Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.4% → 99.7%

Time: 20.1s

Alternatives: 24

Speedup: 7.3×

• 46.8% 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: 70.4% 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, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.3%

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

   4. Applied rewrites 99.7%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 3.3

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

   5. Applied rewrites 3.3%

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

   6. Taylor expanded in x1 around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   8. Applied rewrites 100.0%

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

4. Final simplification 99.8%

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

Alternative 2: 61.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(3 \cdot x1\right) \cdot x1\\ t_1 := \left(\left(x2 \cdot x2\right) \cdot x1\right) \cdot 8\\ t_2 := -1 - x1 \cdot x1\\ t_3 := \left(x2 \cdot 2 + t\_0\right) - x1\\ t_4 := x1 \cdot x1 - -1\\ t_5 := \frac{t\_3}{t\_4}\\ t_6 := x1 - \left(\left(\left(\left(\frac{t\_3}{t\_2} \cdot t\_0 - t\_2 \cdot \left(\left(3 - t\_5\right) \cdot \left(\left(2 \cdot x1\right) \cdot t\_5\right) - \left(4 \cdot t\_5 - 6\right) \cdot \left(x1 \cdot x1\right)\right)\right) - \left(x1 \cdot x1\right) \cdot x1\right) - x1\right) - \frac{\left(t\_0 - x2 \cdot 2\right) - x1}{t\_4} \cdot 3\right)\\ \mathbf{if}\;t\_6 \leq -1 \cdot 10^{+201}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_6 \leq -5 \cdot 10^{-5}:\\ \;\;\;\;-6 \cdot x2\\ \mathbf{elif}\;t\_6 \leq 5 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-19, x1, 9\right), x1, -1\right) \cdot x1\\ \mathbf{elif}\;t\_6 \leq 10^{+190}:\\ \;\;\;\;-6 \cdot x2 + x1\\ \mathbf{elif}\;t\_6 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(9, x1, -1\right) \cdot x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* 3.0 x1) x1))
        (t_1 (* (* (* x2 x2) x1) 8.0))
        (t_2 (- -1.0 (* x1 x1)))
        (t_3 (- (+ (* x2 2.0) t_0) x1))
        (t_4 (- (* x1 x1) -1.0))
        (t_5 (/ t_3 t_4))
        (t_6
         (-
          x1
          (-
           (-
            (-
             (-
              (* (/ t_3 t_2) t_0)
              (*
               t_2
               (-
                (* (- 3.0 t_5) (* (* 2.0 x1) t_5))
                (* (- (* 4.0 t_5) 6.0) (* x1 x1)))))
             (* (* x1 x1) x1))
            x1)
           (* (/ (- (- t_0 (* x2 2.0)) x1) t_4) 3.0)))))
   (if (<= t_6 -1e+201)
     t_1
     (if (<= t_6 -5e-5)
       (* -6.0 x2)
       (if (<= t_6 5e-11)
         (* (fma (fma -19.0 x1 9.0) x1 -1.0) x1)
         (if (<= t_6 1e+190)
           (+ (* -6.0 x2) x1)
           (if (<= t_6 INFINITY) t_1 (* (fma 9.0 x1 -1.0) x1))))))))

C

double code(double x1, double x2) {
	double t_0 = (3.0 * x1) * x1;
	double t_1 = ((x2 * x2) * x1) * 8.0;
	double t_2 = -1.0 - (x1 * x1);
	double t_3 = ((x2 * 2.0) + t_0) - x1;
	double t_4 = (x1 * x1) - -1.0;
	double t_5 = t_3 / t_4;
	double t_6 = x1 - ((((((t_3 / t_2) * t_0) - (t_2 * (((3.0 - t_5) * ((2.0 * x1) * t_5)) - (((4.0 * t_5) - 6.0) * (x1 * x1))))) - ((x1 * x1) * x1)) - x1) - ((((t_0 - (x2 * 2.0)) - x1) / t_4) * 3.0));
	double tmp;
	if (t_6 <= -1e+201) {
		tmp = t_1;
	} else if (t_6 <= -5e-5) {
		tmp = -6.0 * x2;
	} else if (t_6 <= 5e-11) {
		tmp = fma(fma(-19.0, x1, 9.0), x1, -1.0) * x1;
	} else if (t_6 <= 1e+190) {
		tmp = (-6.0 * x2) + x1;
	} else if (t_6 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma(9.0, x1, -1.0) * x1;
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(3.0 * x1) * x1)
	t_1 = Float64(Float64(Float64(x2 * x2) * x1) * 8.0)
	t_2 = Float64(-1.0 - Float64(x1 * x1))
	t_3 = Float64(Float64(Float64(x2 * 2.0) + t_0) - x1)
	t_4 = Float64(Float64(x1 * x1) - -1.0)
	t_5 = Float64(t_3 / t_4)
	t_6 = Float64(x1 - Float64(Float64(Float64(Float64(Float64(Float64(t_3 / t_2) * t_0) - Float64(t_2 * Float64(Float64(Float64(3.0 - t_5) * Float64(Float64(2.0 * x1) * t_5)) - Float64(Float64(Float64(4.0 * t_5) - 6.0) * Float64(x1 * x1))))) - Float64(Float64(x1 * x1) * x1)) - x1) - Float64(Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_4) * 3.0)))
	tmp = 0.0
	if (t_6 <= -1e+201)
		tmp = t_1;
	elseif (t_6 <= -5e-5)
		tmp = Float64(-6.0 * x2);
	elseif (t_6 <= 5e-11)
		tmp = Float64(fma(fma(-19.0, x1, 9.0), x1, -1.0) * x1);
	elseif (t_6 <= 1e+190)
		tmp = Float64(Float64(-6.0 * x2) + x1);
	elseif (t_6 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(fma(9.0, x1, -1.0) * x1);
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(x2 * x2), $MachinePrecision] * x1), $MachinePrecision] * 8.0), $MachinePrecision]}, Block[{t$95$2 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 * x1), $MachinePrecision] - -1.0), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$3 / t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(x1 - N[(N[(N[(N[(N[(N[(t$95$3 / t$95$2), $MachinePrecision] * t$95$0), $MachinePrecision] - N[(t$95$2 * N[(N[(N[(3.0 - t$95$5), $MachinePrecision] * N[(N[(2.0 * x1), $MachinePrecision] * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(4.0 * t$95$5), $MachinePrecision] - 6.0), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] - N[(N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$4), $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$6, -1e+201], t$95$1, If[LessEqual[t$95$6, -5e-5], N[(-6.0 * x2), $MachinePrecision], If[LessEqual[t$95$6, 5e-11], N[(N[(N[(-19.0 * x1 + 9.0), $MachinePrecision] * x1 + -1.0), $MachinePrecision] * x1), $MachinePrecision], If[LessEqual[t$95$6, 1e+190], N[(N[(-6.0 * x2), $MachinePrecision] + x1), $MachinePrecision], If[LessEqual[t$95$6, Infinity], t$95$1, N[(N[(9.0 * x1 + -1.0), $MachinePrecision] * x1), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 5 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)))))) < -1.00000000000000004e201 or 1.0000000000000001e190 < (+.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 99.8%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 4.5

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

   5. Applied rewrites 4.5%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 55.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right)\right), x1, x2 \cdot -6\right)} \]

   9. Taylor expanded in x2 around inf

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

   11. Applied rewrites 53.9%

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

   if -1.00000000000000004e201 < (+.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)))))) < -5.00000000000000024e-5

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 81.0

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

   5. Applied rewrites 81.0%

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

   6. Taylor expanded in x1 around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 81.1

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

   8. Applied rewrites 81.1%

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

   if -5.00000000000000024e-5 < (+.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)))))) < 5.00000000000000018e-11

   1. Initial program 98.9%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 39.8

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

   5. Applied rewrites 39.8%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, 3\right) \cdot x2, 2, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 3, 1\right)\right) - \left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2\right) \cdot 2, 2, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -3\right)\right), x1, 14 \cdot x2\right)\right)\right) - 6, x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right)\right), x1, x2 \cdot -6\right)} \]

   9. Taylor expanded in x2 around 0

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

   11. Applied rewrites 59.6%

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-19, x1, 9\right), x1, -1\right) \cdot \color{blue}{x1} \]

   if 5.00000000000000018e-11 < (+.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)))))) < 1.0000000000000001e190

   1. Initial program 99.0%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 53.4

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

   5. Applied rewrites 53.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 3.3

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

   5. Applied rewrites 3.3%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 67.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right)\right), x1, x2 \cdot -6\right)} \]

   9. Taylor expanded in x2 around 0

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

   11. Applied rewrites 85.7%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 - \left(\left(\left(\left(\frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{-1 - x1 \cdot x1} \cdot \left(\left(3 \cdot x1\right) \cdot x1\right) - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(3 - \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) \cdot \left(\left(2 \cdot x1\right) \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) - \left(4 \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1} - 6\right) \cdot \left(x1 \cdot x1\right)\right)\right) - \left(x1 \cdot x1\right) \cdot x1\right) - x1\right) - \frac{\left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right) - x1}{x1 \cdot x1 - -1} \cdot 3\right) \leq -1 \cdot 10^{+201}:\\ \;\;\;\;\left(\left(x2 \cdot x2\right) \cdot x1\right) \cdot 8\\ \mathbf{elif}\;x1 - \left(\left(\left(\left(\frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{-1 - x1 \cdot x1} \cdot \left(\left(3 \cdot x1\right) \cdot x1\right) - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(3 - \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) \cdot \left(\left(2 \cdot x1\right) \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) - \left(4 \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1} - 6\right) \cdot \left(x1 \cdot x1\right)\right)\right) - \left(x1 \cdot x1\right) \cdot x1\right) - x1\right) - \frac{\left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right) - x1}{x1 \cdot x1 - -1} \cdot 3\right) \leq -5 \cdot 10^{-5}:\\ \;\;\;\;-6 \cdot x2\\ \mathbf{elif}\;x1 - \left(\left(\left(\left(\frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{-1 - x1 \cdot x1} \cdot \left(\left(3 \cdot x1\right) \cdot x1\right) - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(3 - \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) \cdot \left(\left(2 \cdot x1\right) \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) - \left(4 \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1} - 6\right) \cdot \left(x1 \cdot x1\right)\right)\right) - \left(x1 \cdot x1\right) \cdot x1\right) - x1\right) - \frac{\left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right) - x1}{x1 \cdot x1 - -1} \cdot 3\right) \leq 5 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-19, x1, 9\right), x1, -1\right) \cdot x1\\ \mathbf{elif}\;x1 - \left(\left(\left(\left(\frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{-1 - x1 \cdot x1} \cdot \left(\left(3 \cdot x1\right) \cdot x1\right) - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(3 - \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) \cdot \left(\left(2 \cdot x1\right) \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) - \left(4 \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1} - 6\right) \cdot \left(x1 \cdot x1\right)\right)\right) - \left(x1 \cdot x1\right) \cdot x1\right) - x1\right) - \frac{\left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right) - x1}{x1 \cdot x1 - -1} \cdot 3\right) \leq 10^{+190}:\\ \;\;\;\;-6 \cdot x2 + x1\\ \mathbf{elif}\;x1 - \left(\left(\left(\left(\frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{-1 - x1 \cdot x1} \cdot \left(\left(3 \cdot x1\right) \cdot x1\right) - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(3 - \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) \cdot \left(\left(2 \cdot x1\right) \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) - \left(4 \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1} - 6\right) \cdot \left(x1 \cdot x1\right)\right)\right) - \left(x1 \cdot x1\right) \cdot x1\right) - x1\right) - \frac{\left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right) - x1}{x1 \cdot x1 - -1} \cdot 3\right) \leq \infty:\\ \;\;\;\;\left(\left(x2 \cdot x2\right) \cdot x1\right) \cdot 8\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(9, x1, -1\right) \cdot x1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(3 \cdot x1\right) \cdot x1\\ t_1 := \mathsf{fma}\left(9, x1, -1\right) \cdot x1\\ t_2 := \left(\left(x2 \cdot x2\right) \cdot x1\right) \cdot 8\\ t_3 := -1 - x1 \cdot x1\\ t_4 := \left(x2 \cdot 2 + t\_0\right) - x1\\ t_5 := x1 \cdot x1 - -1\\ t_6 := \frac{t\_4}{t\_5}\\ t_7 := x1 - \left(\left(\left(\left(\frac{t\_4}{t\_3} \cdot t\_0 - t\_3 \cdot \left(\left(3 - t\_6\right) \cdot \left(\left(2 \cdot x1\right) \cdot t\_6\right) - \left(4 \cdot t\_6 - 6\right) \cdot \left(x1 \cdot x1\right)\right)\right) - \left(x1 \cdot x1\right) \cdot x1\right) - x1\right) - \frac{\left(t\_0 - x2 \cdot 2\right) - x1}{t\_5} \cdot 3\right)\\ \mathbf{if}\;t\_7 \leq -1 \cdot 10^{+201}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_7 \leq -5 \cdot 10^{-5}:\\ \;\;\;\;-6 \cdot x2\\ \mathbf{elif}\;t\_7 \leq 5 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_7 \leq 10^{+190}:\\ \;\;\;\;-6 \cdot x2 + x1\\ \mathbf{elif}\;t\_7 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* 3.0 x1) x1))
        (t_1 (* (fma 9.0 x1 -1.0) x1))
        (t_2 (* (* (* x2 x2) x1) 8.0))
        (t_3 (- -1.0 (* x1 x1)))
        (t_4 (- (+ (* x2 2.0) t_0) x1))
        (t_5 (- (* x1 x1) -1.0))
        (t_6 (/ t_4 t_5))
        (t_7
         (-
          x1
          (-
           (-
            (-
             (-
              (* (/ t_4 t_3) t_0)
              (*
               t_3
               (-
                (* (- 3.0 t_6) (* (* 2.0 x1) t_6))
                (* (- (* 4.0 t_6) 6.0) (* x1 x1)))))
             (* (* x1 x1) x1))
            x1)
           (* (/ (- (- t_0 (* x2 2.0)) x1) t_5) 3.0)))))
   (if (<= t_7 -1e+201)
     t_2
     (if (<= t_7 -5e-5)
       (* -6.0 x2)
       (if (<= t_7 5e-11)
         t_1
         (if (<= t_7 1e+190)
           (+ (* -6.0 x2) x1)
           (if (<= t_7 INFINITY) t_2 t_1)))))))

C

double code(double x1, double x2) {
	double t_0 = (3.0 * x1) * x1;
	double t_1 = fma(9.0, x1, -1.0) * x1;
	double t_2 = ((x2 * x2) * x1) * 8.0;
	double t_3 = -1.0 - (x1 * x1);
	double t_4 = ((x2 * 2.0) + t_0) - x1;
	double t_5 = (x1 * x1) - -1.0;
	double t_6 = t_4 / t_5;
	double t_7 = x1 - ((((((t_4 / t_3) * t_0) - (t_3 * (((3.0 - t_6) * ((2.0 * x1) * t_6)) - (((4.0 * t_6) - 6.0) * (x1 * x1))))) - ((x1 * x1) * x1)) - x1) - ((((t_0 - (x2 * 2.0)) - x1) / t_5) * 3.0));
	double tmp;
	if (t_7 <= -1e+201) {
		tmp = t_2;
	} else if (t_7 <= -5e-5) {
		tmp = -6.0 * x2;
	} else if (t_7 <= 5e-11) {
		tmp = t_1;
	} else if (t_7 <= 1e+190) {
		tmp = (-6.0 * x2) + x1;
	} else if (t_7 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(3.0 * x1) * x1)
	t_1 = Float64(fma(9.0, x1, -1.0) * x1)
	t_2 = Float64(Float64(Float64(x2 * x2) * x1) * 8.0)
	t_3 = Float64(-1.0 - Float64(x1 * x1))
	t_4 = Float64(Float64(Float64(x2 * 2.0) + t_0) - x1)
	t_5 = Float64(Float64(x1 * x1) - -1.0)
	t_6 = Float64(t_4 / t_5)
	t_7 = Float64(x1 - Float64(Float64(Float64(Float64(Float64(Float64(t_4 / t_3) * t_0) - Float64(t_3 * Float64(Float64(Float64(3.0 - t_6) * Float64(Float64(2.0 * x1) * t_6)) - Float64(Float64(Float64(4.0 * t_6) - 6.0) * Float64(x1 * x1))))) - Float64(Float64(x1 * x1) * x1)) - x1) - Float64(Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_5) * 3.0)))
	tmp = 0.0
	if (t_7 <= -1e+201)
		tmp = t_2;
	elseif (t_7 <= -5e-5)
		tmp = Float64(-6.0 * x2);
	elseif (t_7 <= 5e-11)
		tmp = t_1;
	elseif (t_7 <= 1e+190)
		tmp = Float64(Float64(-6.0 * x2) + x1);
	elseif (t_7 <= Inf)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$1 = N[(N[(9.0 * x1 + -1.0), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x2 * x2), $MachinePrecision] * x1), $MachinePrecision] * 8.0), $MachinePrecision]}, Block[{t$95$3 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 * x1), $MachinePrecision] - -1.0), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$4 / t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(x1 - N[(N[(N[(N[(N[(N[(t$95$4 / t$95$3), $MachinePrecision] * t$95$0), $MachinePrecision] - N[(t$95$3 * N[(N[(N[(3.0 - t$95$6), $MachinePrecision] * N[(N[(2.0 * x1), $MachinePrecision] * t$95$6), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(4.0 * t$95$6), $MachinePrecision] - 6.0), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] - N[(N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$5), $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$7, -1e+201], t$95$2, If[LessEqual[t$95$7, -5e-5], N[(-6.0 * x2), $MachinePrecision], If[LessEqual[t$95$7, 5e-11], t$95$1, If[LessEqual[t$95$7, 1e+190], N[(N[(-6.0 * x2), $MachinePrecision] + x1), $MachinePrecision], If[LessEqual[t$95$7, Infinity], t$95$2, t$95$1]]]]]]]]]]]]]

Derivation

1. Split input into 4 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)))))) < -1.00000000000000004e201 or 1.0000000000000001e190 < (+.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 99.8%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 4.5

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

   5. Applied rewrites 4.5%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 55.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right)\right), x1, x2 \cdot -6\right)} \]

   9. Taylor expanded in x2 around inf

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

   11. Applied rewrites 53.9%

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

   if -1.00000000000000004e201 < (+.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)))))) < -5.00000000000000024e-5

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 81.0

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

   5. Applied rewrites 81.0%

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

   6. Taylor expanded in x1 around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 81.1

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

   8. Applied rewrites 81.1%

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

   if -5.00000000000000024e-5 < (+.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)))))) < 5.00000000000000018e-11 or +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 45.4%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 20.1

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

   5. Applied rewrites 20.1%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 82.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right)\right), x1, x2 \cdot -6\right)} \]

   9. Taylor expanded in x2 around 0

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

   11. Applied rewrites 73.7%

       \[\leadsto \mathsf{fma}\left(9, x1, -1\right) \cdot \color{blue}{x1} \]

   if 5.00000000000000018e-11 < (+.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)))))) < 1.0000000000000001e190

   1. Initial program 99.0%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 53.4

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

   5. Applied rewrites 53.4%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 - \left(\left(\left(\left(\frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{-1 - x1 \cdot x1} \cdot \left(\left(3 \cdot x1\right) \cdot x1\right) - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(3 - \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) \cdot \left(\left(2 \cdot x1\right) \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) - \left(4 \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1} - 6\right) \cdot \left(x1 \cdot x1\right)\right)\right) - \left(x1 \cdot x1\right) \cdot x1\right) - x1\right) - \frac{\left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right) - x1}{x1 \cdot x1 - -1} \cdot 3\right) \leq -1 \cdot 10^{+201}:\\ \;\;\;\;\left(\left(x2 \cdot x2\right) \cdot x1\right) \cdot 8\\ \mathbf{elif}\;x1 - \left(\left(\left(\left(\frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{-1 - x1 \cdot x1} \cdot \left(\left(3 \cdot x1\right) \cdot x1\right) - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(3 - \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) \cdot \left(\left(2 \cdot x1\right) \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) - \left(4 \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1} - 6\right) \cdot \left(x1 \cdot x1\right)\right)\right) - \left(x1 \cdot x1\right) \cdot x1\right) - x1\right) - \frac{\left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right) - x1}{x1 \cdot x1 - -1} \cdot 3\right) \leq -5 \cdot 10^{-5}:\\ \;\;\;\;-6 \cdot x2\\ \mathbf{elif}\;x1 - \left(\left(\left(\left(\frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{-1 - x1 \cdot x1} \cdot \left(\left(3 \cdot x1\right) \cdot x1\right) - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(3 - \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) \cdot \left(\left(2 \cdot x1\right) \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) - \left(4 \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1} - 6\right) \cdot \left(x1 \cdot x1\right)\right)\right) - \left(x1 \cdot x1\right) \cdot x1\right) - x1\right) - \frac{\left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right) - x1}{x1 \cdot x1 - -1} \cdot 3\right) \leq 5 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(9, x1, -1\right) \cdot x1\\ \mathbf{elif}\;x1 - \left(\left(\left(\left(\frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{-1 - x1 \cdot x1} \cdot \left(\left(3 \cdot x1\right) \cdot x1\right) - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(3 - \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) \cdot \left(\left(2 \cdot x1\right) \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) - \left(4 \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1} - 6\right) \cdot \left(x1 \cdot x1\right)\right)\right) - \left(x1 \cdot x1\right) \cdot x1\right) - x1\right) - \frac{\left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right) - x1}{x1 \cdot x1 - -1} \cdot 3\right) \leq 10^{+190}:\\ \;\;\;\;-6 \cdot x2 + x1\\ \mathbf{elif}\;x1 - \left(\left(\left(\left(\frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{-1 - x1 \cdot x1} \cdot \left(\left(3 \cdot x1\right) \cdot x1\right) - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(3 - \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) \cdot \left(\left(2 \cdot x1\right) \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) - \left(4 \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1} - 6\right) \cdot \left(x1 \cdot x1\right)\right)\right) - \left(x1 \cdot x1\right) \cdot x1\right) - x1\right) - \frac{\left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right) - x1}{x1 \cdot x1 - -1} \cdot 3\right) \leq \infty:\\ \;\;\;\;\left(\left(x2 \cdot x2\right) \cdot x1\right) \cdot 8\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(9, x1, -1\right) \cdot x1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(3 \cdot x1\right) \cdot x1\\ t_1 := \left(\left(x2 \cdot x2\right) \cdot x1\right) \cdot 8\\ t_2 := -1 - x1 \cdot x1\\ t_3 := \left(x2 \cdot 2 + t\_0\right) - x1\\ t_4 := x1 \cdot x1 - -1\\ t_5 := \frac{t\_3}{t\_4}\\ t_6 := x1 - \left(\left(\left(\left(\frac{t\_3}{t\_2} \cdot t\_0 - t\_2 \cdot \left(\left(3 - t\_5\right) \cdot \left(\left(2 \cdot x1\right) \cdot t\_5\right) - \left(4 \cdot t\_5 - 6\right) \cdot \left(x1 \cdot x1\right)\right)\right) - \left(x1 \cdot x1\right) \cdot x1\right) - x1\right) - \frac{\left(t\_0 - x2 \cdot 2\right) - x1}{t\_4} \cdot 3\right)\\ \mathbf{if}\;t\_6 \leq -1 \cdot 10^{+201}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_6 \leq 10^{+190}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(9, x1, -1\right), x1, -6 \cdot x2\right)\\ \mathbf{elif}\;t\_6 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(9, x1, -1\right) \cdot x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* 3.0 x1) x1))
        (t_1 (* (* (* x2 x2) x1) 8.0))
        (t_2 (- -1.0 (* x1 x1)))
        (t_3 (- (+ (* x2 2.0) t_0) x1))
        (t_4 (- (* x1 x1) -1.0))
        (t_5 (/ t_3 t_4))
        (t_6
         (-
          x1
          (-
           (-
            (-
             (-
              (* (/ t_3 t_2) t_0)
              (*
               t_2
               (-
                (* (- 3.0 t_5) (* (* 2.0 x1) t_5))
                (* (- (* 4.0 t_5) 6.0) (* x1 x1)))))
             (* (* x1 x1) x1))
            x1)
           (* (/ (- (- t_0 (* x2 2.0)) x1) t_4) 3.0)))))
   (if (<= t_6 -1e+201)
     t_1
     (if (<= t_6 1e+190)
       (fma (fma 9.0 x1 -1.0) x1 (* -6.0 x2))
       (if (<= t_6 INFINITY) t_1 (* (fma 9.0 x1 -1.0) x1))))))

C

double code(double x1, double x2) {
	double t_0 = (3.0 * x1) * x1;
	double t_1 = ((x2 * x2) * x1) * 8.0;
	double t_2 = -1.0 - (x1 * x1);
	double t_3 = ((x2 * 2.0) + t_0) - x1;
	double t_4 = (x1 * x1) - -1.0;
	double t_5 = t_3 / t_4;
	double t_6 = x1 - ((((((t_3 / t_2) * t_0) - (t_2 * (((3.0 - t_5) * ((2.0 * x1) * t_5)) - (((4.0 * t_5) - 6.0) * (x1 * x1))))) - ((x1 * x1) * x1)) - x1) - ((((t_0 - (x2 * 2.0)) - x1) / t_4) * 3.0));
	double tmp;
	if (t_6 <= -1e+201) {
		tmp = t_1;
	} else if (t_6 <= 1e+190) {
		tmp = fma(fma(9.0, x1, -1.0), x1, (-6.0 * x2));
	} else if (t_6 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma(9.0, x1, -1.0) * x1;
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(3.0 * x1) * x1)
	t_1 = Float64(Float64(Float64(x2 * x2) * x1) * 8.0)
	t_2 = Float64(-1.0 - Float64(x1 * x1))
	t_3 = Float64(Float64(Float64(x2 * 2.0) + t_0) - x1)
	t_4 = Float64(Float64(x1 * x1) - -1.0)
	t_5 = Float64(t_3 / t_4)
	t_6 = Float64(x1 - Float64(Float64(Float64(Float64(Float64(Float64(t_3 / t_2) * t_0) - Float64(t_2 * Float64(Float64(Float64(3.0 - t_5) * Float64(Float64(2.0 * x1) * t_5)) - Float64(Float64(Float64(4.0 * t_5) - 6.0) * Float64(x1 * x1))))) - Float64(Float64(x1 * x1) * x1)) - x1) - Float64(Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_4) * 3.0)))
	tmp = 0.0
	if (t_6 <= -1e+201)
		tmp = t_1;
	elseif (t_6 <= 1e+190)
		tmp = fma(fma(9.0, x1, -1.0), x1, Float64(-6.0 * x2));
	elseif (t_6 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(fma(9.0, x1, -1.0) * x1);
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(x2 * x2), $MachinePrecision] * x1), $MachinePrecision] * 8.0), $MachinePrecision]}, Block[{t$95$2 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 * x1), $MachinePrecision] - -1.0), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$3 / t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(x1 - N[(N[(N[(N[(N[(N[(t$95$3 / t$95$2), $MachinePrecision] * t$95$0), $MachinePrecision] - N[(t$95$2 * N[(N[(N[(3.0 - t$95$5), $MachinePrecision] * N[(N[(2.0 * x1), $MachinePrecision] * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(4.0 * t$95$5), $MachinePrecision] - 6.0), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] - N[(N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$4), $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$6, -1e+201], t$95$1, If[LessEqual[t$95$6, 1e+190], N[(N[(9.0 * x1 + -1.0), $MachinePrecision] * x1 + N[(-6.0 * x2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$6, Infinity], t$95$1, N[(N[(9.0 * x1 + -1.0), $MachinePrecision] * x1), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 3 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)))))) < -1.00000000000000004e201 or 1.0000000000000001e190 < (+.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 99.8%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 4.5

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

   5. Applied rewrites 4.5%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 55.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right)\right), x1, x2 \cdot -6\right)} \]

   9. Taylor expanded in x2 around inf

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

   11. Applied rewrites 53.9%

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

   if -1.00000000000000004e201 < (+.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)))))) < 1.0000000000000001e190

   1. Initial program 99.1%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 52.3

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

   5. Applied rewrites 52.3%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 86.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right)\right), x1, x2 \cdot -6\right)} \]

   9. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{fma}\left(9 \cdot x1 - 1, x1, x2 \cdot -6\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 82.5%

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(9, x1, -1\right), x1, x2 \cdot -6\right) \]

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 3.3

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

   5. Applied rewrites 3.3%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 67.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right)\right), x1, x2 \cdot -6\right)} \]

   9. Taylor expanded in x2 around 0

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

   11. Applied rewrites 85.7%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 - \left(\left(\left(\left(\frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{-1 - x1 \cdot x1} \cdot \left(\left(3 \cdot x1\right) \cdot x1\right) - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(3 - \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) \cdot \left(\left(2 \cdot x1\right) \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) - \left(4 \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1} - 6\right) \cdot \left(x1 \cdot x1\right)\right)\right) - \left(x1 \cdot x1\right) \cdot x1\right) - x1\right) - \frac{\left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right) - x1}{x1 \cdot x1 - -1} \cdot 3\right) \leq -1 \cdot 10^{+201}:\\ \;\;\;\;\left(\left(x2 \cdot x2\right) \cdot x1\right) \cdot 8\\ \mathbf{elif}\;x1 - \left(\left(\left(\left(\frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{-1 - x1 \cdot x1} \cdot \left(\left(3 \cdot x1\right) \cdot x1\right) - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(3 - \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) \cdot \left(\left(2 \cdot x1\right) \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) - \left(4 \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1} - 6\right) \cdot \left(x1 \cdot x1\right)\right)\right) - \left(x1 \cdot x1\right) \cdot x1\right) - x1\right) - \frac{\left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right) - x1}{x1 \cdot x1 - -1} \cdot 3\right) \leq 10^{+190}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(9, x1, -1\right), x1, -6 \cdot x2\right)\\ \mathbf{elif}\;x1 - \left(\left(\left(\left(\frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{-1 - x1 \cdot x1} \cdot \left(\left(3 \cdot x1\right) \cdot x1\right) - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(3 - \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) \cdot \left(\left(2 \cdot x1\right) \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) - \left(4 \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1} - 6\right) \cdot \left(x1 \cdot x1\right)\right)\right) - \left(x1 \cdot x1\right) \cdot x1\right) - x1\right) - \frac{\left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right) - x1}{x1 \cdot x1 - -1} \cdot 3\right) \leq \infty:\\ \;\;\;\;\left(\left(x2 \cdot x2\right) \cdot x1\right) \cdot 8\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(9, x1, -1\right) \cdot x1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(3 \cdot x1\right) \cdot x1\\ t_1 := -1 - x1 \cdot x1\\ t_2 := \left(x2 \cdot 2 + t\_0\right) - x1\\ t_3 := x1 \cdot x1 - -1\\ t_4 := \frac{t\_2}{t\_3}\\ t_5 := x1 - \left(\left(\left(\left(\frac{t\_2}{t\_1} \cdot t\_0 - t\_1 \cdot \left(\left(3 - t\_4\right) \cdot \left(\left(2 \cdot x1\right) \cdot t\_4\right) - \left(4 \cdot t\_4 - 6\right) \cdot \left(x1 \cdot x1\right)\right)\right) - \left(x1 \cdot x1\right) \cdot x1\right) - x1\right) - \frac{\left(t\_0 - x2 \cdot 2\right) - x1}{t\_3} \cdot 3\right)\\ \mathbf{if}\;t\_5 \leq -2 \cdot 10^{+67}:\\ \;\;\;\;\mathsf{fma}\left(\left(x2 \cdot x2\right) \cdot 8, x1, -6 \cdot x2\right)\\ \mathbf{elif}\;t\_5 \leq 10^{+78}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(9, x1, -1\right), x1, -6 \cdot x2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot 6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* 3.0 x1) x1))
        (t_1 (- -1.0 (* x1 x1)))
        (t_2 (- (+ (* x2 2.0) t_0) x1))
        (t_3 (- (* x1 x1) -1.0))
        (t_4 (/ t_2 t_3))
        (t_5
         (-
          x1
          (-
           (-
            (-
             (-
              (* (/ t_2 t_1) t_0)
              (*
               t_1
               (-
                (* (- 3.0 t_4) (* (* 2.0 x1) t_4))
                (* (- (* 4.0 t_4) 6.0) (* x1 x1)))))
             (* (* x1 x1) x1))
            x1)
           (* (/ (- (- t_0 (* x2 2.0)) x1) t_3) 3.0)))))
   (if (<= t_5 -2e+67)
     (fma (* (* x2 x2) 8.0) x1 (* -6.0 x2))
     (if (<= t_5 1e+78)
       (fma (fma 9.0 x1 -1.0) x1 (* -6.0 x2))
       (* (* (* x1 x1) (* x1 x1)) 6.0)))))

C

double code(double x1, double x2) {
	double t_0 = (3.0 * x1) * x1;
	double t_1 = -1.0 - (x1 * x1);
	double t_2 = ((x2 * 2.0) + t_0) - x1;
	double t_3 = (x1 * x1) - -1.0;
	double t_4 = t_2 / t_3;
	double t_5 = x1 - ((((((t_2 / t_1) * t_0) - (t_1 * (((3.0 - t_4) * ((2.0 * x1) * t_4)) - (((4.0 * t_4) - 6.0) * (x1 * x1))))) - ((x1 * x1) * x1)) - x1) - ((((t_0 - (x2 * 2.0)) - x1) / t_3) * 3.0));
	double tmp;
	if (t_5 <= -2e+67) {
		tmp = fma(((x2 * x2) * 8.0), x1, (-6.0 * x2));
	} else if (t_5 <= 1e+78) {
		tmp = fma(fma(9.0, x1, -1.0), x1, (-6.0 * x2));
	} else {
		tmp = ((x1 * x1) * (x1 * x1)) * 6.0;
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(3.0 * x1) * x1)
	t_1 = Float64(-1.0 - Float64(x1 * x1))
	t_2 = Float64(Float64(Float64(x2 * 2.0) + t_0) - x1)
	t_3 = Float64(Float64(x1 * x1) - -1.0)
	t_4 = Float64(t_2 / t_3)
	t_5 = Float64(x1 - Float64(Float64(Float64(Float64(Float64(Float64(t_2 / t_1) * t_0) - Float64(t_1 * Float64(Float64(Float64(3.0 - t_4) * Float64(Float64(2.0 * x1) * t_4)) - Float64(Float64(Float64(4.0 * t_4) - 6.0) * Float64(x1 * x1))))) - Float64(Float64(x1 * x1) * x1)) - x1) - Float64(Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_3) * 3.0)))
	tmp = 0.0
	if (t_5 <= -2e+67)
		tmp = fma(Float64(Float64(x2 * x2) * 8.0), x1, Float64(-6.0 * x2));
	elseif (t_5 <= 1e+78)
		tmp = fma(fma(9.0, x1, -1.0), x1, Float64(-6.0 * x2));
	else
		tmp = Float64(Float64(Float64(x1 * x1) * Float64(x1 * x1)) * 6.0);
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$1 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] - -1.0), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(x1 - N[(N[(N[(N[(N[(N[(t$95$2 / t$95$1), $MachinePrecision] * t$95$0), $MachinePrecision] - N[(t$95$1 * N[(N[(N[(3.0 - t$95$4), $MachinePrecision] * N[(N[(2.0 * x1), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(4.0 * t$95$4), $MachinePrecision] - 6.0), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] - N[(N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$5, -2e+67], N[(N[(N[(x2 * x2), $MachinePrecision] * 8.0), $MachinePrecision] * x1 + N[(-6.0 * x2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, 1e+78], N[(N[(9.0 * x1 + -1.0), $MachinePrecision] * x1 + N[(-6.0 * x2), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * 6.0), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 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)))))) < -1.99999999999999997e67

   1. Initial program 99.7%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 36.9

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

   5. Applied rewrites 36.9%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 80.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right)\right), x1, x2 \cdot -6\right)} \]

   9. Taylor expanded in x2 around inf

      \[\leadsto \mathsf{fma}\left(8 \cdot {x2}^{2}, x1, x2 \cdot -6\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 80.7%

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

   if -1.99999999999999997e67 < (+.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)))))) < 1.00000000000000001e78

   1. Initial program 99.1%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 50.9

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

   5. Applied rewrites 50.9%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 94.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right)\right), x1, x2 \cdot -6\right)} \]

   9. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{fma}\left(9 \cdot x1 - 1, x1, x2 \cdot -6\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 92.1%

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(9, x1, -1\right), x1, x2 \cdot -6\right) \]

   if 1.00000000000000001e78 < (+.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 44.8%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 8.5

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

   5. Applied rewrites 8.5%

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

   6. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{6 \cdot {x1}^{4}} \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-pow.f64 75.5

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

   8. Applied rewrites 75.5%

      \[\leadsto \color{blue}{{x1}^{4} \cdot 6} \]
   9. Step-by-step derivation

   10. Applied rewrites 75.5%

       \[\leadsto \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot 6 \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 - \left(\left(\left(\left(\frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{-1 - x1 \cdot x1} \cdot \left(\left(3 \cdot x1\right) \cdot x1\right) - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(3 - \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) \cdot \left(\left(2 \cdot x1\right) \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) - \left(4 \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1} - 6\right) \cdot \left(x1 \cdot x1\right)\right)\right) - \left(x1 \cdot x1\right) \cdot x1\right) - x1\right) - \frac{\left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right) - x1}{x1 \cdot x1 - -1} \cdot 3\right) \leq -2 \cdot 10^{+67}:\\ \;\;\;\;\mathsf{fma}\left(\left(x2 \cdot x2\right) \cdot 8, x1, -6 \cdot x2\right)\\ \mathbf{elif}\;x1 - \left(\left(\left(\left(\frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{-1 - x1 \cdot x1} \cdot \left(\left(3 \cdot x1\right) \cdot x1\right) - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(3 - \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) \cdot \left(\left(2 \cdot x1\right) \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) - \left(4 \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1} - 6\right) \cdot \left(x1 \cdot x1\right)\right)\right) - \left(x1 \cdot x1\right) \cdot x1\right) - x1\right) - \frac{\left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right) - x1}{x1 \cdot x1 - -1} \cdot 3\right) \leq 10^{+78}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(9, x1, -1\right), x1, -6 \cdot x2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot 6\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(3 \cdot x1\right) \cdot x1\\ t_1 := -1 - x1 \cdot x1\\ t_2 := \left(x2 \cdot 2 + t\_0\right) - x1\\ t_3 := x1 \cdot x1 - -1\\ t_4 := \frac{t\_2}{t\_3}\\ t_5 := x1 - \left(\left(\left(\left(\frac{t\_2}{t\_1} \cdot t\_0 - t\_1 \cdot \left(\left(3 - t\_4\right) \cdot \left(\left(2 \cdot x1\right) \cdot t\_4\right) - \left(4 \cdot t\_4 - 6\right) \cdot \left(x1 \cdot x1\right)\right)\right) - \left(x1 \cdot x1\right) \cdot x1\right) - x1\right) - \frac{\left(t\_0 - x2 \cdot 2\right) - x1}{t\_3} \cdot 3\right)\\ \mathbf{if}\;t\_5 \leq -1 \cdot 10^{+201}:\\ \;\;\;\;\left(\left(x2 \cdot x2\right) \cdot x1\right) \cdot 8\\ \mathbf{elif}\;t\_5 \leq 10^{+78}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(9, x1, -1\right), x1, -6 \cdot x2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot 6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* 3.0 x1) x1))
        (t_1 (- -1.0 (* x1 x1)))
        (t_2 (- (+ (* x2 2.0) t_0) x1))
        (t_3 (- (* x1 x1) -1.0))
        (t_4 (/ t_2 t_3))
        (t_5
         (-
          x1
          (-
           (-
            (-
             (-
              (* (/ t_2 t_1) t_0)
              (*
               t_1
               (-
                (* (- 3.0 t_4) (* (* 2.0 x1) t_4))
                (* (- (* 4.0 t_4) 6.0) (* x1 x1)))))
             (* (* x1 x1) x1))
            x1)
           (* (/ (- (- t_0 (* x2 2.0)) x1) t_3) 3.0)))))
   (if (<= t_5 -1e+201)
     (* (* (* x2 x2) x1) 8.0)
     (if (<= t_5 1e+78)
       (fma (fma 9.0 x1 -1.0) x1 (* -6.0 x2))
       (* (* (* x1 x1) (* x1 x1)) 6.0)))))

C

double code(double x1, double x2) {
	double t_0 = (3.0 * x1) * x1;
	double t_1 = -1.0 - (x1 * x1);
	double t_2 = ((x2 * 2.0) + t_0) - x1;
	double t_3 = (x1 * x1) - -1.0;
	double t_4 = t_2 / t_3;
	double t_5 = x1 - ((((((t_2 / t_1) * t_0) - (t_1 * (((3.0 - t_4) * ((2.0 * x1) * t_4)) - (((4.0 * t_4) - 6.0) * (x1 * x1))))) - ((x1 * x1) * x1)) - x1) - ((((t_0 - (x2 * 2.0)) - x1) / t_3) * 3.0));
	double tmp;
	if (t_5 <= -1e+201) {
		tmp = ((x2 * x2) * x1) * 8.0;
	} else if (t_5 <= 1e+78) {
		tmp = fma(fma(9.0, x1, -1.0), x1, (-6.0 * x2));
	} else {
		tmp = ((x1 * x1) * (x1 * x1)) * 6.0;
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(3.0 * x1) * x1)
	t_1 = Float64(-1.0 - Float64(x1 * x1))
	t_2 = Float64(Float64(Float64(x2 * 2.0) + t_0) - x1)
	t_3 = Float64(Float64(x1 * x1) - -1.0)
	t_4 = Float64(t_2 / t_3)
	t_5 = Float64(x1 - Float64(Float64(Float64(Float64(Float64(Float64(t_2 / t_1) * t_0) - Float64(t_1 * Float64(Float64(Float64(3.0 - t_4) * Float64(Float64(2.0 * x1) * t_4)) - Float64(Float64(Float64(4.0 * t_4) - 6.0) * Float64(x1 * x1))))) - Float64(Float64(x1 * x1) * x1)) - x1) - Float64(Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_3) * 3.0)))
	tmp = 0.0
	if (t_5 <= -1e+201)
		tmp = Float64(Float64(Float64(x2 * x2) * x1) * 8.0);
	elseif (t_5 <= 1e+78)
		tmp = fma(fma(9.0, x1, -1.0), x1, Float64(-6.0 * x2));
	else
		tmp = Float64(Float64(Float64(x1 * x1) * Float64(x1 * x1)) * 6.0);
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$1 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] - -1.0), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(x1 - N[(N[(N[(N[(N[(N[(t$95$2 / t$95$1), $MachinePrecision] * t$95$0), $MachinePrecision] - N[(t$95$1 * N[(N[(N[(3.0 - t$95$4), $MachinePrecision] * N[(N[(2.0 * x1), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(4.0 * t$95$4), $MachinePrecision] - 6.0), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] - N[(N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$5, -1e+201], N[(N[(N[(x2 * x2), $MachinePrecision] * x1), $MachinePrecision] * 8.0), $MachinePrecision], If[LessEqual[t$95$5, 1e+78], N[(N[(9.0 * x1 + -1.0), $MachinePrecision] * x1 + N[(-6.0 * x2), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * 6.0), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 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)))))) < -1.00000000000000004e201

   1. Initial program 99.9%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 4.9

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

   5. Applied rewrites 4.9%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 75.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right)\right), x1, x2 \cdot -6\right)} \]

   9. Taylor expanded in x2 around inf

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

   11. Applied rewrites 75.4%

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

   if -1.00000000000000004e201 < (+.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)))))) < 1.00000000000000001e78

   1. Initial program 99.1%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 54.6

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

   5. Applied rewrites 54.6%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 93.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right)\right), x1, x2 \cdot -6\right)} \]

   9. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{fma}\left(9 \cdot x1 - 1, x1, x2 \cdot -6\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 89.5%

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(9, x1, -1\right), x1, x2 \cdot -6\right) \]

   if 1.00000000000000001e78 < (+.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 44.8%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 8.5

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

   5. Applied rewrites 8.5%

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

   6. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{6 \cdot {x1}^{4}} \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-pow.f64 75.5

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

   8. Applied rewrites 75.5%

      \[\leadsto \color{blue}{{x1}^{4} \cdot 6} \]
   9. Step-by-step derivation

   10. Applied rewrites 75.5%

       \[\leadsto \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot 6 \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 - \left(\left(\left(\left(\frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{-1 - x1 \cdot x1} \cdot \left(\left(3 \cdot x1\right) \cdot x1\right) - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(3 - \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) \cdot \left(\left(2 \cdot x1\right) \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) - \left(4 \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1} - 6\right) \cdot \left(x1 \cdot x1\right)\right)\right) - \left(x1 \cdot x1\right) \cdot x1\right) - x1\right) - \frac{\left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right) - x1}{x1 \cdot x1 - -1} \cdot 3\right) \leq -1 \cdot 10^{+201}:\\ \;\;\;\;\left(\left(x2 \cdot x2\right) \cdot x1\right) \cdot 8\\ \mathbf{elif}\;x1 - \left(\left(\left(\left(\frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{-1 - x1 \cdot x1} \cdot \left(\left(3 \cdot x1\right) \cdot x1\right) - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(3 - \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) \cdot \left(\left(2 \cdot x1\right) \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) - \left(4 \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1} - 6\right) \cdot \left(x1 \cdot x1\right)\right)\right) - \left(x1 \cdot x1\right) \cdot x1\right) - x1\right) - \frac{\left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right) - x1}{x1 \cdot x1 - -1} \cdot 3\right) \leq 10^{+78}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(9, x1, -1\right), x1, -6 \cdot x2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot 6\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(3 \cdot x1\right) \cdot x1\\ t_1 := -1 - x1 \cdot x1\\ t_2 := \left(x2 \cdot 2 + t\_0\right) - x1\\ t_3 := x1 \cdot x1 - -1\\ t_4 := \frac{t\_2}{t\_3}\\ t_5 := x1 - \left(\left(\left(\left(\frac{t\_2}{t\_1} \cdot t\_0 - t\_1 \cdot \left(\left(3 - t\_4\right) \cdot \left(\left(2 \cdot x1\right) \cdot t\_4\right) - \left(4 \cdot t\_4 - 6\right) \cdot \left(x1 \cdot x1\right)\right)\right) - \left(x1 \cdot x1\right) \cdot x1\right) - x1\right) - \frac{\left(t\_0 - x2 \cdot 2\right) - x1}{t\_3} \cdot 3\right)\\ \mathbf{if}\;t\_5 \leq -1 \cdot 10^{+201}:\\ \;\;\;\;\left(\left(x2 \cdot x2\right) \cdot x1\right) \cdot 8\\ \mathbf{elif}\;t\_5 \leq 10^{+78}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(9, x1, -1\right), x1, -6 \cdot x2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(6 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(x1 \cdot x1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* 3.0 x1) x1))
        (t_1 (- -1.0 (* x1 x1)))
        (t_2 (- (+ (* x2 2.0) t_0) x1))
        (t_3 (- (* x1 x1) -1.0))
        (t_4 (/ t_2 t_3))
        (t_5
         (-
          x1
          (-
           (-
            (-
             (-
              (* (/ t_2 t_1) t_0)
              (*
               t_1
               (-
                (* (- 3.0 t_4) (* (* 2.0 x1) t_4))
                (* (- (* 4.0 t_4) 6.0) (* x1 x1)))))
             (* (* x1 x1) x1))
            x1)
           (* (/ (- (- t_0 (* x2 2.0)) x1) t_3) 3.0)))))
   (if (<= t_5 -1e+201)
     (* (* (* x2 x2) x1) 8.0)
     (if (<= t_5 1e+78)
       (fma (fma 9.0 x1 -1.0) x1 (* -6.0 x2))
       (* (* 6.0 (* x1 x1)) (* x1 x1))))))

C

double code(double x1, double x2) {
	double t_0 = (3.0 * x1) * x1;
	double t_1 = -1.0 - (x1 * x1);
	double t_2 = ((x2 * 2.0) + t_0) - x1;
	double t_3 = (x1 * x1) - -1.0;
	double t_4 = t_2 / t_3;
	double t_5 = x1 - ((((((t_2 / t_1) * t_0) - (t_1 * (((3.0 - t_4) * ((2.0 * x1) * t_4)) - (((4.0 * t_4) - 6.0) * (x1 * x1))))) - ((x1 * x1) * x1)) - x1) - ((((t_0 - (x2 * 2.0)) - x1) / t_3) * 3.0));
	double tmp;
	if (t_5 <= -1e+201) {
		tmp = ((x2 * x2) * x1) * 8.0;
	} else if (t_5 <= 1e+78) {
		tmp = fma(fma(9.0, x1, -1.0), x1, (-6.0 * x2));
	} else {
		tmp = (6.0 * (x1 * x1)) * (x1 * x1);
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(3.0 * x1) * x1)
	t_1 = Float64(-1.0 - Float64(x1 * x1))
	t_2 = Float64(Float64(Float64(x2 * 2.0) + t_0) - x1)
	t_3 = Float64(Float64(x1 * x1) - -1.0)
	t_4 = Float64(t_2 / t_3)
	t_5 = Float64(x1 - Float64(Float64(Float64(Float64(Float64(Float64(t_2 / t_1) * t_0) - Float64(t_1 * Float64(Float64(Float64(3.0 - t_4) * Float64(Float64(2.0 * x1) * t_4)) - Float64(Float64(Float64(4.0 * t_4) - 6.0) * Float64(x1 * x1))))) - Float64(Float64(x1 * x1) * x1)) - x1) - Float64(Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_3) * 3.0)))
	tmp = 0.0
	if (t_5 <= -1e+201)
		tmp = Float64(Float64(Float64(x2 * x2) * x1) * 8.0);
	elseif (t_5 <= 1e+78)
		tmp = fma(fma(9.0, x1, -1.0), x1, Float64(-6.0 * x2));
	else
		tmp = Float64(Float64(6.0 * Float64(x1 * x1)) * Float64(x1 * x1));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$1 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] - -1.0), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(x1 - N[(N[(N[(N[(N[(N[(t$95$2 / t$95$1), $MachinePrecision] * t$95$0), $MachinePrecision] - N[(t$95$1 * N[(N[(N[(3.0 - t$95$4), $MachinePrecision] * N[(N[(2.0 * x1), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(4.0 * t$95$4), $MachinePrecision] - 6.0), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] - N[(N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$5, -1e+201], N[(N[(N[(x2 * x2), $MachinePrecision] * x1), $MachinePrecision] * 8.0), $MachinePrecision], If[LessEqual[t$95$5, 1e+78], N[(N[(9.0 * x1 + -1.0), $MachinePrecision] * x1 + N[(-6.0 * x2), $MachinePrecision]), $MachinePrecision], N[(N[(6.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 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)))))) < -1.00000000000000004e201

   1. Initial program 99.9%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 4.9

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

   5. Applied rewrites 4.9%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 75.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right)\right), x1, x2 \cdot -6\right)} \]

   9. Taylor expanded in x2 around inf

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

   11. Applied rewrites 75.4%

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

   if -1.00000000000000004e201 < (+.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)))))) < 1.00000000000000001e78

   1. Initial program 99.1%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 54.6

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

   5. Applied rewrites 54.6%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 93.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right)\right), x1, x2 \cdot -6\right)} \]

   9. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{fma}\left(9 \cdot x1 - 1, x1, x2 \cdot -6\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 89.5%

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(9, x1, -1\right), x1, x2 \cdot -6\right) \]

   if 1.00000000000000001e78 < (+.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 44.8%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 8.5

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

   5. Applied rewrites 8.5%

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

   6. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{6 \cdot {x1}^{4}} \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-pow.f64 75.5

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

   8. Applied rewrites 75.5%

      \[\leadsto \color{blue}{{x1}^{4} \cdot 6} \]
   9. Step-by-step derivation

   10. Applied rewrites 75.4%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 - \left(\left(\left(\left(\frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{-1 - x1 \cdot x1} \cdot \left(\left(3 \cdot x1\right) \cdot x1\right) - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(3 - \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) \cdot \left(\left(2 \cdot x1\right) \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) - \left(4 \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1} - 6\right) \cdot \left(x1 \cdot x1\right)\right)\right) - \left(x1 \cdot x1\right) \cdot x1\right) - x1\right) - \frac{\left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right) - x1}{x1 \cdot x1 - -1} \cdot 3\right) \leq -1 \cdot 10^{+201}:\\ \;\;\;\;\left(\left(x2 \cdot x2\right) \cdot x1\right) \cdot 8\\ \mathbf{elif}\;x1 - \left(\left(\left(\left(\frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{-1 - x1 \cdot x1} \cdot \left(\left(3 \cdot x1\right) \cdot x1\right) - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(3 - \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) \cdot \left(\left(2 \cdot x1\right) \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1}\right) - \left(4 \cdot \frac{\left(x2 \cdot 2 + \left(3 \cdot x1\right) \cdot x1\right) - x1}{x1 \cdot x1 - -1} - 6\right) \cdot \left(x1 \cdot x1\right)\right)\right) - \left(x1 \cdot x1\right) \cdot x1\right) - x1\right) - \frac{\left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right) - x1}{x1 \cdot x1 - -1} \cdot 3\right) \leq 10^{+78}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(9, x1, -1\right), x1, -6 \cdot x2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(6 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(x1 \cdot x1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.3%

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

   4. Applied rewrites 99.7%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 3.3

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

   5. Applied rewrites 3.3%

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

   6. Taylor expanded in x1 around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   8. Applied rewrites 100.0%

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

4. Final simplification 99.8%

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

Alternative 9: 98.8% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.3%

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto x1 + \mathsf{fma}\left(x1 \cdot x1, x1, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4, \frac{\mathsf{fma}\left(x2, 2, \left(3 \cdot x1\right) \cdot x1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, -6\right), x1 \cdot x1, \left(\frac{\mathsf{fma}\left(x2, 2, \left(3 \cdot x1\right) \cdot x1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3\right) \cdot \left(\frac{\mathsf{fma}\left(x2, 2, \left(3 \cdot x1\right) \cdot x1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(x1 \cdot 2\right)\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \color{blue}{9 \cdot {x1}^{2}}\right) + \mathsf{fma}\left(\frac{\mathsf{fma}\left(-2, x2, \left(3 \cdot x1\right) \cdot x1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, 3, x1\right)\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. unpow2 N/A

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

      3. lower-*.f64 98.9

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

   7. Applied rewrites 98.9%

      \[\leadsto x1 + \mathsf{fma}\left(x1 \cdot x1, x1, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4, \frac{\mathsf{fma}\left(x2, 2, \left(3 \cdot x1\right) \cdot x1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, -6\right), x1 \cdot x1, \left(\frac{\mathsf{fma}\left(x2, 2, \left(3 \cdot x1\right) \cdot x1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3\right) \cdot \left(\frac{\mathsf{fma}\left(x2, 2, \left(3 \cdot x1\right) \cdot x1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(x1 \cdot 2\right)\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \color{blue}{9 \cdot \left(x1 \cdot x1\right)}\right) + \mathsf{fma}\left(\frac{\mathsf{fma}\left(-2, x2, \left(3 \cdot x1\right) \cdot x1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, 3, x1\right)\right) \]
   8. Step-by-step derivation

      1. lift-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. clear-num N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift-fma.f64 98.9

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

      7. lift-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 98.9

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 98.9

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

   9. Applied rewrites 98.9%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 3.3

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

   5. Applied rewrites 3.3%

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

   6. Taylor expanded in x1 around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   8. Applied rewrites 100.0%

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

4. Final simplification 99.2%

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

Alternative 10: 98.8% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.3%

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto x1 + \mathsf{fma}\left(x1 \cdot x1, x1, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4, \frac{\mathsf{fma}\left(x2, 2, \left(3 \cdot x1\right) \cdot x1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, -6\right), x1 \cdot x1, \left(\frac{\mathsf{fma}\left(x2, 2, \left(3 \cdot x1\right) \cdot x1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3\right) \cdot \left(\frac{\mathsf{fma}\left(x2, 2, \left(3 \cdot x1\right) \cdot x1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(x1 \cdot 2\right)\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \color{blue}{9 \cdot {x1}^{2}}\right) + \mathsf{fma}\left(\frac{\mathsf{fma}\left(-2, x2, \left(3 \cdot x1\right) \cdot x1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, 3, x1\right)\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. unpow2 N/A

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

      3. lower-*.f64 98.9

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

   7. Applied rewrites 98.9%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 3.3

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

   5. Applied rewrites 3.3%

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

   6. Taylor expanded in x1 around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   8. Applied rewrites 100.0%

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

4. Final simplification 99.2%

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

Alternative 11: 94.7% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.3%

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto x1 + \mathsf{fma}\left(x1 \cdot x1, x1, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4, \frac{\mathsf{fma}\left(x2, 2, \left(3 \cdot x1\right) \cdot x1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, -6\right), x1 \cdot x1, \left(\frac{\mathsf{fma}\left(x2, 2, \left(3 \cdot x1\right) \cdot x1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3\right) \cdot \left(\frac{\mathsf{fma}\left(x2, 2, \left(3 \cdot x1\right) \cdot x1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(x1 \cdot 2\right)\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \color{blue}{9 \cdot {x1}^{2}}\right) + \mathsf{fma}\left(\frac{\mathsf{fma}\left(-2, x2, \left(3 \cdot x1\right) \cdot x1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, 3, x1\right)\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. unpow2 N/A

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

      3. lower-*.f64 98.9

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

   7. Applied rewrites 98.9%

      \[\leadsto x1 + \mathsf{fma}\left(x1 \cdot x1, x1, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4, \frac{\mathsf{fma}\left(x2, 2, \left(3 \cdot x1\right) \cdot x1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, -6\right), x1 \cdot x1, \left(\frac{\mathsf{fma}\left(x2, 2, \left(3 \cdot x1\right) \cdot x1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3\right) \cdot \left(\frac{\mathsf{fma}\left(x2, 2, \left(3 \cdot x1\right) \cdot x1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(x1 \cdot 2\right)\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \color{blue}{9 \cdot \left(x1 \cdot x1\right)}\right) + \mathsf{fma}\left(\frac{\mathsf{fma}\left(-2, x2, \left(3 \cdot x1\right) \cdot x1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, 3, x1\right)\right) \]
   8. Step-by-step derivation

      1. lift-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. clear-num N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift-fma.f64 98.9

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

      7. lift-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 98.9

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 98.9

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

   9. Applied rewrites 98.9%

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

   10. Taylor expanded in x1 around 0

       \[\leadsto x1 + \mathsf{fma}\left(x1 \cdot x1, x1, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4, \frac{\mathsf{fma}\left(x2, 2, \left(3 \cdot x1\right) \cdot x1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, -6\right), x1 \cdot x1, \color{blue}{\left(2 \cdot x2 - 3\right)} \cdot \left(\frac{1}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{\mathsf{fma}\left(2, x2, \left(x1 \cdot 3\right) \cdot x1\right) - x1}} \cdot \left(x1 \cdot 2\right)\right)\right), \mathsf{fma}\left(x1, x1, 1\right), 9 \cdot \left(x1 \cdot x1\right)\right) + \mathsf{fma}\left(\frac{\mathsf{fma}\left(-2, x2, \left(3 \cdot x1\right) \cdot x1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, 3, x1\right)\right) \]
   11. Step-by-step derivation

       1. sub-neg N/A

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

       2. metadata-eval N/A

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

       3. lower-fma.f64 94.2

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

   12. Applied rewrites 94.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 3.3

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

   5. Applied rewrites 3.3%

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

   6. Taylor expanded in x1 around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   8. Applied rewrites 100.0%

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

4. Final simplification 95.9%

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

Alternative 12: 95.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -780000000000:\\ \;\;\;\;\left(6 - \frac{3 - \frac{\mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)}{x1}}{x1}\right) \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq 720:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(x2 \cdot x1, 8, \mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, -6\right)\right), x2, \mathsf{fma}\left(9, x1, -1\right) \cdot x1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(2, x2, -3\right)}{x1}, \frac{4}{x1}, \frac{9}{x1 \cdot x1} + 6\right) - \frac{3}{x1}\right) \cdot {x1}^{4} + x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -780000000000.0)
   (*
    (- 6.0 (/ (- 3.0 (/ (fma (fma 2.0 x2 -3.0) 4.0 9.0) x1)) x1))
    (pow x1 4.0))
   (if (<= x1 720.0)
     (fma
      (fma (* x2 x1) 8.0 (fma (fma 12.0 x1 -12.0) x1 -6.0))
      x2
      (* (fma 9.0 x1 -1.0) x1))
     (+
      (*
       (-
        (fma (/ (fma 2.0 x2 -3.0) x1) (/ 4.0 x1) (+ (/ 9.0 (* x1 x1)) 6.0))
        (/ 3.0 x1))
       (pow x1 4.0))
      x1))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -780000000000.0) {
		tmp = (6.0 - ((3.0 - (fma(fma(2.0, x2, -3.0), 4.0, 9.0) / x1)) / x1)) * pow(x1, 4.0);
	} else if (x1 <= 720.0) {
		tmp = fma(fma((x2 * x1), 8.0, fma(fma(12.0, x1, -12.0), x1, -6.0)), x2, (fma(9.0, x1, -1.0) * x1));
	} else {
		tmp = ((fma((fma(2.0, x2, -3.0) / x1), (4.0 / x1), ((9.0 / (x1 * x1)) + 6.0)) - (3.0 / x1)) * pow(x1, 4.0)) + x1;
	}
	return tmp;
}

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -780000000000.0)
		tmp = Float64(Float64(6.0 - Float64(Float64(3.0 - Float64(fma(fma(2.0, x2, -3.0), 4.0, 9.0) / x1)) / x1)) * (x1 ^ 4.0));
	elseif (x1 <= 720.0)
		tmp = fma(fma(Float64(x2 * x1), 8.0, fma(fma(12.0, x1, -12.0), x1, -6.0)), x2, Float64(fma(9.0, x1, -1.0) * x1));
	else
		tmp = Float64(Float64(Float64(fma(Float64(fma(2.0, x2, -3.0) / x1), Float64(4.0 / x1), Float64(Float64(9.0 / Float64(x1 * x1)) + 6.0)) - Float64(3.0 / x1)) * (x1 ^ 4.0)) + x1);
	end
	return tmp
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -780000000000.0], N[(N[(6.0 - N[(N[(3.0 - N[(N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * 4.0 + 9.0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 720.0], N[(N[(N[(x2 * x1), $MachinePrecision] * 8.0 + N[(N[(12.0 * x1 + -12.0), $MachinePrecision] * x1 + -6.0), $MachinePrecision]), $MachinePrecision] * x2 + N[(N[(9.0 * x1 + -1.0), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(2.0 * x2 + -3.0), $MachinePrecision] / x1), $MachinePrecision] * N[(4.0 / x1), $MachinePrecision] + N[(N[(9.0 / N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + 6.0), $MachinePrecision]), $MachinePrecision] - N[(3.0 / x1), $MachinePrecision]), $MachinePrecision] * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -7.8e11

   1. Initial program 28.0%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 0.8

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

   5. Applied rewrites 0.8%

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

   6. Taylor expanded in x1 around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   8. Applied rewrites 94.3%

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

   if -7.8e11 < x1 < 720

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 46.9

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

   5. Applied rewrites 46.9%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 89.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right)\right), x1, x2 \cdot -6\right)} \]

   9. Taylor expanded in x2 around 0

      \[\leadsto x1 \cdot \left(9 \cdot x1 - 1\right) + \color{blue}{x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 99.0%

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

   if 720 < x1

   1. Initial program 44.8%

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

   3. Taylor expanded in x1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 95.2%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -780000000000:\\ \;\;\;\;\left(6 - \frac{3 - \frac{\mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)}{x1}}{x1}\right) \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq 720:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(x2 \cdot x1, 8, \mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, -6\right)\right), x2, \mathsf{fma}\left(9, x1, -1\right) \cdot x1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(2, x2, -3\right)}{x1}, \frac{4}{x1}, \frac{9}{x1 \cdot x1} + 6\right) - \frac{3}{x1}\right) \cdot {x1}^{4} + x1\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 95.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)}{x1}\\ \mathbf{if}\;x1 \leq -780000000000:\\ \;\;\;\;\left(6 - \frac{3 - t\_0}{x1}\right) \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq 720:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(x2 \cdot x1, 8, \mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, -6\right)\right), x2, \mathsf{fma}\left(9, x1, -1\right) \cdot x1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x1 \cdot x1, x1, \left(6 - \frac{4 - t\_0}{x1}\right) \cdot {x1}^{4}\right) + x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (/ (fma (fma 2.0 x2 -3.0) 4.0 9.0) x1)))
   (if (<= x1 -780000000000.0)
     (* (- 6.0 (/ (- 3.0 t_0) x1)) (pow x1 4.0))
     (if (<= x1 720.0)
       (fma
        (fma (* x2 x1) 8.0 (fma (fma 12.0 x1 -12.0) x1 -6.0))
        x2
        (* (fma 9.0 x1 -1.0) x1))
       (+
        (fma (* x1 x1) x1 (* (- 6.0 (/ (- 4.0 t_0) x1)) (pow x1 4.0)))
        x1)))))

C

double code(double x1, double x2) {
	double t_0 = fma(fma(2.0, x2, -3.0), 4.0, 9.0) / x1;
	double tmp;
	if (x1 <= -780000000000.0) {
		tmp = (6.0 - ((3.0 - t_0) / x1)) * pow(x1, 4.0);
	} else if (x1 <= 720.0) {
		tmp = fma(fma((x2 * x1), 8.0, fma(fma(12.0, x1, -12.0), x1, -6.0)), x2, (fma(9.0, x1, -1.0) * x1));
	} else {
		tmp = fma((x1 * x1), x1, ((6.0 - ((4.0 - t_0) / x1)) * pow(x1, 4.0))) + x1;
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(fma(fma(2.0, x2, -3.0), 4.0, 9.0) / x1)
	tmp = 0.0
	if (x1 <= -780000000000.0)
		tmp = Float64(Float64(6.0 - Float64(Float64(3.0 - t_0) / x1)) * (x1 ^ 4.0));
	elseif (x1 <= 720.0)
		tmp = fma(fma(Float64(x2 * x1), 8.0, fma(fma(12.0, x1, -12.0), x1, -6.0)), x2, Float64(fma(9.0, x1, -1.0) * x1));
	else
		tmp = Float64(fma(Float64(x1 * x1), x1, Float64(Float64(6.0 - Float64(Float64(4.0 - t_0) / x1)) * (x1 ^ 4.0))) + x1);
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * 4.0 + 9.0), $MachinePrecision] / x1), $MachinePrecision]}, If[LessEqual[x1, -780000000000.0], N[(N[(6.0 - N[(N[(3.0 - t$95$0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 720.0], N[(N[(N[(x2 * x1), $MachinePrecision] * 8.0 + N[(N[(12.0 * x1 + -12.0), $MachinePrecision] * x1 + -6.0), $MachinePrecision]), $MachinePrecision] * x2 + N[(N[(9.0 * x1 + -1.0), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] * x1 + N[(N[(6.0 - N[(N[(4.0 - t$95$0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -7.8e11

   1. Initial program 28.0%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 0.8

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

   5. Applied rewrites 0.8%

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

   6. Taylor expanded in x1 around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   8. Applied rewrites 94.3%

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

   if -7.8e11 < x1 < 720

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 46.9

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

   5. Applied rewrites 46.9%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 89.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right)\right), x1, x2 \cdot -6\right)} \]

   9. Taylor expanded in x2 around 0

      \[\leadsto x1 \cdot \left(9 \cdot x1 - 1\right) + \color{blue}{x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 99.0%

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

   if 720 < x1

   1. Initial program 44.8%

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

   4. Applied rewrites 48.1%

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

   5. Taylor expanded in x1 around -inf

      \[\leadsto x1 + \mathsf{fma}\left(x1 \cdot x1, x1, \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{4 + -1 \cdot \frac{9 + 4 \cdot \left(2 \cdot x2 - 3\right)}{x1}}{x1}\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   7. Applied rewrites 95.2%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -780000000000:\\ \;\;\;\;\left(6 - \frac{3 - \frac{\mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)}{x1}}{x1}\right) \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq 720:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(x2 \cdot x1, 8, \mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, -6\right)\right), x2, \mathsf{fma}\left(9, x1, -1\right) \cdot x1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x1 \cdot x1, x1, \left(6 - \frac{4 - \frac{\mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)}{x1}}{x1}\right) \cdot {x1}^{4}\right) + x1\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 95.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)\\ \mathbf{if}\;x1 \leq -780000000000:\\ \;\;\;\;\left(6 - \frac{3 - \frac{t\_0}{x1}}{x1}\right) \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq 720:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(x2 \cdot x1, 8, \mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, -6\right)\right), x2, \mathsf{fma}\left(9, x1, -1\right) \cdot x1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x1 \cdot x1, x1, \mathsf{fma}\left(\mathsf{fma}\left(6, x1, -4\right), x1, t\_0\right) \cdot \left(x1 \cdot x1\right)\right) + x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (fma (fma 2.0 x2 -3.0) 4.0 9.0)))
   (if (<= x1 -780000000000.0)
     (* (- 6.0 (/ (- 3.0 (/ t_0 x1)) x1)) (pow x1 4.0))
     (if (<= x1 720.0)
       (fma
        (fma (* x2 x1) 8.0 (fma (fma 12.0 x1 -12.0) x1 -6.0))
        x2
        (* (fma 9.0 x1 -1.0) x1))
       (+
        (fma (* x1 x1) x1 (* (fma (fma 6.0 x1 -4.0) x1 t_0) (* x1 x1)))
        x1)))))

C

double code(double x1, double x2) {
	double t_0 = fma(fma(2.0, x2, -3.0), 4.0, 9.0);
	double tmp;
	if (x1 <= -780000000000.0) {
		tmp = (6.0 - ((3.0 - (t_0 / x1)) / x1)) * pow(x1, 4.0);
	} else if (x1 <= 720.0) {
		tmp = fma(fma((x2 * x1), 8.0, fma(fma(12.0, x1, -12.0), x1, -6.0)), x2, (fma(9.0, x1, -1.0) * x1));
	} else {
		tmp = fma((x1 * x1), x1, (fma(fma(6.0, x1, -4.0), x1, t_0) * (x1 * x1))) + x1;
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = fma(fma(2.0, x2, -3.0), 4.0, 9.0)
	tmp = 0.0
	if (x1 <= -780000000000.0)
		tmp = Float64(Float64(6.0 - Float64(Float64(3.0 - Float64(t_0 / x1)) / x1)) * (x1 ^ 4.0));
	elseif (x1 <= 720.0)
		tmp = fma(fma(Float64(x2 * x1), 8.0, fma(fma(12.0, x1, -12.0), x1, -6.0)), x2, Float64(fma(9.0, x1, -1.0) * x1));
	else
		tmp = Float64(fma(Float64(x1 * x1), x1, Float64(fma(fma(6.0, x1, -4.0), x1, t_0) * Float64(x1 * x1))) + x1);
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * 4.0 + 9.0), $MachinePrecision]}, If[LessEqual[x1, -780000000000.0], N[(N[(6.0 - N[(N[(3.0 - N[(t$95$0 / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 720.0], N[(N[(N[(x2 * x1), $MachinePrecision] * 8.0 + N[(N[(12.0 * x1 + -12.0), $MachinePrecision] * x1 + -6.0), $MachinePrecision]), $MachinePrecision] * x2 + N[(N[(9.0 * x1 + -1.0), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] * x1 + N[(N[(N[(6.0 * x1 + -4.0), $MachinePrecision] * x1 + t$95$0), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -7.8e11

   1. Initial program 28.0%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 0.8

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

   5. Applied rewrites 0.8%

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

   6. Taylor expanded in x1 around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   8. Applied rewrites 94.3%

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

   if -7.8e11 < x1 < 720

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 46.9

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

   5. Applied rewrites 46.9%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 89.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right)\right), x1, x2 \cdot -6\right)} \]

   9. Taylor expanded in x2 around 0

      \[\leadsto x1 \cdot \left(9 \cdot x1 - 1\right) + \color{blue}{x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 99.0%

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

   if 720 < x1

   1. Initial program 44.8%

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

   4. Applied rewrites 48.1%

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

   5. Taylor expanded in x1 around -inf

      \[\leadsto x1 + \mathsf{fma}\left(x1 \cdot x1, x1, \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{4 + -1 \cdot \frac{9 + 4 \cdot \left(2 \cdot x2 - 3\right)}{x1}}{x1}\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   7. Applied rewrites 95.2%

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

   8. Taylor expanded in x1 around 0

      \[\leadsto x1 + \mathsf{fma}\left(x1 \cdot x1, x1, {x1}^{2} \cdot \color{blue}{\left(9 + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(6 \cdot x1 - 4\right)\right)\right)}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 95.1%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -780000000000:\\ \;\;\;\;\left(6 - \frac{3 - \frac{\mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)}{x1}}{x1}\right) \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq 720:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(x2 \cdot x1, 8, \mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, -6\right)\right), x2, \mathsf{fma}\left(9, x1, -1\right) \cdot x1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x1 \cdot x1, x1, \mathsf{fma}\left(\mathsf{fma}\left(6, x1, -4\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)\right) \cdot \left(x1 \cdot x1\right)\right) + x1\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 94.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1050000000000:\\ \;\;\;\;\left(6 - \frac{3}{x1}\right) \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq 720:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(x2 \cdot x1, 8, \mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, -6\right)\right), x2, \mathsf{fma}\left(9, x1, -1\right) \cdot x1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x1 \cdot x1, x1, \mathsf{fma}\left(\mathsf{fma}\left(6, x1, -4\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)\right) \cdot \left(x1 \cdot x1\right)\right) + x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1050000000000.0)
   (* (- 6.0 (/ 3.0 x1)) (pow x1 4.0))
   (if (<= x1 720.0)
     (fma
      (fma (* x2 x1) 8.0 (fma (fma 12.0 x1 -12.0) x1 -6.0))
      x2
      (* (fma 9.0 x1 -1.0) x1))
     (+
      (fma
       (* x1 x1)
       x1
       (*
        (fma (fma 6.0 x1 -4.0) x1 (fma (fma 2.0 x2 -3.0) 4.0 9.0))
        (* x1 x1)))
      x1))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1050000000000.0) {
		tmp = (6.0 - (3.0 / x1)) * pow(x1, 4.0);
	} else if (x1 <= 720.0) {
		tmp = fma(fma((x2 * x1), 8.0, fma(fma(12.0, x1, -12.0), x1, -6.0)), x2, (fma(9.0, x1, -1.0) * x1));
	} else {
		tmp = fma((x1 * x1), x1, (fma(fma(6.0, x1, -4.0), x1, fma(fma(2.0, x2, -3.0), 4.0, 9.0)) * (x1 * x1))) + x1;
	}
	return tmp;
}

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1050000000000.0)
		tmp = Float64(Float64(6.0 - Float64(3.0 / x1)) * (x1 ^ 4.0));
	elseif (x1 <= 720.0)
		tmp = fma(fma(Float64(x2 * x1), 8.0, fma(fma(12.0, x1, -12.0), x1, -6.0)), x2, Float64(fma(9.0, x1, -1.0) * x1));
	else
		tmp = Float64(fma(Float64(x1 * x1), x1, Float64(fma(fma(6.0, x1, -4.0), x1, fma(fma(2.0, x2, -3.0), 4.0, 9.0)) * Float64(x1 * x1))) + x1);
	end
	return tmp
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1050000000000.0], N[(N[(6.0 - N[(3.0 / x1), $MachinePrecision]), $MachinePrecision] * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 720.0], N[(N[(N[(x2 * x1), $MachinePrecision] * 8.0 + N[(N[(12.0 * x1 + -12.0), $MachinePrecision] * x1 + -6.0), $MachinePrecision]), $MachinePrecision] * x2 + N[(N[(9.0 * x1 + -1.0), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] * x1 + N[(N[(N[(6.0 * x1 + -4.0), $MachinePrecision] * x1 + N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * 4.0 + 9.0), $MachinePrecision]), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.05e12

   1. Initial program 28.0%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 0.8

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

   5. Applied rewrites 0.8%

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

   6. Taylor expanded in x1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 N/A

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

      7. lower-pow.f64 90.6

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

   8. Applied rewrites 90.6%

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

   if -1.05e12 < x1 < 720

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 46.9

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

   5. Applied rewrites 46.9%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 89.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right)\right), x1, x2 \cdot -6\right)} \]

   9. Taylor expanded in x2 around 0

      \[\leadsto x1 \cdot \left(9 \cdot x1 - 1\right) + \color{blue}{x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 99.0%

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

   if 720 < x1

   1. Initial program 44.8%

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

   4. Applied rewrites 48.1%

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

   5. Taylor expanded in x1 around -inf

      \[\leadsto x1 + \mathsf{fma}\left(x1 \cdot x1, x1, \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{4 + -1 \cdot \frac{9 + 4 \cdot \left(2 \cdot x2 - 3\right)}{x1}}{x1}\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   7. Applied rewrites 95.2%

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

   8. Taylor expanded in x1 around 0

      \[\leadsto x1 + \mathsf{fma}\left(x1 \cdot x1, x1, {x1}^{2} \cdot \color{blue}{\left(9 + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(6 \cdot x1 - 4\right)\right)\right)}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 95.1%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1050000000000:\\ \;\;\;\;\left(6 - \frac{3}{x1}\right) \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq 720:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(x2 \cdot x1, 8, \mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, -6\right)\right), x2, \mathsf{fma}\left(9, x1, -1\right) \cdot x1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x1 \cdot x1, x1, \mathsf{fma}\left(\mathsf{fma}\left(6, x1, -4\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)\right) \cdot \left(x1 \cdot x1\right)\right) + x1\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 94.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2700000000000:\\ \;\;\;\;{x1}^{4} \cdot 6\\ \mathbf{elif}\;x1 \leq 720:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(x2 \cdot x1, 8, \mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, -6\right)\right), x2, \mathsf{fma}\left(9, x1, -1\right) \cdot x1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x1 \cdot x1, x1, \mathsf{fma}\left(\mathsf{fma}\left(6, x1, -4\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)\right) \cdot \left(x1 \cdot x1\right)\right) + x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -2700000000000.0)
   (* (pow x1 4.0) 6.0)
   (if (<= x1 720.0)
     (fma
      (fma (* x2 x1) 8.0 (fma (fma 12.0 x1 -12.0) x1 -6.0))
      x2
      (* (fma 9.0 x1 -1.0) x1))
     (+
      (fma
       (* x1 x1)
       x1
       (*
        (fma (fma 6.0 x1 -4.0) x1 (fma (fma 2.0 x2 -3.0) 4.0 9.0))
        (* x1 x1)))
      x1))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2700000000000.0) {
		tmp = pow(x1, 4.0) * 6.0;
	} else if (x1 <= 720.0) {
		tmp = fma(fma((x2 * x1), 8.0, fma(fma(12.0, x1, -12.0), x1, -6.0)), x2, (fma(9.0, x1, -1.0) * x1));
	} else {
		tmp = fma((x1 * x1), x1, (fma(fma(6.0, x1, -4.0), x1, fma(fma(2.0, x2, -3.0), 4.0, 9.0)) * (x1 * x1))) + x1;
	}
	return tmp;
}

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -2700000000000.0)
		tmp = Float64((x1 ^ 4.0) * 6.0);
	elseif (x1 <= 720.0)
		tmp = fma(fma(Float64(x2 * x1), 8.0, fma(fma(12.0, x1, -12.0), x1, -6.0)), x2, Float64(fma(9.0, x1, -1.0) * x1));
	else
		tmp = Float64(fma(Float64(x1 * x1), x1, Float64(fma(fma(6.0, x1, -4.0), x1, fma(fma(2.0, x2, -3.0), 4.0, 9.0)) * Float64(x1 * x1))) + x1);
	end
	return tmp
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -2700000000000.0], N[(N[Power[x1, 4.0], $MachinePrecision] * 6.0), $MachinePrecision], If[LessEqual[x1, 720.0], N[(N[(N[(x2 * x1), $MachinePrecision] * 8.0 + N[(N[(12.0 * x1 + -12.0), $MachinePrecision] * x1 + -6.0), $MachinePrecision]), $MachinePrecision] * x2 + N[(N[(9.0 * x1 + -1.0), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] * x1 + N[(N[(N[(6.0 * x1 + -4.0), $MachinePrecision] * x1 + N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * 4.0 + 9.0), $MachinePrecision]), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.7e12

   1. Initial program 28.0%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 0.8

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

   5. Applied rewrites 0.8%

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

   6. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{6 \cdot {x1}^{4}} \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-pow.f64 90.3

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

   8. Applied rewrites 90.3%

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

   if -2.7e12 < x1 < 720

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 46.9

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

   5. Applied rewrites 46.9%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 89.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right)\right), x1, x2 \cdot -6\right)} \]

   9. Taylor expanded in x2 around 0

      \[\leadsto x1 \cdot \left(9 \cdot x1 - 1\right) + \color{blue}{x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 99.0%

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

   if 720 < x1

   1. Initial program 44.8%

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

   4. Applied rewrites 48.1%

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

   5. Taylor expanded in x1 around -inf

      \[\leadsto x1 + \mathsf{fma}\left(x1 \cdot x1, x1, \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{4 + -1 \cdot \frac{9 + 4 \cdot \left(2 \cdot x2 - 3\right)}{x1}}{x1}\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   7. Applied rewrites 95.2%

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

   8. Taylor expanded in x1 around 0

      \[\leadsto x1 + \mathsf{fma}\left(x1 \cdot x1, x1, {x1}^{2} \cdot \color{blue}{\left(9 + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(6 \cdot x1 - 4\right)\right)\right)}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 95.1%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2700000000000:\\ \;\;\;\;{x1}^{4} \cdot 6\\ \mathbf{elif}\;x1 \leq 720:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(x2 \cdot x1, 8, \mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, -6\right)\right), x2, \mathsf{fma}\left(9, x1, -1\right) \cdot x1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x1 \cdot x1, x1, \mathsf{fma}\left(\mathsf{fma}\left(6, x1, -4\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)\right) \cdot \left(x1 \cdot x1\right)\right) + x1\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 94.4% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2700000000000:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot 6\\ \mathbf{elif}\;x1 \leq 720:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(x2 \cdot x1, 8, \mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, -6\right)\right), x2, \mathsf{fma}\left(9, x1, -1\right) \cdot x1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x1 \cdot x1, x1, \mathsf{fma}\left(\mathsf{fma}\left(6, x1, -4\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)\right) \cdot \left(x1 \cdot x1\right)\right) + x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -2700000000000.0)
   (* (* (* x1 x1) (* x1 x1)) 6.0)
   (if (<= x1 720.0)
     (fma
      (fma (* x2 x1) 8.0 (fma (fma 12.0 x1 -12.0) x1 -6.0))
      x2
      (* (fma 9.0 x1 -1.0) x1))
     (+
      (fma
       (* x1 x1)
       x1
       (*
        (fma (fma 6.0 x1 -4.0) x1 (fma (fma 2.0 x2 -3.0) 4.0 9.0))
        (* x1 x1)))
      x1))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2700000000000.0) {
		tmp = ((x1 * x1) * (x1 * x1)) * 6.0;
	} else if (x1 <= 720.0) {
		tmp = fma(fma((x2 * x1), 8.0, fma(fma(12.0, x1, -12.0), x1, -6.0)), x2, (fma(9.0, x1, -1.0) * x1));
	} else {
		tmp = fma((x1 * x1), x1, (fma(fma(6.0, x1, -4.0), x1, fma(fma(2.0, x2, -3.0), 4.0, 9.0)) * (x1 * x1))) + x1;
	}
	return tmp;
}

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -2700000000000.0)
		tmp = Float64(Float64(Float64(x1 * x1) * Float64(x1 * x1)) * 6.0);
	elseif (x1 <= 720.0)
		tmp = fma(fma(Float64(x2 * x1), 8.0, fma(fma(12.0, x1, -12.0), x1, -6.0)), x2, Float64(fma(9.0, x1, -1.0) * x1));
	else
		tmp = Float64(fma(Float64(x1 * x1), x1, Float64(fma(fma(6.0, x1, -4.0), x1, fma(fma(2.0, x2, -3.0), 4.0, 9.0)) * Float64(x1 * x1))) + x1);
	end
	return tmp
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -2700000000000.0], N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * 6.0), $MachinePrecision], If[LessEqual[x1, 720.0], N[(N[(N[(x2 * x1), $MachinePrecision] * 8.0 + N[(N[(12.0 * x1 + -12.0), $MachinePrecision] * x1 + -6.0), $MachinePrecision]), $MachinePrecision] * x2 + N[(N[(9.0 * x1 + -1.0), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] * x1 + N[(N[(N[(6.0 * x1 + -4.0), $MachinePrecision] * x1 + N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * 4.0 + 9.0), $MachinePrecision]), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.7e12

   1. Initial program 28.0%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 0.8

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

   5. Applied rewrites 0.8%

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

   6. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{6 \cdot {x1}^{4}} \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-pow.f64 90.3

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

   8. Applied rewrites 90.3%

      \[\leadsto \color{blue}{{x1}^{4} \cdot 6} \]
   9. Step-by-step derivation

   10. Applied rewrites 90.2%

       \[\leadsto \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot 6 \]

   if -2.7e12 < x1 < 720

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 46.9

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

   5. Applied rewrites 46.9%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 89.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right)\right), x1, x2 \cdot -6\right)} \]

   9. Taylor expanded in x2 around 0

      \[\leadsto x1 \cdot \left(9 \cdot x1 - 1\right) + \color{blue}{x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 99.0%

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

   if 720 < x1

   1. Initial program 44.8%

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

   4. Applied rewrites 48.1%

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

   5. Taylor expanded in x1 around -inf

      \[\leadsto x1 + \mathsf{fma}\left(x1 \cdot x1, x1, \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{4 + -1 \cdot \frac{9 + 4 \cdot \left(2 \cdot x2 - 3\right)}{x1}}{x1}\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   7. Applied rewrites 95.2%

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

   8. Taylor expanded in x1 around 0

      \[\leadsto x1 + \mathsf{fma}\left(x1 \cdot x1, x1, {x1}^{2} \cdot \color{blue}{\left(9 + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(6 \cdot x1 - 4\right)\right)\right)}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 95.1%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2700000000000:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot 6\\ \mathbf{elif}\;x1 \leq 720:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(x2 \cdot x1, 8, \mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, -6\right)\right), x2, \mathsf{fma}\left(9, x1, -1\right) \cdot x1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x1 \cdot x1, x1, \mathsf{fma}\left(\mathsf{fma}\left(6, x1, -4\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)\right) \cdot \left(x1 \cdot x1\right)\right) + x1\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 93.0% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2700000000000:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot 6\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+29}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(x2 \cdot x1, 8, \mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, -6\right)\right), x2, \mathsf{fma}\left(9, x1, -1\right) \cdot x1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(6 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(x1 \cdot x1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -2700000000000.0)
   (* (* (* x1 x1) (* x1 x1)) 6.0)
   (if (<= x1 2e+29)
     (fma
      (fma (* x2 x1) 8.0 (fma (fma 12.0 x1 -12.0) x1 -6.0))
      x2
      (* (fma 9.0 x1 -1.0) x1))
     (* (* 6.0 (* x1 x1)) (* x1 x1)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2700000000000.0) {
		tmp = ((x1 * x1) * (x1 * x1)) * 6.0;
	} else if (x1 <= 2e+29) {
		tmp = fma(fma((x2 * x1), 8.0, fma(fma(12.0, x1, -12.0), x1, -6.0)), x2, (fma(9.0, x1, -1.0) * x1));
	} else {
		tmp = (6.0 * (x1 * x1)) * (x1 * x1);
	}
	return tmp;
}

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -2700000000000.0)
		tmp = Float64(Float64(Float64(x1 * x1) * Float64(x1 * x1)) * 6.0);
	elseif (x1 <= 2e+29)
		tmp = fma(fma(Float64(x2 * x1), 8.0, fma(fma(12.0, x1, -12.0), x1, -6.0)), x2, Float64(fma(9.0, x1, -1.0) * x1));
	else
		tmp = Float64(Float64(6.0 * Float64(x1 * x1)) * Float64(x1 * x1));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -2700000000000.0], N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * 6.0), $MachinePrecision], If[LessEqual[x1, 2e+29], N[(N[(N[(x2 * x1), $MachinePrecision] * 8.0 + N[(N[(12.0 * x1 + -12.0), $MachinePrecision] * x1 + -6.0), $MachinePrecision]), $MachinePrecision] * x2 + N[(N[(9.0 * x1 + -1.0), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision], N[(N[(6.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.7e12

   1. Initial program 28.0%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 0.8

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

   5. Applied rewrites 0.8%

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

   6. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{6 \cdot {x1}^{4}} \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-pow.f64 90.3

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

   8. Applied rewrites 90.3%

      \[\leadsto \color{blue}{{x1}^{4} \cdot 6} \]
   9. Step-by-step derivation

   10. Applied rewrites 90.2%

       \[\leadsto \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot 6 \]

   if -2.7e12 < x1 < 1.99999999999999983e29

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 45.7

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

   5. Applied rewrites 45.7%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 88.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right)\right), x1, x2 \cdot -6\right)} \]

   9. Taylor expanded in x2 around 0

      \[\leadsto x1 \cdot \left(9 \cdot x1 - 1\right) + \color{blue}{x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 97.2%

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

   if 1.99999999999999983e29 < x1

   1. Initial program 41.1%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 5.5

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

   5. Applied rewrites 5.5%

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

   6. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{6 \cdot {x1}^{4}} \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-pow.f64 90.2

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

   8. Applied rewrites 90.2%

      \[\leadsto \color{blue}{{x1}^{4} \cdot 6} \]
   9. Step-by-step derivation

   10. Applied rewrites 90.2%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2700000000000:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot 6\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+29}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(x2 \cdot x1, 8, \mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, -6\right)\right), x2, \mathsf{fma}\left(9, x1, -1\right) \cdot x1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(6 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(x1 \cdot x1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 87.4% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2700000000000:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot 6\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+29}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(9, x1, \mathsf{fma}\left(\mathsf{fma}\left(8, x2, \mathsf{fma}\left(12, x1, -12\right)\right), x2, -1\right)\right), x1, -6 \cdot x2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(6 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(x1 \cdot x1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -2700000000000.0)
   (* (* (* x1 x1) (* x1 x1)) 6.0)
   (if (<= x1 2e+29)
     (fma
      (fma 9.0 x1 (fma (fma 8.0 x2 (fma 12.0 x1 -12.0)) x2 -1.0))
      x1
      (* -6.0 x2))
     (* (* 6.0 (* x1 x1)) (* x1 x1)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2700000000000.0) {
		tmp = ((x1 * x1) * (x1 * x1)) * 6.0;
	} else if (x1 <= 2e+29) {
		tmp = fma(fma(9.0, x1, fma(fma(8.0, x2, fma(12.0, x1, -12.0)), x2, -1.0)), x1, (-6.0 * x2));
	} else {
		tmp = (6.0 * (x1 * x1)) * (x1 * x1);
	}
	return tmp;
}

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -2700000000000.0)
		tmp = Float64(Float64(Float64(x1 * x1) * Float64(x1 * x1)) * 6.0);
	elseif (x1 <= 2e+29)
		tmp = fma(fma(9.0, x1, fma(fma(8.0, x2, fma(12.0, x1, -12.0)), x2, -1.0)), x1, Float64(-6.0 * x2));
	else
		tmp = Float64(Float64(6.0 * Float64(x1 * x1)) * Float64(x1 * x1));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -2700000000000.0], N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * 6.0), $MachinePrecision], If[LessEqual[x1, 2e+29], N[(N[(9.0 * x1 + N[(N[(8.0 * x2 + N[(12.0 * x1 + -12.0), $MachinePrecision]), $MachinePrecision] * x2 + -1.0), $MachinePrecision]), $MachinePrecision] * x1 + N[(-6.0 * x2), $MachinePrecision]), $MachinePrecision], N[(N[(6.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.7e12

   1. Initial program 28.0%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 0.8

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

   5. Applied rewrites 0.8%

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

   6. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{6 \cdot {x1}^{4}} \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-pow.f64 90.3

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

   8. Applied rewrites 90.3%

      \[\leadsto \color{blue}{{x1}^{4} \cdot 6} \]
   9. Step-by-step derivation

   10. Applied rewrites 90.2%

       \[\leadsto \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot 6 \]

   if -2.7e12 < x1 < 1.99999999999999983e29

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 45.7

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

   5. Applied rewrites 45.7%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 88.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right)\right), x1, x2 \cdot -6\right)} \]

   9. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{fma}\left(\left(9 \cdot x1 + x2 \cdot \left(\left(8 \cdot x2 + 12 \cdot x1\right) - 12\right)\right) - 1, x1, x2 \cdot -6\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 88.0%

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(9, x1, \mathsf{fma}\left(\mathsf{fma}\left(8, x2, \mathsf{fma}\left(12, x1, -12\right)\right), x2, -1\right)\right), x1, x2 \cdot -6\right) \]

   if 1.99999999999999983e29 < x1

   1. Initial program 41.1%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 5.5

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

   5. Applied rewrites 5.5%

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

   6. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{6 \cdot {x1}^{4}} \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-pow.f64 90.2

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

   8. Applied rewrites 90.2%

      \[\leadsto \color{blue}{{x1}^{4} \cdot 6} \]
   9. Step-by-step derivation

   10. Applied rewrites 90.2%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2700000000000:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot 6\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+29}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(9, x1, \mathsf{fma}\left(\mathsf{fma}\left(8, x2, \mathsf{fma}\left(12, x1, -12\right)\right), x2, -1\right)\right), x1, -6 \cdot x2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(6 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(x1 \cdot x1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 87.3% accurate, 6.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2700000000000:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot 6\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+29}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(9, x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right)\right), x1, -6 \cdot x2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(6 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(x1 \cdot x1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -2700000000000.0)
   (* (* (* x1 x1) (* x1 x1)) 6.0)
   (if (<= x1 2e+29)
     (fma (fma 9.0 x1 (fma (* (fma 2.0 x2 -3.0) x2) 4.0 -1.0)) x1 (* -6.0 x2))
     (* (* 6.0 (* x1 x1)) (* x1 x1)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2700000000000.0) {
		tmp = ((x1 * x1) * (x1 * x1)) * 6.0;
	} else if (x1 <= 2e+29) {
		tmp = fma(fma(9.0, x1, fma((fma(2.0, x2, -3.0) * x2), 4.0, -1.0)), x1, (-6.0 * x2));
	} else {
		tmp = (6.0 * (x1 * x1)) * (x1 * x1);
	}
	return tmp;
}

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -2700000000000.0)
		tmp = Float64(Float64(Float64(x1 * x1) * Float64(x1 * x1)) * 6.0);
	elseif (x1 <= 2e+29)
		tmp = fma(fma(9.0, x1, fma(Float64(fma(2.0, x2, -3.0) * x2), 4.0, -1.0)), x1, Float64(-6.0 * x2));
	else
		tmp = Float64(Float64(6.0 * Float64(x1 * x1)) * Float64(x1 * x1));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -2700000000000.0], N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * 6.0), $MachinePrecision], If[LessEqual[x1, 2e+29], N[(N[(9.0 * x1 + N[(N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * x2), $MachinePrecision] * 4.0 + -1.0), $MachinePrecision]), $MachinePrecision] * x1 + N[(-6.0 * x2), $MachinePrecision]), $MachinePrecision], N[(N[(6.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.7e12

   1. Initial program 28.0%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 0.8

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

   5. Applied rewrites 0.8%

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

   6. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{6 \cdot {x1}^{4}} \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-pow.f64 90.3

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

   8. Applied rewrites 90.3%

      \[\leadsto \color{blue}{{x1}^{4} \cdot 6} \]
   9. Step-by-step derivation

   10. Applied rewrites 90.2%

       \[\leadsto \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot 6 \]

   if -2.7e12 < x1 < 1.99999999999999983e29

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 45.7

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

   5. Applied rewrites 45.7%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 88.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right)\right), x1, x2 \cdot -6\right)} \]

   9. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(9, x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right)\right), x1, x2 \cdot -6\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 88.0%

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(9, x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right)\right), x1, x2 \cdot -6\right) \]

   if 1.99999999999999983e29 < x1

   1. Initial program 41.1%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 5.5

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

   5. Applied rewrites 5.5%

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

   6. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{6 \cdot {x1}^{4}} \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-pow.f64 90.2

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

   8. Applied rewrites 90.2%

      \[\leadsto \color{blue}{{x1}^{4} \cdot 6} \]
   9. Step-by-step derivation

   10. Applied rewrites 90.2%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2700000000000:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot 6\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+29}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(9, x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right)\right), x1, -6 \cdot x2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(6 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(x1 \cdot x1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 87.4% accurate, 7.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2600000000000:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot 6\\ \mathbf{elif}\;x1 \leq 780:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right), x1, -6 \cdot x2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(6 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(x1 \cdot x1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -2600000000000.0)
   (* (* (* x1 x1) (* x1 x1)) 6.0)
   (if (<= x1 780.0)
     (fma (fma (* (fma 2.0 x2 -3.0) x2) 4.0 -1.0) x1 (* -6.0 x2))
     (* (* 6.0 (* x1 x1)) (* x1 x1)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2600000000000.0) {
		tmp = ((x1 * x1) * (x1 * x1)) * 6.0;
	} else if (x1 <= 780.0) {
		tmp = fma(fma((fma(2.0, x2, -3.0) * x2), 4.0, -1.0), x1, (-6.0 * x2));
	} else {
		tmp = (6.0 * (x1 * x1)) * (x1 * x1);
	}
	return tmp;
}

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -2600000000000.0)
		tmp = Float64(Float64(Float64(x1 * x1) * Float64(x1 * x1)) * 6.0);
	elseif (x1 <= 780.0)
		tmp = fma(fma(Float64(fma(2.0, x2, -3.0) * x2), 4.0, -1.0), x1, Float64(-6.0 * x2));
	else
		tmp = Float64(Float64(6.0 * Float64(x1 * x1)) * Float64(x1 * x1));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -2600000000000.0], N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * 6.0), $MachinePrecision], If[LessEqual[x1, 780.0], N[(N[(N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * x2), $MachinePrecision] * 4.0 + -1.0), $MachinePrecision] * x1 + N[(-6.0 * x2), $MachinePrecision]), $MachinePrecision], N[(N[(6.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.6e12

   1. Initial program 28.0%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 0.8

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

   5. Applied rewrites 0.8%

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

   6. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{6 \cdot {x1}^{4}} \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-pow.f64 90.3

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

   8. Applied rewrites 90.3%

      \[\leadsto \color{blue}{{x1}^{4} \cdot 6} \]
   9. Step-by-step derivation

   10. Applied rewrites 90.2%

       \[\leadsto \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot 6 \]

   if -2.6e12 < x1 < 780

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 46.9

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

   5. Applied rewrites 46.9%

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

   6. Taylor expanded in x1 around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. *-commutative N/A

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

      6. metadata-eval N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 88.7

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

   8. Applied rewrites 88.7%

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

   if 780 < x1

   1. Initial program 44.8%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 5.4

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

   5. Applied rewrites 5.4%

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

   6. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{6 \cdot {x1}^{4}} \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-pow.f64 86.2

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

   8. Applied rewrites 86.2%

      \[\leadsto \color{blue}{{x1}^{4} \cdot 6} \]
   9. Step-by-step derivation

   10. Applied rewrites 86.1%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2600000000000:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot 6\\ \mathbf{elif}\;x1 \leq 780:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right), x1, -6 \cdot x2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(6 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(x1 \cdot x1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 54.4% accurate, 12.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(9, x1, -1\right) \cdot x1\\ \mathbf{if}\;x1 \leq -8.5 \cdot 10^{-96}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 3.45 \cdot 10^{-62}:\\ \;\;\;\;-6 \cdot x2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (fma 9.0 x1 -1.0) x1)))
   (if (<= x1 -8.5e-96) t_0 (if (<= x1 3.45e-62) (* -6.0 x2) t_0))))

C

double code(double x1, double x2) {
	double t_0 = fma(9.0, x1, -1.0) * x1;
	double tmp;
	if (x1 <= -8.5e-96) {
		tmp = t_0;
	} else if (x1 <= 3.45e-62) {
		tmp = -6.0 * x2;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(fma(9.0, x1, -1.0) * x1)
	tmp = 0.0
	if (x1 <= -8.5e-96)
		tmp = t_0;
	elseif (x1 <= 3.45e-62)
		tmp = Float64(-6.0 * x2);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(9.0 * x1 + -1.0), $MachinePrecision] * x1), $MachinePrecision]}, If[LessEqual[x1, -8.5e-96], t$95$0, If[LessEqual[x1, 3.45e-62], N[(-6.0 * x2), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -8.49999999999999983e-96 or 3.44999999999999979e-62 < x1

   1. Initial program 53.6%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 5.1

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

   5. Applied rewrites 5.1%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 65.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right)\right), x1, x2 \cdot -6\right)} \]

   9. Taylor expanded in x2 around 0

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

   11. Applied rewrites 54.9%

       \[\leadsto \mathsf{fma}\left(9, x1, -1\right) \cdot \color{blue}{x1} \]

   if -8.49999999999999983e-96 < x1 < 3.44999999999999979e-62

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 62.5

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

   5. Applied rewrites 62.5%

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

   6. Taylor expanded in x1 around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 62.9

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

   8. Applied rewrites 62.9%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -8.5 \cdot 10^{-96}:\\ \;\;\;\;\mathsf{fma}\left(9, x1, -1\right) \cdot x1\\ \mathbf{elif}\;x1 \leq 3.45 \cdot 10^{-62}:\\ \;\;\;\;-6 \cdot x2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(9, x1, -1\right) \cdot x1\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 26.0% accurate, 33.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.4%

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

3. Taylor expanded in x1 around 0

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

   1. lower-*.f64 27.3

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

5. Applied rewrites 27.3%

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

6. Final simplification 27.3%

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

Alternative 24: 25.8% accurate, 49.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.4%

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

3. Taylor expanded in x1 around 0

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

   1. lower-*.f64 27.3

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

5. Applied rewrites 27.3%

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

6. Taylor expanded in x1 around 0

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

   1. *-commutative N/A

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

   2. lower-*.f64 27.2

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

8. Applied rewrites 27.2%

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

9. Final simplification 27.2%

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

Reproduce

herbie shell --seed 2024242 
(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))))))