Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 69.9% → 99.5%

Time: 58.2s

Precision: binary64

Cost: 103044

• 47.1% of points produce a very large (infinite) output. You may want to add a precondition.

Math

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

↓

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

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

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 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = t_0 + (2.0 * x2);
	double t_3 = (t_2 - x1) / t_1;
	double t_4 = fma(x1, (x1 * 3.0), fma(2.0, x2, -x1));
	double tmp;
	if ((x1 + ((x1 + ((((-1.0 - (x1 * x1)) * (((x1 * x1) * (6.0 - (t_3 * 4.0))) + (((x1 * 2.0) * t_3) * (3.0 + ((x1 - t_2) / t_1))))) + (t_0 * t_3)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)))) <= ((double) INFINITY)) {
		tmp = x1 + fma(3.0, ((t_0 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), fma(x1, (x1 * (t_4 / (fma(x1, x1, 1.0) / 3.0))), (fma(x1, x1, 1.0) * (x1 + ((x1 * (x1 * -6.0)) + ((t_4 / fma(x1, x1, 1.0)) * ((x1 * (-6.0 + (t_4 / (fma(x1, x1, 1.0) / 2.0)))) + ((x1 * x1) * 4.0))))))));
	} else {
		tmp = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + (3.0 * (x2 * -2.0)));
	}
	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 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(t_0 + Float64(2.0 * x2))
	t_3 = Float64(Float64(t_2 - x1) / t_1)
	t_4 = fma(x1, Float64(x1 * 3.0), fma(2.0, x2, Float64(-x1)))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(Float64(-1.0 - Float64(x1 * x1)) * Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(t_3 * 4.0))) + Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(3.0 + Float64(Float64(x1 - t_2) / t_1))))) + Float64(t_0 * t_3)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1)))) <= Inf)
		tmp = Float64(x1 + fma(3.0, Float64(Float64(t_0 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), fma(x1, Float64(x1 * Float64(t_4 / Float64(fma(x1, x1, 1.0) / 3.0))), Float64(fma(x1, x1, 1.0) * Float64(x1 + Float64(Float64(x1 * Float64(x1 * -6.0)) + Float64(Float64(t_4 / fma(x1, x1, 1.0)) * Float64(Float64(x1 * Float64(-6.0 + Float64(t_4 / Float64(fma(x1, x1, 1.0) / 2.0)))) + Float64(Float64(x1 * x1) * 4.0)))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + Float64(3.0 * Float64(x2 * -2.0))));
	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]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(x1 * N[(x1 * 3.0), $MachinePrecision] + N[(2.0 * x2 + (-x1)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(t$95$3 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(3.0 + N[(N[(x1 - t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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], Infinity], N[(x1 + N[(3.0 * N[(N[(t$95$0 - N[(2.0 * x2 + x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * N[(t$95$4 / N[(N[(x1 * x1 + 1.0), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1 + 1.0), $MachinePrecision] * N[(x1 + N[(N[(x1 * N[(x1 * -6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$4 / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x1 * N[(-6.0 + N[(t$95$4 / 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], N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 2 x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)) 3)) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 4 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) 6))) (+.f64 (*.f64 x1 x1) 1)) (*.f64 (*.f64 (*.f64 3 x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 3 (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))))) < +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. 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] 99.4%

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

      +-commutative [=>] 99.4%

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

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

   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%

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

   3. Simplified 0.0%

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

      [Start] 0.0%

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

      *-commutative [=>] 0.0%

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

   4. Taylor expanded in x1 around inf 98.5%

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

4. Final simplification 99.4%

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

Alternatives

Alternative 1
Accuracy	99.5%
Cost	103044

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

Alternative 2
Accuracy	99.3%
Cost	28996

\[\begin{array}{l} t_0 := -1 - x1 \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := t_2 + 2 \cdot x2\\ t_4 := 3 \cdot \frac{\left(t_2 - 2 \cdot x2\right) - x1}{t_1}\\ t_5 := \frac{t_3 - x1}{t_1}\\ t_6 := \left(x1 \cdot 2\right) \cdot t_5\\ t_7 := \left(x1 \cdot x1\right) \cdot \left(6 - t_5 \cdot 4\right)\\ t_8 := \frac{x1 - t_3}{t_1}\\ t_9 := x1 \cdot \left(x1 \cdot x1\right)\\ \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(t_0 \cdot \left(t_7 + t_6 \cdot \left(3 + t_8\right)\right) + t_2 \cdot t_5\right) + t_9\right)\right) + t_4\right) \leq \infty:\\ \;\;\;\;x1 + \left(t_4 - \left(\left(\left(t_2 \cdot t_8 - t_0 \cdot \left(t_7 + t_6 \cdot \left(3 + \left(\mathsf{fma}\left(x1 \cdot 3, x1, 2 \cdot x2\right) - x1\right) \cdot \frac{-1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right)\right) - t_9\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \]

Alternative 3
Accuracy	99.3%
Cost	28996

\[\begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := 3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_0}\\ t_3 := t_1 + 2 \cdot x2\\ t_4 := \frac{t_3 - x1}{t_0}\\ t_5 := \left(x1 \cdot 2\right) \cdot t_4\\ t_6 := \left(x1 \cdot x1\right) \cdot \left(6 - t_4 \cdot 4\right)\\ t_7 := t_1 \cdot t_4\\ t_8 := x1 \cdot \left(x1 \cdot x1\right)\\ \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(\left(-1 - x1 \cdot x1\right) \cdot \left(t_6 + t_5 \cdot \left(3 + \frac{x1 - t_3}{t_0}\right)\right) + t_7\right) + t_8\right)\right) + t_2\right) \leq \infty:\\ \;\;\;\;x1 + \left(t_2 + \left(x1 + \left(t_8 + \left(t_7 - t_0 \cdot \left(t_6 + t_5 \cdot \left(3 + \frac{-1}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right) - x1}}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \]

Alternative 4
Accuracy	99.3%
Cost	16324

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

Alternative 5
Accuracy	86.7%
Cost	7892

\[\begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := t_0 + 2 \cdot x2\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{t_1 - x1}{t_2}\\ t_4 := \left(x1 \cdot x1\right) \cdot \left(6 - t_3 \cdot 4\right)\\ t_5 := 3 - 2 \cdot x2\\ t_6 := x1 \cdot \left(x1 \cdot x1\right)\\ t_7 := \left(x1 \cdot 2\right) \cdot t_3\\ t_8 := x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(t_6 + \left(t_0 \cdot t_3 - t_2 \cdot \left(t_4 + t_7 \cdot \left(\left(\frac{1}{x1} + \frac{3}{x1 \cdot x1}\right) - 2 \cdot \frac{x2}{x1 \cdot x1}\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -4.8 \cdot 10^{+158}:\\ \;\;\;\;x1 + \left(\left(x1 - 4 \cdot \left(x2 \cdot \left(x1 \cdot t_5\right)\right)\right) + \frac{\left(x1 \cdot x1\right) \cdot 9 - \left(x2 \cdot x2\right) \cdot 36}{x1 \cdot -3 - x2 \cdot -6}\right)\\ \mathbf{elif}\;x1 \leq -5.8 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + x1 \cdot -3\right) - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \mathbf{elif}\;x1 \leq -0.78:\\ \;\;\;\;t_8\\ \mathbf{elif}\;x1 \leq 1.15:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_2} + \left(x1 + \left(t_6 - \left(t_0 \cdot \frac{x1 - t_1}{t_2} + t_2 \cdot \left(t_4 + t_7 \cdot t_5\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.1 \cdot 10^{+154}:\\ \;\;\;\;t_8\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot 6}\\ \end{array} \]

Alternative 6
Accuracy	85.9%
Cost	7764

\[\begin{array}{l} t_0 := x1 - 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \left(x2 \cdot x2\right) \cdot 36\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := \frac{\left(t_3 + 2 \cdot x2\right) - x1}{t_1}\\ t_5 := x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_3 \cdot t_4 - t_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - t_4 \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot t_4\right) \cdot \left(\left(\frac{1}{x1} + \frac{3}{x1 \cdot x1}\right) - 2 \cdot \frac{x2}{x1 \cdot x1}\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -4.8 \cdot 10^{+158}:\\ \;\;\;\;x1 + \left(t_0 + \frac{\left(x1 \cdot x1\right) \cdot 9 - t_2}{x1 \cdot -3 - x2 \cdot -6}\right)\\ \mathbf{elif}\;x1 \leq -5.8 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + x1 \cdot -3\right) - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \mathbf{elif}\;x1 \leq -0.55:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x1 \leq 0.33:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_3 - 2 \cdot x2\right) - x1}{t_1} + t_0\right)\\ \mathbf{elif}\;x1 \leq 1.1 \cdot 10^{+154}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - t_2}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 7
Accuracy	85.9%
Cost	7764

\[\begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := 3 - 2 \cdot x2\\ t_2 := x1 \cdot \left(x1 \cdot x1\right)\\ t_3 := \left(x2 \cdot x2\right) \cdot 36\\ t_4 := x1 \cdot \left(x1 \cdot 3\right)\\ t_5 := t_4 + 2 \cdot x2\\ t_6 := \frac{t_5 - x1}{t_0}\\ t_7 := \left(x1 \cdot x1\right) \cdot \left(6 - t_6 \cdot 4\right)\\ t_8 := \left(x1 \cdot 2\right) \cdot t_6\\ t_9 := x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(t_2 + \left(t_4 \cdot t_6 - t_0 \cdot \left(t_7 + t_8 \cdot \left(\left(\frac{1}{x1} + \frac{3}{x1 \cdot x1}\right) - 2 \cdot \frac{x2}{x1 \cdot x1}\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+159}:\\ \;\;\;\;x1 + \left(\left(x1 - 4 \cdot \left(x2 \cdot \left(x1 \cdot t_1\right)\right)\right) + \frac{\left(x1 \cdot x1\right) \cdot 9 - t_3}{x1 \cdot -3 - x2 \cdot -6}\right)\\ \mathbf{elif}\;x1 \leq -5.8 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + x1 \cdot -3\right) - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \mathbf{elif}\;x1 \leq -0.82:\\ \;\;\;\;t_9\\ \mathbf{elif}\;x1 \leq 1.25:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_4 - 2 \cdot x2\right) - x1}{t_0} + \left(x1 + \left(t_2 - \left(t_4 \cdot \frac{x1 - t_5}{t_0} + t_0 \cdot \left(t_7 + t_8 \cdot t_1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.5 \cdot 10^{+153}:\\ \;\;\;\;t_9\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - t_3}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 8
Accuracy	96.6%
Cost	7561

\[\begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := t_1 + 2 \cdot x2\\ t_3 := \frac{x1 - t_2}{t_0}\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+100} \lor \neg \left(x1 \leq 1.06 \cdot 10^{+55}\right):\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_0} + \left(x1 - \left(\left(t_1 \cdot t_3 + t_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{t_2 - x1}{t_0}\right) \cdot \left(3 + t_3\right) - \left(x1 \cdot x1\right) \cdot 6\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \end{array} \]

Alternative 9
Accuracy	80.7%
Cost	6604

\[\begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := \left(x2 \cdot x2\right) \cdot 36\\ t_3 := t_0 + 2 \cdot x2\\ t_4 := 3 \cdot \left(x2 \cdot -2\right)\\ t_5 := x1 - 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ t_6 := x1 \cdot x1 + 1\\ t_7 := \frac{t_3 - x1}{t_6}\\ \mathbf{if}\;x1 \leq -4.8 \cdot 10^{+158}:\\ \;\;\;\;x1 + \left(t_5 + \frac{\left(x1 \cdot x1\right) \cdot 9 - t_2}{x1 \cdot -3 - x2 \cdot -6}\right)\\ \mathbf{elif}\;x1 \leq -5.8 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + x1 \cdot -3\right) - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \mathbf{elif}\;x1 \leq -1.15 \cdot 10^{+29}:\\ \;\;\;\;x1 - \left(\left(\left(\left(t_0 \cdot \frac{x1 - t_3}{t_6} + t_6 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - t_7 \cdot 4\right) - \left(\left(x1 \cdot 2\right) \cdot t_7\right) \cdot \frac{-1}{x1}\right)\right) - t_1\right) - x1\right) - t_4\right)\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{+24}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_6} + t_5\right)\\ \mathbf{elif}\;x1 \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(t_4 + \left(x1 + \left(t_1 + \left(t_0 \cdot t_7 + t_6 \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - t_2}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 10
Accuracy	79.9%
Cost	3924

\[\begin{array}{l} t_0 := \left(x2 \cdot x2\right) \cdot 36\\ t_1 := x1 - 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := x1 \cdot x1 + 1\\ t_4 := x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 - \left(\left(\left(\left(x1 \cdot x1\right) \cdot 6\right) \cdot \left(-1 - x1 \cdot x1\right) - t_2 \cdot \frac{\left(t_2 + 2 \cdot x2\right) - x1}{t_3}\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -4.8 \cdot 10^{+158}:\\ \;\;\;\;x1 + \left(t_1 + \frac{\left(x1 \cdot x1\right) \cdot 9 - t_0}{x1 \cdot -3 - x2 \cdot -6}\right)\\ \mathbf{elif}\;x1 \leq -5.8 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + x1 \cdot -3\right) - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \mathbf{elif}\;x1 \leq -8.5 \cdot 10^{+28}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x1 \leq 5.7 \cdot 10^{+23}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_2 - 2 \cdot x2\right) - x1}{t_3} + t_1\right)\\ \mathbf{elif}\;x1 \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - t_0}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 11
Accuracy	79.9%
Cost	3924

\[\begin{array}{l} t_0 := x1 - 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \left(x2 \cdot x2\right) \cdot 36\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_3 \cdot \frac{\left(t_3 + 2 \cdot x2\right) - x1}{t_1} + t_1 \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -2.15 \cdot 10^{+159}:\\ \;\;\;\;x1 + \left(t_0 + \frac{\left(x1 \cdot x1\right) \cdot 9 - t_2}{x1 \cdot -3 - x2 \cdot -6}\right)\\ \mathbf{elif}\;x1 \leq -5.8 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + x1 \cdot -3\right) - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \mathbf{elif}\;x1 \leq -8.5 \cdot 10^{+28}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x1 \leq 1.3 \cdot 10^{+24}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_3 - 2 \cdot x2\right) - x1}{t_1} + t_0\right)\\ \mathbf{elif}\;x1 \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - t_2}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 12
Accuracy	71.5%
Cost	2636

\[\begin{array}{l} t_0 := \left(x2 \cdot x2\right) \cdot 36\\ t_1 := x1 - 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{if}\;x1 \leq -4.8 \cdot 10^{+158}:\\ \;\;\;\;x1 + \left(t_1 + \frac{\left(x1 \cdot x1\right) \cdot 9 - t_0}{x1 \cdot -3 - x2 \cdot -6}\right)\\ \mathbf{elif}\;x1 \leq -2.45 \cdot 10^{+89}:\\ \;\;\;\;x1 + \left(\left(x1 + x1 \cdot -3\right) - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \mathbf{elif}\;x1 \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - t_0}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 13
Accuracy	67.7%
Cost	2504

\[\begin{array}{l} \mathbf{if}\;x1 \leq -1.9 \cdot 10^{+90}:\\ \;\;\;\;x1 + \left(\left(x1 + x1 \cdot -3\right) - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \mathbf{elif}\;x1 \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 - 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 14
Accuracy	63.3%
Cost	1744

\[\begin{array}{l} t_0 := x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -6.4 \cdot 10^{+81}:\\ \;\;\;\;x1 + \left(\left(x1 + x1 \cdot -3\right) - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \mathbf{elif}\;x1 \leq -2.5 \cdot 10^{-233}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 5.2 \cdot 10^{-245}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 3 \cdot 10^{+170}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 15
Accuracy	66.9%
Cost	1736

\[\begin{array}{l} \mathbf{if}\;x1 \leq -4.3 \cdot 10^{+84}:\\ \;\;\;\;x1 + \left(\left(x1 + x1 \cdot -3\right) - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \mathbf{elif}\;x1 \leq 3 \cdot 10^{+170}:\\ \;\;\;\;x1 + \left(\left(x1 - 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) + \left(x2 \cdot -6 + x1 \cdot -3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 16
Accuracy	60.5%
Cost	1481

\[\begin{array}{l} \mathbf{if}\;x2 \leq -1.35 \lor \neg \left(x2 \leq 2.65 \cdot 10^{+20}\right):\\ \;\;\;\;x1 + \left(\left(x1 - 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) + x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \]

Alternative 17
Accuracy	53.5%
Cost	1357

\[\begin{array}{l} \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+88}:\\ \;\;\;\;x1 + \left(\left(x1 + x1 \cdot -3\right) - x2 \cdot \left(6 - x1 \cdot -12\right)\right)\\ \mathbf{elif}\;x1 \leq -6.2 \cdot 10^{-98} \lor \neg \left(x1 \leq 1.95 \cdot 10^{-171}\right):\\ \;\;\;\;x1 - x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \]

Alternative 18
Accuracy	50.5%
Cost	1225

\[\begin{array}{l} \mathbf{if}\;x1 \leq -4.1 \cdot 10^{-98} \lor \neg \left(x1 \leq 3 \cdot 10^{-171}\right):\\ \;\;\;\;x1 - x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \]

Alternative 19
Accuracy	55.3%
Cost	1225

\[\begin{array}{l} \mathbf{if}\;x2 \leq -27.5 \lor \neg \left(x2 \leq 6.2 \cdot 10^{+16}\right):\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 + 8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \]

Alternative 20
Accuracy	49.8%
Cost	964

\[\begin{array}{l} t_0 := 8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{if}\;x2 \leq -2 \cdot 10^{+73}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + t_0\right)\right)\\ \mathbf{elif}\;x2 \leq 6.8 \cdot 10^{+119}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 21
Accuracy	49.8%
Cost	713

\[\begin{array}{l} \mathbf{if}\;x2 \leq -4.3 \cdot 10^{+73} \lor \neg \left(x2 \leq 1.8 \cdot 10^{+117}\right):\\ \;\;\;\;8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \]

Alternative 22
Accuracy	32.4%
Cost	585

\[\begin{array}{l} \mathbf{if}\;x2 \leq -1.25 \cdot 10^{-115} \lor \neg \left(x2 \leq 1.9 \cdot 10^{-81}\right):\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \]

Alternative 23
Accuracy	32.2%
Cost	456

\[\begin{array}{l} \mathbf{if}\;x2 \leq -2.15 \cdot 10^{-100}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 3 \cdot 10^{-82}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]

Alternative 24
Accuracy	38.9%
Cost	320

\[x2 \cdot -6 - x1 \]

Alternative 25
Accuracy	14.4%
Cost	128

\[-x1 \]

Alternative 26
Accuracy	3.3%
Cost	64

\[x1 \]

Reproduce

herbie shell --seed 2023263 
(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))))))