Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.1% → 99.7%

Time: 36.7s

Precision: binary64

Cost: 61769

• 46.9% of points produce a very large (infinite) output. You may want to add a precondition.

Math

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

↓

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+153} \lor \neg \left(x1 \leq 5 \cdot 10^{+153}\right):\\ \;\;\;\;x1 + \mathsf{fma}\left(3, x1 \cdot \left(x1 \cdot 3\right) - x1, x1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, -2 \cdot x2 - x1, \mathsf{fma}\left(x1, x1 \cdot 9, \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{t_0}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(x1 \cdot \left(-6 + \frac{t_0}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{2}}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :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))))))

↓

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (fma x1 (* x1 3.0) (fma 2.0 x2 (- x1)))))
   (if (or (<= x1 -5e+153) (not (<= x1 5e+153)))
     (+ x1 (fma 3.0 (- (* x1 (* x1 3.0)) x1) x1))
     (+
      x1
      (fma
       3.0
       (- (* -2.0 x2) x1)
       (fma
        x1
        (* x1 9.0)
        (*
         (fma x1 x1 1.0)
         (+
          x1
          (+
           (* x1 (* x1 -6.0))
           (*
            (/ t_0 (fma x1 x1 1.0))
            (+
             (* x1 (+ -6.0 (/ t_0 (/ (fma x1 x1 1.0) 2.0))))
             (* (* x1 x1) 4.0))))))))))))

C

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

↓

double code(double x1, double x2) {
	double t_0 = fma(x1, (x1 * 3.0), fma(2.0, x2, -x1));
	double tmp;
	if ((x1 <= -5e+153) || !(x1 <= 5e+153)) {
		tmp = x1 + fma(3.0, ((x1 * (x1 * 3.0)) - x1), x1);
	} else {
		tmp = x1 + fma(3.0, ((-2.0 * x2) - x1), fma(x1, (x1 * 9.0), (fma(x1, x1, 1.0) * (x1 + ((x1 * (x1 * -6.0)) + ((t_0 / fma(x1, x1, 1.0)) * ((x1 * (-6.0 + (t_0 / (fma(x1, x1, 1.0) / 2.0)))) + ((x1 * x1) * 4.0))))))));
	}
	return tmp;
}

Julia

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

↓

function code(x1, x2)
	t_0 = fma(x1, Float64(x1 * 3.0), fma(2.0, x2, Float64(-x1)))
	tmp = 0.0
	if ((x1 <= -5e+153) || !(x1 <= 5e+153))
		tmp = Float64(x1 + fma(3.0, Float64(Float64(x1 * Float64(x1 * 3.0)) - x1), x1));
	else
		tmp = Float64(x1 + fma(3.0, Float64(Float64(-2.0 * x2) - x1), fma(x1, Float64(x1 * 9.0), Float64(fma(x1, x1, 1.0) * Float64(x1 + Float64(Float64(x1 * Float64(x1 * -6.0)) + Float64(Float64(t_0 / fma(x1, x1, 1.0)) * Float64(Float64(x1 * Float64(-6.0 + Float64(t_0 / Float64(fma(x1, x1, 1.0) / 2.0)))) + Float64(Float64(x1 * x1) * 4.0)))))))));
	end
	return tmp
end

Wolfram

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

↓

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision] + N[(2.0 * x2 + (-x1)), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x1, -5e+153], N[Not[LessEqual[x1, 5e+153]], $MachinePrecision]], N[(x1 + N[(3.0 * N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] + x1), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(3.0 * N[(N[(-2.0 * x2), $MachinePrecision] - x1), $MachinePrecision] + N[(x1 * N[(x1 * 9.0), $MachinePrecision] + N[(N[(x1 * x1 + 1.0), $MachinePrecision] * N[(x1 + N[(N[(x1 * N[(x1 * -6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x1 * N[(-6.0 + N[(t$95$0 / N[(N[(x1 * x1 + 1.0), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 66.0%

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

   4. Simplified 66.0%

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

      [Start] 66.0%	\[ x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right)\right)\right) \]
      +-commutative [=>] 66.0%	\[ x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + -1 \cdot x1\right)}\right) \]
      neg-mul-1 [<=] 66.0%	\[ x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + \color{blue}{\left(-x1\right)}\right)\right) \]
      unsub-neg [=>] 66.0%	\[ x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)}\right) \]
      +-commutative [=>] 66.0%	\[ x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + -2 \cdot x2\right)} - x1\right)\right) \]
      *-commutative [=>] 66.0%	\[ x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{{x1}^{2} \cdot \left(3 - -2 \cdot x2\right)} + -2 \cdot x2\right) - x1\right)\right) \]
      fma-def [=>] 66.0%	\[ x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left({x1}^{2}, 3 - -2 \cdot x2, -2 \cdot x2\right)} - x1\right)\right) \]
      unpow2 [=>] 66.0%	\[ x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(\color{blue}{x1 \cdot x1}, 3 - -2 \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]
      cancel-sign-sub-inv [=>] 66.0%	\[ x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{3 + \left(--2\right) \cdot x2}, -2 \cdot x2\right) - x1\right)\right) \]
      metadata-eval [=>] 66.0%	\[ x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + \color{blue}{2} \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]
      +-commutative [=>] 66.0%	\[ x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{2 \cdot x2 + 3}, -2 \cdot x2\right) - x1\right)\right) \]
      *-commutative [=>] 66.0%	\[ x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, \color{blue}{x2 \cdot -2}\right) - x1\right)\right) \]

   5. Applied egg-rr 66.0%

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

      [Start] 66.0%	\[ x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right) \]
      *-un-lft-identity [=>] 66.0%	\[ x1 + \color{blue}{1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right)} \]
      fma-def [=>] 66.0%	\[ x1 + 1 \cdot \left(\color{blue}{\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right), x1\right)} + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right) \]
      fma-neg [=>] 66.0%	\[ x1 + 1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \color{blue}{\mathsf{fma}\left(2, x2, -3\right)}\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right) \]
      metadata-eval [=>] 66.0%	\[ x1 + 1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, \color{blue}{-3}\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right) \]
      fma-def [=>] 66.0%	\[ x1 + 1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{\mathsf{fma}\left(2, x2, 3\right)}, x2 \cdot -2\right) - x1\right)\right) \]

   6. Simplified 66.0%

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

      [Start] 66.0%	\[ x1 + 1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1\right)\right) \]
      *-lft-identity [=>] 66.0%	\[ x1 + \color{blue}{\left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1\right)\right)} \]
      +-commutative [=>] 66.0%	\[ x1 + \color{blue}{\left(3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1\right) + \mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right)\right)} \]
      fma-def [=>] 66.0%	\[ x1 + \color{blue}{\mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right)\right)} \]
      fma-udef [=>] 66.0%	\[ x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right)\right) + x1}\right) \]
      associate-*r* [=>] 66.0%	\[ x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \color{blue}{\left(4 \cdot x2\right) \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right)} + x1\right) \]
      fma-def [=>] 66.0%	\[ x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \color{blue}{\mathsf{fma}\left(4 \cdot x2, x1 \cdot \mathsf{fma}\left(2, x2, -3\right), x1\right)}\right) \]
      *-commutative [=>] 66.0%	\[ x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \mathsf{fma}\left(\color{blue}{x2 \cdot 4}, x1 \cdot \mathsf{fma}\left(2, x2, -3\right), x1\right)\right) \]

   7. Taylor expanded in x2 around 0 100.0%

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

   8. Simplified 100.0%

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

      [Start] 100.0%	\[ x1 + \left(x1 + 3 \cdot \left(3 \cdot {x1}^{2} - x1\right)\right) \]
      +-commutative [=>] 100.0%	\[ x1 + \color{blue}{\left(3 \cdot \left(3 \cdot {x1}^{2} - x1\right) + x1\right)} \]
      fma-def [=>] 100.0%	\[ x1 + \color{blue}{\mathsf{fma}\left(3, 3 \cdot {x1}^{2} - x1, x1\right)} \]
      *-commutative [=>] 100.0%	\[ x1 + \mathsf{fma}\left(3, \color{blue}{{x1}^{2} \cdot 3} - x1, x1\right) \]
      unpow2 [=>] 100.0%	\[ x1 + \mathsf{fma}\left(3, \color{blue}{\left(x1 \cdot x1\right)} \cdot 3 - x1, x1\right) \]
      associate-*l* [=>] 100.0%	\[ x1 + \mathsf{fma}\left(3, \color{blue}{x1 \cdot \left(x1 \cdot 3\right)} - x1, x1\right) \]

   if -5.00000000000000018e153 < x1 < 5.00000000000000018e153

   1. Initial program 89.5%

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

   2. Simplified 99.7%

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

      [Start] 89.5%

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

      +-commutative [=>] 89.5%

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

   3. Taylor expanded in x1 around inf 98.4%

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

   4. Taylor expanded in x1 around 0 99.7%

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

   5. Simplified 99.7%

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

      [Start] 99.7%	\[ x1 + \mathsf{fma}\left(3, -1 \cdot x1 + -2 \cdot x2, \mathsf{fma}\left(x1, x1 \cdot 9, \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(x1 \cdot \left(-6 + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{2}}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right)\right)\right)\right) \]
      +-commutative [=>] 99.7%	\[ x1 + \mathsf{fma}\left(3, \color{blue}{-2 \cdot x2 + -1 \cdot x1}, \mathsf{fma}\left(x1, x1 \cdot 9, \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(x1 \cdot \left(-6 + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{2}}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right)\right)\right)\right) \]
      neg-mul-1 [<=] 99.7%	\[ x1 + \mathsf{fma}\left(3, -2 \cdot x2 + \color{blue}{\left(-x1\right)}, \mathsf{fma}\left(x1, x1 \cdot 9, \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(x1 \cdot \left(-6 + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{2}}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right)\right)\right)\right) \]
      unsub-neg [=>] 99.7%	\[ x1 + \mathsf{fma}\left(3, \color{blue}{-2 \cdot x2 - x1}, \mathsf{fma}\left(x1, x1 \cdot 9, \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(x1 \cdot \left(-6 + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{2}}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right)\right)\right)\right) \]

3. Recombined 2 regimes into one program.

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+153} \lor \neg \left(x1 \leq 5 \cdot 10^{+153}\right):\\ \;\;\;\;x1 + \mathsf{fma}\left(3, x1 \cdot \left(x1 \cdot 3\right) - x1, x1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, -2 \cdot x2 - x1, \mathsf{fma}\left(x1, x1 \cdot 9, \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(x1 \cdot \left(-6 + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{2}}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right)\right)\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	99.7%
Cost	61769

\[\begin{array}{l} t_0 := \mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+153} \lor \neg \left(x1 \leq 5 \cdot 10^{+153}\right):\\ \;\;\;\;x1 + \mathsf{fma}\left(3, x1 \cdot \left(x1 \cdot 3\right) - x1, x1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, -2 \cdot x2 - x1, \mathsf{fma}\left(x1, x1 \cdot 9, \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{t_0}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(x1 \cdot \left(-6 + \frac{t_0}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{2}}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 2
Accuracy	98.0%
Cost	8524

\[\begin{array}{l} t_0 := 1 + x1 \cdot x1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\left(t_1 + x2 \cdot 2\right) - x1}{t_0}\\ t_3 := x1 + \mathsf{fma}\left(3, t_1 - x1, x1\right)\\ \mathbf{if}\;x1 \leq -7.1 \cdot 10^{+183}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2 - x2 \cdot {x1}^{3}\right)\right)\right) + 3 \cdot \left(-2 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_1 - x2 \cdot 2\right) - x1}{t_0} + \left(x1 + \left(\left(t_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right)\right) + t_1 \cdot t_2\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 3
Accuracy	99.1%
Cost	8524

\[\begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 + \mathsf{fma}\left(3, t_0 - x1, x1\right)\\ t_2 := 1 + x1 \cdot x1\\ t_3 := 3 \cdot \frac{\left(t_0 - x2 \cdot 2\right) - x1}{t_2}\\ t_4 := \frac{\left(t_0 + x2 \cdot 2\right) - x1}{t_2}\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq -2 \cdot 10^{+104}:\\ \;\;\;\;x1 + \left(\left(x1 + {x1}^{4} \cdot 6\right) + t_3\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + \left(\left(t_2 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_4\right) \cdot \left(t_4 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_4 - 6\right)\right) + t_0 \cdot t_4\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Accuracy	97.1%
Cost	8072

\[\begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 + \mathsf{fma}\left(3, t_0 - x1, x1\right)\\ t_2 := 1 + x1 \cdot x1\\ t_3 := \frac{\left(t_0 + x2 \cdot 2\right) - x1}{t_2}\\ \mathbf{if}\;x1 \leq -7.1 \cdot 10^{+183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2 - x2 \cdot {x1}^{3}\right)\right)\right) + 3 \cdot \left(-2 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t_2 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_3\right) \cdot \left(t_3 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_3 - 6\right)\right) + t_0 \cdot t_3\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(-2 \cdot x2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Accuracy	96.8%
Cost	7816

\[\begin{array}{l} t_0 := 1 + x1 \cdot x1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 + \mathsf{fma}\left(3, t_1 - x1, x1\right)\\ t_3 := \frac{\left(t_1 + x2 \cdot 2\right) - x1}{t_0}\\ \mathbf{if}\;x1 \leq -3.2 \cdot 10^{+181}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x1 \leq -3.7 \cdot 10^{+104}:\\ \;\;\;\;x1 + \left(3 \cdot \left(-2 \cdot x2\right) + \left(x1 - 8 \cdot \left({x1}^{3} \cdot \left(x2 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_3\right) \cdot \left(t_3 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_3 - 6\right)\right) + t_1 \cdot t_3\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(-2 \cdot x2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Accuracy	94.8%
Cost	7625

\[\begin{array}{l} t_0 := 1 + x1 \cdot x1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\left(t_1 + x2 \cdot 2\right) - x1}{t_0}\\ \mathbf{if}\;x1 \leq -1.05 \cdot 10^{+103} \lor \neg \left(x1 \leq 4 \cdot 10^{+153}\right):\\ \;\;\;\;x1 + \mathsf{fma}\left(3, t_1 - x1, x1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right)\right) + t_1 \cdot t_2\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(-2 \cdot x2 - x1\right)\right)\\ \end{array} \]

Alternative 7
Accuracy	85.8%
Cost	7369

\[\begin{array}{l} t_0 := 1 + x1 \cdot x1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\left(t_1 + x2 \cdot 2\right) - x1}{t_0}\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102} \lor \neg \left(x1 \leq 4.5 \cdot 10^{+153}\right):\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \mathsf{fma}\left(2, x2, 3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(-2 \cdot x2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t_1 + t_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right) + \left(t_2 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 \cdot 2 - x1\right)\right)\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 8
Accuracy	87.5%
Cost	7369

\[\begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 1 + x1 \cdot x1\\ t_2 := \frac{\left(t_0 + x2 \cdot 2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102} \lor \neg \left(x1 \leq 1.35 \cdot 10^{+154}\right):\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \mathsf{fma}\left(2, x2, 3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - x2 \cdot 2\right) - x1}{t_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_0 \cdot t_2 + t_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 9
Accuracy	89.1%
Cost	7369

\[\begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 1 + x1 \cdot x1\\ t_2 := \frac{\left(t_0 + x2 \cdot 2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102} \lor \neg \left(x1 \leq 1.35 \cdot 10^{+154}\right):\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \mathsf{fma}\left(2, x2, 3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - x2 \cdot 2\right) - x1}{t_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right)\right) + 3 \cdot t_0\right)\right)\right)\right)\\ \end{array} \]

Alternative 10
Accuracy	94.8%
Cost	7369

\[\begin{array}{l} t_0 := 1 + x1 \cdot x1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\left(t_1 + x2 \cdot 2\right) - x1}{t_0}\\ \mathbf{if}\;x1 \leq -6.8 \cdot 10^{+103} \lor \neg \left(x1 \leq 4 \cdot 10^{+153}\right):\\ \;\;\;\;x1 + \mathsf{fma}\left(3, t_1 - x1, x1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_1 - x2 \cdot 2\right) - x1}{t_0} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right)\right) + 3 \cdot t_1\right)\right)\right)\right)\\ \end{array} \]

Alternative 11
Accuracy	75.3%
Cost	5832

\[\begin{array}{l} t_0 := 1 + x1 \cdot x1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\left(t_1 + x2 \cdot 2\right) - x1}{t_0}\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x1 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq 8 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \left(-2 \cdot x2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t_1 + t_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right) + \left(t_2 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 \cdot 2 - x1\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(-2 \cdot x2\right) + \left(x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \end{array} \]

Alternative 12
Accuracy	74.3%
Cost	5448

\[\begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 1 + x1 \cdot x1\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x1 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - x2 \cdot 2\right) - x1}{t_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t_0 + t_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(t_0 + x2 \cdot 2\right) - x1}{t_1} - 6\right) + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(-2 \cdot x2\right) + \left(x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \end{array} \]

Alternative 13
Accuracy	75.0%
Cost	5200

\[\begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 1 + x1 \cdot x1\\ t_2 := 3 \cdot \frac{\left(t_0 - x2 \cdot 2\right) - x1}{t_1}\\ t_3 := x1 + \left(t_2 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t_0 + t_1 \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(t_0 + x2 \cdot 2\right) - x1}{t_1} - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x1 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq -32000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x1 \leq 1.95 \cdot 10^{+26}:\\ \;\;\;\;x1 + \left(t_2 + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(-2 \cdot x2\right) + \left(x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \end{array} \]

Alternative 14
Accuracy	63.0%
Cost	1604

\[\begin{array}{l} \mathbf{if}\;x1 \leq -3.7 \cdot 10^{+104}:\\ \;\;\;\;x1 + \left(x1 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right) + \left(x1 \cdot -3 + x2 \cdot -6\right)\right)\\ \end{array} \]

Alternative 15
Accuracy	63.0%
Cost	1604

\[\begin{array}{l} \mathbf{if}\;x1 \leq -1.15 \cdot 10^{+105}:\\ \;\;\;\;x1 + \left(x1 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(-2 \cdot x2 - x1\right) + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 16
Accuracy	42.6%
Cost	1352

\[\begin{array}{l} \mathbf{if}\;x1 \leq -2.6 \cdot 10^{+57}:\\ \;\;\;\;x1 + \left(x1 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq -7 \cdot 10^{-110}:\\ \;\;\;\;x1 + \left(9 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.6 \cdot 10^{-140}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ \end{array} \]

Alternative 17
Accuracy	57.5%
Cost	1348

\[\begin{array}{l} \mathbf{if}\;x1 \leq -1.05 \cdot 10^{+105}:\\ \;\;\;\;x1 + \left(x1 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right)\right)\\ \end{array} \]

Alternative 18
Accuracy	46.3%
Cost	1220

\[\begin{array}{l} \mathbf{if}\;x1 \leq -3.8 \cdot 10^{+73}:\\ \;\;\;\;x1 + \left(x1 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(-2 \cdot x2\right) + \left(x1 + 8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\\ \end{array} \]

Alternative 19
Accuracy	52.0%
Cost	1220

\[\begin{array}{l} \mathbf{if}\;x1 \leq -9.8 \cdot 10^{+73}:\\ \;\;\;\;x1 + \left(x1 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(-2 \cdot x2\right) + \left(x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \end{array} \]

Alternative 20
Accuracy	42.5%
Cost	973

\[\begin{array}{l} \mathbf{if}\;x1 \leq -3.8 \cdot 10^{+72}:\\ \;\;\;\;x1 + \left(x1 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq -4.4 \cdot 10^{-111} \lor \neg \left(x1 \leq 1.6 \cdot 10^{-140}\right):\\ \;\;\;\;x1 + \left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \]

Alternative 21
Accuracy	37.7%
Cost	841

\[\begin{array}{l} \mathbf{if}\;x2 \leq -2.3 \cdot 10^{+96} \lor \neg \left(x2 \leq 1.75 \cdot 10^{+134}\right):\\ \;\;\;\;x1 + \left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \]

Alternative 22
Accuracy	26.5%
Cost	320

\[x1 + x2 \cdot -6 \]

Alternative 23
Accuracy	3.3%
Cost	192

\[x1 + x1 \]

Reproduce

herbie shell --seed 2023167 
(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))))))