x1
          (+
           9.0
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (-
              (* t_3 t_4)
              (*
               t_0
               (-
                (*
                 (* x1 x1)
                 (+
                  6.0
                  (* 4.0 (- (/ (- 1.0 (/ (- (* 2.0 x2) 3.0) x1)) x1) 3.0))))
                (* (* (* x1 2.0) t_4) (- t_4 3.0)))))))))))
   (if (<= x1 -3.6e+113)
     t_2
     (if (<= x1 -0.029)
       t_5
       (if (<= x1 1.9e-22)
         (+ x1 (+ (* x2 -6.0) (+ t_1 (* x2 (* x2 (* x1 8.0))))))
         (if (<= x1 5e+153) t_5 t_2))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * ((x1 * 9.0) - 2.0);
	double t_2 = x1 + ((x2 * -6.0) + t_1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	double t_5 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_3 * t_4) - (t_0 * (((x1 * x1) * (6.0 + (4.0 * (((1.0 - (((2.0 * x2) - 3.0) / x1)) / x1) - 3.0)))) - (((x1 * 2.0) * t_4) * (t_4 - 3.0))))))));
	double tmp;
	if (x1 <= -3.6e+113) {
		tmp = t_2;
	} else if (x1 <= -0.029) {
		tmp = t_5;
	} else if (x1 <= 1.9e-22) {
		tmp = x1 + ((x2 * -6.0) + (t_1 + (x2 * (x2 * (x1 * 8.0)))));
	} else if (x1 <= 5e+153) {
		tmp = t_5;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * ((x1 * 9.0d0) - 2.0d0)
    t_2 = x1 + ((x2 * (-6.0d0)) + t_1)
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = ((t_3 + (2.0d0 * x2)) - x1) / t_0
    t_5 = x1 + (9.0d0 + (x1 + ((x1 * (x1 * x1)) + ((t_3 * t_4) - (t_0 * (((x1 * x1) * (6.0d0 + (4.0d0 * (((1.0d0 - (((2.0d0 * x2) - 3.0d0) / x1)) / x1) - 3.0d0)))) - (((x1 * 2.0d0) * t_4) * (t_4 - 3.0d0))))))))
    if (x1 <= (-3.6d+113)) then
        tmp = t_2
    else if (x1 <= (-0.029d0)) then
        tmp = t_5
    else if (x1 <= 1.9d-22) then
        tmp = x1 + ((x2 * (-6.0d0)) + (t_1 + (x2 * (x2 * (x1 * 8.0d0)))))
    else if (x1 <= 5d+153) then
        tmp = t_5
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * ((x1 * 9.0) - 2.0);
	double t_2 = x1 + ((x2 * -6.0) + t_1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	double t_5 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_3 * t_4) - (t_0 * (((x1 * x1) * (6.0 + (4.0 * (((1.0 - (((2.0 * x2) - 3.0) / x1)) / x1) - 3.0)))) - (((x1 * 2.0) * t_4) * (t_4 - 3.0))))))));
	double tmp;
	if (x1 <= -3.6e+113) {
		tmp = t_2;
	} else if (x1 <= -0.029) {
		tmp = t_5;
	} else if (x1 <= 1.9e-22) {
		tmp = x1 + ((x2 * -6.0) + (t_1 + (x2 * (x2 * (x1 * 8.0)))));
	} else if (x1 <= 5e+153) {
		tmp = t_5;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * ((x1 * 9.0) - 2.0)
	t_2 = x1 + ((x2 * -6.0) + t_1)
	t_3 = x1 * (x1 * 3.0)
	t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0
	t_5 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_3 * t_4) - (t_0 * (((x1 * x1) * (6.0 + (4.0 * (((1.0 - (((2.0 * x2) - 3.0) / x1)) / x1) - 3.0)))) - (((x1 * 2.0) * t_4) * (t_4 - 3.0))))))))
	tmp = 0
	if x1 <= -3.6e+113:
		tmp = t_2
	elif x1 <= -0.029:
		tmp = t_5
	elif x1 <= 1.9e-22:
		tmp = x1 + ((x2 * -6.0) + (t_1 + (x2 * (x2 * (x1 * 8.0)))))
	elif x1 <= 5e+153:
		tmp = t_5
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))
	t_2 = Float64(x1 + Float64(Float64(x2 * -6.0) + t_1))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(Float64(Float64(t_3 + Float64(2.0 * x2)) - x1) / t_0)
	t_5 = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_3 * t_4) - Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * Float64(Float64(Float64(1.0 - Float64(Float64(Float64(2.0 * x2) - 3.0) / x1)) / x1) - 3.0)))) - Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(t_4 - 3.0)))))))))
	tmp = 0.0
	if (x1 <= -3.6e+113)
		tmp = t_2;
	elseif (x1 <= -0.029)
		tmp = t_5;
	elseif (x1 <= 1.9e-22)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(t_1 + Float64(x2 * Float64(x2 * Float64(x1 * 8.0))))));
	elseif (x1 <= 5e+153)
		tmp = t_5;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * ((x1 * 9.0) - 2.0);
	t_2 = x1 + ((x2 * -6.0) + t_1);
	t_3 = x1 * (x1 * 3.0);
	t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	t_5 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_3 * t_4) - (t_0 * (((x1 * x1) * (6.0 + (4.0 * (((1.0 - (((2.0 * x2) - 3.0) / x1)) / x1) - 3.0)))) - (((x1 * 2.0) * t_4) * (t_4 - 3.0))))))));
	tmp = 0.0;
	if (x1 <= -3.6e+113)
		tmp = t_2;
	elseif (x1 <= -0.029)
		tmp = t_5;
	elseif (x1 <= 1.9e-22)
		tmp = x1 + ((x2 * -6.0) + (t_1 + (x2 * (x2 * (x1 * 8.0)))));
	elseif (x1 <= 5e+153)
		tmp = t_5;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(9.0 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$3 * t$95$4), $MachinePrecision] - N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * N[(N[(N[(1.0 - N[(N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3.6e+113], t$95$2, If[LessEqual[x1, -0.029], t$95$5, If[LessEqual[x1, 1.9e-22], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(t$95$1 + N[(x2 * N[(x2 * N[(x1 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], t$95$5, t$95$2]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.59999999999999992e113 or 5.00000000000000018e153 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 64.2%

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

   6. Taylor expanded in x2 around 0 94.0%

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

      1. *-commutative 94.0%

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

   8. Simplified 94.0%

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

   if -3.59999999999999992e113 < x1 < -0.0290000000000000015 or 1.90000000000000012e-22 < x1 < 5.00000000000000018e153

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around inf 99.0%

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

   4. Taylor expanded in x1 around -inf 98.8%

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

   if -0.0290000000000000015 < x1 < 1.90000000000000012e-22

   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 87.3%

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

   6. Taylor expanded in x2 around 0 87.3%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\color{blue}{15} - 6\right)\right) - 2\right)\right) \]

   7. Taylor expanded in x2 around 0 99.6%

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

   8. Taylor expanded in x2 around inf 99.6%

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

      1. associate-*r* 99.6%

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

      2. *-commutative 99.6%

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

      3. *-commutative 99.6%

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

   10. Simplified 99.6%

       \[\leadsto x1 + \left(-6 \cdot x2 + \left(x1 \cdot \left(9 \cdot x1 - 2\right) + x2 \cdot \color{blue}{\left(x2 \cdot \left(x1 \cdot 8\right)\right)}\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.6 \cdot 10^{+113}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -0.029:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \left(\frac{1 - \frac{2 \cdot x2 - 3}{x1}}{x1} - 3\right)\right) - \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.9 \cdot 10^{-22}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(x2 \cdot \left(x1 \cdot 8\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \left(\frac{1 - \frac{2 \cdot x2 - 3}{x1}}{x1} - 3\right)\right) - \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 - x1 \cdot x1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := x1 \cdot \left(x1 \cdot x1\right)\\ t_4 := x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ t_5 := \left(t\_1 + 2 \cdot x2\right) - x1\\ t_6 := \frac{t\_5}{t\_2}\\ t_7 := \frac{t\_5}{t\_0}\\ t_8 := t\_6 - 3\\ \mathbf{if}\;x1 \leq -3 \cdot 10^{+113}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x1 \leq 1.9 \cdot 10^{-22}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_1 - 2 \cdot x2\right) - x1}{t\_2} + \left(x1 + \left(t\_3 - \left(t\_1 \cdot t\_7 - t\_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_7\right) + t\_8 \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x1 - 2 \cdot x2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(t\_3 + \left(t\_1 \cdot t\_6 - t\_2 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \left(\frac{1 - \frac{2 \cdot x2 - 3}{x1}}{x1} - 3\right)\right) - \left(\left(x1 \cdot 2\right) \cdot t\_6\right) \cdot t\_8\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- -1.0 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* x1 (* x1 x1)))
        (t_4 (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 9.0) 2.0)))))
        (t_5 (- (+ t_1 (* 2.0 x2)) x1))
        (t_6 (/ t_5 t_2))
        (t_7 (/ t_5 t_0))
        (t_8 (- t_6 3.0)))
   (if (<= x1 -3e+113)
     t_4
     (if (<= x1 1.9e-22)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2))
         (+
          x1
          (-
           t_3
           (-
            (* t_1 t_7)
            (*
             t_0
             (+
              (* (* x1 x1) (+ 6.0 (* 4.0 t_7)))
              (* t_8 (* (* x1 2.0) (- x1 (* 2.0 x2)))))))))))
       (if (<= x1 5e+153)
         (+
          x1
          (+
           9.0
           (+
            x1
            (+
             t_3
             (-
              (* t_1 t_6)
              (*
               t_2
               (-
                (*
                 (* x1 x1)
                 (+
                  6.0
                  (* 4.0 (- (/ (- 1.0 (/ (- (* 2.0 x2) 3.0) x1)) x1) 3.0))))
                (* (* (* x1 2.0) t_6) t_8))))))))
         t_4)))))

C

double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = x1 * (x1 * x1);
	double t_4 = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	double t_5 = (t_1 + (2.0 * x2)) - x1;
	double t_6 = t_5 / t_2;
	double t_7 = t_5 / t_0;
	double t_8 = t_6 - 3.0;
	double tmp;
	if (x1 <= -3e+113) {
		tmp = t_4;
	} else if (x1 <= 1.9e-22) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + (t_3 - ((t_1 * t_7) - (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_7))) + (t_8 * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + (9.0 + (x1 + (t_3 + ((t_1 * t_6) - (t_2 * (((x1 * x1) * (6.0 + (4.0 * (((1.0 - (((2.0 * x2) - 3.0) / x1)) / x1) - 3.0)))) - (((x1 * 2.0) * t_6) * t_8)))))));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: tmp
    t_0 = (-1.0d0) - (x1 * x1)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = x1 * (x1 * x1)
    t_4 = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) - 2.0d0)))
    t_5 = (t_1 + (2.0d0 * x2)) - x1
    t_6 = t_5 / t_2
    t_7 = t_5 / t_0
    t_8 = t_6 - 3.0d0
    if (x1 <= (-3d+113)) then
        tmp = t_4
    else if (x1 <= 1.9d-22) then
        tmp = x1 + ((3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_2)) + (x1 + (t_3 - ((t_1 * t_7) - (t_0 * (((x1 * x1) * (6.0d0 + (4.0d0 * t_7))) + (t_8 * ((x1 * 2.0d0) * (x1 - (2.0d0 * x2))))))))))
    else if (x1 <= 5d+153) then
        tmp = x1 + (9.0d0 + (x1 + (t_3 + ((t_1 * t_6) - (t_2 * (((x1 * x1) * (6.0d0 + (4.0d0 * (((1.0d0 - (((2.0d0 * x2) - 3.0d0) / x1)) / x1) - 3.0d0)))) - (((x1 * 2.0d0) * t_6) * t_8)))))))
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = x1 * (x1 * x1);
	double t_4 = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	double t_5 = (t_1 + (2.0 * x2)) - x1;
	double t_6 = t_5 / t_2;
	double t_7 = t_5 / t_0;
	double t_8 = t_6 - 3.0;
	double tmp;
	if (x1 <= -3e+113) {
		tmp = t_4;
	} else if (x1 <= 1.9e-22) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + (t_3 - ((t_1 * t_7) - (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_7))) + (t_8 * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + (9.0 + (x1 + (t_3 + ((t_1 * t_6) - (t_2 * (((x1 * x1) * (6.0 + (4.0 * (((1.0 - (((2.0 * x2) - 3.0) / x1)) / x1) - 3.0)))) - (((x1 * 2.0) * t_6) * t_8)))))));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = -1.0 - (x1 * x1)
	t_1 = x1 * (x1 * 3.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = x1 * (x1 * x1)
	t_4 = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)))
	t_5 = (t_1 + (2.0 * x2)) - x1
	t_6 = t_5 / t_2
	t_7 = t_5 / t_0
	t_8 = t_6 - 3.0
	tmp = 0
	if x1 <= -3e+113:
		tmp = t_4
	elif x1 <= 1.9e-22:
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + (t_3 - ((t_1 * t_7) - (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_7))) + (t_8 * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))))
	elif x1 <= 5e+153:
		tmp = x1 + (9.0 + (x1 + (t_3 + ((t_1 * t_6) - (t_2 * (((x1 * x1) * (6.0 + (4.0 * (((1.0 - (((2.0 * x2) - 3.0) / x1)) / x1) - 3.0)))) - (((x1 * 2.0) * t_6) * t_8)))))))
	else:
		tmp = t_4
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(-1.0 - Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(x1 * Float64(x1 * x1))
	t_4 = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))))
	t_5 = Float64(Float64(t_1 + Float64(2.0 * x2)) - x1)
	t_6 = Float64(t_5 / t_2)
	t_7 = Float64(t_5 / t_0)
	t_8 = Float64(t_6 - 3.0)
	tmp = 0.0
	if (x1 <= -3e+113)
		tmp = t_4;
	elseif (x1 <= 1.9e-22)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2)) + Float64(x1 + Float64(t_3 - Float64(Float64(t_1 * t_7) - Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_7))) + Float64(t_8 * Float64(Float64(x1 * 2.0) * Float64(x1 - Float64(2.0 * x2)))))))))));
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_3 + Float64(Float64(t_1 * t_6) - Float64(t_2 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * Float64(Float64(Float64(1.0 - Float64(Float64(Float64(2.0 * x2) - 3.0) / x1)) / x1) - 3.0)))) - Float64(Float64(Float64(x1 * 2.0) * t_6) * t_8))))))));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = -1.0 - (x1 * x1);
	t_1 = x1 * (x1 * 3.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = x1 * (x1 * x1);
	t_4 = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	t_5 = (t_1 + (2.0 * x2)) - x1;
	t_6 = t_5 / t_2;
	t_7 = t_5 / t_0;
	t_8 = t_6 - 3.0;
	tmp = 0.0;
	if (x1 <= -3e+113)
		tmp = t_4;
	elseif (x1 <= 1.9e-22)
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + (t_3 - ((t_1 * t_7) - (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_7))) + (t_8 * ((x1 * 2.0) * (x1 - (2.0 * x2))))))))));
	elseif (x1 <= 5e+153)
		tmp = x1 + (9.0 + (x1 + (t_3 + ((t_1 * t_6) - (t_2 * (((x1 * x1) * (6.0 + (4.0 * (((1.0 - (((2.0 * x2) - 3.0) / x1)) / x1) - 3.0)))) - (((x1 * 2.0) * t_6) * t_8)))))));
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$5 / t$95$2), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$5 / t$95$0), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$6 - 3.0), $MachinePrecision]}, If[LessEqual[x1, -3e+113], t$95$4, If[LessEqual[x1, 1.9e-22], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$3 - N[(N[(t$95$1 * t$95$7), $MachinePrecision] - N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$8 * N[(N[(x1 * 2.0), $MachinePrecision] * N[(x1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], N[(x1 + N[(9.0 + N[(x1 + N[(t$95$3 + N[(N[(t$95$1 * t$95$6), $MachinePrecision] - N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * N[(N[(N[(1.0 - N[(N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$6), $MachinePrecision] * t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3e113 or 5.00000000000000018e153 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 64.2%

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

   6. Taylor expanded in x2 around 0 94.0%

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

      1. *-commutative 94.0%

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

   8. Simplified 94.0%

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

   if -3e113 < x1 < 1.90000000000000012e-22

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 97.1%

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

      1. +-commutative 97.1%

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

      2. mul-1-neg 97.1%

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

      3. unsub-neg 97.1%

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

   5. Simplified 97.1%

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

   if 1.90000000000000012e-22 < x1 < 5.00000000000000018e153

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around inf 99.5%

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

   4. Taylor expanded in x1 around -inf 99.7%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3 \cdot 10^{+113}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 1.9 \cdot 10^{-22}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x1 - 2 \cdot x2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \left(\frac{1 - \frac{2 \cdot x2 - 3}{x1}}{x1} - 3\right)\right) - \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 94.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot \left(x1 \cdot 9 - 2\right)\\ t_3 := x1 + \left(x2 \cdot -6 + t\_2\right)\\ t_4 := \left(t\_1 + 2 \cdot x2\right) - x1\\ t_5 := \frac{t\_4}{-1 - x1 \cdot x1}\\ t_6 := x1 + \left(9 - \left(\left(\left(t\_1 \cdot t\_5 + t\_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{t\_4}{t\_0}\right) \cdot \frac{\left(1 + \frac{3}{x1}\right) - 2 \cdot \frac{x2}{x1}}{x1} + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_5\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{if}\;x1 \leq -1.2 \cdot 10^{+115}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x1 \leq -0.92:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;x1 \leq 2.2 \cdot 10^{-10}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(t\_2 + x2 \cdot \left(x2 \cdot \left(x1 \cdot 8\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (* x1 (- (* x1 9.0) 2.0)))
        (t_3 (+ x1 (+ (* x2 -6.0) t_2)))
        (t_4 (- (+ t_1 (* 2.0 x2)) x1))
        (t_5 (/ t_4 (- -1.0 (* x1 x1))))
        (t_6
         (+
          x1
          (-
           9.0
           (-
            (-
             (+
              (* t_1 t_5)
              (*
               t_0
               (+
                (*
                 (* (* x1 2.0) (/ t_4 t_0))
                 (/ (- (+ 1.0 (/ 3.0 x1)) (* 2.0 (/ x2 x1))) x1))
                (* (* x1 x1) (+ 6.0 (* 4.0 t_5))))))
             (* x1 (* x1 x1)))
            x1)))))
   (if (<= x1 -1.2e+115)
     t_3
     (if (<= x1 -0.92)
       t_6
       (if (<= x1 2.2e-10)
         (+ x1 (+ (* x2 -6.0) (+ t_2 (* x2 (* x2 (* x1 8.0))))))
         (if (<= x1 5e+153) t_6 t_3))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = x1 * ((x1 * 9.0) - 2.0);
	double t_3 = x1 + ((x2 * -6.0) + t_2);
	double t_4 = (t_1 + (2.0 * x2)) - x1;
	double t_5 = t_4 / (-1.0 - (x1 * x1));
	double t_6 = x1 + (9.0 - ((((t_1 * t_5) + (t_0 * ((((x1 * 2.0) * (t_4 / t_0)) * (((1.0 + (3.0 / x1)) - (2.0 * (x2 / x1))) / x1)) + ((x1 * x1) * (6.0 + (4.0 * t_5)))))) - (x1 * (x1 * x1))) - x1));
	double tmp;
	if (x1 <= -1.2e+115) {
		tmp = t_3;
	} else if (x1 <= -0.92) {
		tmp = t_6;
	} else if (x1 <= 2.2e-10) {
		tmp = x1 + ((x2 * -6.0) + (t_2 + (x2 * (x2 * (x1 * 8.0)))));
	} else if (x1 <= 5e+153) {
		tmp = t_6;
	} else {
		tmp = t_3;
	}
	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 * 3.0d0)
    t_2 = x1 * ((x1 * 9.0d0) - 2.0d0)
    t_3 = x1 + ((x2 * (-6.0d0)) + t_2)
    t_4 = (t_1 + (2.0d0 * x2)) - x1
    t_5 = t_4 / ((-1.0d0) - (x1 * x1))
    t_6 = x1 + (9.0d0 - ((((t_1 * t_5) + (t_0 * ((((x1 * 2.0d0) * (t_4 / t_0)) * (((1.0d0 + (3.0d0 / x1)) - (2.0d0 * (x2 / x1))) / x1)) + ((x1 * x1) * (6.0d0 + (4.0d0 * t_5)))))) - (x1 * (x1 * x1))) - x1))
    if (x1 <= (-1.2d+115)) then
        tmp = t_3
    else if (x1 <= (-0.92d0)) then
        tmp = t_6
    else if (x1 <= 2.2d-10) then
        tmp = x1 + ((x2 * (-6.0d0)) + (t_2 + (x2 * (x2 * (x1 * 8.0d0)))))
    else if (x1 <= 5d+153) then
        tmp = t_6
    else
        tmp = t_3
    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 = x1 * ((x1 * 9.0) - 2.0);
	double t_3 = x1 + ((x2 * -6.0) + t_2);
	double t_4 = (t_1 + (2.0 * x2)) - x1;
	double t_5 = t_4 / (-1.0 - (x1 * x1));
	double t_6 = x1 + (9.0 - ((((t_1 * t_5) + (t_0 * ((((x1 * 2.0) * (t_4 / t_0)) * (((1.0 + (3.0 / x1)) - (2.0 * (x2 / x1))) / x1)) + ((x1 * x1) * (6.0 + (4.0 * t_5)))))) - (x1 * (x1 * x1))) - x1));
	double tmp;
	if (x1 <= -1.2e+115) {
		tmp = t_3;
	} else if (x1 <= -0.92) {
		tmp = t_6;
	} else if (x1 <= 2.2e-10) {
		tmp = x1 + ((x2 * -6.0) + (t_2 + (x2 * (x2 * (x1 * 8.0)))));
	} else if (x1 <= 5e+153) {
		tmp = t_6;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = x1 * ((x1 * 9.0) - 2.0)
	t_3 = x1 + ((x2 * -6.0) + t_2)
	t_4 = (t_1 + (2.0 * x2)) - x1
	t_5 = t_4 / (-1.0 - (x1 * x1))
	t_6 = x1 + (9.0 - ((((t_1 * t_5) + (t_0 * ((((x1 * 2.0) * (t_4 / t_0)) * (((1.0 + (3.0 / x1)) - (2.0 * (x2 / x1))) / x1)) + ((x1 * x1) * (6.0 + (4.0 * t_5)))))) - (x1 * (x1 * x1))) - x1))
	tmp = 0
	if x1 <= -1.2e+115:
		tmp = t_3
	elif x1 <= -0.92:
		tmp = t_6
	elif x1 <= 2.2e-10:
		tmp = x1 + ((x2 * -6.0) + (t_2 + (x2 * (x2 * (x1 * 8.0)))))
	elif x1 <= 5e+153:
		tmp = t_6
	else:
		tmp = t_3
	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(x1 * Float64(Float64(x1 * 9.0) - 2.0))
	t_3 = Float64(x1 + Float64(Float64(x2 * -6.0) + t_2))
	t_4 = Float64(Float64(t_1 + Float64(2.0 * x2)) - x1)
	t_5 = Float64(t_4 / Float64(-1.0 - Float64(x1 * x1)))
	t_6 = Float64(x1 + Float64(9.0 - Float64(Float64(Float64(Float64(t_1 * t_5) + Float64(t_0 * Float64(Float64(Float64(Float64(x1 * 2.0) * Float64(t_4 / t_0)) * Float64(Float64(Float64(1.0 + Float64(3.0 / x1)) - Float64(2.0 * Float64(x2 / x1))) / x1)) + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_5)))))) - Float64(x1 * Float64(x1 * x1))) - x1)))
	tmp = 0.0
	if (x1 <= -1.2e+115)
		tmp = t_3;
	elseif (x1 <= -0.92)
		tmp = t_6;
	elseif (x1 <= 2.2e-10)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(t_2 + Float64(x2 * Float64(x2 * Float64(x1 * 8.0))))));
	elseif (x1 <= 5e+153)
		tmp = t_6;
	else
		tmp = t_3;
	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 = x1 * ((x1 * 9.0) - 2.0);
	t_3 = x1 + ((x2 * -6.0) + t_2);
	t_4 = (t_1 + (2.0 * x2)) - x1;
	t_5 = t_4 / (-1.0 - (x1 * x1));
	t_6 = x1 + (9.0 - ((((t_1 * t_5) + (t_0 * ((((x1 * 2.0) * (t_4 / t_0)) * (((1.0 + (3.0 / x1)) - (2.0 * (x2 / x1))) / x1)) + ((x1 * x1) * (6.0 + (4.0 * t_5)))))) - (x1 * (x1 * x1))) - x1));
	tmp = 0.0;
	if (x1 <= -1.2e+115)
		tmp = t_3;
	elseif (x1 <= -0.92)
		tmp = t_6;
	elseif (x1 <= 2.2e-10)
		tmp = x1 + ((x2 * -6.0) + (t_2 + (x2 * (x2 * (x1 * 8.0)))));
	elseif (x1 <= 5e+153)
		tmp = t_6;
	else
		tmp = t_3;
	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[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(x1 + N[(9.0 - N[(N[(N[(N[(t$95$1 * t$95$5), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(t$95$4 / t$95$0), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(1.0 + N[(3.0 / x1), $MachinePrecision]), $MachinePrecision] - N[(2.0 * N[(x2 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.2e+115], t$95$3, If[LessEqual[x1, -0.92], t$95$6, If[LessEqual[x1, 2.2e-10], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(t$95$2 + N[(x2 * N[(x2 * N[(x1 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], t$95$6, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.2e115 or 5.00000000000000018e153 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 64.2%

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

   6. Taylor expanded in x2 around 0 94.0%

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

      1. *-commutative 94.0%

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

   8. Simplified 94.0%

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

   if -1.2e115 < x1 < -0.92000000000000004 or 2.1999999999999999e-10 < x1 < 5.00000000000000018e153

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around inf 99.0%

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

   4. Taylor expanded in x1 around inf 97.3%

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

      1. associate-*r/ 97.3%

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

      2. metadata-eval 97.3%

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

   6. Simplified 97.3%

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

   if -0.92000000000000004 < x1 < 2.1999999999999999e-10

   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 87.4%

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

   6. Taylor expanded in x2 around 0 87.4%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\color{blue}{15} - 6\right)\right) - 2\right)\right) \]

   7. Taylor expanded in x2 around 0 99.6%

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

   8. Taylor expanded in x2 around inf 99.6%

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

      1. associate-*r* 99.6%

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

      2. *-commutative 99.6%

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

      3. *-commutative 99.6%

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

   10. Simplified 99.6%

       \[\leadsto x1 + \left(-6 \cdot x2 + \left(x1 \cdot \left(9 \cdot x1 - 2\right) + x2 \cdot \color{blue}{\left(x2 \cdot \left(x1 \cdot 8\right)\right)}\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.2 \cdot 10^{+115}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -0.92:\\ \;\;\;\;x1 + \left(9 - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \frac{\left(1 + \frac{3}{x1}\right) - 2 \cdot \frac{x2}{x1}}{x1} + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 2.2 \cdot 10^{-10}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(x2 \cdot \left(x1 \cdot 8\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \frac{\left(1 + \frac{3}{x1}\right) - 2 \cdot \frac{x2}{x1}}{x1} + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 92.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \left(t\_1 + 2 \cdot x2\right) - x1\\ t_3 := x1 \cdot \left(x1 \cdot 9 - 2\right)\\ t_4 := x1 + \left(x2 \cdot -6 + t\_3\right)\\ t_5 := -1 - x1 \cdot x1\\ t_6 := \frac{t\_2}{t\_5}\\ t_7 := \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_6\right)\\ t_8 := x1 \cdot x1 + 1\\ \mathbf{if}\;x1 \leq -6 \cdot 10^{+111}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x1 \leq -0.0024:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(t\_0 + \left(t\_5 \cdot \left(t\_7 + \left(\left(x1 \cdot 2\right) \cdot \frac{t\_2}{t\_8}\right) \cdot \left(3 + t\_6\right)\right) + t\_1 \cdot \left(2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7 \cdot 10^{+18}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(t\_3 + x2 \cdot \left(x2 \cdot \left(x1 \cdot 8\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_1 - 2 \cdot x2\right) - x1}{t\_8} - \left(\left(\left(t\_1 \cdot t\_6 + t\_8 \cdot \left(t\_7 - x1 \cdot 2\right)\right) - t\_0\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (- (+ t_1 (* 2.0 x2)) x1))
        (t_3 (* x1 (- (* x1 9.0) 2.0)))
        (t_4 (+ x1 (+ (* x2 -6.0) t_3)))
        (t_5 (- -1.0 (* x1 x1)))
        (t_6 (/ t_2 t_5))
        (t_7 (* (* x1 x1) (+ 6.0 (* 4.0 t_6))))
        (t_8 (+ (* x1 x1) 1.0)))
   (if (<= x1 -6e+111)
     t_4
     (if (<= x1 -0.0024)
       (+
        x1
        (+
         9.0
         (+
          x1
          (+
           t_0
           (+
            (* t_5 (+ t_7 (* (* (* x1 2.0) (/ t_2 t_8)) (+ 3.0 t_6))))
            (* t_1 (* 2.0 x2)))))))
       (if (<= x1 7e+18)
         (+ x1 (+ (* x2 -6.0) (+ t_3 (* x2 (* x2 (* x1 8.0))))))
         (if (<= x1 5e+153)
           (+
            x1
            (-
             (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_8))
             (- (- (+ (* t_1 t_6) (* t_8 (- t_7 (* x1 2.0)))) t_0) x1)))
           t_4))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (t_1 + (2.0 * x2)) - x1;
	double t_3 = x1 * ((x1 * 9.0) - 2.0);
	double t_4 = x1 + ((x2 * -6.0) + t_3);
	double t_5 = -1.0 - (x1 * x1);
	double t_6 = t_2 / t_5;
	double t_7 = (x1 * x1) * (6.0 + (4.0 * t_6));
	double t_8 = (x1 * x1) + 1.0;
	double tmp;
	if (x1 <= -6e+111) {
		tmp = t_4;
	} else if (x1 <= -0.0024) {
		tmp = x1 + (9.0 + (x1 + (t_0 + ((t_5 * (t_7 + (((x1 * 2.0) * (t_2 / t_8)) * (3.0 + t_6)))) + (t_1 * (2.0 * x2))))));
	} else if (x1 <= 7e+18) {
		tmp = x1 + ((x2 * -6.0) + (t_3 + (x2 * (x2 * (x1 * 8.0)))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_8)) - ((((t_1 * t_6) + (t_8 * (t_7 - (x1 * 2.0)))) - t_0) - x1));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: tmp
    t_0 = x1 * (x1 * x1)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (t_1 + (2.0d0 * x2)) - x1
    t_3 = x1 * ((x1 * 9.0d0) - 2.0d0)
    t_4 = x1 + ((x2 * (-6.0d0)) + t_3)
    t_5 = (-1.0d0) - (x1 * x1)
    t_6 = t_2 / t_5
    t_7 = (x1 * x1) * (6.0d0 + (4.0d0 * t_6))
    t_8 = (x1 * x1) + 1.0d0
    if (x1 <= (-6d+111)) then
        tmp = t_4
    else if (x1 <= (-0.0024d0)) then
        tmp = x1 + (9.0d0 + (x1 + (t_0 + ((t_5 * (t_7 + (((x1 * 2.0d0) * (t_2 / t_8)) * (3.0d0 + t_6)))) + (t_1 * (2.0d0 * x2))))))
    else if (x1 <= 7d+18) then
        tmp = x1 + ((x2 * (-6.0d0)) + (t_3 + (x2 * (x2 * (x1 * 8.0d0)))))
    else if (x1 <= 5d+153) then
        tmp = x1 + ((3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_8)) - ((((t_1 * t_6) + (t_8 * (t_7 - (x1 * 2.0d0)))) - t_0) - x1))
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (t_1 + (2.0 * x2)) - x1;
	double t_3 = x1 * ((x1 * 9.0) - 2.0);
	double t_4 = x1 + ((x2 * -6.0) + t_3);
	double t_5 = -1.0 - (x1 * x1);
	double t_6 = t_2 / t_5;
	double t_7 = (x1 * x1) * (6.0 + (4.0 * t_6));
	double t_8 = (x1 * x1) + 1.0;
	double tmp;
	if (x1 <= -6e+111) {
		tmp = t_4;
	} else if (x1 <= -0.0024) {
		tmp = x1 + (9.0 + (x1 + (t_0 + ((t_5 * (t_7 + (((x1 * 2.0) * (t_2 / t_8)) * (3.0 + t_6)))) + (t_1 * (2.0 * x2))))));
	} else if (x1 <= 7e+18) {
		tmp = x1 + ((x2 * -6.0) + (t_3 + (x2 * (x2 * (x1 * 8.0)))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_8)) - ((((t_1 * t_6) + (t_8 * (t_7 - (x1 * 2.0)))) - t_0) - x1));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = x1 * (x1 * 3.0)
	t_2 = (t_1 + (2.0 * x2)) - x1
	t_3 = x1 * ((x1 * 9.0) - 2.0)
	t_4 = x1 + ((x2 * -6.0) + t_3)
	t_5 = -1.0 - (x1 * x1)
	t_6 = t_2 / t_5
	t_7 = (x1 * x1) * (6.0 + (4.0 * t_6))
	t_8 = (x1 * x1) + 1.0
	tmp = 0
	if x1 <= -6e+111:
		tmp = t_4
	elif x1 <= -0.0024:
		tmp = x1 + (9.0 + (x1 + (t_0 + ((t_5 * (t_7 + (((x1 * 2.0) * (t_2 / t_8)) * (3.0 + t_6)))) + (t_1 * (2.0 * x2))))))
	elif x1 <= 7e+18:
		tmp = x1 + ((x2 * -6.0) + (t_3 + (x2 * (x2 * (x1 * 8.0)))))
	elif x1 <= 5e+153:
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_8)) - ((((t_1 * t_6) + (t_8 * (t_7 - (x1 * 2.0)))) - t_0) - x1))
	else:
		tmp = t_4
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(t_1 + Float64(2.0 * x2)) - x1)
	t_3 = Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))
	t_4 = Float64(x1 + Float64(Float64(x2 * -6.0) + t_3))
	t_5 = Float64(-1.0 - Float64(x1 * x1))
	t_6 = Float64(t_2 / t_5)
	t_7 = Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_6)))
	t_8 = Float64(Float64(x1 * x1) + 1.0)
	tmp = 0.0
	if (x1 <= -6e+111)
		tmp = t_4;
	elseif (x1 <= -0.0024)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_0 + Float64(Float64(t_5 * Float64(t_7 + Float64(Float64(Float64(x1 * 2.0) * Float64(t_2 / t_8)) * Float64(3.0 + t_6)))) + Float64(t_1 * Float64(2.0 * x2)))))));
	elseif (x1 <= 7e+18)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(t_3 + Float64(x2 * Float64(x2 * Float64(x1 * 8.0))))));
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_8)) - Float64(Float64(Float64(Float64(t_1 * t_6) + Float64(t_8 * Float64(t_7 - Float64(x1 * 2.0)))) - t_0) - x1)));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = x1 * (x1 * 3.0);
	t_2 = (t_1 + (2.0 * x2)) - x1;
	t_3 = x1 * ((x1 * 9.0) - 2.0);
	t_4 = x1 + ((x2 * -6.0) + t_3);
	t_5 = -1.0 - (x1 * x1);
	t_6 = t_2 / t_5;
	t_7 = (x1 * x1) * (6.0 + (4.0 * t_6));
	t_8 = (x1 * x1) + 1.0;
	tmp = 0.0;
	if (x1 <= -6e+111)
		tmp = t_4;
	elseif (x1 <= -0.0024)
		tmp = x1 + (9.0 + (x1 + (t_0 + ((t_5 * (t_7 + (((x1 * 2.0) * (t_2 / t_8)) * (3.0 + t_6)))) + (t_1 * (2.0 * x2))))));
	elseif (x1 <= 7e+18)
		tmp = x1 + ((x2 * -6.0) + (t_3 + (x2 * (x2 * (x1 * 8.0)))));
	elseif (x1 <= 5e+153)
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_8)) - ((((t_1 * t_6) + (t_8 * (t_7 - (x1 * 2.0)))) - t_0) - x1));
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$2 / t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, If[LessEqual[x1, -6e+111], t$95$4, If[LessEqual[x1, -0.0024], N[(x1 + N[(9.0 + N[(x1 + N[(t$95$0 + N[(N[(t$95$5 * N[(t$95$7 + N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(t$95$2 / t$95$8), $MachinePrecision]), $MachinePrecision] * N[(3.0 + t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7e+18], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(t$95$3 + N[(x2 * N[(x2 * N[(x1 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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$8), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(t$95$1 * t$95$6), $MachinePrecision] + N[(t$95$8 * N[(t$95$7 - N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -6e111 or 5.00000000000000018e153 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 64.2%

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

   6. Taylor expanded in x2 around 0 94.0%

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

      1. *-commutative 94.0%

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

   8. Simplified 94.0%

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

   if -6e111 < x1 < -0.00239999999999999979

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around inf 98.2%

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

   4. Taylor expanded in x1 around 0 87.8%

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

   if -0.00239999999999999979 < x1 < 7e18

   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 86.0%

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

   6. Taylor expanded in x2 around 0 86.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\color{blue}{15} - 6\right)\right) - 2\right)\right) \]

   7. Taylor expanded in x2 around 0 97.6%

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

   8. Taylor expanded in x2 around inf 97.6%

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

      1. associate-*r* 97.6%

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

      2. *-commutative 97.6%

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

      3. *-commutative 97.6%

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

   10. Simplified 97.6%

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

   if 7e18 < 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 0 79.7%

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

      1. +-commutative 79.7%

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

      2. mul-1-neg 79.7%

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

      3. unsub-neg 79.7%

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

   5. Simplified 79.7%

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

   6. Taylor expanded in x1 around inf 94.4%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6 \cdot 10^{+111}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -0.0024:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(-1 - x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7 \cdot 10^{+18}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(x2 \cdot \left(x1 \cdot 8\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) - x1 \cdot 2\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 91.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := -1 - x1 \cdot x1\\ t_3 := x1 \cdot \left(x1 \cdot 9 - 2\right)\\ t_4 := x1 + \left(x2 \cdot -6 + t\_3\right)\\ t_5 := x1 \cdot \left(x1 \cdot 3\right)\\ t_6 := \left(t\_5 + 2 \cdot x2\right) - x1\\ t_7 := \frac{t\_6}{t\_2}\\ t_8 := \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_7\right)\\ \mathbf{if}\;x1 \leq -1.9 \cdot 10^{+114}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x1 \leq -46:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(t\_1 + \left(t\_5 \cdot \frac{t\_6}{t\_0} + \left(\frac{-1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot t\_7\right) + t\_8\right) \cdot t\_2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7 \cdot 10^{+18}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(t\_3 + x2 \cdot \left(x2 \cdot \left(x1 \cdot 8\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_5 - 2 \cdot x2\right) - x1}{t\_0} - \left(\left(\left(t\_5 \cdot t\_7 + t\_0 \cdot \left(t\_8 - x1 \cdot 2\right)\right) - t\_1\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 x1)))
        (t_2 (- -1.0 (* x1 x1)))
        (t_3 (* x1 (- (* x1 9.0) 2.0)))
        (t_4 (+ x1 (+ (* x2 -6.0) t_3)))
        (t_5 (* x1 (* x1 3.0)))
        (t_6 (- (+ t_5 (* 2.0 x2)) x1))
        (t_7 (/ t_6 t_2))
        (t_8 (* (* x1 x1) (+ 6.0 (* 4.0 t_7)))))
   (if (<= x1 -1.9e+114)
     t_4
     (if (<= x1 -46.0)
       (+
        x1
        (+
         9.0
         (+
          x1
          (+
           t_1
           (+
            (* t_5 (/ t_6 t_0))
            (* (+ (* (/ -1.0 x1) (* (* x1 2.0) t_7)) t_8) t_2))))))
       (if (<= x1 7e+18)
         (+ x1 (+ (* x2 -6.0) (+ t_3 (* x2 (* x2 (* x1 8.0))))))
         (if (<= x1 5e+153)
           (+
            x1
            (-
             (* 3.0 (/ (- (- t_5 (* 2.0 x2)) x1) t_0))
             (- (- (+ (* t_5 t_7) (* t_0 (- t_8 (* x1 2.0)))) t_1) x1)))
           t_4))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * x1);
	double t_2 = -1.0 - (x1 * x1);
	double t_3 = x1 * ((x1 * 9.0) - 2.0);
	double t_4 = x1 + ((x2 * -6.0) + t_3);
	double t_5 = x1 * (x1 * 3.0);
	double t_6 = (t_5 + (2.0 * x2)) - x1;
	double t_7 = t_6 / t_2;
	double t_8 = (x1 * x1) * (6.0 + (4.0 * t_7));
	double tmp;
	if (x1 <= -1.9e+114) {
		tmp = t_4;
	} else if (x1 <= -46.0) {
		tmp = x1 + (9.0 + (x1 + (t_1 + ((t_5 * (t_6 / t_0)) + ((((-1.0 / x1) * ((x1 * 2.0) * t_7)) + t_8) * t_2)))));
	} else if (x1 <= 7e+18) {
		tmp = x1 + ((x2 * -6.0) + (t_3 + (x2 * (x2 * (x1 * 8.0)))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + ((3.0 * (((t_5 - (2.0 * x2)) - x1) / t_0)) - ((((t_5 * t_7) + (t_0 * (t_8 - (x1 * 2.0)))) - t_1) - x1));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * (x1 * x1)
    t_2 = (-1.0d0) - (x1 * x1)
    t_3 = x1 * ((x1 * 9.0d0) - 2.0d0)
    t_4 = x1 + ((x2 * (-6.0d0)) + t_3)
    t_5 = x1 * (x1 * 3.0d0)
    t_6 = (t_5 + (2.0d0 * x2)) - x1
    t_7 = t_6 / t_2
    t_8 = (x1 * x1) * (6.0d0 + (4.0d0 * t_7))
    if (x1 <= (-1.9d+114)) then
        tmp = t_4
    else if (x1 <= (-46.0d0)) then
        tmp = x1 + (9.0d0 + (x1 + (t_1 + ((t_5 * (t_6 / t_0)) + (((((-1.0d0) / x1) * ((x1 * 2.0d0) * t_7)) + t_8) * t_2)))))
    else if (x1 <= 7d+18) then
        tmp = x1 + ((x2 * (-6.0d0)) + (t_3 + (x2 * (x2 * (x1 * 8.0d0)))))
    else if (x1 <= 5d+153) then
        tmp = x1 + ((3.0d0 * (((t_5 - (2.0d0 * x2)) - x1) / t_0)) - ((((t_5 * t_7) + (t_0 * (t_8 - (x1 * 2.0d0)))) - t_1) - x1))
    else
        tmp = t_4
    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 = -1.0 - (x1 * x1);
	double t_3 = x1 * ((x1 * 9.0) - 2.0);
	double t_4 = x1 + ((x2 * -6.0) + t_3);
	double t_5 = x1 * (x1 * 3.0);
	double t_6 = (t_5 + (2.0 * x2)) - x1;
	double t_7 = t_6 / t_2;
	double t_8 = (x1 * x1) * (6.0 + (4.0 * t_7));
	double tmp;
	if (x1 <= -1.9e+114) {
		tmp = t_4;
	} else if (x1 <= -46.0) {
		tmp = x1 + (9.0 + (x1 + (t_1 + ((t_5 * (t_6 / t_0)) + ((((-1.0 / x1) * ((x1 * 2.0) * t_7)) + t_8) * t_2)))));
	} else if (x1 <= 7e+18) {
		tmp = x1 + ((x2 * -6.0) + (t_3 + (x2 * (x2 * (x1 * 8.0)))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + ((3.0 * (((t_5 - (2.0 * x2)) - x1) / t_0)) - ((((t_5 * t_7) + (t_0 * (t_8 - (x1 * 2.0)))) - t_1) - x1));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * x1)
	t_2 = -1.0 - (x1 * x1)
	t_3 = x1 * ((x1 * 9.0) - 2.0)
	t_4 = x1 + ((x2 * -6.0) + t_3)
	t_5 = x1 * (x1 * 3.0)
	t_6 = (t_5 + (2.0 * x2)) - x1
	t_7 = t_6 / t_2
	t_8 = (x1 * x1) * (6.0 + (4.0 * t_7))
	tmp = 0
	if x1 <= -1.9e+114:
		tmp = t_4
	elif x1 <= -46.0:
		tmp = x1 + (9.0 + (x1 + (t_1 + ((t_5 * (t_6 / t_0)) + ((((-1.0 / x1) * ((x1 * 2.0) * t_7)) + t_8) * t_2)))))
	elif x1 <= 7e+18:
		tmp = x1 + ((x2 * -6.0) + (t_3 + (x2 * (x2 * (x1 * 8.0)))))
	elif x1 <= 5e+153:
		tmp = x1 + ((3.0 * (((t_5 - (2.0 * x2)) - x1) / t_0)) - ((((t_5 * t_7) + (t_0 * (t_8 - (x1 * 2.0)))) - t_1) - x1))
	else:
		tmp = t_4
	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(-1.0 - Float64(x1 * x1))
	t_3 = Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))
	t_4 = Float64(x1 + Float64(Float64(x2 * -6.0) + t_3))
	t_5 = Float64(x1 * Float64(x1 * 3.0))
	t_6 = Float64(Float64(t_5 + Float64(2.0 * x2)) - x1)
	t_7 = Float64(t_6 / t_2)
	t_8 = Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_7)))
	tmp = 0.0
	if (x1 <= -1.9e+114)
		tmp = t_4;
	elseif (x1 <= -46.0)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_1 + Float64(Float64(t_5 * Float64(t_6 / t_0)) + Float64(Float64(Float64(Float64(-1.0 / x1) * Float64(Float64(x1 * 2.0) * t_7)) + t_8) * t_2))))));
	elseif (x1 <= 7e+18)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(t_3 + Float64(x2 * Float64(x2 * Float64(x1 * 8.0))))));
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_5 - Float64(2.0 * x2)) - x1) / t_0)) - Float64(Float64(Float64(Float64(t_5 * t_7) + Float64(t_0 * Float64(t_8 - Float64(x1 * 2.0)))) - t_1) - x1)));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * x1);
	t_2 = -1.0 - (x1 * x1);
	t_3 = x1 * ((x1 * 9.0) - 2.0);
	t_4 = x1 + ((x2 * -6.0) + t_3);
	t_5 = x1 * (x1 * 3.0);
	t_6 = (t_5 + (2.0 * x2)) - x1;
	t_7 = t_6 / t_2;
	t_8 = (x1 * x1) * (6.0 + (4.0 * t_7));
	tmp = 0.0;
	if (x1 <= -1.9e+114)
		tmp = t_4;
	elseif (x1 <= -46.0)
		tmp = x1 + (9.0 + (x1 + (t_1 + ((t_5 * (t_6 / t_0)) + ((((-1.0 / x1) * ((x1 * 2.0) * t_7)) + t_8) * t_2)))));
	elseif (x1 <= 7e+18)
		tmp = x1 + ((x2 * -6.0) + (t_3 + (x2 * (x2 * (x1 * 8.0)))));
	elseif (x1 <= 5e+153)
		tmp = x1 + ((3.0 * (((t_5 - (2.0 * x2)) - x1) / t_0)) - ((((t_5 * t_7) + (t_0 * (t_8 - (x1 * 2.0)))) - t_1) - x1));
	else
		tmp = t_4;
	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[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(t$95$5 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$6 / t$95$2), $MachinePrecision]}, Block[{t$95$8 = N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.9e+114], t$95$4, If[LessEqual[x1, -46.0], N[(x1 + N[(9.0 + N[(x1 + N[(t$95$1 + N[(N[(t$95$5 * N[(t$95$6 / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(-1.0 / x1), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision] + t$95$8), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7e+18], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(t$95$3 + N[(x2 * N[(x2 * N[(x1 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$5 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(t$95$5 * t$95$7), $MachinePrecision] + N[(t$95$0 * N[(t$95$8 - N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.9e114 or 5.00000000000000018e153 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 64.2%

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

   6. Taylor expanded in x2 around 0 94.0%

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

      1. *-commutative 94.0%

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

   8. Simplified 94.0%

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

   if -1.9e114 < x1 < -46

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around inf 98.1%

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

   4. Taylor expanded in x1 around inf 89.3%

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

   if -46 < x1 < 7e18

   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 85.5%

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

   6. Taylor expanded in x2 around 0 85.5%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\color{blue}{15} - 6\right)\right) - 2\right)\right) \]

   7. Taylor expanded in x2 around 0 97.0%

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

   8. Taylor expanded in x2 around inf 97.0%

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

      1. associate-*r* 97.0%

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

      2. *-commutative 97.0%

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

      3. *-commutative 97.0%

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

   10. Simplified 97.0%

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

   if 7e18 < 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 0 79.7%

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

      1. +-commutative 79.7%

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

      2. mul-1-neg 79.7%

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

      3. unsub-neg 79.7%

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

   5. Simplified 79.7%

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

   6. Taylor expanded in x1 around inf 94.4%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.9 \cdot 10^{+114}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -46:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(\frac{-1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7 \cdot 10^{+18}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(x2 \cdot \left(x1 \cdot 8\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) - x1 \cdot 2\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 90.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\left(t\_1 + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\\ t_3 := x1 \cdot \left(x1 \cdot 9 - 2\right)\\ t_4 := x1 + \left(x2 \cdot -6 + t\_3\right)\\ t_5 := \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_2\right)\\ t_6 := x1 \cdot x1 + 1\\ t_7 := 3 \cdot \frac{\left(t\_1 - 2 \cdot x2\right) - x1}{t\_6}\\ \mathbf{if}\;x1 \leq -1.25 \cdot 10^{+110}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x1 \leq -21:\\ \;\;\;\;x1 + \left(t\_7 + \left(x1 + \left(t\_0 + \left(t\_1 \cdot \left(2 \cdot x2\right) - t\_6 \cdot \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) + t\_5\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7.1 \cdot 10^{+18}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(t\_3 + x2 \cdot \left(x2 \cdot \left(x1 \cdot 8\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(t\_7 - \left(\left(\left(t\_1 \cdot t\_2 + t\_6 \cdot \left(t\_5 - x1 \cdot 2\right)\right) - t\_0\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (/ (- (+ t_1 (* 2.0 x2)) x1) (- -1.0 (* x1 x1))))
        (t_3 (* x1 (- (* x1 9.0) 2.0)))
        (t_4 (+ x1 (+ (* x2 -6.0) t_3)))
        (t_5 (* (* x1 x1) (+ 6.0 (* 4.0 t_2))))
        (t_6 (+ (* x1 x1) 1.0))
        (t_7 (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_6))))
   (if (<= x1 -1.25e+110)
     t_4
     (if (<= x1 -21.0)
       (+
        x1
        (+
         t_7
         (+
          x1
          (+
           t_0
           (-
            (* t_1 (* 2.0 x2))
            (* t_6 (+ (* 4.0 (* x1 (* x2 (- 3.0 (* 2.0 x2))))) t_5)))))))
       (if (<= x1 7.1e+18)
         (+ x1 (+ (* x2 -6.0) (+ t_3 (* x2 (* x2 (* x1 8.0))))))
         (if (<= x1 5e+153)
           (+
            x1
            (- t_7 (- (- (+ (* t_1 t_2) (* t_6 (- t_5 (* x1 2.0)))) t_0) x1)))
           t_4))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (2.0 * x2)) - x1) / (-1.0 - (x1 * x1));
	double t_3 = x1 * ((x1 * 9.0) - 2.0);
	double t_4 = x1 + ((x2 * -6.0) + t_3);
	double t_5 = (x1 * x1) * (6.0 + (4.0 * t_2));
	double t_6 = (x1 * x1) + 1.0;
	double t_7 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_6);
	double tmp;
	if (x1 <= -1.25e+110) {
		tmp = t_4;
	} else if (x1 <= -21.0) {
		tmp = x1 + (t_7 + (x1 + (t_0 + ((t_1 * (2.0 * x2)) - (t_6 * ((4.0 * (x1 * (x2 * (3.0 - (2.0 * x2))))) + t_5))))));
	} else if (x1 <= 7.1e+18) {
		tmp = x1 + ((x2 * -6.0) + (t_3 + (x2 * (x2 * (x1 * 8.0)))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + (t_7 - ((((t_1 * t_2) + (t_6 * (t_5 - (x1 * 2.0)))) - t_0) - x1));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = x1 * (x1 * x1)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = ((t_1 + (2.0d0 * x2)) - x1) / ((-1.0d0) - (x1 * x1))
    t_3 = x1 * ((x1 * 9.0d0) - 2.0d0)
    t_4 = x1 + ((x2 * (-6.0d0)) + t_3)
    t_5 = (x1 * x1) * (6.0d0 + (4.0d0 * t_2))
    t_6 = (x1 * x1) + 1.0d0
    t_7 = 3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_6)
    if (x1 <= (-1.25d+110)) then
        tmp = t_4
    else if (x1 <= (-21.0d0)) then
        tmp = x1 + (t_7 + (x1 + (t_0 + ((t_1 * (2.0d0 * x2)) - (t_6 * ((4.0d0 * (x1 * (x2 * (3.0d0 - (2.0d0 * x2))))) + t_5))))))
    else if (x1 <= 7.1d+18) then
        tmp = x1 + ((x2 * (-6.0d0)) + (t_3 + (x2 * (x2 * (x1 * 8.0d0)))))
    else if (x1 <= 5d+153) then
        tmp = x1 + (t_7 - ((((t_1 * t_2) + (t_6 * (t_5 - (x1 * 2.0d0)))) - t_0) - x1))
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (2.0 * x2)) - x1) / (-1.0 - (x1 * x1));
	double t_3 = x1 * ((x1 * 9.0) - 2.0);
	double t_4 = x1 + ((x2 * -6.0) + t_3);
	double t_5 = (x1 * x1) * (6.0 + (4.0 * t_2));
	double t_6 = (x1 * x1) + 1.0;
	double t_7 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_6);
	double tmp;
	if (x1 <= -1.25e+110) {
		tmp = t_4;
	} else if (x1 <= -21.0) {
		tmp = x1 + (t_7 + (x1 + (t_0 + ((t_1 * (2.0 * x2)) - (t_6 * ((4.0 * (x1 * (x2 * (3.0 - (2.0 * x2))))) + t_5))))));
	} else if (x1 <= 7.1e+18) {
		tmp = x1 + ((x2 * -6.0) + (t_3 + (x2 * (x2 * (x1 * 8.0)))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + (t_7 - ((((t_1 * t_2) + (t_6 * (t_5 - (x1 * 2.0)))) - t_0) - x1));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = x1 * (x1 * 3.0)
	t_2 = ((t_1 + (2.0 * x2)) - x1) / (-1.0 - (x1 * x1))
	t_3 = x1 * ((x1 * 9.0) - 2.0)
	t_4 = x1 + ((x2 * -6.0) + t_3)
	t_5 = (x1 * x1) * (6.0 + (4.0 * t_2))
	t_6 = (x1 * x1) + 1.0
	t_7 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_6)
	tmp = 0
	if x1 <= -1.25e+110:
		tmp = t_4
	elif x1 <= -21.0:
		tmp = x1 + (t_7 + (x1 + (t_0 + ((t_1 * (2.0 * x2)) - (t_6 * ((4.0 * (x1 * (x2 * (3.0 - (2.0 * x2))))) + t_5))))))
	elif x1 <= 7.1e+18:
		tmp = x1 + ((x2 * -6.0) + (t_3 + (x2 * (x2 * (x1 * 8.0)))))
	elif x1 <= 5e+153:
		tmp = x1 + (t_7 - ((((t_1 * t_2) + (t_6 * (t_5 - (x1 * 2.0)))) - t_0) - x1))
	else:
		tmp = t_4
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / Float64(-1.0 - Float64(x1 * x1)))
	t_3 = Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))
	t_4 = Float64(x1 + Float64(Float64(x2 * -6.0) + t_3))
	t_5 = Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_2)))
	t_6 = Float64(Float64(x1 * x1) + 1.0)
	t_7 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_6))
	tmp = 0.0
	if (x1 <= -1.25e+110)
		tmp = t_4;
	elseif (x1 <= -21.0)
		tmp = Float64(x1 + Float64(t_7 + Float64(x1 + Float64(t_0 + Float64(Float64(t_1 * Float64(2.0 * x2)) - Float64(t_6 * Float64(Float64(4.0 * Float64(x1 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))) + t_5)))))));
	elseif (x1 <= 7.1e+18)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(t_3 + Float64(x2 * Float64(x2 * Float64(x1 * 8.0))))));
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + Float64(t_7 - Float64(Float64(Float64(Float64(t_1 * t_2) + Float64(t_6 * Float64(t_5 - Float64(x1 * 2.0)))) - t_0) - x1)));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = x1 * (x1 * 3.0);
	t_2 = ((t_1 + (2.0 * x2)) - x1) / (-1.0 - (x1 * x1));
	t_3 = x1 * ((x1 * 9.0) - 2.0);
	t_4 = x1 + ((x2 * -6.0) + t_3);
	t_5 = (x1 * x1) * (6.0 + (4.0 * t_2));
	t_6 = (x1 * x1) + 1.0;
	t_7 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_6);
	tmp = 0.0;
	if (x1 <= -1.25e+110)
		tmp = t_4;
	elseif (x1 <= -21.0)
		tmp = x1 + (t_7 + (x1 + (t_0 + ((t_1 * (2.0 * x2)) - (t_6 * ((4.0 * (x1 * (x2 * (3.0 - (2.0 * x2))))) + t_5))))));
	elseif (x1 <= 7.1e+18)
		tmp = x1 + ((x2 * -6.0) + (t_3 + (x2 * (x2 * (x1 * 8.0)))));
	elseif (x1 <= 5e+153)
		tmp = x1 + (t_7 - ((((t_1 * t_2) + (t_6 * (t_5 - (x1 * 2.0)))) - t_0) - x1));
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$7 = N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$6), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.25e+110], t$95$4, If[LessEqual[x1, -21.0], N[(x1 + N[(t$95$7 + N[(x1 + N[(t$95$0 + N[(N[(t$95$1 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - N[(t$95$6 * N[(N[(4.0 * N[(x1 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7.1e+18], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(t$95$3 + N[(x2 * N[(x2 * N[(x1 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], N[(x1 + N[(t$95$7 - N[(N[(N[(N[(t$95$1 * t$95$2), $MachinePrecision] + N[(t$95$6 * N[(t$95$5 - N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.24999999999999995e110 or 5.00000000000000018e153 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 64.2%

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

   6. Taylor expanded in x2 around 0 94.0%

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

      1. *-commutative 94.0%

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

   8. Simplified 94.0%

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

   if -1.24999999999999995e110 < x1 < -21

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around 0 88.5%

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

      1. +-commutative 88.5%

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

      2. mul-1-neg 88.5%

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

      3. unsub-neg 88.5%

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

   5. Simplified 88.5%

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

   6. Taylor expanded in x1 around 0 86.6%

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

   7. Taylor expanded in x1 around 0 86.8%

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

   if -21 < x1 < 7.1e18

   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 85.5%

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

   6. Taylor expanded in x2 around 0 85.5%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\color{blue}{15} - 6\right)\right) - 2\right)\right) \]

   7. Taylor expanded in x2 around 0 97.0%

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

   8. Taylor expanded in x2 around inf 97.0%

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

      1. associate-*r* 97.0%

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

      2. *-commutative 97.0%

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

      3. *-commutative 97.0%

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

   10. Simplified 97.0%

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

   if 7.1e18 < 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 0 79.7%

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

      1. +-commutative 79.7%

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

      2. mul-1-neg 79.7%

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

      3. unsub-neg 79.7%

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

   5. Simplified 79.7%

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

   6. Taylor expanded in x1 around inf 94.4%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.25 \cdot 10^{+110}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -21:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right) - \left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7.1 \cdot 10^{+18}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(x2 \cdot \left(x1 \cdot 8\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) - x1 \cdot 2\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 90.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\left(t\_1 + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\\ t_3 := x1 \cdot \left(x1 \cdot 9 - 2\right)\\ t_4 := x1 + \left(x2 \cdot -6 + t\_3\right)\\ t_5 := x1 \cdot x1 + 1\\ t_6 := t\_5 \cdot \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_2\right)\right)\\ \mathbf{if}\;x1 \leq -7.6 \cdot 10^{+112}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x1 \leq -21:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_1 - 2 \cdot x2\right) - x1}{t\_5} + \left(x1 + \left(t\_0 + \left(t\_1 \cdot \left(2 \cdot x2\right) - t\_6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 220000:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(t\_3 + x2 \cdot \left(x2 \cdot \left(x1 \cdot 8\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - \left(\left(t\_1 \cdot t\_2 + t\_6\right) - t\_0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (/ (- (+ t_1 (* 2.0 x2)) x1) (- -1.0 (* x1 x1))))
        (t_3 (* x1 (- (* x1 9.0) 2.0)))
        (t_4 (+ x1 (+ (* x2 -6.0) t_3)))
        (t_5 (+ (* x1 x1) 1.0))
        (t_6
         (*
          t_5
          (+
           (* 4.0 (* x1 (* x2 (- 3.0 (* 2.0 x2)))))
           (* (* x1 x1) (+ 6.0 (* 4.0 t_2)))))))
   (if (<= x1 -7.6e+112)
     t_4
     (if (<= x1 -21.0)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_5))
         (+ x1 (+ t_0 (- (* t_1 (* 2.0 x2)) t_6)))))
       (if (<= x1 220000.0)
         (+ x1 (+ (* x2 -6.0) (+ t_3 (* x2 (* x2 (* x1 8.0))))))
         (if (<= x1 5e+153)
           (+ x1 (+ 9.0 (- x1 (- (+ (* t_1 t_2) t_6) t_0))))
           t_4))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (2.0 * x2)) - x1) / (-1.0 - (x1 * x1));
	double t_3 = x1 * ((x1 * 9.0) - 2.0);
	double t_4 = x1 + ((x2 * -6.0) + t_3);
	double t_5 = (x1 * x1) + 1.0;
	double t_6 = t_5 * ((4.0 * (x1 * (x2 * (3.0 - (2.0 * x2))))) + ((x1 * x1) * (6.0 + (4.0 * t_2))));
	double tmp;
	if (x1 <= -7.6e+112) {
		tmp = t_4;
	} else if (x1 <= -21.0) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_5)) + (x1 + (t_0 + ((t_1 * (2.0 * x2)) - t_6))));
	} else if (x1 <= 220000.0) {
		tmp = x1 + ((x2 * -6.0) + (t_3 + (x2 * (x2 * (x1 * 8.0)))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + (9.0 + (x1 - (((t_1 * t_2) + t_6) - t_0)));
	} else {
		tmp = t_4;
	}
	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 * x1)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = ((t_1 + (2.0d0 * x2)) - x1) / ((-1.0d0) - (x1 * x1))
    t_3 = x1 * ((x1 * 9.0d0) - 2.0d0)
    t_4 = x1 + ((x2 * (-6.0d0)) + t_3)
    t_5 = (x1 * x1) + 1.0d0
    t_6 = t_5 * ((4.0d0 * (x1 * (x2 * (3.0d0 - (2.0d0 * x2))))) + ((x1 * x1) * (6.0d0 + (4.0d0 * t_2))))
    if (x1 <= (-7.6d+112)) then
        tmp = t_4
    else if (x1 <= (-21.0d0)) then
        tmp = x1 + ((3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_5)) + (x1 + (t_0 + ((t_1 * (2.0d0 * x2)) - t_6))))
    else if (x1 <= 220000.0d0) then
        tmp = x1 + ((x2 * (-6.0d0)) + (t_3 + (x2 * (x2 * (x1 * 8.0d0)))))
    else if (x1 <= 5d+153) then
        tmp = x1 + (9.0d0 + (x1 - (((t_1 * t_2) + t_6) - t_0)))
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (2.0 * x2)) - x1) / (-1.0 - (x1 * x1));
	double t_3 = x1 * ((x1 * 9.0) - 2.0);
	double t_4 = x1 + ((x2 * -6.0) + t_3);
	double t_5 = (x1 * x1) + 1.0;
	double t_6 = t_5 * ((4.0 * (x1 * (x2 * (3.0 - (2.0 * x2))))) + ((x1 * x1) * (6.0 + (4.0 * t_2))));
	double tmp;
	if (x1 <= -7.6e+112) {
		tmp = t_4;
	} else if (x1 <= -21.0) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_5)) + (x1 + (t_0 + ((t_1 * (2.0 * x2)) - t_6))));
	} else if (x1 <= 220000.0) {
		tmp = x1 + ((x2 * -6.0) + (t_3 + (x2 * (x2 * (x1 * 8.0)))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + (9.0 + (x1 - (((t_1 * t_2) + t_6) - t_0)));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = x1 * (x1 * 3.0)
	t_2 = ((t_1 + (2.0 * x2)) - x1) / (-1.0 - (x1 * x1))
	t_3 = x1 * ((x1 * 9.0) - 2.0)
	t_4 = x1 + ((x2 * -6.0) + t_3)
	t_5 = (x1 * x1) + 1.0
	t_6 = t_5 * ((4.0 * (x1 * (x2 * (3.0 - (2.0 * x2))))) + ((x1 * x1) * (6.0 + (4.0 * t_2))))
	tmp = 0
	if x1 <= -7.6e+112:
		tmp = t_4
	elif x1 <= -21.0:
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_5)) + (x1 + (t_0 + ((t_1 * (2.0 * x2)) - t_6))))
	elif x1 <= 220000.0:
		tmp = x1 + ((x2 * -6.0) + (t_3 + (x2 * (x2 * (x1 * 8.0)))))
	elif x1 <= 5e+153:
		tmp = x1 + (9.0 + (x1 - (((t_1 * t_2) + t_6) - t_0)))
	else:
		tmp = t_4
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / Float64(-1.0 - Float64(x1 * x1)))
	t_3 = Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))
	t_4 = Float64(x1 + Float64(Float64(x2 * -6.0) + t_3))
	t_5 = Float64(Float64(x1 * x1) + 1.0)
	t_6 = Float64(t_5 * Float64(Float64(4.0 * Float64(x1 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))) + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_2)))))
	tmp = 0.0
	if (x1 <= -7.6e+112)
		tmp = t_4;
	elseif (x1 <= -21.0)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_5)) + Float64(x1 + Float64(t_0 + Float64(Float64(t_1 * Float64(2.0 * x2)) - t_6)))));
	elseif (x1 <= 220000.0)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(t_3 + Float64(x2 * Float64(x2 * Float64(x1 * 8.0))))));
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 - Float64(Float64(Float64(t_1 * t_2) + t_6) - t_0))));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = x1 * (x1 * 3.0);
	t_2 = ((t_1 + (2.0 * x2)) - x1) / (-1.0 - (x1 * x1));
	t_3 = x1 * ((x1 * 9.0) - 2.0);
	t_4 = x1 + ((x2 * -6.0) + t_3);
	t_5 = (x1 * x1) + 1.0;
	t_6 = t_5 * ((4.0 * (x1 * (x2 * (3.0 - (2.0 * x2))))) + ((x1 * x1) * (6.0 + (4.0 * t_2))));
	tmp = 0.0;
	if (x1 <= -7.6e+112)
		tmp = t_4;
	elseif (x1 <= -21.0)
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_5)) + (x1 + (t_0 + ((t_1 * (2.0 * x2)) - t_6))));
	elseif (x1 <= 220000.0)
		tmp = x1 + ((x2 * -6.0) + (t_3 + (x2 * (x2 * (x1 * 8.0)))));
	elseif (x1 <= 5e+153)
		tmp = x1 + (9.0 + (x1 - (((t_1 * t_2) + t_6) - t_0)));
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$5 * N[(N[(4.0 * N[(x1 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -7.6e+112], t$95$4, If[LessEqual[x1, -21.0], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$5), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$0 + N[(N[(t$95$1 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 220000.0], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(t$95$3 + N[(x2 * N[(x2 * N[(x1 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], N[(x1 + N[(9.0 + N[(x1 - N[(N[(N[(t$95$1 * t$95$2), $MachinePrecision] + t$95$6), $MachinePrecision] - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -7.60000000000000015e112 or 5.00000000000000018e153 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 64.2%

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

   6. Taylor expanded in x2 around 0 94.0%

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

      1. *-commutative 94.0%

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

   8. Simplified 94.0%

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

   if -7.60000000000000015e112 < x1 < -21

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around 0 88.5%

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

      1. +-commutative 88.5%

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

      2. mul-1-neg 88.5%

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

      3. unsub-neg 88.5%

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

   5. Simplified 88.5%

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

   6. Taylor expanded in x1 around 0 86.6%

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

   7. Taylor expanded in x1 around 0 86.8%

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

   if -21 < x1 < 2.2e5

   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 86.5%

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

   6. Taylor expanded in x2 around 0 86.5%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\color{blue}{15} - 6\right)\right) - 2\right)\right) \]

   7. Taylor expanded in x2 around 0 98.3%

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

   8. Taylor expanded in x2 around inf 98.3%

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

      1. associate-*r* 98.3%

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

      2. *-commutative 98.3%

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

      3. *-commutative 98.3%

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

   10. Simplified 98.3%

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

   if 2.2e5 < 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 0 78.4%

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

      1. +-commutative 78.4%

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

      2. mul-1-neg 78.4%

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

      3. unsub-neg 78.4%

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

   5. Simplified 78.4%

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

   6. Taylor expanded in x1 around 0 75.6%

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

   7. Taylor expanded in x1 around inf 75.6%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.6 \cdot 10^{+112}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -21:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right) - \left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 220000:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(x2 \cdot \left(x1 \cdot 8\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - \left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 91.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot \left(x1 \cdot 9 - 2\right)\\ t_2 := x1 + \left(x2 \cdot -6 + t\_1\right)\\ t_3 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\\ t_4 := x1 + \left(9 + \left(x1 - \left(\left(t\_0 \cdot t\_3 + \left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -1.25 \cdot 10^{+114}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq -21:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x1 \leq 220000:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(t\_1 + x2 \cdot \left(x2 \cdot \left(x1 \cdot 8\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (* x1 (- (* x1 9.0) 2.0)))
        (t_2 (+ x1 (+ (* x2 -6.0) t_1)))
        (t_3 (/ (- (+ t_0 (* 2.0 x2)) x1) (- -1.0 (* x1 x1))))
        (t_4
         (+
          x1
          (+
           9.0
           (-
            x1
            (-
             (+
              (* t_0 t_3)
              (*
               (+ (* x1 x1) 1.0)
               (+
                (* 4.0 (* x1 (* x2 (- 3.0 (* 2.0 x2)))))
                (* (* x1 x1) (+ 6.0 (* 4.0 t_3))))))
             (* x1 (* x1 x1))))))))
   (if (<= x1 -1.25e+114)
     t_2
     (if (<= x1 -21.0)
       t_4
       (if (<= x1 220000.0)
         (+ x1 (+ (* x2 -6.0) (+ t_1 (* x2 (* x2 (* x1 8.0))))))
         (if (<= x1 5e+153) t_4 t_2))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * ((x1 * 9.0) - 2.0);
	double t_2 = x1 + ((x2 * -6.0) + t_1);
	double t_3 = ((t_0 + (2.0 * x2)) - x1) / (-1.0 - (x1 * x1));
	double t_4 = x1 + (9.0 + (x1 - (((t_0 * t_3) + (((x1 * x1) + 1.0) * ((4.0 * (x1 * (x2 * (3.0 - (2.0 * x2))))) + ((x1 * x1) * (6.0 + (4.0 * t_3)))))) - (x1 * (x1 * x1)))));
	double tmp;
	if (x1 <= -1.25e+114) {
		tmp = t_2;
	} else if (x1 <= -21.0) {
		tmp = t_4;
	} else if (x1 <= 220000.0) {
		tmp = x1 + ((x2 * -6.0) + (t_1 + (x2 * (x2 * (x1 * 8.0)))));
	} else if (x1 <= 5e+153) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = x1 * ((x1 * 9.0d0) - 2.0d0)
    t_2 = x1 + ((x2 * (-6.0d0)) + t_1)
    t_3 = ((t_0 + (2.0d0 * x2)) - x1) / ((-1.0d0) - (x1 * x1))
    t_4 = x1 + (9.0d0 + (x1 - (((t_0 * t_3) + (((x1 * x1) + 1.0d0) * ((4.0d0 * (x1 * (x2 * (3.0d0 - (2.0d0 * x2))))) + ((x1 * x1) * (6.0d0 + (4.0d0 * t_3)))))) - (x1 * (x1 * x1)))))
    if (x1 <= (-1.25d+114)) then
        tmp = t_2
    else if (x1 <= (-21.0d0)) then
        tmp = t_4
    else if (x1 <= 220000.0d0) then
        tmp = x1 + ((x2 * (-6.0d0)) + (t_1 + (x2 * (x2 * (x1 * 8.0d0)))))
    else if (x1 <= 5d+153) then
        tmp = t_4
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * ((x1 * 9.0) - 2.0);
	double t_2 = x1 + ((x2 * -6.0) + t_1);
	double t_3 = ((t_0 + (2.0 * x2)) - x1) / (-1.0 - (x1 * x1));
	double t_4 = x1 + (9.0 + (x1 - (((t_0 * t_3) + (((x1 * x1) + 1.0) * ((4.0 * (x1 * (x2 * (3.0 - (2.0 * x2))))) + ((x1 * x1) * (6.0 + (4.0 * t_3)))))) - (x1 * (x1 * x1)))));
	double tmp;
	if (x1 <= -1.25e+114) {
		tmp = t_2;
	} else if (x1 <= -21.0) {
		tmp = t_4;
	} else if (x1 <= 220000.0) {
		tmp = x1 + ((x2 * -6.0) + (t_1 + (x2 * (x2 * (x1 * 8.0)))));
	} else if (x1 <= 5e+153) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = x1 * ((x1 * 9.0) - 2.0)
	t_2 = x1 + ((x2 * -6.0) + t_1)
	t_3 = ((t_0 + (2.0 * x2)) - x1) / (-1.0 - (x1 * x1))
	t_4 = x1 + (9.0 + (x1 - (((t_0 * t_3) + (((x1 * x1) + 1.0) * ((4.0 * (x1 * (x2 * (3.0 - (2.0 * x2))))) + ((x1 * x1) * (6.0 + (4.0 * t_3)))))) - (x1 * (x1 * x1)))))
	tmp = 0
	if x1 <= -1.25e+114:
		tmp = t_2
	elif x1 <= -21.0:
		tmp = t_4
	elif x1 <= 220000.0:
		tmp = x1 + ((x2 * -6.0) + (t_1 + (x2 * (x2 * (x1 * 8.0)))))
	elif x1 <= 5e+153:
		tmp = t_4
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))
	t_2 = Float64(x1 + Float64(Float64(x2 * -6.0) + t_1))
	t_3 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / Float64(-1.0 - Float64(x1 * x1)))
	t_4 = Float64(x1 + Float64(9.0 + Float64(x1 - Float64(Float64(Float64(t_0 * t_3) + Float64(Float64(Float64(x1 * x1) + 1.0) * Float64(Float64(4.0 * Float64(x1 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))) + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_3)))))) - Float64(x1 * Float64(x1 * x1))))))
	tmp = 0.0
	if (x1 <= -1.25e+114)
		tmp = t_2;
	elseif (x1 <= -21.0)
		tmp = t_4;
	elseif (x1 <= 220000.0)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(t_1 + Float64(x2 * Float64(x2 * Float64(x1 * 8.0))))));
	elseif (x1 <= 5e+153)
		tmp = t_4;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = x1 * ((x1 * 9.0) - 2.0);
	t_2 = x1 + ((x2 * -6.0) + t_1);
	t_3 = ((t_0 + (2.0 * x2)) - x1) / (-1.0 - (x1 * x1));
	t_4 = x1 + (9.0 + (x1 - (((t_0 * t_3) + (((x1 * x1) + 1.0) * ((4.0 * (x1 * (x2 * (3.0 - (2.0 * x2))))) + ((x1 * x1) * (6.0 + (4.0 * t_3)))))) - (x1 * (x1 * x1)))));
	tmp = 0.0;
	if (x1 <= -1.25e+114)
		tmp = t_2;
	elseif (x1 <= -21.0)
		tmp = t_4;
	elseif (x1 <= 220000.0)
		tmp = x1 + ((x2 * -6.0) + (t_1 + (x2 * (x2 * (x1 * 8.0)))));
	elseif (x1 <= 5e+153)
		tmp = t_4;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(9.0 + N[(x1 - N[(N[(N[(t$95$0 * t$95$3), $MachinePrecision] + N[(N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision] * N[(N[(4.0 * N[(x1 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.25e+114], t$95$2, If[LessEqual[x1, -21.0], t$95$4, If[LessEqual[x1, 220000.0], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(t$95$1 + N[(x2 * N[(x2 * N[(x1 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], t$95$4, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.25e114 or 5.00000000000000018e153 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 64.2%

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

   6. Taylor expanded in x2 around 0 94.0%

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

      1. *-commutative 94.0%

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

   8. Simplified 94.0%

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

   if -1.25e114 < x1 < -21 or 2.2e5 < x1 < 5.00000000000000018e153

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around 0 82.4%

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

      1. +-commutative 82.4%

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

      2. mul-1-neg 82.4%

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

      3. unsub-neg 82.4%

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

   5. Simplified 82.4%

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

   6. Taylor expanded in x1 around 0 80.0%

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

   7. Taylor expanded in x1 around inf 80.0%

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

   if -21 < x1 < 2.2e5

   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 86.5%

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

   6. Taylor expanded in x2 around 0 86.5%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\color{blue}{15} - 6\right)\right) - 2\right)\right) \]

   7. Taylor expanded in x2 around 0 98.3%

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

   8. Taylor expanded in x2 around inf 98.3%

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

      1. associate-*r* 98.3%

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

      2. *-commutative 98.3%

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

      3. *-commutative 98.3%

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

   10. Simplified 98.3%

       \[\leadsto x1 + \left(-6 \cdot x2 + \left(x1 \cdot \left(9 \cdot x1 - 2\right) + x2 \cdot \color{blue}{\left(x2 \cdot \left(x1 \cdot 8\right)\right)}\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.25 \cdot 10^{+114}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -21:\\ \;\;\;\;x1 + \left(9 + \left(x1 - \left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 220000:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(x2 \cdot \left(x1 \cdot 8\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - \left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 83.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ \mathbf{if}\;x1 \leq -6.1 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{+97}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 - x1 \cdot 9\right) - x2 \cdot \left(x2 \cdot \left(-12 \cdot \frac{x1}{x2} + x1 \cdot 8\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_2 \cdot \frac{\left(t\_2 + 2 \cdot x2\right) - x1}{t\_0} + t\_0 \cdot \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 9.0) 2.0)))))
        (t_2 (* x1 (* x1 3.0))))
   (if (<= x1 -6.1e+125)
     t_1
     (if (<= x1 6e+97)
       (-
        x1
        (-
         (-
          (* x1 (- 2.0 (* x1 9.0)))
          (* x2 (* x2 (+ (* -12.0 (/ x1 x2)) (* x1 8.0)))))
         (* x2 -6.0)))
       (if (<= x1 4.5e+153)
         (+
          x1
          (+
           9.0
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* t_2 (/ (- (+ t_2 (* 2.0 x2)) x1) t_0))
              (* t_0 (* 4.0 (* x1 (* x2 (- (* 2.0 x2) 3.0))))))))))
         t_1)))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	double t_2 = x1 * (x1 * 3.0);
	double tmp;
	if (x1 <= -6.1e+125) {
		tmp = t_1;
	} else if (x1 <= 6e+97) {
		tmp = x1 - (((x1 * (2.0 - (x1 * 9.0))) - (x2 * (x2 * ((-12.0 * (x1 / x2)) + (x1 * 8.0))))) - (x2 * -6.0));
	} else if (x1 <= 4.5e+153) {
		tmp = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * (((t_2 + (2.0 * x2)) - x1) / t_0)) + (t_0 * (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0)))))))));
	} 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) :: t_2
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) - 2.0d0)))
    t_2 = x1 * (x1 * 3.0d0)
    if (x1 <= (-6.1d+125)) then
        tmp = t_1
    else if (x1 <= 6d+97) then
        tmp = x1 - (((x1 * (2.0d0 - (x1 * 9.0d0))) - (x2 * (x2 * (((-12.0d0) * (x1 / x2)) + (x1 * 8.0d0))))) - (x2 * (-6.0d0)))
    else if (x1 <= 4.5d+153) then
        tmp = x1 + (9.0d0 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * (((t_2 + (2.0d0 * x2)) - x1) / t_0)) + (t_0 * (4.0d0 * (x1 * (x2 * ((2.0d0 * x2) - 3.0d0)))))))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	double t_2 = x1 * (x1 * 3.0);
	double tmp;
	if (x1 <= -6.1e+125) {
		tmp = t_1;
	} else if (x1 <= 6e+97) {
		tmp = x1 - (((x1 * (2.0 - (x1 * 9.0))) - (x2 * (x2 * ((-12.0 * (x1 / x2)) + (x1 * 8.0))))) - (x2 * -6.0));
	} else if (x1 <= 4.5e+153) {
		tmp = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * (((t_2 + (2.0 * x2)) - x1) / t_0)) + (t_0 * (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0)))))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)))
	t_2 = x1 * (x1 * 3.0)
	tmp = 0
	if x1 <= -6.1e+125:
		tmp = t_1
	elif x1 <= 6e+97:
		tmp = x1 - (((x1 * (2.0 - (x1 * 9.0))) - (x2 * (x2 * ((-12.0 * (x1 / x2)) + (x1 * 8.0))))) - (x2 * -6.0))
	elif x1 <= 4.5e+153:
		tmp = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * (((t_2 + (2.0 * x2)) - x1) / t_0)) + (t_0 * (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0)))))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	tmp = 0.0
	if (x1 <= -6.1e+125)
		tmp = t_1;
	elseif (x1 <= 6e+97)
		tmp = Float64(x1 - Float64(Float64(Float64(x1 * Float64(2.0 - Float64(x1 * 9.0))) - Float64(x2 * Float64(x2 * Float64(Float64(-12.0 * Float64(x1 / x2)) + Float64(x1 * 8.0))))) - Float64(x2 * -6.0)));
	elseif (x1 <= 4.5e+153)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_2 * Float64(Float64(Float64(t_2 + Float64(2.0 * x2)) - x1) / t_0)) + Float64(t_0 * Float64(4.0 * Float64(x1 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	t_2 = x1 * (x1 * 3.0);
	tmp = 0.0;
	if (x1 <= -6.1e+125)
		tmp = t_1;
	elseif (x1 <= 6e+97)
		tmp = x1 - (((x1 * (2.0 - (x1 * 9.0))) - (x2 * (x2 * ((-12.0 * (x1 / x2)) + (x1 * 8.0))))) - (x2 * -6.0));
	elseif (x1 <= 4.5e+153)
		tmp = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * (((t_2 + (2.0 * x2)) - x1) / t_0)) + (t_0 * (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0)))))))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -6.1e+125], t$95$1, If[LessEqual[x1, 6e+97], N[(x1 - N[(N[(N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * N[(x2 * N[(N[(-12.0 * N[(x1 / x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.5e+153], N[(x1 + N[(9.0 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(4.0 * N[(x1 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -6.09999999999999977e125 or 4.5000000000000001e153 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 65.1%

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

   6. Taylor expanded in x2 around 0 95.4%

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

      1. *-commutative 95.4%

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

   8. Simplified 95.4%

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

   if -6.09999999999999977e125 < x1 < 5.9999999999999997e97

   1. Initial program 98.9%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in x1 around 0 67.8%

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

   6. Taylor expanded in x2 around 0 67.8%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\color{blue}{15} - 6\right)\right) - 2\right)\right) \]

   7. Taylor expanded in x2 around 0 76.4%

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

   8. Taylor expanded in x2 around inf 76.9%

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

   if 5.9999999999999997e97 < x1 < 4.5000000000000001e153

   1. Initial program 100.0%

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

   3. Taylor expanded in x1 around inf 100.0%

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

   4. Taylor expanded in x1 around 0 90.9%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6.1 \cdot 10^{+125}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{+97}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 - x1 \cdot 9\right) - x2 \cdot \left(x2 \cdot \left(-12 \cdot \frac{x1}{x2} + x1 \cdot 8\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 80.8% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.9 \cdot 10^{+108}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 1.85 \cdot 10^{-22}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x2 \cdot \left(12 - x2 \cdot 8\right) - x1 \cdot 9\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -2.9e+108)
   (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 9.0) 2.0))))
   (if (<= x1 1.85e-22)
     (- (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0)) x1)
     (+
      x1
      (-
       (* x2 -6.0)
       (* x1 (+ 2.0 (- (* x2 (- 12.0 (* x2 8.0))) (* x1 9.0)))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.9e+108) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	} else if (x1 <= 1.85e-22) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x2 * (12.0 - (x2 * 8.0))) - (x1 * 9.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-2.9d+108)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) - 2.0d0)))
    else if (x1 <= 1.85d-22) then
        tmp = (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)) - x1
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((x2 * (12.0d0 - (x2 * 8.0d0))) - (x1 * 9.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.9e+108) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	} else if (x1 <= 1.85e-22) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x2 * (12.0 - (x2 * 8.0))) - (x1 * 9.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -2.9e+108:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)))
	elif x1 <= 1.85e-22:
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x2 * (12.0 - (x2 * 8.0))) - (x1 * 9.0)))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -2.9e+108)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))));
	elseif (x1 <= 1.85e-22)
		tmp = Float64(Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0)) - x1);
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(x2 * Float64(12.0 - Float64(x2 * 8.0))) - Float64(x1 * 9.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -2.9e+108)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	elseif (x1 <= 1.85e-22)
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x2 * (12.0 - (x2 * 8.0))) - (x1 * 9.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -2.9e+108], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.85e-22], 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[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(N[(x2 * N[(12.0 - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.90000000000000007e108

   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 63.2%

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

   6. Taylor expanded in x2 around 0 89.5%

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

      1. *-commutative 89.5%

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

   8. Simplified 89.5%

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

   if -2.90000000000000007e108 < x1 < 1.85e-22

   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 76.1%

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

      1. fma-define 76.2%

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

      2. associate-*r* 76.2%

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

      3. fma-neg 76.2%

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

      4. fma-neg 76.2%

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

      5. metadata-eval 76.2%

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

      6. metadata-eval 76.2%

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

   7. Simplified 76.2%

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

   8. Taylor expanded in x2 around 0 86.3%

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

   if 1.85e-22 < x1

   1. Initial program 60.3%

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

   3. Simplified 60.3%

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

   5. Taylor expanded in x1 around 0 39.2%

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

   6. Taylor expanded in x2 around 0 53.2%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\color{blue}{15} - 6\right)\right) - 2\right)\right) \]

   7. Taylor expanded in x2 around 0 53.2%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{\left(9 \cdot x1 + x2 \cdot \left(8 \cdot x2 - 12\right)\right)} - 2\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.9 \cdot 10^{+108}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 1.85 \cdot 10^{-22}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x2 \cdot \left(12 - x2 \cdot 8\right) - x1 \cdot 9\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 52.9% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -8 \cdot 10^{+44}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{elif}\;x1 \leq -4.4 \cdot 10^{-39} \lor \neg \left(x1 \leq 1.95 \cdot 10^{-151}\right):\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot \left(x2 \cdot 8 - 12\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -8e+44)
   (* x1 (+ -1.0 (* x2 -12.0)))
   (if (or (<= x1 -4.4e-39) (not (<= x1 1.95e-151)))
     (* x1 (+ -1.0 (* x2 (- (* x2 8.0) 12.0))))
     (- (* x2 -6.0) x1))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -8e+44) {
		tmp = x1 * (-1.0 + (x2 * -12.0));
	} else if ((x1 <= -4.4e-39) || !(x1 <= 1.95e-151)) {
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)));
	} else {
		tmp = (x2 * -6.0) - x1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-8d+44)) then
        tmp = x1 * ((-1.0d0) + (x2 * (-12.0d0)))
    else if ((x1 <= (-4.4d-39)) .or. (.not. (x1 <= 1.95d-151))) then
        tmp = x1 * ((-1.0d0) + (x2 * ((x2 * 8.0d0) - 12.0d0)))
    else
        tmp = (x2 * (-6.0d0)) - x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -8e+44) {
		tmp = x1 * (-1.0 + (x2 * -12.0));
	} else if ((x1 <= -4.4e-39) || !(x1 <= 1.95e-151)) {
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)));
	} else {
		tmp = (x2 * -6.0) - x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -8e+44:
		tmp = x1 * (-1.0 + (x2 * -12.0))
	elif (x1 <= -4.4e-39) or not (x1 <= 1.95e-151):
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)))
	else:
		tmp = (x2 * -6.0) - x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -8e+44)
		tmp = Float64(x1 * Float64(-1.0 + Float64(x2 * -12.0)));
	elseif ((x1 <= -4.4e-39) || !(x1 <= 1.95e-151))
		tmp = Float64(x1 * Float64(-1.0 + Float64(x2 * Float64(Float64(x2 * 8.0) - 12.0))));
	else
		tmp = Float64(Float64(x2 * -6.0) - x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -8e+44)
		tmp = x1 * (-1.0 + (x2 * -12.0));
	elseif ((x1 <= -4.4e-39) || ~((x1 <= 1.95e-151)))
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)));
	else
		tmp = (x2 * -6.0) - x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -8e+44], N[(x1 * N[(-1.0 + N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x1, -4.4e-39], N[Not[LessEqual[x1, 1.95e-151]], $MachinePrecision]], N[(x1 * N[(-1.0 + N[(x2 * N[(N[(x2 * 8.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -8.0000000000000007e44

   1. Initial program 27.0%

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

   3. Simplified 26.9%

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

   5. Taylor expanded in x1 around 0 7.7%

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

      1. fma-define 7.7%

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

      2. associate-*r* 7.7%

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

      3. fma-neg 7.7%

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

      4. fma-neg 7.7%

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

      5. metadata-eval 7.7%

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

      6. metadata-eval 7.7%

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

   7. Simplified 7.7%

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

   8. Taylor expanded in x2 around 0 20.8%

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

   9. Taylor expanded in x1 around inf 20.8%

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

   if -8.0000000000000007e44 < x1 < -4.40000000000000002e-39 or 1.95000000000000003e-151 < x1

   1. Initial program 77.2%

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

   3. Simplified 77.4%

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

   5. Taylor expanded in x1 around 0 49.6%

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

      1. fma-define 49.6%

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

      2. associate-*r* 49.6%

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

      3. fma-neg 49.6%

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

      4. fma-neg 49.6%

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

      5. metadata-eval 49.6%

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

      6. metadata-eval 49.6%

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

   7. Simplified 49.6%

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

   8. Taylor expanded in x2 around 0 49.6%

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

   9. Taylor expanded in x1 around inf 42.4%

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

   if -4.40000000000000002e-39 < x1 < 1.95000000000000003e-151

   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 84.3%

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

      1. fma-define 84.5%

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

      2. associate-*r* 84.5%

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

      3. fma-neg 84.5%

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

      4. fma-neg 84.5%

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

      5. metadata-eval 84.5%

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

      6. metadata-eval 84.5%

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

   7. Simplified 84.5%

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

   8. Taylor expanded in x2 around 0 80.7%

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

   9. Taylor expanded in x1 around 0 80.7%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -8 \cdot 10^{+44}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{elif}\;x1 \leq -4.4 \cdot 10^{-39} \lor \neg \left(x1 \leq 1.95 \cdot 10^{-151}\right):\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot \left(x2 \cdot 8 - 12\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 81.1% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 9 - 2\right)\\ \mathbf{if}\;x1 \leq -2.02 \cdot 10^{+127}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + t\_0\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(t\_0 + x2 \cdot \left(x2 \cdot \left(x1 \cdot 8\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (- (* x1 9.0) 2.0))))
   (if (<= x1 -2.02e+127)
     (+ x1 (+ (* x2 -6.0) t_0))
     (+ x1 (+ (* x2 -6.0) (+ t_0 (* x2 (* x2 (* x1 8.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 9.0) - 2.0);
	double tmp;
	if (x1 <= -2.02e+127) {
		tmp = x1 + ((x2 * -6.0) + t_0);
	} else {
		tmp = x1 + ((x2 * -6.0) + (t_0 + (x2 * (x2 * (x1 * 8.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 * ((x1 * 9.0d0) - 2.0d0)
    if (x1 <= (-2.02d+127)) then
        tmp = x1 + ((x2 * (-6.0d0)) + t_0)
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (t_0 + (x2 * (x2 * (x1 * 8.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 9.0) - 2.0);
	double tmp;
	if (x1 <= -2.02e+127) {
		tmp = x1 + ((x2 * -6.0) + t_0);
	} else {
		tmp = x1 + ((x2 * -6.0) + (t_0 + (x2 * (x2 * (x1 * 8.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((x1 * 9.0) - 2.0)
	tmp = 0
	if x1 <= -2.02e+127:
		tmp = x1 + ((x2 * -6.0) + t_0)
	else:
		tmp = x1 + ((x2 * -6.0) + (t_0 + (x2 * (x2 * (x1 * 8.0)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))
	tmp = 0.0
	if (x1 <= -2.02e+127)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + t_0));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(t_0 + Float64(x2 * Float64(x2 * Float64(x1 * 8.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((x1 * 9.0) - 2.0);
	tmp = 0.0;
	if (x1 <= -2.02e+127)
		tmp = x1 + ((x2 * -6.0) + t_0);
	else
		tmp = x1 + ((x2 * -6.0) + (t_0 + (x2 * (x2 * (x1 * 8.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.02e+127], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(t$95$0 + N[(x2 * N[(x2 * N[(x1 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -2.0200000000000001e127

   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 66.7%

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

   6. Taylor expanded in x2 around 0 94.5%

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

      1. *-commutative 94.5%

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

   8. Simplified 94.5%

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

   if -2.0200000000000001e127 < x1

   1. Initial program 87.0%

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

   3. Simplified 87.1%

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

   5. Taylor expanded in x1 around 0 65.0%

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

   6. Taylor expanded in x2 around 0 69.1%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\color{blue}{15} - 6\right)\right) - 2\right)\right) \]

   7. Taylor expanded in x2 around 0 76.3%

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

   8. Taylor expanded in x2 around inf 76.3%

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

      1. associate-*r* 76.3%

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

      2. *-commutative 76.3%

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

      3. *-commutative 76.3%

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

   10. Simplified 76.3%

       \[\leadsto x1 + \left(-6 \cdot x2 + \left(x1 \cdot \left(9 \cdot x1 - 2\right) + x2 \cdot \color{blue}{\left(x2 \cdot \left(x1 \cdot 8\right)\right)}\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.02 \cdot 10^{+127}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(x2 \cdot \left(x1 \cdot 8\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 80.3% accurate, 5.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -3.6 \cdot 10^{+114} \lor \neg \left(x1 \leq 7 \cdot 10^{+151}\right):\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -3.6e+114) (not (<= x1 7e+151)))
   (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 9.0) 2.0))))
   (- (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0)) x1)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -3.6e+114) || !(x1 <= 7e+151)) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	} else {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-3.6d+114)) .or. (.not. (x1 <= 7d+151))) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) - 2.0d0)))
    else
        tmp = (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)) - x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -3.6e+114) || !(x1 <= 7e+151)) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	} else {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -3.6e+114) or not (x1 <= 7e+151):
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)))
	else:
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -3.6e+114) || !(x1 <= 7e+151))
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))));
	else
		tmp = Float64(Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0)) - x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -3.6e+114) || ~((x1 <= 7e+151)))
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	else
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -3.6e+114], N[Not[LessEqual[x1, 7e+151]], $MachinePrecision]], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if x1 < -3.6000000000000001e114 or 7.0000000000000006e151 < x1

   1. Initial program 1.6%

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

   3. Simplified 1.6%

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

   5. Taylor expanded in x1 around 0 63.3%

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

   6. Taylor expanded in x2 around 0 92.7%

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

      1. *-commutative 92.7%

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

   8. Simplified 92.7%

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

   if -3.6000000000000001e114 < x1 < 7.0000000000000006e151

   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 64.9%

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

      1. fma-define 65.0%

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

      2. associate-*r* 65.0%

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

      3. fma-neg 65.0%

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

      4. fma-neg 65.0%

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

      5. metadata-eval 65.0%

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

      6. metadata-eval 65.0%

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

   7. Simplified 65.0%

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

   8. Taylor expanded in x2 around 0 73.0%

      \[\leadsto \color{blue}{-1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.6 \cdot 10^{+114} \lor \neg \left(x1 \leq 7 \cdot 10^{+151}\right):\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 74.5% accurate, 5.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.3 \cdot 10^{+116} \lor \neg \left(x1 \leq 7 \cdot 10^{+151}\right):\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x2 \cdot \left(x2 \cdot 8 - 12\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -1.3e+116) (not (<= x1 7e+151)))
   (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 9.0) 2.0))))
   (+ (* x2 -6.0) (* x1 (+ -1.0 (* x2 (- (* x2 8.0) 12.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -1.3e+116) || !(x1 <= 7e+151)) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-1.3d+116)) .or. (.not. (x1 <= 7d+151))) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) - 2.0d0)))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x2 * ((x2 * 8.0d0) - 12.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -1.3e+116) || !(x1 <= 7e+151)) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -1.3e+116) or not (x1 <= 7e+151):
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)))
	else:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -1.3e+116) || !(x1 <= 7e+151))
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x2 * Float64(Float64(x2 * 8.0) - 12.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -1.3e+116) || ~((x1 <= 7e+151)))
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	else
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -1.3e+116], N[Not[LessEqual[x1, 7e+151]], $MachinePrecision]], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.29999999999999993e116 or 7.0000000000000006e151 < x1

   1. Initial program 1.6%

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

   3. Simplified 1.6%

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

   5. Taylor expanded in x1 around 0 63.3%

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

   6. Taylor expanded in x2 around 0 92.7%

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

      1. *-commutative 92.7%

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

   8. Simplified 92.7%

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

   if -1.29999999999999993e116 < x1 < 7.0000000000000006e151

   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 64.9%

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

      1. fma-define 65.0%

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

      2. associate-*r* 65.0%

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

      3. fma-neg 65.0%

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

      4. fma-neg 65.0%

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

      5. metadata-eval 65.0%

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

      6. metadata-eval 65.0%

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

   7. Simplified 65.0%

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

   8. Taylor expanded in x2 around 0 65.0%

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

   9. Taylor expanded in x1 around 0 64.9%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(x2 \cdot \left(8 \cdot x2 - 12\right) - 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.3 \cdot 10^{+116} \lor \neg \left(x1 \leq 7 \cdot 10^{+151}\right):\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x2 \cdot \left(x2 \cdot 8 - 12\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 68.2% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -1.8 \cdot 10^{+148} \lor \neg \left(x2 \leq 4.6 \cdot 10^{+209}\right):\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot \left(x2 \cdot 8 - 12\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -1.8e+148) (not (<= x2 4.6e+209)))
   (* x1 (+ -1.0 (* x2 (- (* x2 8.0) 12.0))))
   (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 9.0) 2.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.8e+148) || !(x2 <= 4.6e+209)) {
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-1.8d+148)) .or. (.not. (x2 <= 4.6d+209))) then
        tmp = x1 * ((-1.0d0) + (x2 * ((x2 * 8.0d0) - 12.0d0)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.8e+148) || !(x2 <= 4.6e+209)) {
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -1.8e+148) or not (x2 <= 4.6e+209):
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -1.8e+148) || !(x2 <= 4.6e+209))
		tmp = Float64(x1 * Float64(-1.0 + Float64(x2 * Float64(Float64(x2 * 8.0) - 12.0))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -1.8e+148) || ~((x2 <= 4.6e+209)))
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -1.8e+148], N[Not[LessEqual[x2, 4.6e+209]], $MachinePrecision]], N[(x1 * N[(-1.0 + N[(x2 * N[(N[(x2 * 8.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -1.80000000000000003e148 or 4.60000000000000019e209 < x2

   1. Initial program 78.7%

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

   3. Simplified 78.7%

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

   5. Taylor expanded in x1 around 0 59.2%

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

      1. fma-define 59.2%

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

      2. associate-*r* 59.2%

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

      3. fma-neg 59.2%

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

      4. fma-neg 59.2%

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

      5. metadata-eval 59.2%

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

      6. metadata-eval 59.2%

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

   7. Simplified 59.2%

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

   8. Taylor expanded in x2 around 0 59.2%

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

   9. Taylor expanded in x1 around inf 59.2%

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

   if -1.80000000000000003e148 < x2 < 4.60000000000000019e209

   1. Initial program 75.1%

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

   3. Simplified 75.2%

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

   5. Taylor expanded in x1 around 0 67.5%

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

   6. Taylor expanded in x2 around 0 69.5%

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

      1. *-commutative 69.5%

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

   8. Simplified 69.5%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.8 \cdot 10^{+148} \lor \neg \left(x2 \leq 4.6 \cdot 10^{+209}\right):\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot \left(x2 \cdot 8 - 12\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 43.1% accurate, 6.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -2.1 \cdot 10^{-9}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right)\\ \mathbf{elif}\;x2 \leq 4.8 \cdot 10^{+206}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot \left(\left(-12\right) - \frac{6}{x1}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 -2.1e-9)
   (* x2 (- (* x1 -12.0) 6.0))
   (if (<= x2 4.8e+206)
     (- (* x2 -6.0) x1)
     (* x1 (* x2 (- (- 12.0) (/ 6.0 x1)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= -2.1e-9) {
		tmp = x2 * ((x1 * -12.0) - 6.0);
	} else if (x2 <= 4.8e+206) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = x1 * (x2 * (-12.0 - (6.0 / x1)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x2 <= (-2.1d-9)) then
        tmp = x2 * ((x1 * (-12.0d0)) - 6.0d0)
    else if (x2 <= 4.8d+206) then
        tmp = (x2 * (-6.0d0)) - x1
    else
        tmp = x1 * (x2 * (-12.0d0 - (6.0d0 / x1)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x2 <= -2.1e-9) {
		tmp = x2 * ((x1 * -12.0) - 6.0);
	} else if (x2 <= 4.8e+206) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = x1 * (x2 * (-12.0 - (6.0 / x1)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= -2.1e-9:
		tmp = x2 * ((x1 * -12.0) - 6.0)
	elif x2 <= 4.8e+206:
		tmp = (x2 * -6.0) - x1
	else:
		tmp = x1 * (x2 * (-12.0 - (6.0 / x1)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= -2.1e-9)
		tmp = Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0));
	elseif (x2 <= 4.8e+206)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	else
		tmp = Float64(x1 * Float64(x2 * Float64(Float64(-12.0) - Float64(6.0 / x1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= -2.1e-9)
		tmp = x2 * ((x1 * -12.0) - 6.0);
	elseif (x2 <= 4.8e+206)
		tmp = (x2 * -6.0) - x1;
	else
		tmp = x1 * (x2 * (-12.0 - (6.0 / x1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, -2.1e-9], N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x2, 4.8e+206], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], N[(x1 * N[(x2 * N[((-12.0) - N[(6.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -2.10000000000000019e-9

   1. Initial program 79.0%

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

   3. Simplified 79.1%

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

   5. Taylor expanded in x1 around 0 61.5%

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

      1. fma-define 61.6%

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

      2. associate-*r* 61.6%

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

      3. fma-neg 61.6%

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

      4. fma-neg 61.6%

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

      5. metadata-eval 61.6%

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

      6. metadata-eval 61.6%

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

   7. Simplified 61.6%

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

   8. Taylor expanded in x2 around 0 39.5%

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

   9. Taylor expanded in x2 around inf 39.6%

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

   if -2.10000000000000019e-9 < x2 < 4.7999999999999999e206

   1. Initial program 76.0%

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

   3. Simplified 76.2%

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

   5. Taylor expanded in x1 around 0 50.4%

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

      1. fma-define 50.5%

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

      2. associate-*r* 50.5%

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

      3. fma-neg 50.5%

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

      4. fma-neg 50.5%

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

      5. metadata-eval 50.5%

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

      6. metadata-eval 50.5%

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

   7. Simplified 50.5%

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

   8. Taylor expanded in x2 around 0 47.1%

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

   9. Taylor expanded in x1 around 0 47.1%

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

   if 4.7999999999999999e206 < x2

   1. Initial program 61.1%

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

   3. Simplified 61.1%

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

   5. Taylor expanded in x1 around 0 61.6%

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

      1. fma-define 61.6%

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

      2. associate-*r* 61.6%

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

      3. fma-neg 61.6%

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

      4. fma-neg 61.6%

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

      5. metadata-eval 61.6%

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

      6. metadata-eval 61.6%

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

   7. Simplified 61.6%

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

   8. Taylor expanded in x2 around 0 36.0%

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

   9. Taylor expanded in x1 around inf 50.8%

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

   10. Taylor expanded in x2 around inf 50.8%

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

       1. associate-*r* 50.8%

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

       2. neg-mul-1 50.8%

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

       3. associate-*r/ 50.8%

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

       4. metadata-eval 50.8%

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

   12. Simplified 50.8%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -2.1 \cdot 10^{-9}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right)\\ \mathbf{elif}\;x2 \leq 4.8 \cdot 10^{+206}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot \left(\left(-12\right) - \frac{6}{x1}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 37.4% accurate, 7.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -8.5 \cdot 10^{-236} \lor \neg \left(x2 \leq 1.36 \cdot 10^{-120}\right):\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -8.5e-236) (not (<= x2 1.36e-120)))
   (* x2 (- (* x1 -12.0) 6.0))
   (* x1 (+ -1.0 (* x2 -12.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -8.5e-236) || !(x2 <= 1.36e-120)) {
		tmp = x2 * ((x1 * -12.0) - 6.0);
	} else {
		tmp = x1 * (-1.0 + (x2 * -12.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-8.5d-236)) .or. (.not. (x2 <= 1.36d-120))) then
        tmp = x2 * ((x1 * (-12.0d0)) - 6.0d0)
    else
        tmp = x1 * ((-1.0d0) + (x2 * (-12.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -8.5e-236) || !(x2 <= 1.36e-120)) {
		tmp = x2 * ((x1 * -12.0) - 6.0);
	} else {
		tmp = x1 * (-1.0 + (x2 * -12.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -8.5e-236) or not (x2 <= 1.36e-120):
		tmp = x2 * ((x1 * -12.0) - 6.0)
	else:
		tmp = x1 * (-1.0 + (x2 * -12.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -8.5e-236) || !(x2 <= 1.36e-120))
		tmp = Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0));
	else
		tmp = Float64(x1 * Float64(-1.0 + Float64(x2 * -12.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -8.5e-236) || ~((x2 <= 1.36e-120)))
		tmp = x2 * ((x1 * -12.0) - 6.0);
	else
		tmp = x1 * (-1.0 + (x2 * -12.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -8.5e-236], N[Not[LessEqual[x2, 1.36e-120]], $MachinePrecision]], N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision], N[(x1 * N[(-1.0 + N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -8.49999999999999929e-236 or 1.36000000000000001e-120 < x2

   1. Initial program 74.6%

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

   3. Simplified 74.6%

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

   5. Taylor expanded in x1 around 0 54.9%

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

      1. fma-define 55.0%

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

      2. associate-*r* 55.0%

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

      3. fma-neg 55.0%

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

      4. fma-neg 55.0%

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

      5. metadata-eval 55.0%

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

      6. metadata-eval 55.0%

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

   7. Simplified 55.0%

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

   8. Taylor expanded in x2 around 0 42.7%

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

   9. Taylor expanded in x2 around inf 37.4%

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

   if -8.49999999999999929e-236 < x2 < 1.36000000000000001e-120

   1. Initial program 80.2%

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

   3. Simplified 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 50.8%

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

      1. fma-define 50.8%

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

      2. associate-*r* 50.8%

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

      3. fma-neg 50.8%

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

      4. fma-neg 50.8%

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

      5. metadata-eval 50.8%

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

      6. metadata-eval 50.8%

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

   7. Simplified 50.8%

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

   8. Taylor expanded in x2 around 0 50.8%

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

   9. Taylor expanded in x1 around inf 40.7%

      \[\leadsto \color{blue}{x1 \cdot \left(-12 \cdot x2 - 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -8.5 \cdot 10^{-236} \lor \neg \left(x2 \leq 1.36 \cdot 10^{-120}\right):\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 36.0% accurate, 7.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -5.2 \cdot 10^{-109} \lor \neg \left(x1 \leq 5 \cdot 10^{-102}\right):\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -5.2e-109) (not (<= x1 5e-102)))
   (* x1 (+ -1.0 (* x2 -12.0)))
   (* x2 -6.0)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -5.2e-109) || !(x1 <= 5e-102)) {
		tmp = x1 * (-1.0 + (x2 * -12.0));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-5.2d-109)) .or. (.not. (x1 <= 5d-102))) then
        tmp = x1 * ((-1.0d0) + (x2 * (-12.0d0)))
    else
        tmp = x2 * (-6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -5.2e-109) || !(x1 <= 5e-102)) {
		tmp = x1 * (-1.0 + (x2 * -12.0));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -5.2e-109) or not (x1 <= 5e-102):
		tmp = x1 * (-1.0 + (x2 * -12.0))
	else:
		tmp = x2 * -6.0
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -5.2e-109) || !(x1 <= 5e-102))
		tmp = Float64(x1 * Float64(-1.0 + Float64(x2 * -12.0)));
	else
		tmp = Float64(x2 * -6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -5.2e-109) || ~((x1 <= 5e-102)))
		tmp = x1 * (-1.0 + (x2 * -12.0));
	else
		tmp = x2 * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -5.2e-109], N[Not[LessEqual[x1, 5e-102]], $MachinePrecision]], N[(x1 * N[(-1.0 + N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * -6.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -5.1999999999999997e-109 or 5.00000000000000026e-102 < x1

   1. Initial program 63.2%

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

   3. Simplified 63.4%

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

   5. Taylor expanded in x1 around 0 38.0%

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

      1. fma-define 38.0%

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

      2. associate-*r* 38.0%

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

      3. fma-neg 38.0%

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

      4. fma-neg 38.0%

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

      5. metadata-eval 38.0%

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

      6. metadata-eval 38.0%

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

   7. Simplified 38.0%

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

   8. Taylor expanded in x2 around 0 28.0%

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

   9. Taylor expanded in x1 around inf 21.4%

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

   if -5.1999999999999997e-109 < x1 < 5.00000000000000026e-102

   1. Initial program 99.6%

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

   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 66.0%

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

      1. *-commutative 66.0%

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

   7. Simplified 66.0%

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

4. Final simplification 36.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.2 \cdot 10^{-109} \lor \neg \left(x1 \leq 5 \cdot 10^{-102}\right):\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 44.3% accurate, 7.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -3.4 \cdot 10^{-25}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{elif}\;x1 \leq 220000:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -3.4e-25)
   (* x1 (+ -1.0 (* x2 -12.0)))
   (if (<= x1 220000.0) (- (* x2 -6.0) x1) (* x2 (- (* x1 -12.0) 6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3.4e-25) {
		tmp = x1 * (-1.0 + (x2 * -12.0));
	} else if (x1 <= 220000.0) {
		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 <= (-3.4d-25)) then
        tmp = x1 * ((-1.0d0) + (x2 * (-12.0d0)))
    else if (x1 <= 220000.0d0) 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 <= -3.4e-25) {
		tmp = x1 * (-1.0 + (x2 * -12.0));
	} else if (x1 <= 220000.0) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = x2 * ((x1 * -12.0) - 6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -3.4e-25:
		tmp = x1 * (-1.0 + (x2 * -12.0))
	elif x1 <= 220000.0:
		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 <= -3.4e-25)
		tmp = Float64(x1 * Float64(-1.0 + Float64(x2 * -12.0)));
	elseif (x1 <= 220000.0)
		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 <= -3.4e-25)
		tmp = x1 * (-1.0 + (x2 * -12.0));
	elseif (x1 <= 220000.0)
		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, -3.4e-25], N[(x1 * N[(-1.0 + N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 220000.0], 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 3 regimes

2. if x1 < -3.40000000000000002e-25

   1. Initial program 46.7%

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

   3. Simplified 46.7%

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

   5. Taylor expanded in x1 around 0 17.4%

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

      1. fma-define 17.4%

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

      2. associate-*r* 17.4%

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

      3. fma-neg 17.4%

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

      4. fma-neg 17.4%

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

      5. metadata-eval 17.4%

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

      6. metadata-eval 17.4%

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

   7. Simplified 17.4%

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

   8. Taylor expanded in x2 around 0 19.4%

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

   9. Taylor expanded in x1 around inf 19.6%

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

   if -3.40000000000000002e-25 < x1 < 2.2e5

   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 99.7%

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

   5. Taylor expanded in x1 around 0 86.7%

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

      1. fma-define 86.8%

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

      2. associate-*r* 86.8%

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

      3. fma-neg 86.8%

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

      4. fma-neg 86.8%

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

      5. metadata-eval 86.8%

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

      6. metadata-eval 86.8%

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

   7. Simplified 86.8%

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

   8. Taylor expanded in x2 around 0 74.1%

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

   9. Taylor expanded in x1 around 0 74.1%

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

   if 2.2e5 < x1

   1. Initial program 57.7%

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

   3. Simplified 57.7%

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

   5. Taylor expanded in x1 around 0 25.9%

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

      1. fma-define 25.9%

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

      2. associate-*r* 25.9%

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

      3. fma-neg 25.9%

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

      4. fma-neg 25.9%

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

      5. metadata-eval 25.9%

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

      6. metadata-eval 25.9%

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

   7. Simplified 25.9%

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

   8. Taylor expanded in x2 around 0 9.6%

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

   9. Taylor expanded in x2 around inf 10.6%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.4 \cdot 10^{-25}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{elif}\;x1 \leq 220000:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 56.6% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq 1.95 \cdot 10^{-151}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 - \frac{x1}{x2}\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot \left(x2 \cdot 8 - 12\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 1.95e-151)
   (* x2 (- (- (* x1 -12.0) (/ x1 x2)) 6.0))
   (* x1 (+ -1.0 (* x2 (- (* x2 8.0) 12.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= 1.95e-151) {
		tmp = x2 * (((x1 * -12.0) - (x1 / x2)) - 6.0);
	} else {
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= 1.95d-151) then
        tmp = x2 * (((x1 * (-12.0d0)) - (x1 / x2)) - 6.0d0)
    else
        tmp = x1 * ((-1.0d0) + (x2 * ((x2 * 8.0d0) - 12.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= 1.95e-151) {
		tmp = x2 * (((x1 * -12.0) - (x1 / x2)) - 6.0);
	} else {
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= 1.95e-151:
		tmp = x2 * (((x1 * -12.0) - (x1 / x2)) - 6.0)
	else:
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= 1.95e-151)
		tmp = Float64(x2 * Float64(Float64(Float64(x1 * -12.0) - Float64(x1 / x2)) - 6.0));
	else
		tmp = Float64(x1 * Float64(-1.0 + Float64(x2 * Float64(Float64(x2 * 8.0) - 12.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= 1.95e-151)
		tmp = x2 * (((x1 * -12.0) - (x1 / x2)) - 6.0);
	else
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, 1.95e-151], N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] - N[(x1 / x2), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision], N[(x1 * N[(-1.0 + N[(x2 * N[(N[(x2 * 8.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < 1.95000000000000003e-151

   1. Initial program 77.8%

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

   3. Simplified 78.0%

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

   5. Taylor expanded in x1 around 0 57.2%

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

      1. fma-define 57.3%

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

      2. associate-*r* 57.3%

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

      3. fma-neg 57.3%

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

      4. fma-neg 57.3%

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

      5. metadata-eval 57.3%

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

      6. metadata-eval 57.3%

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

   7. Simplified 57.3%

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

   8. Taylor expanded in x2 around 0 55.5%

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

   9. Taylor expanded in x2 around inf 62.4%

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

   if 1.95000000000000003e-151 < x1

   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 72.3%

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

   5. Taylor expanded in x1 around 0 48.7%

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

      1. fma-define 48.7%

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

      2. associate-*r* 48.7%

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

      3. fma-neg 48.7%

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

      4. fma-neg 48.7%

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

      5. metadata-eval 48.7%

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

      6. metadata-eval 48.7%

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

   7. Simplified 48.7%

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

   8. Taylor expanded in x2 around 0 48.7%

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

   9. Taylor expanded in x1 around inf 40.9%

      \[\leadsto \color{blue}{x1 \cdot \left(x2 \cdot \left(8 \cdot x2 - 12\right) - 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq 1.95 \cdot 10^{-151}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 - \frac{x1}{x2}\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot \left(x2 \cdot 8 - 12\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 51.3% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq 1.95 \cdot 10^{-151}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot \left(x2 \cdot 8 - 12\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 1.95e-151)
   (- (* x2 (- (* x1 -12.0) 6.0)) x1)
   (* x1 (+ -1.0 (* x2 (- (* x2 8.0) 12.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= 1.95e-151) {
		tmp = (x2 * ((x1 * -12.0) - 6.0)) - x1;
	} else {
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= 1.95d-151) then
        tmp = (x2 * ((x1 * (-12.0d0)) - 6.0d0)) - x1
    else
        tmp = x1 * ((-1.0d0) + (x2 * ((x2 * 8.0d0) - 12.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= 1.95e-151) {
		tmp = (x2 * ((x1 * -12.0) - 6.0)) - x1;
	} else {
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= 1.95e-151:
		tmp = (x2 * ((x1 * -12.0) - 6.0)) - x1
	else:
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= 1.95e-151)
		tmp = Float64(Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)) - x1);
	else
		tmp = Float64(x1 * Float64(-1.0 + Float64(x2 * Float64(Float64(x2 * 8.0) - 12.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= 1.95e-151)
		tmp = (x2 * ((x1 * -12.0) - 6.0)) - x1;
	else
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, 1.95e-151], N[(N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], N[(x1 * N[(-1.0 + N[(x2 * N[(N[(x2 * 8.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < 1.95000000000000003e-151

   1. Initial program 77.8%

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

   3. Simplified 78.0%

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

   5. Taylor expanded in x1 around 0 57.2%

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

      1. fma-define 57.3%

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

      2. associate-*r* 57.3%

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

      3. fma-neg 57.3%

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

      4. fma-neg 57.3%

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

      5. metadata-eval 57.3%

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

      6. metadata-eval 57.3%

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

   7. Simplified 57.3%

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

   8. Taylor expanded in x2 around 0 55.5%

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

   if 1.95000000000000003e-151 < x1

   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 72.3%

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

   5. Taylor expanded in x1 around 0 48.7%

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

      1. fma-define 48.7%

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

      2. associate-*r* 48.7%

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

      3. fma-neg 48.7%

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

      4. fma-neg 48.7%

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

      5. metadata-eval 48.7%

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

      6. metadata-eval 48.7%

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

   7. Simplified 48.7%

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

   8. Taylor expanded in x2 around 0 48.7%

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

   9. Taylor expanded in x1 around inf 40.9%

      \[\leadsto \color{blue}{x1 \cdot \left(x2 \cdot \left(8 \cdot x2 - 12\right) - 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq 1.95 \cdot 10^{-151}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot \left(x2 \cdot 8 - 12\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 31.2% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -8.5 \cdot 10^{-236} \lor \neg \left(x2 \leq 4.2 \cdot 10^{-120}\right):\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -8.5e-236) (not (<= x2 4.2e-120))) (* x2 -6.0) (- x1)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -8.5e-236) || !(x2 <= 4.2e-120)) {
		tmp = x2 * -6.0;
	} else {
		tmp = -x1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-8.5d-236)) .or. (.not. (x2 <= 4.2d-120))) then
        tmp = x2 * (-6.0d0)
    else
        tmp = -x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -8.5e-236) || !(x2 <= 4.2e-120)) {
		tmp = x2 * -6.0;
	} else {
		tmp = -x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -8.5e-236) or not (x2 <= 4.2e-120):
		tmp = x2 * -6.0
	else:
		tmp = -x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -8.5e-236) || !(x2 <= 4.2e-120))
		tmp = Float64(x2 * -6.0);
	else
		tmp = Float64(-x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -8.5e-236) || ~((x2 <= 4.2e-120)))
		tmp = x2 * -6.0;
	else
		tmp = -x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -8.5e-236], N[Not[LessEqual[x2, 4.2e-120]], $MachinePrecision]], N[(x2 * -6.0), $MachinePrecision], (-x1)]

Derivation

1. Split input into 2 regimes

2. if x2 < -8.49999999999999929e-236 or 4.2000000000000001e-120 < x2

   1. Initial program 74.6%

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

   3. Simplified 74.6%

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

   5. Taylor expanded in x1 around 0 30.9%

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

      1. *-commutative 30.9%

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

   7. Simplified 30.9%

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

   if -8.49999999999999929e-236 < x2 < 4.2000000000000001e-120

   1. Initial program 80.2%

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

   3. Simplified 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 50.8%

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

      1. fma-define 50.8%

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

      2. associate-*r* 50.8%

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

      3. fma-neg 50.8%

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

      4. fma-neg 50.8%

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

      5. metadata-eval 50.8%

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

      6. metadata-eval 50.8%

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

   7. Simplified 50.8%

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

   8. Taylor expanded in x2 around 0 50.8%

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

   9. Taylor expanded in x2 around 0 40.7%

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

       1. neg-mul-1 40.7%

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

   11. Simplified 40.7%

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

4. Final simplification 33.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -8.5 \cdot 10^{-236} \lor \neg \left(x2 \leq 4.2 \cdot 10^{-120}\right):\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 13.8% accurate, 63.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x1, x2):
	return -x1

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 75.7%

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

3. Simplified 75.9%

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

5. Taylor expanded in x1 around 0 54.1%

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

   1. fma-define 54.1%

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

   2. associate-*r* 54.1%

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

   3. fma-neg 54.1%

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

   4. fma-neg 54.1%

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

   5. metadata-eval 54.1%

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

   6. metadata-eval 54.1%

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

7. Simplified 54.1%

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

8. Taylor expanded in x2 around 0 44.3%

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

9. Taylor expanded in x2 around 0 13.0%

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

    1. neg-mul-1 13.0%

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

11. Simplified 13.0%

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

Reproduce

herbie shell --seed 2024146 
(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))))))