Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.6% → 99.5%

Time: 20.2s

Alternatives: 18

Speedup: 7.3×

• 46.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 70.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* 3.0 x1) x1))
        (t_1 (- -1.0 (* x1 x1)))
        (t_2 (fma (* x1 x1) 3.0 (fma 2.0 x2 (- x1))))
        (t_3 (/ t_2 (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_1) t_0)
             (*
              t_1
              (-
               (* (- 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 (* x1 x1) (fma t_3 4.0 -6.0) (* (- t_3 3.0) (* (* 2.0 x1) t_3)))
       (fma x1 x1 1.0)
       (fma
        (* x1 x1)
        (fma t_2 (/ 3.0 (fma x1 x1 1.0)) x1)
        (fma (/ (- (fma -2.0 x2 t_0) x1) (fma x1 x1 1.0)) 3.0 x1)))
      x1)
     (+ (* (pow x1 4.0) 6.0) 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 = fma((x1 * x1), 3.0, fma(2.0, x2, -x1));
	double t_3 = t_2 / 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_1) * t_0) - (t_1 * (((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((x1 * x1), fma(t_3, 4.0, -6.0), ((t_3 - 3.0) * ((2.0 * x1) * t_3))), fma(x1, x1, 1.0), fma((x1 * x1), fma(t_2, (3.0 / fma(x1, x1, 1.0)), x1), fma(((fma(-2.0, x2, t_0) - x1) / fma(x1, x1, 1.0)), 3.0, x1))) + x1;
	} else {
		tmp = (pow(x1, 4.0) * 6.0) + 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 = fma(Float64(x1 * x1), 3.0, fma(2.0, x2, Float64(-x1)))
	t_3 = Float64(t_2 / 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_1) * t_0) - Float64(t_1 * 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(fma(Float64(x1 * x1), fma(t_3, 4.0, -6.0), Float64(Float64(t_3 - 3.0) * Float64(Float64(2.0 * x1) * t_3))), fma(x1, x1, 1.0), fma(Float64(x1 * x1), fma(t_2, Float64(3.0 / fma(x1, x1, 1.0)), x1), fma(Float64(Float64(fma(-2.0, x2, t_0) - x1) / fma(x1, x1, 1.0)), 3.0, x1))) + x1);
	else
		tmp = Float64(Float64((x1 ^ 4.0) * 6.0) + 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[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] * 3.0 + N[(2.0 * x2 + (-x1)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / 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$1), $MachinePrecision] * t$95$0), $MachinePrecision] - N[(t$95$1 * 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[(x1 * x1), $MachinePrecision] * N[(t$95$3 * 4.0 + -6.0), $MachinePrecision] + N[(N[(t$95$3 - 3.0), $MachinePrecision] * N[(N[(2.0 * x1), $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x1 * x1 + 1.0), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(t$95$2 * N[(3.0 / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] + x1), $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[(N[Power[x1, 4.0], $MachinePrecision] * 6.0), $MachinePrecision] + x1), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

   4. Applied rewrites 99.6%

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

   6. Applied rewrites 99.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-pow.f64 98.6

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

   5. Applied rewrites 98.6%

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

4. Final simplification 99.4%

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

Alternative 2: 31.1% accurate, 0.9× speedup

Math

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

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)
     (* -6.0 x2)
     (+ (* 12.0 (* x2 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 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 = -6.0 * x2;
	} else {
		tmp = (12.0 * (x2 * x1)) + x1;
	}
	return tmp;
}

Java

public static 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.POSITIVE_INFINITY) {
		tmp = -6.0 * x2;
	} else {
		tmp = (12.0 * (x2 * x1)) + x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	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
	tmp = 0
	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))) <= math.inf:
		tmp = -6.0 * x2
	else:
		tmp = (12.0 * (x2 * 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)
	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(-6.0 * x2);
	else
		tmp = Float64(Float64(12.0 * Float64(x2 * x1)) + x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	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;
	tmp = 0.0;
	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))) <= Inf)
		tmp = -6.0 * x2;
	else
		tmp = (12.0 * (x2 * x1)) + x1;
	end
	tmp_2 = 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[(-6.0 * x2), $MachinePrecision], N[(N[(12.0 * N[(x2 * x1), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0

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

      1. lower-*.f64 30.7

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

   5. Applied rewrites 30.7%

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

   6. Taylor expanded in x1 around 0

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

      1. lower-*.f64 30.9

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

   8. Applied rewrites 30.9%

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

   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 -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 98.6%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 15.7%

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

   9. Taylor expanded in x2 around inf

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

   11. Applied rewrites 16.5%

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

4. Final simplification 26.8%

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

Alternative 3: 97.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(3 \cdot x1\right) \cdot x1\\ t_1 := \frac{\mathsf{fma}\left(x2, 2, t\_0\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\\ t_2 := \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)\\ \mathbf{if}\;x1 \leq -3.5 \cdot 10^{+55}:\\ \;\;\;\;\left(6 - \frac{3 - \frac{t\_2}{x1}}{x1}\right) \cdot {x1}^{4} + x1\\ \mathbf{elif}\;x1 \leq 8000:\\ \;\;\;\;\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(-2, x2, t\_0\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, 3, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4, t\_1, -6\right), x1 \cdot x1, \left(t\_1 \cdot \left(2 \cdot x1\right)\right) \cdot \left(t\_1 - 3\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \frac{\left(\left(x1 \cdot x1\right) \cdot x2\right) \cdot 6}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right) + x1\right) + x1\\ \mathbf{else}:\\ \;\;\;\;\left(6 - \frac{3 - \frac{t\_2 - \frac{\mathsf{fma}\left(2, x2, -3\right) \cdot -6}{x1}}{x1}}{x1}\right) \cdot {x1}^{4} + x1\\ \end{array} \end{array} \]

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 (fma (fma 2.0 x2 -3.0) 4.0 9.0)))
   (if (<= x1 -3.5e+55)
     (+ (* (- 6.0 (/ (- 3.0 (/ t_2 x1)) x1)) (pow x1 4.0)) x1)
     (if (<= x1 8000.0)
       (+
        (+
         (fma
          (/ (- (fma -2.0 x2 t_0) x1) (fma x1 x1 1.0))
          3.0
          (fma
           (fma
            (fma 4.0 t_1 -6.0)
            (* x1 x1)
            (* (* t_1 (* 2.0 x1)) (- t_1 3.0)))
           (fma x1 x1 1.0)
           (/ (* (* (* x1 x1) x2) 6.0) (fma x1 x1 1.0))))
         x1)
        x1)
       (+
        (*
         (-
          6.0
          (/ (- 3.0 (/ (- t_2 (/ (* (fma 2.0 x2 -3.0) -6.0) x1)) x1)) x1))
         (pow x1 4.0))
        x1)))))

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 = fma(fma(2.0, x2, -3.0), 4.0, 9.0);
	double tmp;
	if (x1 <= -3.5e+55) {
		tmp = ((6.0 - ((3.0 - (t_2 / x1)) / x1)) * pow(x1, 4.0)) + x1;
	} else if (x1 <= 8000.0) {
		tmp = (fma(((fma(-2.0, x2, t_0) - x1) / fma(x1, x1, 1.0)), 3.0, fma(fma(fma(4.0, t_1, -6.0), (x1 * x1), ((t_1 * (2.0 * x1)) * (t_1 - 3.0))), fma(x1, x1, 1.0), ((((x1 * x1) * x2) * 6.0) / fma(x1, x1, 1.0)))) + x1) + x1;
	} else {
		tmp = ((6.0 - ((3.0 - ((t_2 - ((fma(2.0, x2, -3.0) * -6.0) / x1)) / x1)) / x1)) * pow(x1, 4.0)) + x1;
	}
	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 = fma(fma(2.0, x2, -3.0), 4.0, 9.0)
	tmp = 0.0
	if (x1 <= -3.5e+55)
		tmp = Float64(Float64(Float64(6.0 - Float64(Float64(3.0 - Float64(t_2 / x1)) / x1)) * (x1 ^ 4.0)) + x1);
	elseif (x1 <= 8000.0)
		tmp = Float64(Float64(fma(Float64(Float64(fma(-2.0, x2, t_0) - x1) / fma(x1, x1, 1.0)), 3.0, fma(fma(fma(4.0, t_1, -6.0), Float64(x1 * x1), Float64(Float64(t_1 * Float64(2.0 * x1)) * Float64(t_1 - 3.0))), fma(x1, x1, 1.0), Float64(Float64(Float64(Float64(x1 * x1) * x2) * 6.0) / fma(x1, x1, 1.0)))) + x1) + x1);
	else
		tmp = Float64(Float64(Float64(6.0 - Float64(Float64(3.0 - Float64(Float64(t_2 - Float64(Float64(fma(2.0, x2, -3.0) * -6.0) / x1)) / x1)) / x1)) * (x1 ^ 4.0)) + 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 * 2.0 + t$95$0), $MachinePrecision] - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * 4.0 + 9.0), $MachinePrecision]}, If[LessEqual[x1, -3.5e+55], N[(N[(N[(6.0 - N[(N[(3.0 - N[(t$95$2 / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision], If[LessEqual[x1, 8000.0], N[(N[(N[(N[(N[(N[(-2.0 * x2 + t$95$0), $MachinePrecision] - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] * 3.0 + N[(N[(N[(4.0 * t$95$1 + -6.0), $MachinePrecision] * N[(x1 * x1), $MachinePrecision] + N[(N[(t$95$1 * N[(2.0 * x1), $MachinePrecision]), $MachinePrecision] * N[(t$95$1 - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x1 * x1 + 1.0), $MachinePrecision] + N[(N[(N[(N[(x1 * x1), $MachinePrecision] * x2), $MachinePrecision] * 6.0), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision] + x1), $MachinePrecision], N[(N[(N[(6.0 - N[(N[(3.0 - N[(N[(t$95$2 - N[(N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * -6.0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.5000000000000001e55

   1. Initial program 27.6%

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

   3. Taylor expanded in x1 around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 100.0%

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

   if -3.5000000000000001e55 < x1 < 8e3

   1. Initial program 98.7%

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

   4. Applied rewrites 98.7%

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

   5. Taylor expanded in x2 around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 N/A

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

      8. +-commutative N/A

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

      9. unpow2 N/A

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

      10. lower-fma.f64 97.3

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

   7. Applied rewrites 97.3%

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

   if 8e3 < x1

   1. Initial program 45.7%

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

   3. Taylor expanded in x1 around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 98.6%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.5 \cdot 10^{+55}:\\ \;\;\;\;\left(6 - \frac{3 - \frac{\mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)}{x1}}{x1}\right) \cdot {x1}^{4} + x1\\ \mathbf{elif}\;x1 \leq 8000:\\ \;\;\;\;\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(-2, x2, \left(3 \cdot x1\right) \cdot x1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, 3, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4, \frac{\mathsf{fma}\left(x2, 2, \left(3 \cdot x1\right) \cdot x1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, -6\right), x1 \cdot x1, \left(\frac{\mathsf{fma}\left(x2, 2, \left(3 \cdot x1\right) \cdot x1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(2 \cdot x1\right)\right) \cdot \left(\frac{\mathsf{fma}\left(x2, 2, \left(3 \cdot x1\right) \cdot x1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \frac{\left(\left(x1 \cdot x1\right) \cdot x2\right) \cdot 6}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right) + x1\right) + x1\\ \mathbf{else}:\\ \;\;\;\;\left(6 - \frac{3 - \frac{\mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right) - \frac{\mathsf{fma}\left(2, x2, -3\right) \cdot -6}{x1}}{x1}}{x1}\right) \cdot {x1}^{4} + x1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)\\ t_1 := \left(3 \cdot x1\right) \cdot x1\\ t_2 := \frac{\mathsf{fma}\left(x2, 2, t\_1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\\ \mathbf{if}\;x1 \leq -7.2 \cdot 10^{+19}:\\ \;\;\;\;\left(6 - \frac{3 - \frac{t\_0}{x1}}{x1}\right) \cdot {x1}^{4} + x1\\ \mathbf{elif}\;x1 \leq 390:\\ \;\;\;\;\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(-2, x2, t\_1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, 3, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, 3\right), x1, -1\right), x1, x2 \cdot 2\right), -6\right), x1 \cdot x1, \left(t\_2 \cdot \left(2 \cdot x1\right)\right) \cdot \left(t\_2 - 3\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, 3\right) \cdot x1, 3, -2\right), x1, 6 \cdot x2\right) \cdot \left(x1 \cdot x1\right)\right)\right) + x1\right) + x1\\ \mathbf{else}:\\ \;\;\;\;\left(6 - \frac{3 - \frac{t\_0 - \frac{\mathsf{fma}\left(2, x2, -3\right) \cdot -6}{x1}}{x1}}{x1}\right) \cdot {x1}^{4} + x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (fma (fma 2.0 x2 -3.0) 4.0 9.0))
        (t_1 (* (* 3.0 x1) x1))
        (t_2 (/ (- (fma x2 2.0 t_1) x1) (fma x1 x1 1.0))))
   (if (<= x1 -7.2e+19)
     (+ (* (- 6.0 (/ (- 3.0 (/ t_0 x1)) x1)) (pow x1 4.0)) x1)
     (if (<= x1 390.0)
       (+
        (+
         (fma
          (/ (- (fma -2.0 x2 t_1) x1) (fma x1 x1 1.0))
          3.0
          (fma
           (fma
            (fma 4.0 (fma (fma (fma -2.0 x2 3.0) x1 -1.0) x1 (* x2 2.0)) -6.0)
            (* x1 x1)
            (* (* t_2 (* 2.0 x1)) (- t_2 3.0)))
           (fma x1 x1 1.0)
           (*
            (fma (fma (* (fma -2.0 x2 3.0) x1) 3.0 -2.0) x1 (* 6.0 x2))
            (* x1 x1))))
         x1)
        x1)
       (+
        (*
         (-
          6.0
          (/ (- 3.0 (/ (- t_0 (/ (* (fma 2.0 x2 -3.0) -6.0) x1)) x1)) 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);
	double t_1 = (3.0 * x1) * x1;
	double t_2 = (fma(x2, 2.0, t_1) - x1) / fma(x1, x1, 1.0);
	double tmp;
	if (x1 <= -7.2e+19) {
		tmp = ((6.0 - ((3.0 - (t_0 / x1)) / x1)) * pow(x1, 4.0)) + x1;
	} else if (x1 <= 390.0) {
		tmp = (fma(((fma(-2.0, x2, t_1) - x1) / fma(x1, x1, 1.0)), 3.0, fma(fma(fma(4.0, fma(fma(fma(-2.0, x2, 3.0), x1, -1.0), x1, (x2 * 2.0)), -6.0), (x1 * x1), ((t_2 * (2.0 * x1)) * (t_2 - 3.0))), fma(x1, x1, 1.0), (fma(fma((fma(-2.0, x2, 3.0) * x1), 3.0, -2.0), x1, (6.0 * x2)) * (x1 * x1)))) + x1) + x1;
	} else {
		tmp = ((6.0 - ((3.0 - ((t_0 - ((fma(2.0, x2, -3.0) * -6.0) / x1)) / x1)) / x1)) * pow(x1, 4.0)) + x1;
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = fma(fma(2.0, x2, -3.0), 4.0, 9.0)
	t_1 = Float64(Float64(3.0 * x1) * x1)
	t_2 = Float64(Float64(fma(x2, 2.0, t_1) - x1) / fma(x1, x1, 1.0))
	tmp = 0.0
	if (x1 <= -7.2e+19)
		tmp = Float64(Float64(Float64(6.0 - Float64(Float64(3.0 - Float64(t_0 / x1)) / x1)) * (x1 ^ 4.0)) + x1);
	elseif (x1 <= 390.0)
		tmp = Float64(Float64(fma(Float64(Float64(fma(-2.0, x2, t_1) - x1) / fma(x1, x1, 1.0)), 3.0, fma(fma(fma(4.0, fma(fma(fma(-2.0, x2, 3.0), x1, -1.0), x1, Float64(x2 * 2.0)), -6.0), Float64(x1 * x1), Float64(Float64(t_2 * Float64(2.0 * x1)) * Float64(t_2 - 3.0))), fma(x1, x1, 1.0), Float64(fma(fma(Float64(fma(-2.0, x2, 3.0) * x1), 3.0, -2.0), x1, Float64(6.0 * x2)) * Float64(x1 * x1)))) + x1) + x1);
	else
		tmp = Float64(Float64(Float64(6.0 - Float64(Float64(3.0 - Float64(Float64(t_0 - Float64(Float64(fma(2.0, x2, -3.0) * -6.0) / x1)) / x1)) / x1)) * (x1 ^ 4.0)) + 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]}, Block[{t$95$1 = N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x2 * 2.0 + t$95$1), $MachinePrecision] - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -7.2e+19], N[(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] + x1), $MachinePrecision], If[LessEqual[x1, 390.0], N[(N[(N[(N[(N[(N[(-2.0 * x2 + t$95$1), $MachinePrecision] - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] * 3.0 + N[(N[(N[(4.0 * N[(N[(N[(-2.0 * x2 + 3.0), $MachinePrecision] * x1 + -1.0), $MachinePrecision] * x1 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] + -6.0), $MachinePrecision] * N[(x1 * x1), $MachinePrecision] + N[(N[(t$95$2 * N[(2.0 * x1), $MachinePrecision]), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x1 * x1 + 1.0), $MachinePrecision] + N[(N[(N[(N[(N[(-2.0 * x2 + 3.0), $MachinePrecision] * x1), $MachinePrecision] * 3.0 + -2.0), $MachinePrecision] * x1 + N[(6.0 * x2), $MachinePrecision]), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision] + x1), $MachinePrecision], N[(N[(N[(6.0 - N[(N[(3.0 - N[(N[(t$95$0 - N[(N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * -6.0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -7.2e19

   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 -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 96.3%

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

   if -7.2e19 < x1 < 390

   1. Initial program 98.6%

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

   4. Applied rewrites 98.7%

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

   5. Taylor expanded in x1 around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. *-commutative N/A

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

      8. metadata-eval N/A

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

      9. lower-fma.f64 N/A

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

      10. cancel-sign-sub-inv N/A

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

      11. metadata-eval N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. unpow2 N/A

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

   7. Applied rewrites 97.6%

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

   8. Taylor expanded in x1 around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. lower-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-*.f64 97.5

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

   10. Applied rewrites 97.5%

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

   if 390 < x1

   1. Initial program 45.7%

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

   3. Taylor expanded in x1 around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 98.6%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.2 \cdot 10^{+19}:\\ \;\;\;\;\left(6 - \frac{3 - \frac{\mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)}{x1}}{x1}\right) \cdot {x1}^{4} + x1\\ \mathbf{elif}\;x1 \leq 390:\\ \;\;\;\;\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(-2, x2, \left(3 \cdot x1\right) \cdot x1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, 3, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, 3\right), x1, -1\right), x1, x2 \cdot 2\right), -6\right), x1 \cdot x1, \left(\frac{\mathsf{fma}\left(x2, 2, \left(3 \cdot x1\right) \cdot x1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(2 \cdot x1\right)\right) \cdot \left(\frac{\mathsf{fma}\left(x2, 2, \left(3 \cdot x1\right) \cdot x1\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, 3\right) \cdot x1, 3, -2\right), x1, 6 \cdot x2\right) \cdot \left(x1 \cdot x1\right)\right)\right) + x1\right) + x1\\ \mathbf{else}:\\ \;\;\;\;\left(6 - \frac{3 - \frac{\mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right) - \frac{\mathsf{fma}\left(2, x2, -3\right) \cdot -6}{x1}}{x1}}{x1}\right) \cdot {x1}^{4} + x1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)\\ \mathbf{if}\;x1 \leq -7.2 \cdot 10^{+19}:\\ \;\;\;\;\left(6 - \frac{3 - \frac{t\_0}{x1}}{x1}\right) \cdot {x1}^{4} + x1\\ \mathbf{elif}\;x1 \leq 9.6:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -12\right), x1, \left(x2 \cdot x1\right) \cdot 8\right) \cdot x2 + x1\right) - \frac{x1 - \left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right)}{x1 \cdot x1 - -1} \cdot 3\right) + x1\\ \mathbf{else}:\\ \;\;\;\;\left(6 - \frac{3 - \frac{t\_0 - \frac{\mathsf{fma}\left(2, x2, -3\right) \cdot -6}{x1}}{x1}}{x1}\right) \cdot {x1}^{4} + x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (fma (fma 2.0 x2 -3.0) 4.0 9.0)))
   (if (<= x1 -7.2e+19)
     (+ (* (- 6.0 (/ (- 3.0 (/ t_0 x1)) x1)) (pow x1 4.0)) x1)
     (if (<= x1 9.6)
       (+
        (-
         (+ (* (fma (fma 6.0 x1 -12.0) x1 (* (* x2 x1) 8.0)) x2) x1)
         (*
          (/ (- x1 (- (* (* 3.0 x1) x1) (* x2 2.0))) (- (* x1 x1) -1.0))
          3.0))
        x1)
       (+
        (*
         (-
          6.0
          (/ (- 3.0 (/ (- t_0 (/ (* (fma 2.0 x2 -3.0) -6.0) x1)) x1)) 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);
	double tmp;
	if (x1 <= -7.2e+19) {
		tmp = ((6.0 - ((3.0 - (t_0 / x1)) / x1)) * pow(x1, 4.0)) + x1;
	} else if (x1 <= 9.6) {
		tmp = (((fma(fma(6.0, x1, -12.0), x1, ((x2 * x1) * 8.0)) * x2) + x1) - (((x1 - (((3.0 * x1) * x1) - (x2 * 2.0))) / ((x1 * x1) - -1.0)) * 3.0)) + x1;
	} else {
		tmp = ((6.0 - ((3.0 - ((t_0 - ((fma(2.0, x2, -3.0) * -6.0) / x1)) / x1)) / x1)) * pow(x1, 4.0)) + 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 <= -7.2e+19)
		tmp = Float64(Float64(Float64(6.0 - Float64(Float64(3.0 - Float64(t_0 / x1)) / x1)) * (x1 ^ 4.0)) + x1);
	elseif (x1 <= 9.6)
		tmp = Float64(Float64(Float64(Float64(fma(fma(6.0, x1, -12.0), x1, Float64(Float64(x2 * x1) * 8.0)) * x2) + x1) - Float64(Float64(Float64(x1 - Float64(Float64(Float64(3.0 * x1) * x1) - Float64(x2 * 2.0))) / Float64(Float64(x1 * x1) - -1.0)) * 3.0)) + x1);
	else
		tmp = Float64(Float64(Float64(6.0 - Float64(Float64(3.0 - Float64(Float64(t_0 - Float64(Float64(fma(2.0, x2, -3.0) * -6.0) / x1)) / x1)) / x1)) * (x1 ^ 4.0)) + 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, -7.2e+19], N[(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] + x1), $MachinePrecision], If[LessEqual[x1, 9.6], N[(N[(N[(N[(N[(N[(6.0 * x1 + -12.0), $MachinePrecision] * x1 + N[(N[(x2 * x1), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision] * x2), $MachinePrecision] + x1), $MachinePrecision] - N[(N[(N[(x1 - N[(N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision] - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision], N[(N[(N[(6.0 - N[(N[(3.0 - N[(N[(t$95$0 - N[(N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * -6.0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -7.2e19

   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 -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 96.3%

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

   if -7.2e19 < x1 < 9.59999999999999964

   1. Initial program 98.6%

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

   3. Taylor expanded in x1 around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 83.3%

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

   6. Taylor expanded in x2 around 0

      \[\leadsto x1 + \left(\left(x2 \cdot \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 95.8%

      \[\leadsto x1 + \left(\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -12\right), x1, \left(x1 \cdot x2\right) \cdot 8\right) \cdot \color{blue}{x2} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if 9.59999999999999964 < x1

   1. Initial program 45.7%

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

   3. Taylor expanded in x1 around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 98.6%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.2 \cdot 10^{+19}:\\ \;\;\;\;\left(6 - \frac{3 - \frac{\mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)}{x1}}{x1}\right) \cdot {x1}^{4} + x1\\ \mathbf{elif}\;x1 \leq 9.6:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -12\right), x1, \left(x2 \cdot x1\right) \cdot 8\right) \cdot x2 + x1\right) - \frac{x1 - \left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right)}{x1 \cdot x1 - -1} \cdot 3\right) + x1\\ \mathbf{else}:\\ \;\;\;\;\left(6 - \frac{3 - \frac{\mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right) - \frac{\mathsf{fma}\left(2, x2, -3\right) \cdot -6}{x1}}{x1}}{x1}\right) \cdot {x1}^{4} + x1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)\\ \mathbf{if}\;x1 \leq -7.2 \cdot 10^{+19}:\\ \;\;\;\;\left(6 - \frac{3 - \frac{t\_0}{x1}}{x1}\right) \cdot {x1}^{4} + x1\\ \mathbf{elif}\;x1 \leq 9.6:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -12\right), x1, \left(x2 \cdot x1\right) \cdot 8\right) \cdot x2 + x1\right) - \frac{x1 - \left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right)}{x1 \cdot x1 - -1} \cdot 3\right) + x1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -3\right), x1, t\_0\right), x1, \mathsf{fma}\left(2, x2, -3\right) \cdot 6\right) \cdot x1 + x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (fma (fma 2.0 x2 -3.0) 4.0 9.0)))
   (if (<= x1 -7.2e+19)
     (+ (* (- 6.0 (/ (- 3.0 (/ t_0 x1)) x1)) (pow x1 4.0)) x1)
     (if (<= x1 9.6)
       (+
        (-
         (+ (* (fma (fma 6.0 x1 -12.0) x1 (* (* x2 x1) 8.0)) x2) x1)
         (*
          (/ (- x1 (- (* (* 3.0 x1) x1) (* x2 2.0))) (- (* x1 x1) -1.0))
          3.0))
        x1)
       (+
        (*
         (fma (fma (fma 6.0 x1 -3.0) x1 t_0) x1 (* (fma 2.0 x2 -3.0) 6.0))
         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 <= -7.2e+19) {
		tmp = ((6.0 - ((3.0 - (t_0 / x1)) / x1)) * pow(x1, 4.0)) + x1;
	} else if (x1 <= 9.6) {
		tmp = (((fma(fma(6.0, x1, -12.0), x1, ((x2 * x1) * 8.0)) * x2) + x1) - (((x1 - (((3.0 * x1) * x1) - (x2 * 2.0))) / ((x1 * x1) - -1.0)) * 3.0)) + x1;
	} else {
		tmp = (fma(fma(fma(6.0, x1, -3.0), x1, t_0), x1, (fma(2.0, x2, -3.0) * 6.0)) * 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 <= -7.2e+19)
		tmp = Float64(Float64(Float64(6.0 - Float64(Float64(3.0 - Float64(t_0 / x1)) / x1)) * (x1 ^ 4.0)) + x1);
	elseif (x1 <= 9.6)
		tmp = Float64(Float64(Float64(Float64(fma(fma(6.0, x1, -12.0), x1, Float64(Float64(x2 * x1) * 8.0)) * x2) + x1) - Float64(Float64(Float64(x1 - Float64(Float64(Float64(3.0 * x1) * x1) - Float64(x2 * 2.0))) / Float64(Float64(x1 * x1) - -1.0)) * 3.0)) + x1);
	else
		tmp = Float64(Float64(fma(fma(fma(6.0, x1, -3.0), x1, t_0), x1, Float64(fma(2.0, x2, -3.0) * 6.0)) * 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, -7.2e+19], N[(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] + x1), $MachinePrecision], If[LessEqual[x1, 9.6], N[(N[(N[(N[(N[(N[(6.0 * x1 + -12.0), $MachinePrecision] * x1 + N[(N[(x2 * x1), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision] * x2), $MachinePrecision] + x1), $MachinePrecision] - N[(N[(N[(x1 - N[(N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision] - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision], N[(N[(N[(N[(N[(6.0 * x1 + -3.0), $MachinePrecision] * x1 + t$95$0), $MachinePrecision] * x1 + N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] * x1), $MachinePrecision] + x1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -7.2e19

   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 -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 96.3%

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

   if -7.2e19 < x1 < 9.59999999999999964

   1. Initial program 98.6%

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

   3. Taylor expanded in x1 around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 83.3%

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

   6. Taylor expanded in x2 around 0

      \[\leadsto x1 + \left(\left(x2 \cdot \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 95.8%

      \[\leadsto x1 + \left(\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -12\right), x1, \left(x1 \cdot x2\right) \cdot 8\right) \cdot \color{blue}{x2} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if 9.59999999999999964 < x1

   1. Initial program 45.7%

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

   3. Taylor expanded in x1 around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 98.6%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 98.5%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.2 \cdot 10^{+19}:\\ \;\;\;\;\left(6 - \frac{3 - \frac{\mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)}{x1}}{x1}\right) \cdot {x1}^{4} + x1\\ \mathbf{elif}\;x1 \leq 9.6:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -12\right), x1, \left(x2 \cdot x1\right) \cdot 8\right) \cdot x2 + x1\right) - \frac{x1 - \left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right)}{x1 \cdot x1 - -1} \cdot 3\right) + x1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -3\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)\right), x1, \mathsf{fma}\left(2, x2, -3\right) \cdot 6\right) \cdot x1 + x1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.3% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -3\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)\right), x1, \mathsf{fma}\left(2, x2, -3\right) \cdot 6\right) \cdot x1 + x1\\ \mathbf{if}\;x1 \leq -7.2 \cdot 10^{+19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 9.6:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -12\right), x1, \left(x2 \cdot x1\right) \cdot 8\right) \cdot x2 + x1\right) - \frac{x1 - \left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right)}{x1 \cdot x1 - -1} \cdot 3\right) + x1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (+
          (*
           (fma
            (fma (fma 6.0 x1 -3.0) x1 (fma (fma 2.0 x2 -3.0) 4.0 9.0))
            x1
            (* (fma 2.0 x2 -3.0) 6.0))
           x1)
          x1)))
   (if (<= x1 -7.2e+19)
     t_0
     (if (<= x1 9.6)
       (+
        (-
         (+ (* (fma (fma 6.0 x1 -12.0) x1 (* (* x2 x1) 8.0)) x2) x1)
         (*
          (/ (- x1 (- (* (* 3.0 x1) x1) (* x2 2.0))) (- (* x1 x1) -1.0))
          3.0))
        x1)
       t_0))))

C

double code(double x1, double x2) {
	double t_0 = (fma(fma(fma(6.0, x1, -3.0), x1, fma(fma(2.0, x2, -3.0), 4.0, 9.0)), x1, (fma(2.0, x2, -3.0) * 6.0)) * x1) + x1;
	double tmp;
	if (x1 <= -7.2e+19) {
		tmp = t_0;
	} else if (x1 <= 9.6) {
		tmp = (((fma(fma(6.0, x1, -12.0), x1, ((x2 * x1) * 8.0)) * x2) + x1) - (((x1 - (((3.0 * x1) * x1) - (x2 * 2.0))) / ((x1 * x1) - -1.0)) * 3.0)) + x1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(fma(fma(fma(6.0, x1, -3.0), x1, fma(fma(2.0, x2, -3.0), 4.0, 9.0)), x1, Float64(fma(2.0, x2, -3.0) * 6.0)) * x1) + x1)
	tmp = 0.0
	if (x1 <= -7.2e+19)
		tmp = t_0;
	elseif (x1 <= 9.6)
		tmp = Float64(Float64(Float64(Float64(fma(fma(6.0, x1, -12.0), x1, Float64(Float64(x2 * x1) * 8.0)) * x2) + x1) - Float64(Float64(Float64(x1 - Float64(Float64(Float64(3.0 * x1) * x1) - Float64(x2 * 2.0))) / Float64(Float64(x1 * x1) - -1.0)) * 3.0)) + x1);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(N[(N[(N[(6.0 * x1 + -3.0), $MachinePrecision] * x1 + N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * 4.0 + 9.0), $MachinePrecision]), $MachinePrecision] * x1 + N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] * x1), $MachinePrecision] + x1), $MachinePrecision]}, If[LessEqual[x1, -7.2e+19], t$95$0, If[LessEqual[x1, 9.6], N[(N[(N[(N[(N[(N[(6.0 * x1 + -12.0), $MachinePrecision] * x1 + N[(N[(x2 * x1), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision] * x2), $MachinePrecision] + x1), $MachinePrecision] - N[(N[(N[(x1 - N[(N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision] - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -7.2e19 or 9.59999999999999964 < x1

   1. Initial program 43.8%

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

   3. Taylor expanded in x1 around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 97.6%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 97.5%

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

   if -7.2e19 < x1 < 9.59999999999999964

   1. Initial program 98.6%

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

   3. Taylor expanded in x1 around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 83.3%

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

   6. Taylor expanded in x2 around 0

      \[\leadsto x1 + \left(\left(x2 \cdot \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 95.8%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.2 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -3\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)\right), x1, \mathsf{fma}\left(2, x2, -3\right) \cdot 6\right) \cdot x1 + x1\\ \mathbf{elif}\;x1 \leq 9.6:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -12\right), x1, \left(x2 \cdot x1\right) \cdot 8\right) \cdot x2 + x1\right) - \frac{x1 - \left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right)}{x1 \cdot x1 - -1} \cdot 3\right) + x1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -3\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)\right), x1, \mathsf{fma}\left(2, x2, -3\right) \cdot 6\right) \cdot x1 + x1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 95.4% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -3\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)\right), x1, \mathsf{fma}\left(2, x2, -3\right) \cdot 6\right) \cdot x1 + x1\\ \mathbf{if}\;x1 \leq -7.2 \cdot 10^{+19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 9.6:\\ \;\;\;\;\left(\mathsf{fma}\left(\mathsf{fma}\left(3 - -2 \cdot x2, x1, -1\right), x1, -2 \cdot x2\right) \cdot 3 + \left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -12\right), x1, \left(x2 \cdot x1\right) \cdot 8\right) \cdot x2 + x1\right)\right) + x1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (+
          (*
           (fma
            (fma (fma 6.0 x1 -3.0) x1 (fma (fma 2.0 x2 -3.0) 4.0 9.0))
            x1
            (* (fma 2.0 x2 -3.0) 6.0))
           x1)
          x1)))
   (if (<= x1 -7.2e+19)
     t_0
     (if (<= x1 9.6)
       (+
        (+
         (* (fma (fma (- 3.0 (* -2.0 x2)) x1 -1.0) x1 (* -2.0 x2)) 3.0)
         (+ (* (fma (fma 6.0 x1 -12.0) x1 (* (* x2 x1) 8.0)) x2) x1))
        x1)
       t_0))))

C

double code(double x1, double x2) {
	double t_0 = (fma(fma(fma(6.0, x1, -3.0), x1, fma(fma(2.0, x2, -3.0), 4.0, 9.0)), x1, (fma(2.0, x2, -3.0) * 6.0)) * x1) + x1;
	double tmp;
	if (x1 <= -7.2e+19) {
		tmp = t_0;
	} else if (x1 <= 9.6) {
		tmp = ((fma(fma((3.0 - (-2.0 * x2)), x1, -1.0), x1, (-2.0 * x2)) * 3.0) + ((fma(fma(6.0, x1, -12.0), x1, ((x2 * x1) * 8.0)) * x2) + x1)) + x1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(fma(fma(fma(6.0, x1, -3.0), x1, fma(fma(2.0, x2, -3.0), 4.0, 9.0)), x1, Float64(fma(2.0, x2, -3.0) * 6.0)) * x1) + x1)
	tmp = 0.0
	if (x1 <= -7.2e+19)
		tmp = t_0;
	elseif (x1 <= 9.6)
		tmp = Float64(Float64(Float64(fma(fma(Float64(3.0 - Float64(-2.0 * x2)), x1, -1.0), x1, Float64(-2.0 * x2)) * 3.0) + Float64(Float64(fma(fma(6.0, x1, -12.0), x1, Float64(Float64(x2 * x1) * 8.0)) * x2) + x1)) + x1);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(N[(N[(N[(6.0 * x1 + -3.0), $MachinePrecision] * x1 + N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * 4.0 + 9.0), $MachinePrecision]), $MachinePrecision] * x1 + N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] * x1), $MachinePrecision] + x1), $MachinePrecision]}, If[LessEqual[x1, -7.2e+19], t$95$0, If[LessEqual[x1, 9.6], N[(N[(N[(N[(N[(N[(3.0 - N[(-2.0 * x2), $MachinePrecision]), $MachinePrecision] * x1 + -1.0), $MachinePrecision] * x1 + N[(-2.0 * x2), $MachinePrecision]), $MachinePrecision] * 3.0), $MachinePrecision] + N[(N[(N[(N[(6.0 * x1 + -12.0), $MachinePrecision] * x1 + N[(N[(x2 * x1), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision] * x2), $MachinePrecision] + x1), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -7.2e19 or 9.59999999999999964 < x1

   1. Initial program 43.8%

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

   3. Taylor expanded in x1 around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 97.6%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 97.5%

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

   if -7.2e19 < x1 < 9.59999999999999964

   1. Initial program 98.6%

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

   3. Taylor expanded in x1 around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 83.3%

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

   6. Taylor expanded in x2 around inf

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

   8. Applied rewrites 84.1%

      \[\leadsto x1 + \left(\left(\left(\left(x2 \cdot x2\right) \cdot 8\right) \cdot x1 + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   9. Taylor expanded in x1 around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. lower-fma.f64 N/A

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

       4. sub-neg N/A

          \[\leadsto x1 + \left(\left(\left(\left(x2 \cdot x2\right) \cdot 8\right) \cdot x1 + x1\right) + 3 \cdot \mathsf{fma}\left(\color{blue}{x1 \cdot \left(3 - -2 \cdot x2\right) + \left(\mathsf{neg}\left(1\right)\right)}, x1, -2 \cdot x2\right)\right) \]

       5. *-commutative N/A

          \[\leadsto x1 + \left(\left(\left(\left(x2 \cdot x2\right) \cdot 8\right) \cdot x1 + x1\right) + 3 \cdot \mathsf{fma}\left(\color{blue}{\left(3 - -2 \cdot x2\right) \cdot x1} + \left(\mathsf{neg}\left(1\right)\right), x1, -2 \cdot x2\right)\right) \]

       6. metadata-eval N/A

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

       7. lower-fma.f64 N/A

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

       8. lower--.f64 N/A

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

       9. lower-*.f64 N/A

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

       10. lower-*.f64 83.4

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

   11. Applied rewrites 83.4%

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

   12. Taylor expanded in x2 around 0

       \[\leadsto x1 + \left(\left(x2 \cdot \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right)} + x1\right) + 3 \cdot \mathsf{fma}\left(\mathsf{fma}\left(3 - -2 \cdot x2, x1, -1\right), x1, -2 \cdot x2\right)\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 95.1%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.2 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -3\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)\right), x1, \mathsf{fma}\left(2, x2, -3\right) \cdot 6\right) \cdot x1 + x1\\ \mathbf{elif}\;x1 \leq 9.6:\\ \;\;\;\;\left(\mathsf{fma}\left(\mathsf{fma}\left(3 - -2 \cdot x2, x1, -1\right), x1, -2 \cdot x2\right) \cdot 3 + \left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -12\right), x1, \left(x2 \cdot x1\right) \cdot 8\right) \cdot x2 + x1\right)\right) + x1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -3\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)\right), x1, \mathsf{fma}\left(2, x2, -3\right) \cdot 6\right) \cdot x1 + x1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.3% accurate, 3.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -3\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)\right), x1, \mathsf{fma}\left(2, x2, -3\right) \cdot 6\right) \cdot x1 + x1\\ \mathbf{if}\;x1 \leq -7.2 \cdot 10^{+19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 9.6:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(3 \cdot x1, x1, -2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, 3, \left(\left(x2 \cdot x2\right) \cdot 8\right) \cdot x1 + x1\right) + x1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (+
          (*
           (fma
            (fma (fma 6.0 x1 -3.0) x1 (fma (fma 2.0 x2 -3.0) 4.0 9.0))
            x1
            (* (fma 2.0 x2 -3.0) 6.0))
           x1)
          x1)))
   (if (<= x1 -7.2e+19)
     t_0
     (if (<= x1 9.6)
       (+
        (fma
         (/ (- (fma (* 3.0 x1) x1 (* -2.0 x2)) x1) (fma x1 x1 1.0))
         3.0
         (+ (* (* (* x2 x2) 8.0) x1) x1))
        x1)
       t_0))))

C

double code(double x1, double x2) {
	double t_0 = (fma(fma(fma(6.0, x1, -3.0), x1, fma(fma(2.0, x2, -3.0), 4.0, 9.0)), x1, (fma(2.0, x2, -3.0) * 6.0)) * x1) + x1;
	double tmp;
	if (x1 <= -7.2e+19) {
		tmp = t_0;
	} else if (x1 <= 9.6) {
		tmp = fma(((fma((3.0 * x1), x1, (-2.0 * x2)) - x1) / fma(x1, x1, 1.0)), 3.0, ((((x2 * x2) * 8.0) * x1) + x1)) + x1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(fma(fma(fma(6.0, x1, -3.0), x1, fma(fma(2.0, x2, -3.0), 4.0, 9.0)), x1, Float64(fma(2.0, x2, -3.0) * 6.0)) * x1) + x1)
	tmp = 0.0
	if (x1 <= -7.2e+19)
		tmp = t_0;
	elseif (x1 <= 9.6)
		tmp = Float64(fma(Float64(Float64(fma(Float64(3.0 * x1), x1, Float64(-2.0 * x2)) - x1) / fma(x1, x1, 1.0)), 3.0, Float64(Float64(Float64(Float64(x2 * x2) * 8.0) * x1) + x1)) + x1);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(N[(N[(N[(6.0 * x1 + -3.0), $MachinePrecision] * x1 + N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * 4.0 + 9.0), $MachinePrecision]), $MachinePrecision] * x1 + N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] * x1), $MachinePrecision] + x1), $MachinePrecision]}, If[LessEqual[x1, -7.2e+19], t$95$0, If[LessEqual[x1, 9.6], N[(N[(N[(N[(N[(N[(3.0 * x1), $MachinePrecision] * x1 + N[(-2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] * 3.0 + N[(N[(N[(N[(x2 * x2), $MachinePrecision] * 8.0), $MachinePrecision] * x1), $MachinePrecision] + x1), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -7.2e19 or 9.59999999999999964 < x1

   1. Initial program 43.8%

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

   3. Taylor expanded in x1 around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 97.6%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 97.5%

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

   if -7.2e19 < x1 < 9.59999999999999964

   1. Initial program 98.6%

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

   3. Taylor expanded in x1 around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 83.3%

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

   6. Taylor expanded in x2 around inf

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

   8. Applied rewrites 84.1%

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

      1. lift-+.f64 N/A

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

   10. Applied rewrites 84.3%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.2 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -3\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)\right), x1, \mathsf{fma}\left(2, x2, -3\right) \cdot 6\right) \cdot x1 + x1\\ \mathbf{elif}\;x1 \leq 9.6:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(3 \cdot x1, x1, -2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, 3, \left(\left(x2 \cdot x2\right) \cdot 8\right) \cdot x1 + x1\right) + x1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -3\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)\right), x1, \mathsf{fma}\left(2, x2, -3\right) \cdot 6\right) \cdot x1 + x1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.2% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -3\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)\right), x1, \mathsf{fma}\left(2, x2, -3\right) \cdot 6\right) \cdot x1 + x1\\ \mathbf{if}\;x1 \leq -7.2 \cdot 10^{+19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 9.6:\\ \;\;\;\;\left(\left(\left(\left(x2 \cdot x2\right) \cdot 8\right) \cdot x1 + x1\right) - \frac{x1 - \left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right)}{1} \cdot 3\right) + x1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (+
          (*
           (fma
            (fma (fma 6.0 x1 -3.0) x1 (fma (fma 2.0 x2 -3.0) 4.0 9.0))
            x1
            (* (fma 2.0 x2 -3.0) 6.0))
           x1)
          x1)))
   (if (<= x1 -7.2e+19)
     t_0
     (if (<= x1 9.6)
       (+
        (-
         (+ (* (* (* x2 x2) 8.0) x1) x1)
         (* (/ (- x1 (- (* (* 3.0 x1) x1) (* x2 2.0))) 1.0) 3.0))
        x1)
       t_0))))

C

double code(double x1, double x2) {
	double t_0 = (fma(fma(fma(6.0, x1, -3.0), x1, fma(fma(2.0, x2, -3.0), 4.0, 9.0)), x1, (fma(2.0, x2, -3.0) * 6.0)) * x1) + x1;
	double tmp;
	if (x1 <= -7.2e+19) {
		tmp = t_0;
	} else if (x1 <= 9.6) {
		tmp = (((((x2 * x2) * 8.0) * x1) + x1) - (((x1 - (((3.0 * x1) * x1) - (x2 * 2.0))) / 1.0) * 3.0)) + x1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(fma(fma(fma(6.0, x1, -3.0), x1, fma(fma(2.0, x2, -3.0), 4.0, 9.0)), x1, Float64(fma(2.0, x2, -3.0) * 6.0)) * x1) + x1)
	tmp = 0.0
	if (x1 <= -7.2e+19)
		tmp = t_0;
	elseif (x1 <= 9.6)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(x2 * x2) * 8.0) * x1) + x1) - Float64(Float64(Float64(x1 - Float64(Float64(Float64(3.0 * x1) * x1) - Float64(x2 * 2.0))) / 1.0) * 3.0)) + x1);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(N[(N[(N[(6.0 * x1 + -3.0), $MachinePrecision] * x1 + N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * 4.0 + 9.0), $MachinePrecision]), $MachinePrecision] * x1 + N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] * x1), $MachinePrecision] + x1), $MachinePrecision]}, If[LessEqual[x1, -7.2e+19], t$95$0, If[LessEqual[x1, 9.6], N[(N[(N[(N[(N[(N[(x2 * x2), $MachinePrecision] * 8.0), $MachinePrecision] * x1), $MachinePrecision] + x1), $MachinePrecision] - N[(N[(N[(x1 - N[(N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision] - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 1.0), $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -7.2e19 or 9.59999999999999964 < x1

   1. Initial program 43.8%

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

   3. Taylor expanded in x1 around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 97.6%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 97.5%

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

   if -7.2e19 < x1 < 9.59999999999999964

   1. Initial program 98.6%

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

   3. Taylor expanded in x1 around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 83.3%

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

   6. Taylor expanded in x2 around inf

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

   8. Applied rewrites 84.1%

      \[\leadsto x1 + \left(\left(\left(\left(x2 \cdot x2\right) \cdot 8\right) \cdot x1 + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   9. Taylor expanded in x1 around 0

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

   11. Applied rewrites 84.1%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.2 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -3\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)\right), x1, \mathsf{fma}\left(2, x2, -3\right) \cdot 6\right) \cdot x1 + x1\\ \mathbf{elif}\;x1 \leq 9.6:\\ \;\;\;\;\left(\left(\left(\left(x2 \cdot x2\right) \cdot 8\right) \cdot x1 + x1\right) - \frac{x1 - \left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right)}{1} \cdot 3\right) + x1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -3\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)\right), x1, \mathsf{fma}\left(2, x2, -3\right) \cdot 6\right) \cdot x1 + x1\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 89.2% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -3\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)\right), x1, \mathsf{fma}\left(2, x2, -3\right) \cdot 6\right) \cdot x1 + x1\\ \mathbf{if}\;x1 \leq -7.2 \cdot 10^{+19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 9.6:\\ \;\;\;\;\left(\mathsf{fma}\left(\mathsf{fma}\left(3, x1, -1\right), x1, -2 \cdot x2\right) \cdot 3 + \left(\left(\left(x2 \cdot x2\right) \cdot 8\right) \cdot x1 + x1\right)\right) + x1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (+
          (*
           (fma
            (fma (fma 6.0 x1 -3.0) x1 (fma (fma 2.0 x2 -3.0) 4.0 9.0))
            x1
            (* (fma 2.0 x2 -3.0) 6.0))
           x1)
          x1)))
   (if (<= x1 -7.2e+19)
     t_0
     (if (<= x1 9.6)
       (+
        (+
         (* (fma (fma 3.0 x1 -1.0) x1 (* -2.0 x2)) 3.0)
         (+ (* (* (* x2 x2) 8.0) x1) x1))
        x1)
       t_0))))

C

double code(double x1, double x2) {
	double t_0 = (fma(fma(fma(6.0, x1, -3.0), x1, fma(fma(2.0, x2, -3.0), 4.0, 9.0)), x1, (fma(2.0, x2, -3.0) * 6.0)) * x1) + x1;
	double tmp;
	if (x1 <= -7.2e+19) {
		tmp = t_0;
	} else if (x1 <= 9.6) {
		tmp = ((fma(fma(3.0, x1, -1.0), x1, (-2.0 * x2)) * 3.0) + ((((x2 * x2) * 8.0) * x1) + x1)) + x1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(fma(fma(fma(6.0, x1, -3.0), x1, fma(fma(2.0, x2, -3.0), 4.0, 9.0)), x1, Float64(fma(2.0, x2, -3.0) * 6.0)) * x1) + x1)
	tmp = 0.0
	if (x1 <= -7.2e+19)
		tmp = t_0;
	elseif (x1 <= 9.6)
		tmp = Float64(Float64(Float64(fma(fma(3.0, x1, -1.0), x1, Float64(-2.0 * x2)) * 3.0) + Float64(Float64(Float64(Float64(x2 * x2) * 8.0) * x1) + x1)) + x1);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(N[(N[(N[(6.0 * x1 + -3.0), $MachinePrecision] * x1 + N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * 4.0 + 9.0), $MachinePrecision]), $MachinePrecision] * x1 + N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] * x1), $MachinePrecision] + x1), $MachinePrecision]}, If[LessEqual[x1, -7.2e+19], t$95$0, If[LessEqual[x1, 9.6], N[(N[(N[(N[(N[(3.0 * x1 + -1.0), $MachinePrecision] * x1 + N[(-2.0 * x2), $MachinePrecision]), $MachinePrecision] * 3.0), $MachinePrecision] + N[(N[(N[(N[(x2 * x2), $MachinePrecision] * 8.0), $MachinePrecision] * x1), $MachinePrecision] + x1), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -7.2e19 or 9.59999999999999964 < x1

   1. Initial program 43.8%

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

   3. Taylor expanded in x1 around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 97.6%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 97.5%

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

   if -7.2e19 < x1 < 9.59999999999999964

   1. Initial program 98.6%

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

   3. Taylor expanded in x1 around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 83.3%

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

   6. Taylor expanded in x2 around inf

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

   8. Applied rewrites 84.1%

      \[\leadsto x1 + \left(\left(\left(\left(x2 \cdot x2\right) \cdot 8\right) \cdot x1 + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   9. Taylor expanded in x1 around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. lower-fma.f64 N/A

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

       4. sub-neg N/A

          \[\leadsto x1 + \left(\left(\left(\left(x2 \cdot x2\right) \cdot 8\right) \cdot x1 + x1\right) + 3 \cdot \mathsf{fma}\left(\color{blue}{x1 \cdot \left(3 - -2 \cdot x2\right) + \left(\mathsf{neg}\left(1\right)\right)}, x1, -2 \cdot x2\right)\right) \]

       5. *-commutative N/A

          \[\leadsto x1 + \left(\left(\left(\left(x2 \cdot x2\right) \cdot 8\right) \cdot x1 + x1\right) + 3 \cdot \mathsf{fma}\left(\color{blue}{\left(3 - -2 \cdot x2\right) \cdot x1} + \left(\mathsf{neg}\left(1\right)\right), x1, -2 \cdot x2\right)\right) \]

       6. metadata-eval N/A

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

       7. lower-fma.f64 N/A

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

       8. lower--.f64 N/A

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

       9. lower-*.f64 N/A

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

       10. lower-*.f64 83.4

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

   11. Applied rewrites 83.4%

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

   12. Taylor expanded in x2 around 0

       \[\leadsto x1 + \left(\left(\left(\left(x2 \cdot x2\right) \cdot 8\right) \cdot x1 + x1\right) + 3 \cdot \mathsf{fma}\left(\mathsf{fma}\left(3, x1, -1\right), x1, -2 \cdot x2\right)\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 84.1%

       \[\leadsto x1 + \left(\left(\left(\left(x2 \cdot x2\right) \cdot 8\right) \cdot x1 + x1\right) + 3 \cdot \mathsf{fma}\left(\mathsf{fma}\left(3, x1, -1\right), x1, -2 \cdot x2\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.2 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -3\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)\right), x1, \mathsf{fma}\left(2, x2, -3\right) \cdot 6\right) \cdot x1 + x1\\ \mathbf{elif}\;x1 \leq 9.6:\\ \;\;\;\;\left(\mathsf{fma}\left(\mathsf{fma}\left(3, x1, -1\right), x1, -2 \cdot x2\right) \cdot 3 + \left(\left(\left(x2 \cdot x2\right) \cdot 8\right) \cdot x1 + x1\right)\right) + x1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -3\right), x1, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)\right), x1, \mathsf{fma}\left(2, x2, -3\right) \cdot 6\right) \cdot x1 + x1\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 87.1% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot 6\\ \mathbf{if}\;x1 \leq -7.2 \cdot 10^{+19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 20.5:\\ \;\;\;\;\left(\mathsf{fma}\left(\mathsf{fma}\left(3, x1, -1\right), x1, -2 \cdot x2\right) \cdot 3 + \left(\left(\left(x2 \cdot x2\right) \cdot 8\right) \cdot x1 + x1\right)\right) + x1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* (* x1 x1) (* x1 x1)) 6.0)))
   (if (<= x1 -7.2e+19)
     t_0
     (if (<= x1 20.5)
       (+
        (+
         (* (fma (fma 3.0 x1 -1.0) x1 (* -2.0 x2)) 3.0)
         (+ (* (* (* x2 x2) 8.0) x1) x1))
        x1)
       t_0))))

C

double code(double x1, double x2) {
	double t_0 = ((x1 * x1) * (x1 * x1)) * 6.0;
	double tmp;
	if (x1 <= -7.2e+19) {
		tmp = t_0;
	} else if (x1 <= 20.5) {
		tmp = ((fma(fma(3.0, x1, -1.0), x1, (-2.0 * x2)) * 3.0) + ((((x2 * x2) * 8.0) * x1) + x1)) + x1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(Float64(x1 * x1) * Float64(x1 * x1)) * 6.0)
	tmp = 0.0
	if (x1 <= -7.2e+19)
		tmp = t_0;
	elseif (x1 <= 20.5)
		tmp = Float64(Float64(Float64(fma(fma(3.0, x1, -1.0), x1, Float64(-2.0 * x2)) * 3.0) + Float64(Float64(Float64(Float64(x2 * x2) * 8.0) * x1) + x1)) + x1);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * 6.0), $MachinePrecision]}, If[LessEqual[x1, -7.2e+19], t$95$0, If[LessEqual[x1, 20.5], N[(N[(N[(N[(N[(3.0 * x1 + -1.0), $MachinePrecision] * x1 + N[(-2.0 * x2), $MachinePrecision]), $MachinePrecision] * 3.0), $MachinePrecision] + N[(N[(N[(N[(x2 * x2), $MachinePrecision] * 8.0), $MachinePrecision] * x1), $MachinePrecision] + x1), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -7.2e19 or 20.5 < x1

   1. Initial program 43.8%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   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 3.8

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

   5. Applied rewrites 3.8%

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

   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 94.3

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

   8. Applied rewrites 94.3%

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

   10. Applied rewrites 94.3%

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

   if -7.2e19 < x1 < 20.5

   1. Initial program 98.6%

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

   3. Taylor expanded in x1 around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 83.3%

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

   6. Taylor expanded in x2 around inf

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

   8. Applied rewrites 84.1%

      \[\leadsto x1 + \left(\left(\left(\left(x2 \cdot x2\right) \cdot 8\right) \cdot x1 + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   9. Taylor expanded in x1 around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. lower-fma.f64 N/A

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

       4. sub-neg N/A

          \[\leadsto x1 + \left(\left(\left(\left(x2 \cdot x2\right) \cdot 8\right) \cdot x1 + x1\right) + 3 \cdot \mathsf{fma}\left(\color{blue}{x1 \cdot \left(3 - -2 \cdot x2\right) + \left(\mathsf{neg}\left(1\right)\right)}, x1, -2 \cdot x2\right)\right) \]

       5. *-commutative N/A

          \[\leadsto x1 + \left(\left(\left(\left(x2 \cdot x2\right) \cdot 8\right) \cdot x1 + x1\right) + 3 \cdot \mathsf{fma}\left(\color{blue}{\left(3 - -2 \cdot x2\right) \cdot x1} + \left(\mathsf{neg}\left(1\right)\right), x1, -2 \cdot x2\right)\right) \]

       6. metadata-eval N/A

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

       7. lower-fma.f64 N/A

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

       8. lower--.f64 N/A

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

       9. lower-*.f64 N/A

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

       10. lower-*.f64 83.4

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

   11. Applied rewrites 83.4%

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

   12. Taylor expanded in x2 around 0

       \[\leadsto x1 + \left(\left(\left(\left(x2 \cdot x2\right) \cdot 8\right) \cdot x1 + x1\right) + 3 \cdot \mathsf{fma}\left(\mathsf{fma}\left(3, x1, -1\right), x1, -2 \cdot x2\right)\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 84.1%

       \[\leadsto x1 + \left(\left(\left(\left(x2 \cdot x2\right) \cdot 8\right) \cdot x1 + x1\right) + 3 \cdot \mathsf{fma}\left(\mathsf{fma}\left(3, x1, -1\right), x1, -2 \cdot x2\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.2 \cdot 10^{+19}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot 6\\ \mathbf{elif}\;x1 \leq 20.5:\\ \;\;\;\;\left(\mathsf{fma}\left(\mathsf{fma}\left(3, x1, -1\right), x1, -2 \cdot x2\right) \cdot 3 + \left(\left(\left(x2 \cdot x2\right) \cdot 8\right) \cdot x1 + x1\right)\right) + x1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot 6\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 87.0% accurate, 7.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot 6\\ \mathbf{if}\;x1 \leq -7.2 \cdot 10^{+19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 9.6:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, -1\right), x1, -6 \cdot x2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* (* x1 x1) (* x1 x1)) 6.0)))
   (if (<= x1 -7.2e+19)
     t_0
     (if (<= x1 9.6)
       (fma (fma (* (fma 2.0 x2 -3.0) x2) 4.0 -1.0) x1 (* -6.0 x2))
       t_0))))

C

double code(double x1, double x2) {
	double t_0 = ((x1 * x1) * (x1 * x1)) * 6.0;
	double tmp;
	if (x1 <= -7.2e+19) {
		tmp = t_0;
	} else if (x1 <= 9.6) {
		tmp = fma(fma((fma(2.0, x2, -3.0) * x2), 4.0, -1.0), x1, (-6.0 * x2));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(Float64(x1 * x1) * Float64(x1 * x1)) * 6.0)
	tmp = 0.0
	if (x1 <= -7.2e+19)
		tmp = t_0;
	elseif (x1 <= 9.6)
		tmp = fma(fma(Float64(fma(2.0, x2, -3.0) * x2), 4.0, -1.0), x1, Float64(-6.0 * x2));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * 6.0), $MachinePrecision]}, If[LessEqual[x1, -7.2e+19], t$95$0, If[LessEqual[x1, 9.6], N[(N[(N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * x2), $MachinePrecision] * 4.0 + -1.0), $MachinePrecision] * x1 + N[(-6.0 * x2), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -7.2e19 or 9.59999999999999964 < x1

   1. Initial program 43.8%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   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 3.8

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

   5. Applied rewrites 3.8%

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

   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 94.3

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

   8. Applied rewrites 94.3%

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

   10. Applied rewrites 94.3%

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

   if -7.2e19 < x1 < 9.59999999999999964

   1. Initial program 98.6%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   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 43.3

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

   5. Applied rewrites 43.3%

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

   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. lower-*.f64 83.5

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

   8. Applied rewrites 83.5%

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

Alternative 14: 69.0% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot 6\\ \mathbf{if}\;x1 \leq -1.02 \cdot 10^{-39}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 0.026:\\ \;\;\;\;-6 \cdot x2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* (* x1 x1) (* x1 x1)) 6.0)))
   (if (<= x1 -1.02e-39) t_0 (if (<= x1 0.026) (* -6.0 x2) t_0))))

C

double code(double x1, double x2) {
	double t_0 = ((x1 * x1) * (x1 * x1)) * 6.0;
	double tmp;
	if (x1 <= -1.02e-39) {
		tmp = t_0;
	} else if (x1 <= 0.026) {
		tmp = -6.0 * x2;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((x1 * x1) * (x1 * x1)) * 6.0d0
    if (x1 <= (-1.02d-39)) then
        tmp = t_0
    else if (x1 <= 0.026d0) then
        tmp = (-6.0d0) * x2
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = ((x1 * x1) * (x1 * x1)) * 6.0;
	double tmp;
	if (x1 <= -1.02e-39) {
		tmp = t_0;
	} else if (x1 <= 0.026) {
		tmp = -6.0 * x2;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = ((x1 * x1) * (x1 * x1)) * 6.0
	tmp = 0
	if x1 <= -1.02e-39:
		tmp = t_0
	elif x1 <= 0.026:
		tmp = -6.0 * x2
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(Float64(x1 * x1) * Float64(x1 * x1)) * 6.0)
	tmp = 0.0
	if (x1 <= -1.02e-39)
		tmp = t_0;
	elseif (x1 <= 0.026)
		tmp = Float64(-6.0 * x2);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = ((x1 * x1) * (x1 * x1)) * 6.0;
	tmp = 0.0;
	if (x1 <= -1.02e-39)
		tmp = t_0;
	elseif (x1 <= 0.026)
		tmp = -6.0 * x2;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * 6.0), $MachinePrecision]}, If[LessEqual[x1, -1.02e-39], t$95$0, If[LessEqual[x1, 0.026], N[(-6.0 * x2), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.02000000000000007e-39 or 0.0259999999999999988 < x1

   1. Initial program 50.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   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 3.5

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

   5. Applied rewrites 3.5%

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

   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 84.7

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

   8. Applied rewrites 84.7%

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

   10. Applied rewrites 84.7%

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

   if -1.02000000000000007e-39 < x1 < 0.0259999999999999988

   1. Initial program 98.6%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   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 49.2

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

   5. Applied rewrites 49.2%

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

   6. Taylor expanded in x1 around 0

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

      1. lower-*.f64 49.6

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

   8. Applied rewrites 49.6%

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

Alternative 15: 69.0% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(6 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(x1 \cdot x1\right)\\ \mathbf{if}\;x1 \leq -1.02 \cdot 10^{-39}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 0.026:\\ \;\;\;\;-6 \cdot x2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* 6.0 (* x1 x1)) (* x1 x1))))
   (if (<= x1 -1.02e-39) t_0 (if (<= x1 0.026) (* -6.0 x2) t_0))))

C

double code(double x1, double x2) {
	double t_0 = (6.0 * (x1 * x1)) * (x1 * x1);
	double tmp;
	if (x1 <= -1.02e-39) {
		tmp = t_0;
	} else if (x1 <= 0.026) {
		tmp = -6.0 * x2;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (6.0d0 * (x1 * x1)) * (x1 * x1)
    if (x1 <= (-1.02d-39)) then
        tmp = t_0
    else if (x1 <= 0.026d0) then
        tmp = (-6.0d0) * x2
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (6.0 * (x1 * x1)) * (x1 * x1);
	double tmp;
	if (x1 <= -1.02e-39) {
		tmp = t_0;
	} else if (x1 <= 0.026) {
		tmp = -6.0 * x2;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (6.0 * (x1 * x1)) * (x1 * x1)
	tmp = 0
	if x1 <= -1.02e-39:
		tmp = t_0
	elif x1 <= 0.026:
		tmp = -6.0 * x2
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(6.0 * Float64(x1 * x1)) * Float64(x1 * x1))
	tmp = 0.0
	if (x1 <= -1.02e-39)
		tmp = t_0;
	elseif (x1 <= 0.026)
		tmp = Float64(-6.0 * x2);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (6.0 * (x1 * x1)) * (x1 * x1);
	tmp = 0.0;
	if (x1 <= -1.02e-39)
		tmp = t_0;
	elseif (x1 <= 0.026)
		tmp = -6.0 * x2;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(6.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.02e-39], t$95$0, If[LessEqual[x1, 0.026], N[(-6.0 * x2), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.02000000000000007e-39 or 0.0259999999999999988 < x1

   1. Initial program 50.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   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 3.5

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

   5. Applied rewrites 3.5%

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

   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 84.7

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

   8. Applied rewrites 84.7%

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

   10. Applied rewrites 84.6%

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

   if -1.02000000000000007e-39 < x1 < 0.0259999999999999988

   1. Initial program 98.6%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   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 49.2

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

   5. Applied rewrites 49.2%

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

   6. Taylor expanded in x1 around 0

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

      1. lower-*.f64 49.6

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

   8. Applied rewrites 49.6%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.02 \cdot 10^{-39}:\\ \;\;\;\;\left(6 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(x1 \cdot x1\right)\\ \mathbf{elif}\;x1 \leq 0.026:\\ \;\;\;\;-6 \cdot x2\\ \mathbf{else}:\\ \;\;\;\;\left(6 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(x1 \cdot x1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 45.6% accurate, 11.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.06 \cdot 10^{-44}:\\ \;\;\;\;\left(-\mathsf{fma}\left(-12, x2, 18\right)\right) \cdot x1 + x1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x1 \cdot x1, x1, -6 \cdot x2\right) + x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.06e-44)
   (+ (* (- (fma -12.0 x2 18.0)) x1) x1)
   (+ (fma (* x1 x1) x1 (* -6.0 x2)) x1)))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.06e-44) {
		tmp = (-fma(-12.0, x2, 18.0) * x1) + x1;
	} else {
		tmp = fma((x1 * x1), x1, (-6.0 * x2)) + x1;
	}
	return tmp;
}

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.06e-44)
		tmp = Float64(Float64(Float64(-fma(-12.0, x2, 18.0)) * x1) + x1);
	else
		tmp = Float64(fma(Float64(x1 * x1), x1, Float64(-6.0 * x2)) + x1);
	end
	return tmp
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.06e-44], N[(N[((-N[(-12.0 * x2 + 18.0), $MachinePrecision]) * x1), $MachinePrecision] + x1), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] * x1 + N[(-6.0 * x2), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.0599999999999999e-44

   1. Initial program 53.9%

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

   3. Taylor expanded in x1 around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 78.5%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 12.1%

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

      1. lift-+.f64 N/A

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

   10. Applied rewrites 12.1%

       \[\leadsto \color{blue}{\left(-\mathsf{fma}\left(-12, x2, 18\right)\right) \cdot x1 + x1} \]

   if -1.0599999999999999e-44 < x1

   1. Initial program 77.8%

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

   4. Applied rewrites 78.0%

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

   5. Taylor expanded in x1 around 0

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

      1. lower-*.f64 61.1

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

   7. Applied rewrites 61.1%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.06 \cdot 10^{-44}:\\ \;\;\;\;\left(-\mathsf{fma}\left(-12, x2, 18\right)\right) \cdot x1 + x1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x1 \cdot x1, x1, -6 \cdot x2\right) + x1\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 26.6% 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 23.7

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

5. Applied rewrites 23.7%

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

6. Final simplification 23.7%

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

Alternative 18: 26.5% 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 23.7

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

5. Applied rewrites 23.7%

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

6. Taylor expanded in x1 around 0

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

   1. lower-*.f64 23.3

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

8. Applied rewrites 23.3%

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

Reproduce

herbie shell --seed 2024276 
(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))))))