Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.6% → 99.7%

Time: 33.4s

Alternatives: 23

Speedup: 5.3×

• 46.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 70.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   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%

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

   6. Taylor expanded in x1 around 0 100.0%

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

4. Final simplification 99.7%

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

Alternative 2: 99.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 - (2.0 * x2);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	double t_4 = x1 + ((x1 + (((t_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + (t_1 * t_3)) + (x1 * (x1 * x1)))) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)));
	double tmp;
	if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else {
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_0)))) - (x1 * (((4.0 * t_0) + (x1 * (3.0 - (x1 * 6.0)))) - 9.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 - (2.0 * x2)
	t_1 = x1 * (x1 * 3.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2
	t_4 = x1 + ((x1 + (((t_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + (t_1 * t_3)) + (x1 * (x1 * x1)))) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)))
	tmp = 0
	if t_4 <= math.inf:
		tmp = t_4
	else:
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_0)))) - (x1 * (((4.0 * t_0) + (x1 * (3.0 - (x1 * 6.0)))) - 9.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 - Float64(2.0 * x2))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_2)
	t_4 = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_2 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(t_3 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0)))) + Float64(t_1 * t_3)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2))))
	tmp = 0.0
	if (t_4 <= Inf)
		tmp = t_4;
	else
		tmp = Float64(x1 * Float64(Float64(-1.0 - Float64(-2.0 * Float64(1.0 - Float64(3.0 * t_0)))) - Float64(x1 * Float64(Float64(Float64(4.0 * t_0) + Float64(x1 * Float64(3.0 - Float64(x1 * 6.0)))) - 9.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 - (2.0 * x2);
	t_1 = x1 * (x1 * 3.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	t_4 = x1 + ((x1 + (((t_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + (t_1 * t_3)) + (x1 * (x1 * x1)))) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)));
	tmp = 0.0;
	if (t_4 <= Inf)
		tmp = t_4;
	else
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_0)))) - (x1 * (((4.0 * t_0) + (x1 * (3.0 - (x1 * 6.0)))) - 9.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$2 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, Infinity], t$95$4, N[(x1 * N[(N[(-1.0 - N[(-2.0 * N[(1.0 - N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(N[(N[(4.0 * t$95$0), $MachinePrecision] + N[(x1 * N[(3.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 9.0), $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 -inf 100.0%

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

   6. Taylor expanded in x1 around 0 100.0%

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

4. Final simplification 99.5%

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

Alternative 3: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 - 2 \cdot x2\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 \cdot \left(x1 \cdot x1\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := \left(t\_3 + 2 \cdot x2\right) - x1\\ t_5 := \frac{t\_4}{t\_1}\\ t_6 := \left(x1 \cdot x1\right) \cdot \left(t\_5 \cdot 4 - 6\right)\\ t_7 := t\_5 - 3\\ \mathbf{if}\;x1 \leq -9.2 \cdot 10^{+49}:\\ \;\;\;\;x1 \cdot \left(\left(-1 - -2 \cdot \left(1 - 3 \cdot t\_0\right)\right) - x1 \cdot \left(\left(4 \cdot t\_0 + x1 \cdot \left(3 - x1 \cdot 6\right)\right) - 9\right)\right)\\ \mathbf{elif}\;x1 \leq 1.5 \cdot 10^{-8}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_3 - 2 \cdot x2\right) - x1}{t\_1} + \left(x1 + \left(t\_2 - \left(t\_3 \cdot \frac{t\_4}{-1 - x1 \cdot x1} + t\_1 \cdot \left(t\_7 \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x1 - 2 \cdot x2\right)\right) - t\_6\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(t\_2 + \left(t\_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_5\right) \cdot t\_7 + t\_6\right) + t\_3 \cdot \left(3 - \frac{1 + \frac{t\_0}{x1}}{x1}\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- 3.0 (* 2.0 x2)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* x1 (* x1 x1)))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (- (+ t_3 (* 2.0 x2)) x1))
        (t_5 (/ t_4 t_1))
        (t_6 (* (* x1 x1) (- (* t_5 4.0) 6.0)))
        (t_7 (- t_5 3.0)))
   (if (<= x1 -9.2e+49)
     (*
      x1
      (-
       (- -1.0 (* -2.0 (- 1.0 (* 3.0 t_0))))
       (* x1 (- (+ (* 4.0 t_0) (* x1 (- 3.0 (* x1 6.0)))) 9.0))))
     (if (<= x1 1.5e-8)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_3 (* 2.0 x2)) x1) t_1))
         (+
          x1
          (-
           t_2
           (+
            (* t_3 (/ t_4 (- -1.0 (* x1 x1))))
            (* t_1 (- (* t_7 (* (* x1 2.0) (- x1 (* 2.0 x2)))) t_6)))))))
       (if (<= x1 5e+153)
         (+
          x1
          (+
           9.0
           (+
            x1
            (+
             t_2
             (+
              (* t_1 (+ (* (* (* x1 2.0) t_5) t_7) t_6))
              (* t_3 (- 3.0 (/ (+ 1.0 (/ t_0 x1)) x1))))))))
         (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 9.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 - (2.0 * x2);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = (t_3 + (2.0 * x2)) - x1;
	double t_5 = t_4 / t_1;
	double t_6 = (x1 * x1) * ((t_5 * 4.0) - 6.0);
	double t_7 = t_5 - 3.0;
	double tmp;
	if (x1 <= -9.2e+49) {
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_0)))) - (x1 * (((4.0 * t_0) + (x1 * (3.0 - (x1 * 6.0)))) - 9.0)));
	} else if (x1 <= 1.5e-8) {
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_1)) + (x1 + (t_2 - ((t_3 * (t_4 / (-1.0 - (x1 * x1)))) + (t_1 * ((t_7 * ((x1 * 2.0) * (x1 - (2.0 * x2)))) - t_6))))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + (9.0 + (x1 + (t_2 + ((t_1 * ((((x1 * 2.0) * t_5) * t_7) + t_6)) + (t_3 * (3.0 - ((1.0 + (t_0 / x1)) / x1)))))));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: 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 = 3.0d0 - (2.0d0 * x2)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = x1 * (x1 * x1)
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = (t_3 + (2.0d0 * x2)) - x1
    t_5 = t_4 / t_1
    t_6 = (x1 * x1) * ((t_5 * 4.0d0) - 6.0d0)
    t_7 = t_5 - 3.0d0
    if (x1 <= (-9.2d+49)) then
        tmp = x1 * (((-1.0d0) - ((-2.0d0) * (1.0d0 - (3.0d0 * t_0)))) - (x1 * (((4.0d0 * t_0) + (x1 * (3.0d0 - (x1 * 6.0d0)))) - 9.0d0)))
    else if (x1 <= 1.5d-8) then
        tmp = x1 + ((3.0d0 * (((t_3 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + (t_2 - ((t_3 * (t_4 / ((-1.0d0) - (x1 * x1)))) + (t_1 * ((t_7 * ((x1 * 2.0d0) * (x1 - (2.0d0 * x2)))) - t_6))))))
    else if (x1 <= 5d+153) then
        tmp = x1 + (9.0d0 + (x1 + (t_2 + ((t_1 * ((((x1 * 2.0d0) * t_5) * t_7) + t_6)) + (t_3 * (3.0d0 - ((1.0d0 + (t_0 / x1)) / x1)))))))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * 9.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 - (2.0 * x2);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = (t_3 + (2.0 * x2)) - x1;
	double t_5 = t_4 / t_1;
	double t_6 = (x1 * x1) * ((t_5 * 4.0) - 6.0);
	double t_7 = t_5 - 3.0;
	double tmp;
	if (x1 <= -9.2e+49) {
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_0)))) - (x1 * (((4.0 * t_0) + (x1 * (3.0 - (x1 * 6.0)))) - 9.0)));
	} else if (x1 <= 1.5e-8) {
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_1)) + (x1 + (t_2 - ((t_3 * (t_4 / (-1.0 - (x1 * x1)))) + (t_1 * ((t_7 * ((x1 * 2.0) * (x1 - (2.0 * x2)))) - t_6))))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + (9.0 + (x1 + (t_2 + ((t_1 * ((((x1 * 2.0) * t_5) * t_7) + t_6)) + (t_3 * (3.0 - ((1.0 + (t_0 / x1)) / x1)))))));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 - (2.0 * x2)
	t_1 = (x1 * x1) + 1.0
	t_2 = x1 * (x1 * x1)
	t_3 = x1 * (x1 * 3.0)
	t_4 = (t_3 + (2.0 * x2)) - x1
	t_5 = t_4 / t_1
	t_6 = (x1 * x1) * ((t_5 * 4.0) - 6.0)
	t_7 = t_5 - 3.0
	tmp = 0
	if x1 <= -9.2e+49:
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_0)))) - (x1 * (((4.0 * t_0) + (x1 * (3.0 - (x1 * 6.0)))) - 9.0)))
	elif x1 <= 1.5e-8:
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_1)) + (x1 + (t_2 - ((t_3 * (t_4 / (-1.0 - (x1 * x1)))) + (t_1 * ((t_7 * ((x1 * 2.0) * (x1 - (2.0 * x2)))) - t_6))))))
	elif x1 <= 5e+153:
		tmp = x1 + (9.0 + (x1 + (t_2 + ((t_1 * ((((x1 * 2.0) * t_5) * t_7) + t_6)) + (t_3 * (3.0 - ((1.0 + (t_0 / x1)) / x1)))))))
	else:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 - Float64(2.0 * x2))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(x1 * Float64(x1 * x1))
	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_1)
	t_6 = Float64(Float64(x1 * x1) * Float64(Float64(t_5 * 4.0) - 6.0))
	t_7 = Float64(t_5 - 3.0)
	tmp = 0.0
	if (x1 <= -9.2e+49)
		tmp = Float64(x1 * Float64(Float64(-1.0 - Float64(-2.0 * Float64(1.0 - Float64(3.0 * t_0)))) - Float64(x1 * Float64(Float64(Float64(4.0 * t_0) + Float64(x1 * Float64(3.0 - Float64(x1 * 6.0)))) - 9.0))));
	elseif (x1 <= 1.5e-8)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_3 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(t_2 - Float64(Float64(t_3 * Float64(t_4 / Float64(-1.0 - Float64(x1 * x1)))) + Float64(t_1 * Float64(Float64(t_7 * Float64(Float64(x1 * 2.0) * Float64(x1 - Float64(2.0 * x2)))) - t_6)))))));
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_2 + Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_5) * t_7) + t_6)) + Float64(t_3 * Float64(3.0 - Float64(Float64(1.0 + Float64(t_0 / x1)) / x1))))))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 - (2.0 * x2);
	t_1 = (x1 * x1) + 1.0;
	t_2 = x1 * (x1 * x1);
	t_3 = x1 * (x1 * 3.0);
	t_4 = (t_3 + (2.0 * x2)) - x1;
	t_5 = t_4 / t_1;
	t_6 = (x1 * x1) * ((t_5 * 4.0) - 6.0);
	t_7 = t_5 - 3.0;
	tmp = 0.0;
	if (x1 <= -9.2e+49)
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_0)))) - (x1 * (((4.0 * t_0) + (x1 * (3.0 - (x1 * 6.0)))) - 9.0)));
	elseif (x1 <= 1.5e-8)
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_1)) + (x1 + (t_2 - ((t_3 * (t_4 / (-1.0 - (x1 * x1)))) + (t_1 * ((t_7 * ((x1 * 2.0) * (x1 - (2.0 * x2)))) - t_6))))));
	elseif (x1 <= 5e+153)
		tmp = x1 + (9.0 + (x1 + (t_2 + ((t_1 * ((((x1 * 2.0) * t_5) * t_7) + t_6)) + (t_3 * (3.0 - ((1.0 + (t_0 / x1)) / x1)))))));
	else
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / t$95$1), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$5 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$5 - 3.0), $MachinePrecision]}, If[LessEqual[x1, -9.2e+49], N[(x1 * N[(N[(-1.0 - N[(-2.0 * N[(1.0 - N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(N[(N[(4.0 * t$95$0), $MachinePrecision] + N[(x1 * N[(3.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.5e-8], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$3 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$2 - N[(N[(t$95$3 * N[(t$95$4 / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(N[(t$95$7 * N[(N[(x1 * 2.0), $MachinePrecision] * N[(x1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], N[(x1 + N[(9.0 + N[(x1 + N[(t$95$2 + N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$5), $MachinePrecision] * t$95$7), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 * N[(3.0 - N[(N[(1.0 + N[(t$95$0 / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -9.20000000000000008e49

   1. Initial program 28.6%

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

   3. Simplified 28.6%

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

   5. Taylor expanded in x1 around -inf 99.9%

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

   6. Taylor expanded in x1 around 0 99.9%

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

   if -9.20000000000000008e49 < x1 < 1.49999999999999987e-8

   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 98.4%

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

      1. +-commutative 98.4%

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

      2. mul-1-neg 98.4%

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

      3. unsub-neg 98.4%

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

   5. Simplified 98.4%

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

   if 1.49999999999999987e-8 < x1 < 5.00000000000000018e153

   1. Initial program 99.2%

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

   3. Taylor expanded in x1 around inf 95.8%

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

   4. Taylor expanded in x1 around -inf 99.1%

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

   if 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 90.3%

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

   6. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9.2 \cdot 10^{+49}:\\ \;\;\;\;x1 \cdot \left(\left(-1 - -2 \cdot \left(1 - 3 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1 \cdot \left(\left(4 \cdot \left(3 - 2 \cdot x2\right) + x1 \cdot \left(3 - x1 \cdot 6\right)\right) - 9\right)\right)\\ \mathbf{elif}\;x1 \leq 1.5 \cdot 10^{-8}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x1 - 2 \cdot x2\right)\right) - \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 - \frac{1 + \frac{3 - 2 \cdot x2}{x1}}{x1}\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 - 2 \cdot x2\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot \left(-1 + x1 \cdot 9\right)\\ t_3 := x1 \cdot x1 + 1\\ t_4 := \frac{\left(t\_1 + 2 \cdot x2\right) - x1}{t\_3}\\ \mathbf{if}\;x1 \leq -1150:\\ \;\;\;\;x1 \cdot \left(\left(-1 - -2 \cdot \left(1 - 3 \cdot t\_0\right)\right) - x1 \cdot \left(\left(4 \cdot t\_0 + x1 \cdot \left(3 - x1 \cdot 6\right)\right) - 9\right)\right)\\ \mathbf{elif}\;x1 \leq 0.3:\\ \;\;\;\;x2 \cdot -6 + \left(t\_2 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t\_3 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_4\right) \cdot \left(t\_4 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t\_4 \cdot 4 - 6\right)\right) + t\_1 \cdot t\_4\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- 3.0 (* 2.0 x2)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (* x1 (+ -1.0 (* x1 9.0))))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (/ (- (+ t_1 (* 2.0 x2)) x1) t_3)))
   (if (<= x1 -1150.0)
     (*
      x1
      (-
       (- -1.0 (* -2.0 (- 1.0 (* 3.0 t_0))))
       (* x1 (- (+ (* 4.0 t_0) (* x1 (- 3.0 (* x1 6.0)))) 9.0))))
     (if (<= x1 0.3)
       (+ (* x2 -6.0) (+ t_2 (* x2 (+ (* x1 -12.0) (* 8.0 (* x1 x2))))))
       (if (<= x1 5e+153)
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               t_3
               (+
                (* (* (* x1 2.0) t_4) (- t_4 3.0))
                (* (* x1 x1) (- (* t_4 4.0) 6.0))))
              (* t_1 t_4))
             (* x1 (* x1 x1))))
           9.0))
         (+ (* x2 -6.0) t_2))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 - (2.0 * x2);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = x1 * (-1.0 + (x1 * 9.0));
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = ((t_1 + (2.0 * x2)) - x1) / t_3;
	double tmp;
	if (x1 <= -1150.0) {
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_0)))) - (x1 * (((4.0 * t_0) + (x1 * (3.0 - (x1 * 6.0)))) - 9.0)));
	} else if (x1 <= 0.3) {
		tmp = (x2 * -6.0) + (t_2 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2)))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + ((x1 + (((t_3 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + (t_1 * t_4)) + (x1 * (x1 * x1)))) + 9.0);
	} else {
		tmp = (x2 * -6.0) + t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = 3.0d0 - (2.0d0 * x2)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = x1 * ((-1.0d0) + (x1 * 9.0d0))
    t_3 = (x1 * x1) + 1.0d0
    t_4 = ((t_1 + (2.0d0 * x2)) - x1) / t_3
    if (x1 <= (-1150.0d0)) then
        tmp = x1 * (((-1.0d0) - ((-2.0d0) * (1.0d0 - (3.0d0 * t_0)))) - (x1 * (((4.0d0 * t_0) + (x1 * (3.0d0 - (x1 * 6.0d0)))) - 9.0d0)))
    else if (x1 <= 0.3d0) then
        tmp = (x2 * (-6.0d0)) + (t_2 + (x2 * ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2)))))
    else if (x1 <= 5d+153) then
        tmp = x1 + ((x1 + (((t_3 * ((((x1 * 2.0d0) * t_4) * (t_4 - 3.0d0)) + ((x1 * x1) * ((t_4 * 4.0d0) - 6.0d0)))) + (t_1 * t_4)) + (x1 * (x1 * x1)))) + 9.0d0)
    else
        tmp = (x2 * (-6.0d0)) + t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 - (2.0 * x2);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = x1 * (-1.0 + (x1 * 9.0));
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = ((t_1 + (2.0 * x2)) - x1) / t_3;
	double tmp;
	if (x1 <= -1150.0) {
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_0)))) - (x1 * (((4.0 * t_0) + (x1 * (3.0 - (x1 * 6.0)))) - 9.0)));
	} else if (x1 <= 0.3) {
		tmp = (x2 * -6.0) + (t_2 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2)))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + ((x1 + (((t_3 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + (t_1 * t_4)) + (x1 * (x1 * x1)))) + 9.0);
	} else {
		tmp = (x2 * -6.0) + t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 - (2.0 * x2)
	t_1 = x1 * (x1 * 3.0)
	t_2 = x1 * (-1.0 + (x1 * 9.0))
	t_3 = (x1 * x1) + 1.0
	t_4 = ((t_1 + (2.0 * x2)) - x1) / t_3
	tmp = 0
	if x1 <= -1150.0:
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_0)))) - (x1 * (((4.0 * t_0) + (x1 * (3.0 - (x1 * 6.0)))) - 9.0)))
	elif x1 <= 0.3:
		tmp = (x2 * -6.0) + (t_2 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2)))))
	elif x1 <= 5e+153:
		tmp = x1 + ((x1 + (((t_3 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + (t_1 * t_4)) + (x1 * (x1 * x1)))) + 9.0)
	else:
		tmp = (x2 * -6.0) + t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 - Float64(2.0 * x2))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0)))
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_3)
	tmp = 0.0
	if (x1 <= -1150.0)
		tmp = Float64(x1 * Float64(Float64(-1.0 - Float64(-2.0 * Float64(1.0 - Float64(3.0 * t_0)))) - Float64(x1 * Float64(Float64(Float64(4.0 * t_0) + Float64(x1 * Float64(3.0 - Float64(x1 * 6.0)))) - 9.0))));
	elseif (x1 <= 0.3)
		tmp = Float64(Float64(x2 * -6.0) + Float64(t_2 + Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))))));
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_3 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(t_4 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_4 * 4.0) - 6.0)))) + Float64(t_1 * t_4)) + Float64(x1 * Float64(x1 * x1)))) + 9.0));
	else
		tmp = Float64(Float64(x2 * -6.0) + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 - (2.0 * x2);
	t_1 = x1 * (x1 * 3.0);
	t_2 = x1 * (-1.0 + (x1 * 9.0));
	t_3 = (x1 * x1) + 1.0;
	t_4 = ((t_1 + (2.0 * x2)) - x1) / t_3;
	tmp = 0.0;
	if (x1 <= -1150.0)
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_0)))) - (x1 * (((4.0 * t_0) + (x1 * (3.0 - (x1 * 6.0)))) - 9.0)));
	elseif (x1 <= 0.3)
		tmp = (x2 * -6.0) + (t_2 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2)))));
	elseif (x1 <= 5e+153)
		tmp = x1 + ((x1 + (((t_3 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + (t_1 * t_4)) + (x1 * (x1 * x1)))) + 9.0);
	else
		tmp = (x2 * -6.0) + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, If[LessEqual[x1, -1150.0], N[(x1 * N[(N[(-1.0 - N[(-2.0 * N[(1.0 - N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(N[(N[(4.0 * t$95$0), $MachinePrecision] + N[(x1 * N[(3.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.3], N[(N[(x2 * -6.0), $MachinePrecision] + N[(t$95$2 + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$3 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$4 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + t$95$2), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1150

   1. Initial program 37.9%

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

   3. Simplified 37.9%

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

   5. Taylor expanded in x1 around -inf 95.4%

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

   6. Taylor expanded in x1 around 0 95.3%

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

   if -1150 < x1 < 0.299999999999999989

   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 85.7%

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

   6. Taylor expanded in x2 around 0 85.7%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\color{blue}{15} - 6\right)\right) - 1\right) \]

   7. Taylor expanded in x2 around 0 99.1%

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

   if 0.299999999999999989 < x1 < 5.00000000000000018e153

   1. Initial program 99.6%

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

   3. Taylor expanded in x1 around inf 99.2%

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

      1. metadata-eval 99.2%

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

   5. Applied egg-rr 99.2%

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

   if 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 90.3%

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

   6. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1150:\\ \;\;\;\;x1 \cdot \left(\left(-1 - -2 \cdot \left(1 - 3 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1 \cdot \left(\left(4 \cdot \left(3 - 2 \cdot x2\right) + x1 \cdot \left(3 - x1 \cdot 6\right)\right) - 9\right)\right)\\ \mathbf{elif}\;x1 \leq 0.3:\\ \;\;\;\;x2 \cdot -6 + \left(x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := 3 - 2 \cdot x2\\ t_3 := x1 \cdot x1 + 1\\ t_4 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_3}\\ t_5 := \left(x1 \cdot x1\right) \cdot \left(t\_4 \cdot 4 - 6\right)\\ t_6 := \left(x1 \cdot 2\right) \cdot t\_4\\ \mathbf{if}\;x1 \leq -4 \cdot 10^{+49}:\\ \;\;\;\;x1 \cdot \left(\left(-1 - -2 \cdot \left(1 - 3 \cdot t\_2\right)\right) - x1 \cdot \left(\left(4 \cdot t\_2 + x1 \cdot \left(3 - x1 \cdot 6\right)\right) - 9\right)\right)\\ \mathbf{elif}\;x1 \leq 1.5 \cdot 10^{-8}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_3} + \left(x1 + \left(t\_1 + \left(t\_0 \cdot t\_4 - \left(t\_5 + t\_6 \cdot \left(2 \cdot x2 - 3\right)\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(t\_1 + \left(t\_3 \cdot \left(t\_6 \cdot \left(t\_4 - 3\right) + t\_5\right) + t\_0 \cdot \left(3 - \frac{1 + \frac{t\_2}{x1}}{x1}\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (* x1 (* x1 x1)))
        (t_2 (- 3.0 (* 2.0 x2)))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (/ (- (+ t_0 (* 2.0 x2)) x1) t_3))
        (t_5 (* (* x1 x1) (- (* t_4 4.0) 6.0)))
        (t_6 (* (* x1 2.0) t_4)))
   (if (<= x1 -4e+49)
     (*
      x1
      (-
       (- -1.0 (* -2.0 (- 1.0 (* 3.0 t_2))))
       (* x1 (- (+ (* 4.0 t_2) (* x1 (- 3.0 (* x1 6.0)))) 9.0))))
     (if (<= x1 1.5e-8)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_3))
         (+
          x1
          (+
           t_1
           (-
            (* t_0 t_4)
            (* (+ t_5 (* t_6 (- (* 2.0 x2) 3.0))) (- -1.0 (* x1 x1))))))))
       (if (<= x1 5e+153)
         (+
          x1
          (+
           9.0
           (+
            x1
            (+
             t_1
             (+
              (* t_3 (+ (* t_6 (- t_4 3.0)) t_5))
              (* t_0 (- 3.0 (/ (+ 1.0 (/ t_2 x1)) x1))))))))
         (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 9.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * (x1 * x1);
	double t_2 = 3.0 - (2.0 * x2);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = ((t_0 + (2.0 * x2)) - x1) / t_3;
	double t_5 = (x1 * x1) * ((t_4 * 4.0) - 6.0);
	double t_6 = (x1 * 2.0) * t_4;
	double tmp;
	if (x1 <= -4e+49) {
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_2)))) - (x1 * (((4.0 * t_2) + (x1 * (3.0 - (x1 * 6.0)))) - 9.0)));
	} else if (x1 <= 1.5e-8) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3)) + (x1 + (t_1 + ((t_0 * t_4) - ((t_5 + (t_6 * ((2.0 * x2) - 3.0))) * (-1.0 - (x1 * x1)))))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + (9.0 + (x1 + (t_1 + ((t_3 * ((t_6 * (t_4 - 3.0)) + t_5)) + (t_0 * (3.0 - ((1.0 + (t_2 / x1)) / x1)))))));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: 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 * 3.0d0)
    t_1 = x1 * (x1 * x1)
    t_2 = 3.0d0 - (2.0d0 * x2)
    t_3 = (x1 * x1) + 1.0d0
    t_4 = ((t_0 + (2.0d0 * x2)) - x1) / t_3
    t_5 = (x1 * x1) * ((t_4 * 4.0d0) - 6.0d0)
    t_6 = (x1 * 2.0d0) * t_4
    if (x1 <= (-4d+49)) then
        tmp = x1 * (((-1.0d0) - ((-2.0d0) * (1.0d0 - (3.0d0 * t_2)))) - (x1 * (((4.0d0 * t_2) + (x1 * (3.0d0 - (x1 * 6.0d0)))) - 9.0d0)))
    else if (x1 <= 1.5d-8) then
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_3)) + (x1 + (t_1 + ((t_0 * t_4) - ((t_5 + (t_6 * ((2.0d0 * x2) - 3.0d0))) * ((-1.0d0) - (x1 * x1)))))))
    else if (x1 <= 5d+153) then
        tmp = x1 + (9.0d0 + (x1 + (t_1 + ((t_3 * ((t_6 * (t_4 - 3.0d0)) + t_5)) + (t_0 * (3.0d0 - ((1.0d0 + (t_2 / x1)) / x1)))))))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * 9.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * (x1 * x1);
	double t_2 = 3.0 - (2.0 * x2);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = ((t_0 + (2.0 * x2)) - x1) / t_3;
	double t_5 = (x1 * x1) * ((t_4 * 4.0) - 6.0);
	double t_6 = (x1 * 2.0) * t_4;
	double tmp;
	if (x1 <= -4e+49) {
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_2)))) - (x1 * (((4.0 * t_2) + (x1 * (3.0 - (x1 * 6.0)))) - 9.0)));
	} else if (x1 <= 1.5e-8) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3)) + (x1 + (t_1 + ((t_0 * t_4) - ((t_5 + (t_6 * ((2.0 * x2) - 3.0))) * (-1.0 - (x1 * x1)))))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + (9.0 + (x1 + (t_1 + ((t_3 * ((t_6 * (t_4 - 3.0)) + t_5)) + (t_0 * (3.0 - ((1.0 + (t_2 / x1)) / x1)))))));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = x1 * (x1 * x1)
	t_2 = 3.0 - (2.0 * x2)
	t_3 = (x1 * x1) + 1.0
	t_4 = ((t_0 + (2.0 * x2)) - x1) / t_3
	t_5 = (x1 * x1) * ((t_4 * 4.0) - 6.0)
	t_6 = (x1 * 2.0) * t_4
	tmp = 0
	if x1 <= -4e+49:
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_2)))) - (x1 * (((4.0 * t_2) + (x1 * (3.0 - (x1 * 6.0)))) - 9.0)))
	elif x1 <= 1.5e-8:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3)) + (x1 + (t_1 + ((t_0 * t_4) - ((t_5 + (t_6 * ((2.0 * x2) - 3.0))) * (-1.0 - (x1 * x1)))))))
	elif x1 <= 5e+153:
		tmp = x1 + (9.0 + (x1 + (t_1 + ((t_3 * ((t_6 * (t_4 - 3.0)) + t_5)) + (t_0 * (3.0 - ((1.0 + (t_2 / x1)) / x1)))))))
	else:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(x1 * Float64(x1 * x1))
	t_2 = Float64(3.0 - Float64(2.0 * x2))
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_3)
	t_5 = Float64(Float64(x1 * x1) * Float64(Float64(t_4 * 4.0) - 6.0))
	t_6 = Float64(Float64(x1 * 2.0) * t_4)
	tmp = 0.0
	if (x1 <= -4e+49)
		tmp = Float64(x1 * Float64(Float64(-1.0 - Float64(-2.0 * Float64(1.0 - Float64(3.0 * t_2)))) - Float64(x1 * Float64(Float64(Float64(4.0 * t_2) + Float64(x1 * Float64(3.0 - Float64(x1 * 6.0)))) - 9.0))));
	elseif (x1 <= 1.5e-8)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_3)) + Float64(x1 + Float64(t_1 + Float64(Float64(t_0 * t_4) - Float64(Float64(t_5 + Float64(t_6 * Float64(Float64(2.0 * x2) - 3.0))) * Float64(-1.0 - Float64(x1 * x1))))))));
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_1 + Float64(Float64(t_3 * Float64(Float64(t_6 * Float64(t_4 - 3.0)) + t_5)) + Float64(t_0 * Float64(3.0 - Float64(Float64(1.0 + Float64(t_2 / x1)) / x1))))))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = x1 * (x1 * x1);
	t_2 = 3.0 - (2.0 * x2);
	t_3 = (x1 * x1) + 1.0;
	t_4 = ((t_0 + (2.0 * x2)) - x1) / t_3;
	t_5 = (x1 * x1) * ((t_4 * 4.0) - 6.0);
	t_6 = (x1 * 2.0) * t_4;
	tmp = 0.0;
	if (x1 <= -4e+49)
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_2)))) - (x1 * (((4.0 * t_2) + (x1 * (3.0 - (x1 * 6.0)))) - 9.0)));
	elseif (x1 <= 1.5e-8)
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3)) + (x1 + (t_1 + ((t_0 * t_4) - ((t_5 + (t_6 * ((2.0 * x2) - 3.0))) * (-1.0 - (x1 * x1)))))));
	elseif (x1 <= 5e+153)
		tmp = x1 + (9.0 + (x1 + (t_1 + ((t_3 * ((t_6 * (t_4 - 3.0)) + t_5)) + (t_0 * (3.0 - ((1.0 + (t_2 / x1)) / x1)))))));
	else
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$4 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision]}, If[LessEqual[x1, -4e+49], N[(x1 * N[(N[(-1.0 - N[(-2.0 * N[(1.0 - N[(3.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(N[(N[(4.0 * t$95$2), $MachinePrecision] + N[(x1 * N[(3.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.5e-8], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$1 + N[(N[(t$95$0 * t$95$4), $MachinePrecision] - N[(N[(t$95$5 + N[(t$95$6 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $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 * N[(N[(t$95$6 * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(3.0 - N[(N[(1.0 + N[(t$95$2 / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -3.99999999999999979e49

   1. Initial program 28.6%

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

   3. Simplified 28.6%

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

   5. Taylor expanded in x1 around -inf 99.9%

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

   6. Taylor expanded in x1 around 0 99.9%

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

   if -3.99999999999999979e49 < x1 < 1.49999999999999987e-8

   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 98.3%

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

   if 1.49999999999999987e-8 < x1 < 5.00000000000000018e153

   1. Initial program 99.2%

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

   3. Taylor expanded in x1 around inf 95.8%

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

   4. Taylor expanded in x1 around -inf 99.1%

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

   if 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 90.3%

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

   6. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+49}:\\ \;\;\;\;x1 \cdot \left(\left(-1 - -2 \cdot \left(1 - 3 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1 \cdot \left(\left(4 \cdot \left(3 - 2 \cdot x2\right) + x1 \cdot \left(3 - x1 \cdot 6\right)\right) - 9\right)\right)\\ \mathbf{elif}\;x1 \leq 1.5 \cdot 10^{-8}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(2 \cdot x2 - 3\right)\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 - \frac{1 + \frac{3 - 2 \cdot x2}{x1}}{x1}\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 - 2 \cdot x2\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 \cdot \left(-1 + x1 \cdot 9\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := \left(t\_3 + 2 \cdot x2\right) - x1\\ t_5 := \frac{t\_4}{t\_1}\\ \mathbf{if}\;x1 \leq -68:\\ \;\;\;\;x1 \cdot \left(\left(-1 - -2 \cdot \left(1 - 3 \cdot t\_0\right)\right) - x1 \cdot \left(\left(4 \cdot t\_0 + x1 \cdot \left(3 - x1 \cdot 6\right)\right) - 9\right)\right)\\ \mathbf{elif}\;x1 \leq 1.5 \cdot 10^{-8}:\\ \;\;\;\;x2 \cdot -6 + \left(t\_2 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_3 \cdot \left(3 - \frac{1 + \frac{t\_0}{x1}}{x1}\right) - t\_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_5\right) \cdot \left(3 + \frac{t\_4}{-1 - x1 \cdot x1}\right) - \left(x1 \cdot x1\right) \cdot \left(t\_5 \cdot 4 - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- 3.0 (* 2.0 x2)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* x1 (+ -1.0 (* x1 9.0))))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (- (+ t_3 (* 2.0 x2)) x1))
        (t_5 (/ t_4 t_1)))
   (if (<= x1 -68.0)
     (*
      x1
      (-
       (- -1.0 (* -2.0 (- 1.0 (* 3.0 t_0))))
       (* x1 (- (+ (* 4.0 t_0) (* x1 (- 3.0 (* x1 6.0)))) 9.0))))
     (if (<= x1 1.5e-8)
       (+ (* x2 -6.0) (+ t_2 (* x2 (+ (* x1 -12.0) (* 8.0 (* x1 x2))))))
       (if (<= x1 5e+153)
         (+
          x1
          (+
           9.0
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (-
              (* t_3 (- 3.0 (/ (+ 1.0 (/ t_0 x1)) x1)))
              (*
               t_1
               (-
                (* (* (* x1 2.0) t_5) (+ 3.0 (/ t_4 (- -1.0 (* x1 x1)))))
                (* (* x1 x1) (- (* t_5 4.0) 6.0)))))))))
         (+ (* x2 -6.0) t_2))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 - (2.0 * x2);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 * (-1.0 + (x1 * 9.0));
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = (t_3 + (2.0 * x2)) - x1;
	double t_5 = t_4 / t_1;
	double tmp;
	if (x1 <= -68.0) {
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_0)))) - (x1 * (((4.0 * t_0) + (x1 * (3.0 - (x1 * 6.0)))) - 9.0)));
	} else if (x1 <= 1.5e-8) {
		tmp = (x2 * -6.0) + (t_2 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2)))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_3 * (3.0 - ((1.0 + (t_0 / x1)) / x1))) - (t_1 * ((((x1 * 2.0) * t_5) * (3.0 + (t_4 / (-1.0 - (x1 * x1))))) - ((x1 * x1) * ((t_5 * 4.0) - 6.0))))))));
	} else {
		tmp = (x2 * -6.0) + t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = 3.0d0 - (2.0d0 * x2)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = x1 * ((-1.0d0) + (x1 * 9.0d0))
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = (t_3 + (2.0d0 * x2)) - x1
    t_5 = t_4 / t_1
    if (x1 <= (-68.0d0)) then
        tmp = x1 * (((-1.0d0) - ((-2.0d0) * (1.0d0 - (3.0d0 * t_0)))) - (x1 * (((4.0d0 * t_0) + (x1 * (3.0d0 - (x1 * 6.0d0)))) - 9.0d0)))
    else if (x1 <= 1.5d-8) then
        tmp = (x2 * (-6.0d0)) + (t_2 + (x2 * ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2)))))
    else if (x1 <= 5d+153) then
        tmp = x1 + (9.0d0 + (x1 + ((x1 * (x1 * x1)) + ((t_3 * (3.0d0 - ((1.0d0 + (t_0 / x1)) / x1))) - (t_1 * ((((x1 * 2.0d0) * t_5) * (3.0d0 + (t_4 / ((-1.0d0) - (x1 * x1))))) - ((x1 * x1) * ((t_5 * 4.0d0) - 6.0d0))))))))
    else
        tmp = (x2 * (-6.0d0)) + t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 - (2.0 * x2);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 * (-1.0 + (x1 * 9.0));
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = (t_3 + (2.0 * x2)) - x1;
	double t_5 = t_4 / t_1;
	double tmp;
	if (x1 <= -68.0) {
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_0)))) - (x1 * (((4.0 * t_0) + (x1 * (3.0 - (x1 * 6.0)))) - 9.0)));
	} else if (x1 <= 1.5e-8) {
		tmp = (x2 * -6.0) + (t_2 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2)))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_3 * (3.0 - ((1.0 + (t_0 / x1)) / x1))) - (t_1 * ((((x1 * 2.0) * t_5) * (3.0 + (t_4 / (-1.0 - (x1 * x1))))) - ((x1 * x1) * ((t_5 * 4.0) - 6.0))))))));
	} else {
		tmp = (x2 * -6.0) + t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 - (2.0 * x2)
	t_1 = (x1 * x1) + 1.0
	t_2 = x1 * (-1.0 + (x1 * 9.0))
	t_3 = x1 * (x1 * 3.0)
	t_4 = (t_3 + (2.0 * x2)) - x1
	t_5 = t_4 / t_1
	tmp = 0
	if x1 <= -68.0:
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_0)))) - (x1 * (((4.0 * t_0) + (x1 * (3.0 - (x1 * 6.0)))) - 9.0)))
	elif x1 <= 1.5e-8:
		tmp = (x2 * -6.0) + (t_2 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2)))))
	elif x1 <= 5e+153:
		tmp = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_3 * (3.0 - ((1.0 + (t_0 / x1)) / x1))) - (t_1 * ((((x1 * 2.0) * t_5) * (3.0 + (t_4 / (-1.0 - (x1 * x1))))) - ((x1 * x1) * ((t_5 * 4.0) - 6.0))))))))
	else:
		tmp = (x2 * -6.0) + t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 - Float64(2.0 * x2))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0)))
	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_1)
	tmp = 0.0
	if (x1 <= -68.0)
		tmp = Float64(x1 * Float64(Float64(-1.0 - Float64(-2.0 * Float64(1.0 - Float64(3.0 * t_0)))) - Float64(x1 * Float64(Float64(Float64(4.0 * t_0) + Float64(x1 * Float64(3.0 - Float64(x1 * 6.0)))) - 9.0))));
	elseif (x1 <= 1.5e-8)
		tmp = Float64(Float64(x2 * -6.0) + Float64(t_2 + Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))))));
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_3 * Float64(3.0 - Float64(Float64(1.0 + Float64(t_0 / x1)) / x1))) - Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_5) * Float64(3.0 + Float64(t_4 / Float64(-1.0 - Float64(x1 * x1))))) - Float64(Float64(x1 * x1) * Float64(Float64(t_5 * 4.0) - 6.0)))))))));
	else
		tmp = Float64(Float64(x2 * -6.0) + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 - (2.0 * x2);
	t_1 = (x1 * x1) + 1.0;
	t_2 = x1 * (-1.0 + (x1 * 9.0));
	t_3 = x1 * (x1 * 3.0);
	t_4 = (t_3 + (2.0 * x2)) - x1;
	t_5 = t_4 / t_1;
	tmp = 0.0;
	if (x1 <= -68.0)
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_0)))) - (x1 * (((4.0 * t_0) + (x1 * (3.0 - (x1 * 6.0)))) - 9.0)));
	elseif (x1 <= 1.5e-8)
		tmp = (x2 * -6.0) + (t_2 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2)))));
	elseif (x1 <= 5e+153)
		tmp = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_3 * (3.0 - ((1.0 + (t_0 / x1)) / x1))) - (t_1 * ((((x1 * 2.0) * t_5) * (3.0 + (t_4 / (-1.0 - (x1 * x1))))) - ((x1 * x1) * ((t_5 * 4.0) - 6.0))))))));
	else
		tmp = (x2 * -6.0) + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $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$1), $MachinePrecision]}, If[LessEqual[x1, -68.0], N[(x1 * N[(N[(-1.0 - N[(-2.0 * N[(1.0 - N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(N[(N[(4.0 * t$95$0), $MachinePrecision] + N[(x1 * N[(3.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.5e-8], N[(N[(x2 * -6.0), $MachinePrecision] + N[(t$95$2 + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], N[(x1 + N[(9.0 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$3 * N[(3.0 - N[(N[(1.0 + N[(t$95$0 / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$5), $MachinePrecision] * N[(3.0 + N[(t$95$4 / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$5 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + t$95$2), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -68

   1. Initial program 37.9%

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

   3. Simplified 37.9%

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

   5. Taylor expanded in x1 around -inf 95.4%

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

   6. Taylor expanded in x1 around 0 95.3%

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

   if -68 < x1 < 1.49999999999999987e-8

   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 99.8%

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

   5. Taylor expanded in x1 around 0 86.1%

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

   6. Taylor expanded in x2 around 0 86.1%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\color{blue}{15} - 6\right)\right) - 1\right) \]

   7. Taylor expanded in x2 around 0 99.8%

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

   if 1.49999999999999987e-8 < x1 < 5.00000000000000018e153

   1. Initial program 99.2%

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

   3. Taylor expanded in x1 around inf 95.8%

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

   4. Taylor expanded in x1 around -inf 99.1%

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

   if 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 90.3%

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

   6. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -68:\\ \;\;\;\;x1 \cdot \left(\left(-1 - -2 \cdot \left(1 - 3 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1 \cdot \left(\left(4 \cdot \left(3 - 2 \cdot x2\right) + x1 \cdot \left(3 - x1 \cdot 6\right)\right) - 9\right)\right)\\ \mathbf{elif}\;x1 \leq 1.5 \cdot 10^{-8}:\\ \;\;\;\;x2 \cdot -6 + \left(x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 - \frac{1 + \frac{3 - 2 \cdot x2}{x1}}{x1}\right) - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) - \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 - 2 \cdot x2\\ t_1 := x1 \cdot \left(-1 + x1 \cdot 9\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \frac{\left(t\_2 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\\ \mathbf{if}\;x1 \leq -1650:\\ \;\;\;\;x1 \cdot \left(\left(-1 - -2 \cdot \left(1 - 3 \cdot t\_0\right)\right) - x1 \cdot \left(\left(4 \cdot t\_0 + x1 \cdot \left(3 - x1 \cdot 6\right)\right) - 9\right)\right)\\ \mathbf{elif}\;x1 \leq 1.95:\\ \;\;\;\;x2 \cdot -6 + \left(t\_1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_2 \cdot t\_3 - \left(\left(x1 \cdot x1\right) \cdot \left(t\_3 \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot t\_3\right) \cdot \frac{2 \cdot \frac{x2}{x1} + \left(-1 - \frac{3}{x1}\right)}{x1}\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- 3.0 (* 2.0 x2)))
        (t_1 (* x1 (+ -1.0 (* x1 9.0))))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (/ (- (+ t_2 (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))))
   (if (<= x1 -1650.0)
     (*
      x1
      (-
       (- -1.0 (* -2.0 (- 1.0 (* 3.0 t_0))))
       (* x1 (- (+ (* 4.0 t_0) (* x1 (- 3.0 (* x1 6.0)))) 9.0))))
     (if (<= x1 1.95)
       (+ (* x2 -6.0) (+ t_1 (* x2 (+ (* x1 -12.0) (* 8.0 (* x1 x2))))))
       (if (<= x1 5e+153)
         (+
          x1
          (+
           9.0
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (-
              (* t_2 t_3)
              (*
               (+
                (* (* x1 x1) (- (* t_3 4.0) 6.0))
                (*
                 (* (* x1 2.0) t_3)
                 (/ (+ (* 2.0 (/ x2 x1)) (- -1.0 (/ 3.0 x1))) x1)))
               (- -1.0 (* x1 x1))))))))
         (+ (* x2 -6.0) t_1))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 - (2.0 * x2);
	double t_1 = x1 * (-1.0 + (x1 * 9.0));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = ((t_2 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0);
	double tmp;
	if (x1 <= -1650.0) {
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_0)))) - (x1 * (((4.0 * t_0) + (x1 * (3.0 - (x1 * 6.0)))) - 9.0)));
	} else if (x1 <= 1.95) {
		tmp = (x2 * -6.0) + (t_1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2)))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_3) - ((((x1 * x1) * ((t_3 * 4.0) - 6.0)) + (((x1 * 2.0) * t_3) * (((2.0 * (x2 / x1)) + (-1.0 - (3.0 / x1))) / x1))) * (-1.0 - (x1 * x1)))))));
	} else {
		tmp = (x2 * -6.0) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = 3.0d0 - (2.0d0 * x2)
    t_1 = x1 * ((-1.0d0) + (x1 * 9.0d0))
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = ((t_2 + (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0)
    if (x1 <= (-1650.0d0)) then
        tmp = x1 * (((-1.0d0) - ((-2.0d0) * (1.0d0 - (3.0d0 * t_0)))) - (x1 * (((4.0d0 * t_0) + (x1 * (3.0d0 - (x1 * 6.0d0)))) - 9.0d0)))
    else if (x1 <= 1.95d0) then
        tmp = (x2 * (-6.0d0)) + (t_1 + (x2 * ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2)))))
    else if (x1 <= 5d+153) then
        tmp = x1 + (9.0d0 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_3) - ((((x1 * x1) * ((t_3 * 4.0d0) - 6.0d0)) + (((x1 * 2.0d0) * t_3) * (((2.0d0 * (x2 / x1)) + ((-1.0d0) - (3.0d0 / x1))) / x1))) * ((-1.0d0) - (x1 * x1)))))))
    else
        tmp = (x2 * (-6.0d0)) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 - (2.0 * x2);
	double t_1 = x1 * (-1.0 + (x1 * 9.0));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = ((t_2 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0);
	double tmp;
	if (x1 <= -1650.0) {
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_0)))) - (x1 * (((4.0 * t_0) + (x1 * (3.0 - (x1 * 6.0)))) - 9.0)));
	} else if (x1 <= 1.95) {
		tmp = (x2 * -6.0) + (t_1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2)))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_3) - ((((x1 * x1) * ((t_3 * 4.0) - 6.0)) + (((x1 * 2.0) * t_3) * (((2.0 * (x2 / x1)) + (-1.0 - (3.0 / x1))) / x1))) * (-1.0 - (x1 * x1)))))));
	} else {
		tmp = (x2 * -6.0) + t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 - (2.0 * x2)
	t_1 = x1 * (-1.0 + (x1 * 9.0))
	t_2 = x1 * (x1 * 3.0)
	t_3 = ((t_2 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0)
	tmp = 0
	if x1 <= -1650.0:
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_0)))) - (x1 * (((4.0 * t_0) + (x1 * (3.0 - (x1 * 6.0)))) - 9.0)))
	elif x1 <= 1.95:
		tmp = (x2 * -6.0) + (t_1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2)))))
	elif x1 <= 5e+153:
		tmp = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_3) - ((((x1 * x1) * ((t_3 * 4.0) - 6.0)) + (((x1 * 2.0) * t_3) * (((2.0 * (x2 / x1)) + (-1.0 - (3.0 / x1))) / x1))) * (-1.0 - (x1 * x1)))))))
	else:
		tmp = (x2 * -6.0) + t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 - Float64(2.0 * x2))
	t_1 = Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0)))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(Float64(t_2 + Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))
	tmp = 0.0
	if (x1 <= -1650.0)
		tmp = Float64(x1 * Float64(Float64(-1.0 - Float64(-2.0 * Float64(1.0 - Float64(3.0 * t_0)))) - Float64(x1 * Float64(Float64(Float64(4.0 * t_0) + Float64(x1 * Float64(3.0 - Float64(x1 * 6.0)))) - 9.0))));
	elseif (x1 <= 1.95)
		tmp = Float64(Float64(x2 * -6.0) + Float64(t_1 + Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))))));
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_2 * t_3) - Float64(Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0)) + Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(Float64(Float64(2.0 * Float64(x2 / x1)) + Float64(-1.0 - Float64(3.0 / x1))) / x1))) * Float64(-1.0 - Float64(x1 * x1))))))));
	else
		tmp = Float64(Float64(x2 * -6.0) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 - (2.0 * x2);
	t_1 = x1 * (-1.0 + (x1 * 9.0));
	t_2 = x1 * (x1 * 3.0);
	t_3 = ((t_2 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0);
	tmp = 0.0;
	if (x1 <= -1650.0)
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_0)))) - (x1 * (((4.0 * t_0) + (x1 * (3.0 - (x1 * 6.0)))) - 9.0)));
	elseif (x1 <= 1.95)
		tmp = (x2 * -6.0) + (t_1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2)))));
	elseif (x1 <= 5e+153)
		tmp = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_3) - ((((x1 * x1) * ((t_3 * 4.0) - 6.0)) + (((x1 * 2.0) * t_3) * (((2.0 * (x2 / x1)) + (-1.0 - (3.0 / x1))) / x1))) * (-1.0 - (x1 * x1)))))));
	else
		tmp = (x2 * -6.0) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1650.0], N[(x1 * N[(N[(-1.0 - N[(-2.0 * N[(1.0 - N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(N[(N[(4.0 * t$95$0), $MachinePrecision] + N[(x1 * N[(3.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.95], N[(N[(x2 * -6.0), $MachinePrecision] + N[(t$95$1 + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], N[(x1 + N[(9.0 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * t$95$3), $MachinePrecision] - N[(N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(N[(N[(2.0 * N[(x2 / x1), $MachinePrecision]), $MachinePrecision] + N[(-1.0 - N[(3.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1650

   1. Initial program 37.9%

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

   3. Simplified 37.9%

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

   5. Taylor expanded in x1 around -inf 95.4%

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

   6. Taylor expanded in x1 around 0 95.3%

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

   if -1650 < x1 < 1.94999999999999996

   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 85.7%

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

   6. Taylor expanded in x2 around 0 85.7%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\color{blue}{15} - 6\right)\right) - 1\right) \]

   7. Taylor expanded in x2 around 0 99.1%

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

   if 1.94999999999999996 < x1 < 5.00000000000000018e153

   1. Initial program 99.6%

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

   3. Taylor expanded in x1 around inf 99.2%

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

   4. Taylor expanded in x1 around inf 98.5%

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

      1. associate-*r/ 98.5%

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

      2. metadata-eval 98.5%

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

   6. Simplified 98.5%

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

   if 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 90.3%

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

   6. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1650:\\ \;\;\;\;x1 \cdot \left(\left(-1 - -2 \cdot \left(1 - 3 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1 \cdot \left(\left(4 \cdot \left(3 - 2 \cdot x2\right) + x1 \cdot \left(3 - x1 \cdot 6\right)\right) - 9\right)\right)\\ \mathbf{elif}\;x1 \leq 1.95:\\ \;\;\;\;x2 \cdot -6 + \left(x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \frac{2 \cdot \frac{x2}{x1} + \left(-1 - \frac{3}{x1}\right)}{x1}\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 95.9% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 - 2 \cdot x2\\ \mathbf{if}\;x1 \leq -185 \lor \neg \left(x1 \leq 0.29\right):\\ \;\;\;\;x1 \cdot \left(\left(-1 - -2 \cdot \left(1 - 3 \cdot t\_0\right)\right) - x1 \cdot \left(\left(4 \cdot t\_0 + x1 \cdot \left(3 - x1 \cdot 6\right)\right) - 9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + \left(x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- 3.0 (* 2.0 x2))))
   (if (or (<= x1 -185.0) (not (<= x1 0.29)))
     (*
      x1
      (-
       (- -1.0 (* -2.0 (- 1.0 (* 3.0 t_0))))
       (* x1 (- (+ (* 4.0 t_0) (* x1 (- 3.0 (* x1 6.0)))) 9.0))))
     (+
      (* x2 -6.0)
      (+
       (* x1 (+ -1.0 (* x1 9.0)))
       (* x2 (+ (* x1 -12.0) (* 8.0 (* x1 x2)))))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 - (2.0 * x2);
	double tmp;
	if ((x1 <= -185.0) || !(x1 <= 0.29)) {
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_0)))) - (x1 * (((4.0 * t_0) + (x1 * (3.0 - (x1 * 6.0)))) - 9.0)));
	} else {
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 3.0d0 - (2.0d0 * x2)
    if ((x1 <= (-185.0d0)) .or. (.not. (x1 <= 0.29d0))) then
        tmp = x1 * (((-1.0d0) - ((-2.0d0) * (1.0d0 - (3.0d0 * t_0)))) - (x1 * (((4.0d0 * t_0) + (x1 * (3.0d0 - (x1 * 6.0d0)))) - 9.0d0)))
    else
        tmp = (x2 * (-6.0d0)) + ((x1 * ((-1.0d0) + (x1 * 9.0d0))) + (x2 * ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 - (2.0 * x2);
	double tmp;
	if ((x1 <= -185.0) || !(x1 <= 0.29)) {
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_0)))) - (x1 * (((4.0 * t_0) + (x1 * (3.0 - (x1 * 6.0)))) - 9.0)));
	} else {
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 - (2.0 * x2)
	tmp = 0
	if (x1 <= -185.0) or not (x1 <= 0.29):
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_0)))) - (x1 * (((4.0 * t_0) + (x1 * (3.0 - (x1 * 6.0)))) - 9.0)))
	else:
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 - Float64(2.0 * x2))
	tmp = 0.0
	if ((x1 <= -185.0) || !(x1 <= 0.29))
		tmp = Float64(x1 * Float64(Float64(-1.0 - Float64(-2.0 * Float64(1.0 - Float64(3.0 * t_0)))) - Float64(x1 * Float64(Float64(Float64(4.0 * t_0) + Float64(x1 * Float64(3.0 - Float64(x1 * 6.0)))) - 9.0))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))) + Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 - (2.0 * x2);
	tmp = 0.0;
	if ((x1 <= -185.0) || ~((x1 <= 0.29)))
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_0)))) - (x1 * (((4.0 * t_0) + (x1 * (3.0 - (x1 * 6.0)))) - 9.0)));
	else
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x1, -185.0], N[Not[LessEqual[x1, 0.29]], $MachinePrecision]], N[(x1 * N[(N[(-1.0 - N[(-2.0 * N[(1.0 - N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(N[(N[(4.0 * t$95$0), $MachinePrecision] + N[(x1 * N[(3.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -185 or 0.28999999999999998 < x1

   1. Initial program 41.3%

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

   3. Simplified 41.3%

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

   5. Taylor expanded in x1 around -inf 91.8%

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

   6. Taylor expanded in x1 around 0 91.7%

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

   if -185 < x1 < 0.28999999999999998

   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 99.8%

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

   5. Taylor expanded in x1 around 0 86.3%

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

   6. Taylor expanded in x2 around 0 86.3%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\color{blue}{15} - 6\right)\right) - 1\right) \]

   7. Taylor expanded in x2 around 0 99.8%

      \[\leadsto -6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(9 \cdot x1 - 1\right) + x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -185 \lor \neg \left(x1 \leq 0.29\right):\\ \;\;\;\;x1 \cdot \left(\left(-1 - -2 \cdot \left(1 - 3 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1 \cdot \left(\left(4 \cdot \left(3 - 2 \cdot x2\right) + x1 \cdot \left(3 - x1 \cdot 6\right)\right) - 9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + \left(x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.8% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \mathbf{if}\;x1 \leq -7.8 \cdot 10^{+155}:\\ \;\;\;\;x2 \cdot -6 + t\_0\\ \mathbf{elif}\;x1 \leq -1.06 \cdot 10^{+51}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x2 \cdot \left(9 \cdot \frac{x1}{x2} + x1 \cdot 12\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + \left(t\_0 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ -1.0 (* x1 9.0)))))
   (if (<= x1 -7.8e+155)
     (+ (* x2 -6.0) t_0)
     (if (<= x1 -1.06e+51)
       (+
        (* x2 -6.0)
        (*
         x1
         (+
          -1.0
          (+
           (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))
           (* x2 (+ (* 9.0 (/ x1 x2)) (* x1 12.0)))))))
       (+ (* x2 -6.0) (+ t_0 (* x2 (+ (* x1 -12.0) (* 8.0 (* x1 x2))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (-1.0 + (x1 * 9.0));
	double tmp;
	if (x1 <= -7.8e+155) {
		tmp = (x2 * -6.0) + t_0;
	} else if (x1 <= -1.06e+51) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x2 * ((9.0 * (x1 / x2)) + (x1 * 12.0))))));
	} else {
		tmp = (x2 * -6.0) + (t_0 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 * ((-1.0d0) + (x1 * 9.0d0))
    if (x1 <= (-7.8d+155)) then
        tmp = (x2 * (-6.0d0)) + t_0
    else if (x1 <= (-1.06d+51)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + (x2 * ((9.0d0 * (x1 / x2)) + (x1 * 12.0d0))))))
    else
        tmp = (x2 * (-6.0d0)) + (t_0 + (x2 * ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (-1.0 + (x1 * 9.0));
	double tmp;
	if (x1 <= -7.8e+155) {
		tmp = (x2 * -6.0) + t_0;
	} else if (x1 <= -1.06e+51) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x2 * ((9.0 * (x1 / x2)) + (x1 * 12.0))))));
	} else {
		tmp = (x2 * -6.0) + (t_0 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (-1.0 + (x1 * 9.0))
	tmp = 0
	if x1 <= -7.8e+155:
		tmp = (x2 * -6.0) + t_0
	elif x1 <= -1.06e+51:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x2 * ((9.0 * (x1 / x2)) + (x1 * 12.0))))))
	else:
		tmp = (x2 * -6.0) + (t_0 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0)))
	tmp = 0.0
	if (x1 <= -7.8e+155)
		tmp = Float64(Float64(x2 * -6.0) + t_0);
	elseif (x1 <= -1.06e+51)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) + Float64(x2 * Float64(Float64(9.0 * Float64(x1 / x2)) + Float64(x1 * 12.0)))))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(t_0 + Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (-1.0 + (x1 * 9.0));
	tmp = 0.0;
	if (x1 <= -7.8e+155)
		tmp = (x2 * -6.0) + t_0;
	elseif (x1 <= -1.06e+51)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x2 * ((9.0 * (x1 / x2)) + (x1 * 12.0))))));
	else
		tmp = (x2 * -6.0) + (t_0 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -7.8e+155], N[(N[(x2 * -6.0), $MachinePrecision] + t$95$0), $MachinePrecision], If[LessEqual[x1, -1.06e+51], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(9.0 * N[(x1 / x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(t$95$0 + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -7.7999999999999996e155

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 70.0%

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

   6. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   if -7.7999999999999996e155 < x1 < -1.06000000000000004e51

   1. Initial program 58.3%

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

   3. Simplified 58.3%

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

   5. Taylor expanded in x1 around 0 24.6%

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

   6. Taylor expanded in x2 around 0 24.6%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\color{blue}{\left(15 + 12 \cdot x2\right)} - 6\right)\right) - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 24.6%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(15 + \color{blue}{x2 \cdot 12}\right) - 6\right)\right) - 1\right) \]

   8. Simplified 24.6%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\color{blue}{\left(15 + x2 \cdot 12\right)} - 6\right)\right) - 1\right) \]

   9. Taylor expanded in x2 around inf 40.9%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + \color{blue}{x2 \cdot \left(9 \cdot \frac{x1}{x2} + 12 \cdot x1\right)}\right) - 1\right) \]

   if -1.06000000000000004e51 < x1

   1. Initial program 83.7%

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

   3. Simplified 84.0%

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

   5. Taylor expanded in x1 around 0 75.5%

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

   6. Taylor expanded in x2 around 0 79.7%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\color{blue}{15} - 6\right)\right) - 1\right) \]

   7. Taylor expanded in x2 around 0 88.7%

      \[\leadsto -6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(9 \cdot x1 - 1\right) + x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.8 \cdot 10^{+155}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -1.06 \cdot 10^{+51}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x2 \cdot \left(9 \cdot \frac{x1}{x2} + x1 \cdot 12\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + \left(x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 83.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 - 2 \cdot x2\\ \mathbf{if}\;x1 \leq -8.6 \cdot 10^{+49}:\\ \;\;\;\;x1 \cdot \left(\left(-1 - -2 \cdot \left(1 - 3 \cdot t\_0\right)\right) - x1 \cdot \left(\left(4 \cdot t\_0 - x1 \cdot -3\right) - 9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + \left(x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- 3.0 (* 2.0 x2))))
   (if (<= x1 -8.6e+49)
     (*
      x1
      (-
       (- -1.0 (* -2.0 (- 1.0 (* 3.0 t_0))))
       (* x1 (- (- (* 4.0 t_0) (* x1 -3.0)) 9.0))))
     (+
      (* x2 -6.0)
      (+
       (* x1 (+ -1.0 (* x1 9.0)))
       (* x2 (+ (* x1 -12.0) (* 8.0 (* x1 x2)))))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 - (2.0 * x2);
	double tmp;
	if (x1 <= -8.6e+49) {
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_0)))) - (x1 * (((4.0 * t_0) - (x1 * -3.0)) - 9.0)));
	} else {
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 3.0d0 - (2.0d0 * x2)
    if (x1 <= (-8.6d+49)) then
        tmp = x1 * (((-1.0d0) - ((-2.0d0) * (1.0d0 - (3.0d0 * t_0)))) - (x1 * (((4.0d0 * t_0) - (x1 * (-3.0d0))) - 9.0d0)))
    else
        tmp = (x2 * (-6.0d0)) + ((x1 * ((-1.0d0) + (x1 * 9.0d0))) + (x2 * ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 - (2.0 * x2);
	double tmp;
	if (x1 <= -8.6e+49) {
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_0)))) - (x1 * (((4.0 * t_0) - (x1 * -3.0)) - 9.0)));
	} else {
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 - (2.0 * x2)
	tmp = 0
	if x1 <= -8.6e+49:
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_0)))) - (x1 * (((4.0 * t_0) - (x1 * -3.0)) - 9.0)))
	else:
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 - Float64(2.0 * x2))
	tmp = 0.0
	if (x1 <= -8.6e+49)
		tmp = Float64(x1 * Float64(Float64(-1.0 - Float64(-2.0 * Float64(1.0 - Float64(3.0 * t_0)))) - Float64(x1 * Float64(Float64(Float64(4.0 * t_0) - Float64(x1 * -3.0)) - 9.0))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))) + Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 - (2.0 * x2);
	tmp = 0.0;
	if (x1 <= -8.6e+49)
		tmp = x1 * ((-1.0 - (-2.0 * (1.0 - (3.0 * t_0)))) - (x1 * (((4.0 * t_0) - (x1 * -3.0)) - 9.0)));
	else
		tmp = (x2 * -6.0) + ((x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -8.6e+49], N[(x1 * N[(N[(-1.0 - N[(-2.0 * N[(1.0 - N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(N[(N[(4.0 * t$95$0), $MachinePrecision] - N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision] - 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -8.5999999999999998e49

   1. Initial program 28.6%

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

   3. Simplified 28.6%

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

   5. Taylor expanded in x1 around -inf 99.9%

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

   6. Taylor expanded in x1 around 0 79.6%

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

   if -8.5999999999999998e49 < x1

   1. Initial program 83.7%

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

   3. Simplified 84.0%

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

   5. Taylor expanded in x1 around 0 75.5%

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

   6. Taylor expanded in x2 around 0 79.7%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\color{blue}{15} - 6\right)\right) - 1\right) \]

   7. Taylor expanded in x2 around 0 88.7%

      \[\leadsto -6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(9 \cdot x1 - 1\right) + x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -8.6 \cdot 10^{+49}:\\ \;\;\;\;x1 \cdot \left(\left(-1 - -2 \cdot \left(1 - 3 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1 \cdot \left(\left(4 \cdot \left(3 - 2 \cdot x2\right) - x1 \cdot -3\right) - 9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + \left(x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 80.8% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+117}:\\ \;\;\;\;x2 \cdot -6 + t\_0\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + \left(t\_0 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ -1.0 (* x1 9.0)))))
   (if (<= x1 -9.5e+117)
     (+ (* x2 -6.0) t_0)
     (+ (* x2 -6.0) (+ t_0 (* x2 (+ (* x1 -12.0) (* 8.0 (* x1 x2)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (-1.0 + (x1 * 9.0));
	double tmp;
	if (x1 <= -9.5e+117) {
		tmp = (x2 * -6.0) + t_0;
	} else {
		tmp = (x2 * -6.0) + (t_0 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 * ((-1.0d0) + (x1 * 9.0d0))
    if (x1 <= (-9.5d+117)) then
        tmp = (x2 * (-6.0d0)) + t_0
    else
        tmp = (x2 * (-6.0d0)) + (t_0 + (x2 * ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (-1.0 + (x1 * 9.0));
	double tmp;
	if (x1 <= -9.5e+117) {
		tmp = (x2 * -6.0) + t_0;
	} else {
		tmp = (x2 * -6.0) + (t_0 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (-1.0 + (x1 * 9.0))
	tmp = 0
	if x1 <= -9.5e+117:
		tmp = (x2 * -6.0) + t_0
	else:
		tmp = (x2 * -6.0) + (t_0 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0)))
	tmp = 0.0
	if (x1 <= -9.5e+117)
		tmp = Float64(Float64(x2 * -6.0) + t_0);
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(t_0 + Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (-1.0 + (x1 * 9.0));
	tmp = 0.0;
	if (x1 <= -9.5e+117)
		tmp = (x2 * -6.0) + t_0;
	else
		tmp = (x2 * -6.0) + (t_0 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -9.5e+117], N[(N[(x2 * -6.0), $MachinePrecision] + t$95$0), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(t$95$0 + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -9.50000000000000041e117

   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 65.4%

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

   6. Taylor expanded in x2 around 0 85.0%

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

      1. *-commutative 85.0%

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

   8. Simplified 85.0%

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

   if -9.50000000000000041e117 < x1

   1. Initial program 83.0%

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

   3. Simplified 83.2%

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

   5. Taylor expanded in x1 around 0 69.7%

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

   6. Taylor expanded in x2 around 0 73.4%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\color{blue}{15} - 6\right)\right) - 1\right) \]

   7. Taylor expanded in x2 around 0 81.5%

      \[\leadsto -6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(9 \cdot x1 - 1\right) + x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+117}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + \left(x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 74.2% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.95 \cdot 10^{+116} \lor \neg \left(x1 \leq 3.5 \cdot 10^{+152}\right):\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -1.95e+116) (not (<= x1 3.5e+152)))
   (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 9.0))))
   (+ (* x2 -6.0) (* x1 (+ -1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -1.95e+116) || !(x1 <= 3.5e+152)) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	}
	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+116)) .or. (.not. (x1 <= 3.5d+152))) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * 9.0d0)))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -1.95e+116) || !(x1 <= 3.5e+152)) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -1.95e+116) or not (x1 <= 3.5e+152):
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)))
	else:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -1.95e+116) || !(x1 <= 3.5e+152))
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -1.95e+116) || ~((x1 <= 3.5e+152)))
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	else
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -1.95e+116], N[Not[LessEqual[x1, 3.5e+152]], $MachinePrecision]], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.95000000000000016e116 or 3.49999999999999981e152 < x1

   1. Initial program 1.4%

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

   3. Simplified 1.4%

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

   5. Taylor expanded in x1 around 0 75.9%

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

   6. Taylor expanded in x2 around 0 90.7%

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

      1. *-commutative 90.7%

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

   8. Simplified 90.7%

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

   if -1.95000000000000016e116 < x1 < 3.49999999999999981e152

   1. Initial program 96.7%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in x1 around 0 68.8%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.95 \cdot 10^{+116} \lor \neg \left(x1 \leq 3.5 \cdot 10^{+152}\right):\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 80.8% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \mathbf{if}\;x1 \leq -1.85 \cdot 10^{+121}:\\ \;\;\;\;x2 \cdot -6 + t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_0 + x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ -1.0 (* x1 9.0)))))
   (if (<= x1 -1.85e+121)
     (+ (* x2 -6.0) t_0)
     (+ t_0 (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (-1.0 + (x1 * 9.0));
	double tmp;
	if (x1 <= -1.85e+121) {
		tmp = (x2 * -6.0) + t_0;
	} else {
		tmp = t_0 + (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 * ((-1.0d0) + (x1 * 9.0d0))
    if (x1 <= (-1.85d+121)) then
        tmp = (x2 * (-6.0d0)) + t_0
    else
        tmp = t_0 + (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (-1.0 + (x1 * 9.0));
	double tmp;
	if (x1 <= -1.85e+121) {
		tmp = (x2 * -6.0) + t_0;
	} else {
		tmp = t_0 + (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (-1.0 + (x1 * 9.0))
	tmp = 0
	if x1 <= -1.85e+121:
		tmp = (x2 * -6.0) + t_0
	else:
		tmp = t_0 + (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0)))
	tmp = 0.0
	if (x1 <= -1.85e+121)
		tmp = Float64(Float64(x2 * -6.0) + t_0);
	else
		tmp = Float64(t_0 + Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (-1.0 + (x1 * 9.0));
	tmp = 0.0;
	if (x1 <= -1.85e+121)
		tmp = (x2 * -6.0) + t_0;
	else
		tmp = t_0 + (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.85e+121], N[(N[(x2 * -6.0), $MachinePrecision] + t$95$0), $MachinePrecision], N[(t$95$0 + N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.85000000000000006e121

   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 65.4%

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

   6. Taylor expanded in x2 around 0 85.0%

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

      1. *-commutative 85.0%

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

   8. Simplified 85.0%

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

   if -1.85000000000000006e121 < x1

   1. Initial program 83.0%

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

   3. Simplified 83.2%

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

   5. Taylor expanded in x1 around 0 69.7%

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

   6. Taylor expanded in x2 around 0 73.4%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\color{blue}{15} - 6\right)\right) - 1\right) \]

   7. Taylor expanded in x2 around 0 81.5%

      \[\leadsto \color{blue}{x1 \cdot \left(9 \cdot x1 - 1\right) + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.85 \cdot 10^{+121}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 41.2% accurate, 5.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.35 \cdot 10^{-12}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot 12 + \frac{x1}{x2} \cdot -17\right)\\ \mathbf{elif}\;x1 \leq -1.8 \cdot 10^{-138} \lor \neg \left(x1 \leq 6 \cdot 10^{-127}\right):\\ \;\;\;\;x1 \cdot \left(-1 - -2 \cdot \left(x2 \cdot 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.35e-12)
   (* x2 (+ (* x1 12.0) (* (/ x1 x2) -17.0)))
   (if (or (<= x1 -1.8e-138) (not (<= x1 6e-127)))
     (* x1 (- -1.0 (* -2.0 (* x2 6.0))))
     (* x2 -6.0))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.35e-12) {
		tmp = x2 * ((x1 * 12.0) + ((x1 / x2) * -17.0));
	} else if ((x1 <= -1.8e-138) || !(x1 <= 6e-127)) {
		tmp = x1 * (-1.0 - (-2.0 * (x2 * 6.0)));
	} 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 <= (-1.35d-12)) then
        tmp = x2 * ((x1 * 12.0d0) + ((x1 / x2) * (-17.0d0)))
    else if ((x1 <= (-1.8d-138)) .or. (.not. (x1 <= 6d-127))) then
        tmp = x1 * ((-1.0d0) - ((-2.0d0) * (x2 * 6.0d0)))
    else
        tmp = x2 * (-6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.35e-12) {
		tmp = x2 * ((x1 * 12.0) + ((x1 / x2) * -17.0));
	} else if ((x1 <= -1.8e-138) || !(x1 <= 6e-127)) {
		tmp = x1 * (-1.0 - (-2.0 * (x2 * 6.0)));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.35e-12:
		tmp = x2 * ((x1 * 12.0) + ((x1 / x2) * -17.0))
	elif (x1 <= -1.8e-138) or not (x1 <= 6e-127):
		tmp = x1 * (-1.0 - (-2.0 * (x2 * 6.0)))
	else:
		tmp = x2 * -6.0
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.35e-12)
		tmp = Float64(x2 * Float64(Float64(x1 * 12.0) + Float64(Float64(x1 / x2) * -17.0)));
	elseif ((x1 <= -1.8e-138) || !(x1 <= 6e-127))
		tmp = Float64(x1 * Float64(-1.0 - Float64(-2.0 * Float64(x2 * 6.0))));
	else
		tmp = Float64(x2 * -6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -1.35e-12)
		tmp = x2 * ((x1 * 12.0) + ((x1 / x2) * -17.0));
	elseif ((x1 <= -1.8e-138) || ~((x1 <= 6e-127)))
		tmp = x1 * (-1.0 - (-2.0 * (x2 * 6.0)));
	else
		tmp = x2 * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.35e-12], N[(x2 * N[(N[(x1 * 12.0), $MachinePrecision] + N[(N[(x1 / x2), $MachinePrecision] * -17.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x1, -1.8e-138], N[Not[LessEqual[x1, 6e-127]], $MachinePrecision]], N[(x1 * N[(-1.0 - N[(-2.0 * N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * -6.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.3499999999999999e-12

   1. Initial program 39.7%

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

   3. Simplified 39.7%

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

   5. Taylor expanded in x1 around -inf 92.9%

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

   6. Taylor expanded in x1 around 0 12.6%

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

   7. Taylor expanded in x2 around inf 35.5%

      \[\leadsto \color{blue}{x2 \cdot \left(-17 \cdot \frac{x1}{x2} + 12 \cdot x1\right)} \]

   if -1.3499999999999999e-12 < x1 < -1.80000000000000009e-138 or 6.00000000000000017e-127 < x1

   1. Initial program 71.7%

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

   3. Simplified 72.0%

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

   5. Taylor expanded in x1 around -inf 47.6%

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

   6. Taylor expanded in x1 around 0 15.0%

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

   7. Taylor expanded in x2 around inf 34.3%

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

      1. *-commutative 34.3%

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

   9. Simplified 34.3%

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

   if -1.80000000000000009e-138 < x1 < 6.00000000000000017e-127

   1. Initial program 99.7%

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

   3. Simplified 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 69.9%

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

      1. *-commutative 69.9%

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

   7. Simplified 69.9%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.35 \cdot 10^{-12}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot 12 + \frac{x1}{x2} \cdot -17\right)\\ \mathbf{elif}\;x1 \leq -1.8 \cdot 10^{-138} \lor \neg \left(x1 \leq 6 \cdot 10^{-127}\right):\\ \;\;\;\;x1 \cdot \left(-1 - -2 \cdot \left(x2 \cdot 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 75.0% accurate, 5.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -8.2 \cdot 10^{+114}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 - \left(x2 \cdot \left(12 - x2 \cdot 8\right) - x1 \cdot 9\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -8.2e+114)
   (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 9.0))))
   (+ (* x2 -6.0) (* x1 (- -1.0 (- (* x2 (- 12.0 (* x2 8.0))) (* x1 9.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -8.2e+114) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 - ((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 <= (-8.2d+114)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * 9.0d0)))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) - ((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 <= -8.2e+114) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 - ((x2 * (12.0 - (x2 * 8.0))) - (x1 * 9.0))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -8.2e+114:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)))
	else:
		tmp = (x2 * -6.0) + (x1 * (-1.0 - ((x2 * (12.0 - (x2 * 8.0))) - (x1 * 9.0))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -8.2e+114)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 - 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 <= -8.2e+114)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	else
		tmp = (x2 * -6.0) + (x1 * (-1.0 - ((x2 * (12.0 - (x2 * 8.0))) - (x1 * 9.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -8.2e+114], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 - N[(N[(x2 * N[(12.0 - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -8.2000000000000001e114

   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 65.4%

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

   6. Taylor expanded in x2 around 0 85.0%

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

      1. *-commutative 85.0%

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

   8. Simplified 85.0%

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

   if -8.2000000000000001e114 < x1

   1. Initial program 83.0%

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

   3. Simplified 83.2%

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

   5. Taylor expanded in x1 around 0 69.7%

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

   6. Taylor expanded in x2 around 0 73.4%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\color{blue}{15} - 6\right)\right) - 1\right) \]

   7. Taylor expanded in x2 around 0 73.4%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{\left(9 \cdot x1 + x2 \cdot \left(8 \cdot x2 - 12\right)\right)} - 1\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -8.2 \cdot 10^{+114}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 - \left(x2 \cdot \left(12 - x2 \cdot 8\right) - x1 \cdot 9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 64.9% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;2 \cdot x2 \leq 5 \cdot 10^{-82}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(x1 \cdot -12 - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x2 \cdot 12\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= (* 2.0 x2) 5e-82)
   (+ (* x1 (+ -1.0 (* x1 9.0))) (* x2 (- (* x1 -12.0) 6.0)))
   (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 (+ 9.0 (* x2 12.0))))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((2.0 * x2) <= 5e-82) {
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((x1 * -12.0) - 6.0));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (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 ((2.0d0 * x2) <= 5d-82) then
        tmp = (x1 * ((-1.0d0) + (x1 * 9.0d0))) + (x2 * ((x1 * (-12.0d0)) - 6.0d0))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * (9.0d0 + (x2 * 12.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((2.0 * x2) <= 5e-82) {
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((x1 * -12.0) - 6.0));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x2 * 12.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (2.0 * x2) <= 5e-82:
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((x1 * -12.0) - 6.0))
	else:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x2 * 12.0)))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (Float64(2.0 * x2) <= 5e-82)
		tmp = Float64(Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))) + Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x2 * 12.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((2.0 * x2) <= 5e-82)
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * ((x1 * -12.0) - 6.0));
	else
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x2 * 12.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[N[(2.0 * x2), $MachinePrecision], 5e-82], N[(N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x2 * 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 #s(literal 2 binary64) x2) < 4.9999999999999998e-82

   1. Initial program 73.3%

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

   3. Simplified 73.6%

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

   5. Taylor expanded in x1 around 0 68.0%

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

   6. Taylor expanded in x2 around 0 73.8%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\color{blue}{15} - 6\right)\right) - 1\right) \]

   7. Taylor expanded in x2 around 0 65.8%

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

   if 4.9999999999999998e-82 < (*.f64 #s(literal 2 binary64) x2)

   1. Initial program 66.0%

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

   3. Simplified 66.1%

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

   5. Taylor expanded in x1 around 0 71.6%

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

   6. Taylor expanded in x2 around 0 71.6%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\color{blue}{\left(15 + 12 \cdot x2\right)} - 6\right)\right) - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 71.6%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(15 + \color{blue}{x2 \cdot 12}\right) - 6\right)\right) - 1\right) \]

   8. Simplified 71.6%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\color{blue}{\left(15 + x2 \cdot 12\right)} - 6\right)\right) - 1\right) \]

   9. Taylor expanded in x1 around inf 65.4%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + 12 \cdot x2\right)} - 1\right) \]
   10. Step-by-step derivation

       1. *-commutative 65.4%

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

   11. Simplified 65.4%

       \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x2 \cdot 12\right)} - 1\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;2 \cdot x2 \leq 5 \cdot 10^{-82}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(x1 \cdot -12 - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x2 \cdot 12\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 66.5% accurate, 6.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq 5.2 \cdot 10^{+34}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x2 \cdot 12\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 5.2e+34)
   (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 9.0))))
   (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 (+ 9.0 (* x2 12.0))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= 5.2e+34) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (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 <= 5.2d+34) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * 9.0d0)))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * (9.0d0 + (x2 * 12.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x2 <= 5.2e+34) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x2 * 12.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= 5.2e+34:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)))
	else:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x2 * 12.0)))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= 5.2e+34)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x2 * 12.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= 5.2e+34)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	else
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x2 * 12.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, 5.2e+34], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x2 * 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < 5.19999999999999995e34

   1. Initial program 72.5%

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

   3. Simplified 72.7%

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

   5. Taylor expanded in x1 around 0 68.6%

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

   6. Taylor expanded in x2 around 0 64.8%

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

      1. *-commutative 64.8%

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

   8. Simplified 64.8%

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

   if 5.19999999999999995e34 < x2

   1. Initial program 66.0%

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

   3. Simplified 66.0%

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

   5. Taylor expanded in x1 around 0 71.0%

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

   6. Taylor expanded in x2 around 0 71.0%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\color{blue}{\left(15 + 12 \cdot x2\right)} - 6\right)\right) - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 71.0%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(15 + \color{blue}{x2 \cdot 12}\right) - 6\right)\right) - 1\right) \]

   8. Simplified 71.0%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\color{blue}{\left(15 + x2 \cdot 12\right)} - 6\right)\right) - 1\right) \]

   9. Taylor expanded in x1 around inf 64.2%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + 12 \cdot x2\right)} - 1\right) \]
   10. Step-by-step derivation

       1. *-commutative 64.2%

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

   11. Simplified 64.2%

       \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x2 \cdot 12\right)} - 1\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq 5.2 \cdot 10^{+34}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x2 \cdot 12\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 36.0% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -4.8 \cdot 10^{-138} \lor \neg \left(x1 \leq 3.9 \cdot 10^{-127}\right):\\ \;\;\;\;x1 \cdot \left(-1 - -2 \cdot \left(x2 \cdot 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -4.8e-138) (not (<= x1 3.9e-127)))
   (* x1 (- -1.0 (* -2.0 (* x2 6.0))))
   (* x2 -6.0)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -4.8e-138) || !(x1 <= 3.9e-127)) {
		tmp = x1 * (-1.0 - (-2.0 * (x2 * 6.0)));
	} 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 <= (-4.8d-138)) .or. (.not. (x1 <= 3.9d-127))) then
        tmp = x1 * ((-1.0d0) - ((-2.0d0) * (x2 * 6.0d0)))
    else
        tmp = x2 * (-6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -4.8e-138) || !(x1 <= 3.9e-127)) {
		tmp = x1 * (-1.0 - (-2.0 * (x2 * 6.0)));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -4.8e-138) or not (x1 <= 3.9e-127):
		tmp = x1 * (-1.0 - (-2.0 * (x2 * 6.0)))
	else:
		tmp = x2 * -6.0
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -4.8e-138) || !(x1 <= 3.9e-127))
		tmp = Float64(x1 * Float64(-1.0 - Float64(-2.0 * Float64(x2 * 6.0))));
	else
		tmp = Float64(x2 * -6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -4.8e-138) || ~((x1 <= 3.9e-127)))
		tmp = x1 * (-1.0 - (-2.0 * (x2 * 6.0)));
	else
		tmp = x2 * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -4.8e-138], N[Not[LessEqual[x1, 3.9e-127]], $MachinePrecision]], N[(x1 * N[(-1.0 - N[(-2.0 * N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * -6.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -4.7999999999999998e-138 or 3.89999999999999966e-127 < x1

   1. Initial program 59.4%

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

   3. Simplified 59.6%

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

   5. Taylor expanded in x1 around -inf 65.0%

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

   6. Taylor expanded in x1 around 0 14.1%

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

   7. Taylor expanded in x2 around inf 25.5%

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

      1. *-commutative 25.5%

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

   9. Simplified 25.5%

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

   if -4.7999999999999998e-138 < x1 < 3.89999999999999966e-127

   1. Initial program 99.7%

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

   3. Simplified 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 69.9%

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

      1. *-commutative 69.9%

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

   7. Simplified 69.9%

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

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.8 \cdot 10^{-138} \lor \neg \left(x1 \leq 3.9 \cdot 10^{-127}\right):\\ \;\;\;\;x1 \cdot \left(-1 - -2 \cdot \left(x2 \cdot 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 32.0% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -6000 \lor \neg \left(x1 \leq 8.2 \cdot 10^{+97}\right):\\ \;\;\;\;\left(x1 \cdot x2\right) \cdot 12\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -6000.0) (not (<= x1 8.2e+97)))
   (* (* x1 x2) 12.0)
   (* x2 -6.0)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -6000.0) || !(x1 <= 8.2e+97)) {
		tmp = (x1 * 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 <= (-6000.0d0)) .or. (.not. (x1 <= 8.2d+97))) then
        tmp = (x1 * 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 <= -6000.0) || !(x1 <= 8.2e+97)) {
		tmp = (x1 * x2) * 12.0;
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -6000.0) or not (x1 <= 8.2e+97):
		tmp = (x1 * x2) * 12.0
	else:
		tmp = x2 * -6.0
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -6000.0) || !(x1 <= 8.2e+97))
		tmp = Float64(Float64(x1 * 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 <= -6000.0) || ~((x1 <= 8.2e+97)))
		tmp = (x1 * x2) * 12.0;
	else
		tmp = x2 * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -6000.0], N[Not[LessEqual[x1, 8.2e+97]], $MachinePrecision]], N[(N[(x1 * x2), $MachinePrecision] * 12.0), $MachinePrecision], N[(x2 * -6.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -6e3 or 8.19999999999999977e97 < x1

   1. Initial program 30.3%

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

   3. Simplified 30.3%

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

   5. Taylor expanded in x1 around -inf 97.1%

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

   6. Taylor expanded in x1 around 0 19.0%

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

   7. Taylor expanded in x2 around inf 17.0%

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

   if -6e3 < x1 < 8.19999999999999977e97

   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 40.9%

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

      1. *-commutative 40.9%

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

   7. Simplified 40.9%

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

4. Final simplification 31.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6000 \lor \neg \left(x1 \leq 8.2 \cdot 10^{+97}\right):\\ \;\;\;\;\left(x1 \cdot x2\right) \cdot 12\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 32.4% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x1 \cdot x2\right) \cdot 12\\ \mathbf{if}\;x1 \leq -4.2 \cdot 10^{-54}:\\ \;\;\;\;x1 \cdot -17 + t\_0\\ \mathbf{elif}\;x1 \leq 8.2 \cdot 10^{+97}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* x1 x2) 12.0)))
   (if (<= x1 -4.2e-54)
     (+ (* x1 -17.0) t_0)
     (if (<= x1 8.2e+97) (* x2 -6.0) t_0))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x2) * 12.0;
	double tmp;
	if (x1 <= -4.2e-54) {
		tmp = (x1 * -17.0) + t_0;
	} else if (x1 <= 8.2e+97) {
		tmp = x2 * -6.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x1 * x2) * 12.0d0
    if (x1 <= (-4.2d-54)) then
        tmp = (x1 * (-17.0d0)) + t_0
    else if (x1 <= 8.2d+97) then
        tmp = x2 * (-6.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x2) * 12.0;
	double tmp;
	if (x1 <= -4.2e-54) {
		tmp = (x1 * -17.0) + t_0;
	} else if (x1 <= 8.2e+97) {
		tmp = x2 * -6.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x2) * 12.0
	tmp = 0
	if x1 <= -4.2e-54:
		tmp = (x1 * -17.0) + t_0
	elif x1 <= 8.2e+97:
		tmp = x2 * -6.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x2) * 12.0)
	tmp = 0.0
	if (x1 <= -4.2e-54)
		tmp = Float64(Float64(x1 * -17.0) + t_0);
	elseif (x1 <= 8.2e+97)
		tmp = Float64(x2 * -6.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x2) * 12.0;
	tmp = 0.0;
	if (x1 <= -4.2e-54)
		tmp = (x1 * -17.0) + t_0;
	elseif (x1 <= 8.2e+97)
		tmp = x2 * -6.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x2), $MachinePrecision] * 12.0), $MachinePrecision]}, If[LessEqual[x1, -4.2e-54], N[(N[(x1 * -17.0), $MachinePrecision] + t$95$0), $MachinePrecision], If[LessEqual[x1, 8.2e+97], N[(x2 * -6.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4.2e-54

   1. Initial program 47.1%

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

   3. Simplified 47.3%

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

   5. Taylor expanded in x1 around -inf 82.5%

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

   6. Taylor expanded in x1 around 0 12.3%

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

   7. Taylor expanded in x2 around 0 12.3%

      \[\leadsto \color{blue}{-17 \cdot x1 + 12 \cdot \left(x1 \cdot x2\right)} \]

   if -4.2e-54 < x1 < 8.19999999999999977e97

   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 44.2%

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

      1. *-commutative 44.2%

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

   7. Simplified 44.2%

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

   if 8.19999999999999977e97 < x1

   1. Initial program 18.4%

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

   3. Simplified 18.4%

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

   5. Taylor expanded in x1 around -inf 100.0%

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

   6. Taylor expanded in x1 around 0 29.8%

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

   7. Taylor expanded in x2 around inf 30.9%

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

4. Final simplification 32.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.2 \cdot 10^{-54}:\\ \;\;\;\;x1 \cdot -17 + \left(x1 \cdot x2\right) \cdot 12\\ \mathbf{elif}\;x1 \leq 8.2 \cdot 10^{+97}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;\left(x1 \cdot x2\right) \cdot 12\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 64.1% accurate, 11.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.0%

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

3. Simplified 71.2%

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

5. Taylor expanded in x1 around 0 69.1%

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

6. Taylor expanded in x2 around 0 62.5%

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

   1. *-commutative 62.5%

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

8. Simplified 62.5%

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

9. Final simplification 62.5%

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

Alternative 22: 26.3% accurate, 42.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.0%

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

3. Simplified 71.2%

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

5. Taylor expanded in x1 around 0 24.9%

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

   1. *-commutative 24.9%

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

7. Simplified 24.9%

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

Alternative 23: 4.6% accurate, 42.3× speedup

Math

\[\begin{array}{l} \\ x1 \cdot -17 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (* x1 -17.0))

C

double code(double x1, double x2) {
	return x1 * -17.0;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x1 * (-17.0d0)
end function

Java

public static double code(double x1, double x2) {
	return x1 * -17.0;
}

Python

def code(x1, x2):
	return x1 * -17.0

Julia

function code(x1, x2)
	return Float64(x1 * -17.0)
end

MATLAB

function tmp = code(x1, x2)
	tmp = x1 * -17.0;
end

Wolfram

code[x1_, x2_] := N[(x1 * -17.0), $MachinePrecision]

Derivation

1. Initial program 71.0%

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

3. Simplified 71.2%

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

5. Taylor expanded in x1 around -inf 46.2%

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

6. Taylor expanded in x1 around 0 11.4%

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

7. Taylor expanded in x2 around 0 5.1%

   \[\leadsto \color{blue}{-17 \cdot x1} \]
8. Step-by-step derivation

   1. *-commutative 5.1%

      \[\leadsto \color{blue}{x1 \cdot -17} \]

9. Simplified 5.1%

   \[\leadsto \color{blue}{x1 \cdot -17} \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024116 
(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))))))