Rosa's FloatVsDoubleBenchmark

Average Error: 0.5 → 1.2

Time: 1.0min

Precision: binary64

Cost: 8392

Math

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

↓

\[\begin{array}{l} t_0 := 3 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 + \left(4 \cdot \left(\left(x2 \cdot 2 - 3\right) \cdot \left(x2 \cdot x1\right)\right) + x2 \cdot -6\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_2}\\ \mathbf{if}\;2 \cdot x2 \leq -2 \cdot 10^{+165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;2 \cdot x2 \leq 5 \cdot 10^{+152}:\\ \;\;\;\;\left(t_2 \cdot \left(x1 \cdot \left(x1 \cdot \left(t_3 \cdot 4 - 6\right) + 2 \cdot \left(t_3 \cdot \left(t_3 - 3\right)\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot x1 + x1 \cdot \left(3 \cdot t_3\right)\right) + 3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_2}\right)\right) + \left(x1 + x1\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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 (* 3.0 (* x1 x1)))
        (t_1 (+ x1 (+ (* 4.0 (* (- (* x2 2.0) 3.0) (* x2 x1))) (* x2 -6.0))))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (/ (- (+ t_0 (* 2.0 x2)) x1) t_2)))
   (if (<= (* 2.0 x2) -2e+165)
     t_1
     (if (<= (* 2.0 x2) 5e+152)
       (+
        (+
         (*
          t_2
          (* x1 (+ (* x1 (- (* t_3 4.0) 6.0)) (* 2.0 (* t_3 (- t_3 3.0))))))
         (+
          (* x1 (+ (* x1 x1) (* x1 (* 3.0 t_3))))
          (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_2))))
        (+ x1 x1))
       t_1))))

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 = 3.0 * (x1 * x1);
	double t_1 = x1 + ((4.0 * (((x2 * 2.0) - 3.0) * (x2 * x1))) + (x2 * -6.0));
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	double tmp;
	if ((2.0 * x2) <= -2e+165) {
		tmp = t_1;
	} else if ((2.0 * x2) <= 5e+152) {
		tmp = ((t_2 * (x1 * ((x1 * ((t_3 * 4.0) - 6.0)) + (2.0 * (t_3 * (t_3 - 3.0)))))) + ((x1 * ((x1 * x1) + (x1 * (3.0 * t_3)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)))) + (x1 + x1);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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

↓

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = 3.0d0 * (x1 * x1)
    t_1 = x1 + ((4.0d0 * (((x2 * 2.0d0) - 3.0d0) * (x2 * x1))) + (x2 * (-6.0d0)))
    t_2 = (x1 * x1) + 1.0d0
    t_3 = ((t_0 + (2.0d0 * x2)) - x1) / t_2
    if ((2.0d0 * x2) <= (-2d+165)) then
        tmp = t_1
    else if ((2.0d0 * x2) <= 5d+152) then
        tmp = ((t_2 * (x1 * ((x1 * ((t_3 * 4.0d0) - 6.0d0)) + (2.0d0 * (t_3 * (t_3 - 3.0d0)))))) + ((x1 * ((x1 * x1) + (x1 * (3.0d0 * t_3)))) + (3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_2)))) + (x1 + x1)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static 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))));
}

↓

public static double code(double x1, double x2) {
	double t_0 = 3.0 * (x1 * x1);
	double t_1 = x1 + ((4.0 * (((x2 * 2.0) - 3.0) * (x2 * x1))) + (x2 * -6.0));
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	double tmp;
	if ((2.0 * x2) <= -2e+165) {
		tmp = t_1;
	} else if ((2.0 * x2) <= 5e+152) {
		tmp = ((t_2 * (x1 * ((x1 * ((t_3 * 4.0) - 6.0)) + (2.0 * (t_3 * (t_3 - 3.0)))))) + ((x1 * ((x1 * x1) + (x1 * (3.0 * t_3)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)))) + (x1 + x1);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, 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))))

↓

def code(x1, x2):
	t_0 = 3.0 * (x1 * x1)
	t_1 = x1 + ((4.0 * (((x2 * 2.0) - 3.0) * (x2 * x1))) + (x2 * -6.0))
	t_2 = (x1 * x1) + 1.0
	t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2
	tmp = 0
	if (2.0 * x2) <= -2e+165:
		tmp = t_1
	elif (2.0 * x2) <= 5e+152:
		tmp = ((t_2 * (x1 * ((x1 * ((t_3 * 4.0) - 6.0)) + (2.0 * (t_3 * (t_3 - 3.0)))))) + ((x1 * ((x1 * x1) + (x1 * (3.0 * t_3)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)))) + (x1 + x1)
	else:
		tmp = t_1
	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(3.0 * Float64(x1 * x1))
	t_1 = Float64(x1 + Float64(Float64(4.0 * Float64(Float64(Float64(x2 * 2.0) - 3.0) * Float64(x2 * x1))) + Float64(x2 * -6.0)))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_2)
	tmp = 0.0
	if (Float64(2.0 * x2) <= -2e+165)
		tmp = t_1;
	elseif (Float64(2.0 * x2) <= 5e+152)
		tmp = Float64(Float64(Float64(t_2 * Float64(x1 * Float64(Float64(x1 * Float64(Float64(t_3 * 4.0) - 6.0)) + Float64(2.0 * Float64(t_3 * Float64(t_3 - 3.0)))))) + Float64(Float64(x1 * Float64(Float64(x1 * x1) + Float64(x1 * Float64(3.0 * t_3)))) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_2)))) + Float64(x1 + x1));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp = code(x1, x2)
	tmp = 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))));
end

↓

function tmp_2 = code(x1, x2)
	t_0 = 3.0 * (x1 * x1);
	t_1 = x1 + ((4.0 * (((x2 * 2.0) - 3.0) * (x2 * x1))) + (x2 * -6.0));
	t_2 = (x1 * x1) + 1.0;
	t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	tmp = 0.0;
	if ((2.0 * x2) <= -2e+165)
		tmp = t_1;
	elseif ((2.0 * x2) <= 5e+152)
		tmp = ((t_2 * (x1 * ((x1 * ((t_3 * 4.0) - 6.0)) + (2.0 * (t_3 * (t_3 - 3.0)))))) + ((x1 * ((x1 * x1) + (x1 * (3.0 * t_3)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)))) + (x1 + x1);
	else
		tmp = t_1;
	end
	tmp_2 = 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[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(N[(4.0 * N[(N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision] * N[(x2 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[N[(2.0 * x2), $MachinePrecision], -2e+165], t$95$1, If[LessEqual[N[(2.0 * x2), $MachinePrecision], 5e+152], N[(N[(N[(t$95$2 * N[(x1 * N[(N[(x1 * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(t$95$3 * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * x1), $MachinePrecision] + N[(x1 * N[(3.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + x1), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 2 x2) < -1.9999999999999998e165 or 5e152 < (*.f64 2 x2)

   1. Initial program 0.2

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

   2. Simplified 60.8

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

      [Start] 0.2

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

      rational_best-simplify-1 [=>] 0.2

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

   3. Taylor expanded in x1 around 0 2.6

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

   4. Simplified 2.6

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

      [Start] 2.6	\[ x1 + \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + \left(x1 + 3 \cdot \frac{x1 + \left(2 \cdot x2 - 3 \cdot \left(x1 \cdot x1\right)\right)}{-1 - x1 \cdot x1}\right)\right) \]
      rational_best-simplify-2 [=>] 2.6	\[ x1 + \left(4 \cdot \left(x2 \cdot \color{blue}{\left(\left(2 \cdot x2 - 3\right) \cdot x1\right)}\right) + \left(x1 + 3 \cdot \frac{x1 + \left(2 \cdot x2 - 3 \cdot \left(x1 \cdot x1\right)\right)}{-1 - x1 \cdot x1}\right)\right) \]
      rational_best-simplify-44 [=>] 2.6	\[ x1 + \left(4 \cdot \color{blue}{\left(\left(2 \cdot x2 - 3\right) \cdot \left(x2 \cdot x1\right)\right)} + \left(x1 + 3 \cdot \frac{x1 + \left(2 \cdot x2 - 3 \cdot \left(x1 \cdot x1\right)\right)}{-1 - x1 \cdot x1}\right)\right) \]
      rational_best-simplify-2 [=>] 2.6	\[ x1 + \left(4 \cdot \left(\left(\color{blue}{x2 \cdot 2} - 3\right) \cdot \left(x2 \cdot x1\right)\right) + \left(x1 + 3 \cdot \frac{x1 + \left(2 \cdot x2 - 3 \cdot \left(x1 \cdot x1\right)\right)}{-1 - x1 \cdot x1}\right)\right) \]

   5. Taylor expanded in x1 around 0 2.6

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

   6. Simplified 2.6

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

      [Start] 2.6	\[ x1 + \left(4 \cdot \left(\left(x2 \cdot 2 - 3\right) \cdot \left(x2 \cdot x1\right)\right) + -6 \cdot x2\right) \]
      rational_best-simplify-2 [=>] 2.6	\[ x1 + \left(4 \cdot \left(\left(x2 \cdot 2 - 3\right) \cdot \left(x2 \cdot x1\right)\right) + \color{blue}{x2 \cdot -6}\right) \]

   if -1.9999999999999998e165 < (*.f64 2 x2) < 5e152

   1. Initial program 0.6

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

   2. Simplified 1.0

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

      [Start] 0.6

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

      rational_best-simplify-1 [=>] 0.6

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

3. Recombined 2 regimes into one program.

4. Final simplification 1.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;2 \cdot x2 \leq -2 \cdot 10^{+165}:\\ \;\;\;\;x1 + \left(4 \cdot \left(\left(x2 \cdot 2 - 3\right) \cdot \left(x2 \cdot x1\right)\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;2 \cdot x2 \leq 5 \cdot 10^{+152}:\\ \;\;\;\;\left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot \left(\frac{\left(3 \cdot \left(x1 \cdot x1\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + 2 \cdot \left(\frac{\left(3 \cdot \left(x1 \cdot x1\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot \left(\frac{\left(3 \cdot \left(x1 \cdot x1\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right)\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot x1 + x1 \cdot \left(3 \cdot \frac{\left(3 \cdot \left(x1 \cdot x1\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\right) + 3 \cdot \frac{\left(3 \cdot \left(x1 \cdot x1\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\right) + \left(x1 + x1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(4 \cdot \left(\left(x2 \cdot 2 - 3\right) \cdot \left(x2 \cdot x1\right)\right) + x2 \cdot -6\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	0.5
Cost	8000

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

Alternative 2
Error	0.7
Cost	7880

\[\begin{array}{l} t_0 := 3 \cdot \left(x1 \cdot x1\right)\\ t_1 := -1 - x1 \cdot x1\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_2}\\ t_4 := x1 + \left(x1 \cdot \left(x1 \cdot \left(x1 + 3 \cdot t_3\right) + t_2 \cdot \left(x1 \cdot \left(t_3 \cdot 4 - 6\right) + 2 \cdot \left(t_3 \cdot \left(t_3 - 3\right)\right)\right)\right) + \left(x1 + 3 \cdot \frac{x1 + \left(2 \cdot x2 - t_0\right)}{t_1}\right)\right)\\ \mathbf{if}\;x1 \leq -2.1 \cdot 10^{-9}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{-65}:\\ \;\;\;\;x1 + \left(4 \cdot \left(\left(x2 \cdot 2 - 3\right) \cdot \left(x2 \cdot x1\right)\right) + \left(x1 + \left(\left(x2 + x2\right) + \left(x1 + x1 \cdot \left(-3 \cdot x1\right)\right)\right) \cdot \frac{3}{t_1}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 3
Error	0.7
Cost	7880

\[\begin{array}{l} t_0 := 3 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := -1 - x1 \cdot x1\\ t_3 := x1 + 3 \cdot \frac{x1 + \left(2 \cdot x2 - t_0\right)}{t_2}\\ t_4 := \frac{x1 - \left(x2 + \left(x2 + t_0\right)\right)}{t_2}\\ t_5 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{-9}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x1 \cdot \left(x1 + 3 \cdot t_5\right) + t_1 \cdot \left(x1 \cdot \left(t_5 \cdot 4 - 6\right) + 2 \cdot \left(t_5 \cdot \left(t_5 - 3\right)\right)\right)\right) + t_3\right)\\ \mathbf{elif}\;x1 \leq 10^{-65}:\\ \;\;\;\;x1 + \left(4 \cdot \left(\left(x2 \cdot 2 - 3\right) \cdot \left(x2 \cdot x1\right)\right) + \left(x1 + \left(\left(x2 + x2\right) + \left(x1 + x1 \cdot \left(-3 \cdot x1\right)\right)\right) \cdot \frac{3}{t_2}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x1 \cdot \left(x1 + t_4 \cdot 3\right) + \left(1 + x1 \cdot x1\right) \cdot \left(x1 \cdot \left(t_4 \cdot 4 - 6\right) + \left(t_4 - 3\right) \cdot \left(2 \cdot t_4\right)\right)\right) + t_3\right)\\ \end{array} \]

Alternative 4
Error	0.7
Cost	7880

\[\begin{array}{l} t_0 := -1 - x1 \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{2 \cdot x2 + \left(\left(x1 \cdot x1\right) \cdot 3 - x1\right)}{t_1}\\ t_3 := 3 \cdot \left(x1 \cdot x1\right)\\ t_4 := \frac{x1 - \left(x2 + \left(x2 + t_3\right)\right)}{t_0}\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{-12}:\\ \;\;\;\;x1 + \left(3 \cdot \left(\frac{x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot -3\right)\right)}{t_0} + \left(x1 \cdot x1\right) \cdot \frac{2 \cdot x2 + \left(x1 \cdot \left(x1 \cdot 3\right) - x1\right)}{t_1}\right) + \left(\frac{x1 \cdot \left(1 + \left(x1 \cdot \left(t_2 \cdot 4 - 6\right) + \left(t_2 - 3\right) \cdot \left(2 \cdot t_2\right)\right)\right)}{\frac{1}{t_1}} + 0\right)\right)\\ \mathbf{elif}\;x1 \leq 2.05 \cdot 10^{-64}:\\ \;\;\;\;x1 + \left(4 \cdot \left(\left(x2 \cdot 2 - 3\right) \cdot \left(x2 \cdot x1\right)\right) + \left(x1 + \left(\left(x2 + x2\right) + \left(x1 + x1 \cdot \left(-3 \cdot x1\right)\right)\right) \cdot \frac{3}{t_0}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x1 \cdot \left(x1 + t_4 \cdot 3\right) + \left(1 + x1 \cdot x1\right) \cdot \left(x1 \cdot \left(t_4 \cdot 4 - 6\right) + \left(t_4 - 3\right) \cdot \left(2 \cdot t_4\right)\right)\right) + \left(x1 + 3 \cdot \frac{x1 + \left(2 \cdot x2 - t_3\right)}{t_0}\right)\right)\\ \end{array} \]

Alternative 5
Error	0.7
Cost	7752

\[\begin{array}{l} t_0 := -1 - x1 \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{2 \cdot x2 + \left(x1 \cdot \left(x1 \cdot 3\right) - x1\right)}{t_1}\\ t_3 := x1 + \left(3 \cdot \left(\frac{x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot -3\right)\right)}{t_0} + \left(x1 \cdot x1\right) \cdot t_2\right) + x1 \cdot \left(t_1 \cdot \left(1 + \left(x1 \cdot \left(t_2 \cdot 4 - 6\right) + 2 \cdot \left(t_2 \cdot \left(t_2 - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{-11}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x1 \leq 10^{-65}:\\ \;\;\;\;x1 + \left(4 \cdot \left(\left(x2 \cdot 2 - 3\right) \cdot \left(x2 \cdot x1\right)\right) + \left(x1 + \left(\left(x2 + x2\right) + \left(x1 + x1 \cdot \left(-3 \cdot x1\right)\right)\right) \cdot \frac{3}{t_0}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 6
Error	0.7
Cost	7752

\[\begin{array}{l} t_0 := -1 - x1 \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot -3\right)\right)}{t_0}\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := \frac{2 \cdot x2 + \left(t_3 - x1\right)}{t_1}\\ t_5 := \frac{\left(t_3 + 2 \cdot x2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -2 \cdot 10^{-8}:\\ \;\;\;\;x1 + \left(3 \cdot \left(t_2 + \left(x1 \cdot x1\right) \cdot t_5\right) + t_1 \cdot \left(x1 + x1 \cdot \left(x1 \cdot \left(t_5 \cdot 4 - 6\right) + 2 \cdot \left(t_5 \cdot \left(t_5 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.5 \cdot 10^{-64}:\\ \;\;\;\;x1 + \left(4 \cdot \left(\left(x2 \cdot 2 - 3\right) \cdot \left(x2 \cdot x1\right)\right) + \left(x1 + \left(\left(x2 + x2\right) + \left(x1 + x1 \cdot \left(-3 \cdot x1\right)\right)\right) \cdot \frac{3}{t_0}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(t_2 + \left(x1 \cdot x1\right) \cdot t_4\right) + x1 \cdot \left(t_1 \cdot \left(1 + \left(x1 \cdot \left(t_4 \cdot 4 - 6\right) + 2 \cdot \left(t_4 \cdot \left(t_4 - 3\right)\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 7
Error	2.6
Cost	6600

\[\begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot -3\right)\\ t_1 := -1 - x1 \cdot x1\\ t_2 := x2 \cdot 2 - 3\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := x1 \cdot x1 + 1\\ t_5 := \frac{\left(t_3 + 2 \cdot x2\right) - x1}{t_4}\\ \mathbf{if}\;x1 \leq -3.6:\\ \;\;\;\;x1 + \left(3 \cdot \left(\frac{x1 + \left(2 \cdot x2 + t_0\right)}{t_1} + \left(x1 \cdot x1\right) \cdot t_5\right) + t_4 \cdot \left(x1 + x1 \cdot \left(\left(x1 \cdot 6 + \frac{6 + t_2 \cdot -4}{-x1}\right) - 4\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.3:\\ \;\;\;\;x1 + \left(4 \cdot \left(t_2 \cdot \left(x2 \cdot x1\right)\right) + \left(x1 + 3 \cdot \left(\left(\left(x2 + x2\right) + \left(x1 + t_0\right)\right) \cdot \left(\frac{3}{t_1} - 2 \cdot \frac{-1}{t_4}\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x1 + \left(t_4 \cdot \left(\left(\left(1 + 3 \cdot \left(\left(x2 + x2\right) + -3\right)\right) \cdot \frac{2}{x1} - 6\right) + \left(x1 \cdot x1\right) \cdot \left(t_5 \cdot 4 - 6\right)\right) + x1 \cdot \left(x1 \cdot x1 + x1 \cdot \left(t_5 \cdot 3\right)\right)\right)\right) + \left(x1 + 3 \cdot \frac{\left(t_3 - 2 \cdot x2\right) - x1}{t_4}\right)\\ \end{array} \]

Alternative 8
Error	2.6
Cost	5128

\[\begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot -3\right)\\ t_1 := -1 - x1 \cdot x1\\ t_2 := x2 \cdot 2 - 3\\ t_3 := \left(x1 \cdot 6 + \frac{6 + t_2 \cdot -4}{-x1}\right) - 4\\ t_4 := 3 \cdot \left(x1 \cdot x1\right)\\ t_5 := x1 \cdot x1 + 1\\ \mathbf{if}\;x1 \leq -3.5:\\ \;\;\;\;x1 + \left(3 \cdot \left(\frac{x1 + \left(2 \cdot x2 + t_0\right)}{t_1} + \left(x1 \cdot x1\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{t_5}\right) + t_5 \cdot \left(x1 + x1 \cdot t_3\right)\right)\\ \mathbf{elif}\;x1 \leq 0.43:\\ \;\;\;\;x1 + \left(4 \cdot \left(t_2 \cdot \left(x2 \cdot x1\right)\right) + \left(x1 + 3 \cdot \left(\left(\left(x2 + x2\right) + \left(x1 + t_0\right)\right) \cdot \left(\frac{3}{t_1} - 2 \cdot \frac{-1}{t_5}\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(t_5 \cdot t_3\right) + \left(x1 \cdot \left(x1 \cdot \left(3 \cdot \frac{\left(t_4 + 2 \cdot x2\right) - x1}{t_5} + x1\right)\right) + \left(x1 + 3 \cdot \frac{x1 + \left(2 \cdot x2 - t_4\right)}{t_1}\right)\right)\right)\\ \end{array} \]

Alternative 9
Error	2.6
Cost	4872

\[\begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot -3\right)\\ t_1 := -1 - x1 \cdot x1\\ t_2 := x2 \cdot 2 - 3\\ t_3 := x1 \cdot x1 + 1\\ t_4 := x1 + \left(3 \cdot \left(\frac{x1 + \left(2 \cdot x2 + t_0\right)}{t_1} + \left(x1 \cdot x1\right) \cdot \frac{2 \cdot x2 + \left(x1 \cdot \left(x1 \cdot 3\right) - x1\right)}{t_3}\right) + x1 \cdot \left(t_3 \cdot \left(1 + \left(\left(x1 \cdot 6 + \frac{6 + t_2 \cdot -4}{-x1}\right) - 4\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -2:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x1 \leq 0.31:\\ \;\;\;\;x1 + \left(4 \cdot \left(t_2 \cdot \left(x2 \cdot x1\right)\right) + \left(x1 + 3 \cdot \left(\left(\left(x2 + x2\right) + \left(x1 + t_0\right)\right) \cdot \left(\frac{3}{t_1} - 2 \cdot \frac{-1}{t_3}\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 10
Error	2.6
Cost	4872

\[\begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot -3\right)\\ t_1 := -1 - x1 \cdot x1\\ t_2 := x2 \cdot 2 - 3\\ t_3 := \left(x1 \cdot 6 + \frac{6 + t_2 \cdot -4}{-x1}\right) - 4\\ t_4 := x1 \cdot x1 + 1\\ t_5 := \frac{x1 + \left(2 \cdot x2 + t_0\right)}{t_1}\\ t_6 := x1 \cdot \left(x1 \cdot 3\right)\\ \mathbf{if}\;x1 \leq -2.7:\\ \;\;\;\;x1 + \left(3 \cdot \left(t_5 + \left(x1 \cdot x1\right) \cdot \frac{\left(t_6 + 2 \cdot x2\right) - x1}{t_4}\right) + t_4 \cdot \left(x1 + x1 \cdot t_3\right)\right)\\ \mathbf{elif}\;x1 \leq 0.31:\\ \;\;\;\;x1 + \left(4 \cdot \left(t_2 \cdot \left(x2 \cdot x1\right)\right) + \left(x1 + 3 \cdot \left(\left(\left(x2 + x2\right) + \left(x1 + t_0\right)\right) \cdot \left(\frac{3}{t_1} - 2 \cdot \frac{-1}{t_4}\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(t_5 + \left(x1 \cdot x1\right) \cdot \frac{2 \cdot x2 + \left(t_6 - x1\right)}{t_4}\right) + x1 \cdot \left(t_4 \cdot \left(1 + t_3\right)\right)\right)\\ \end{array} \]

Alternative 11
Error	2.7
Cost	4680

\[\begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := \left(x1 + \left(t_0 \cdot \left(-6 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{x2 + \left(x2 + x1 \cdot \left(-1 + x1 \cdot 3\right)\right)}{1 + x1 \cdot x1} - 6\right)\right) + x1 \cdot \left(x1 \cdot x1 + \left(x1 \cdot 9 - 3\right)\right)\right)\right) + \left(x1 + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{t_0}\right)\\ \mathbf{if}\;x1 \leq -1.9:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq 0.355:\\ \;\;\;\;x1 + \left(4 \cdot \left(\left(x2 \cdot 2 - 3\right) \cdot \left(x2 \cdot x1\right)\right) + \left(x1 + 3 \cdot \left(\left(\left(x2 + x2\right) + \left(x1 + x1 \cdot \left(x1 \cdot -3\right)\right)\right) \cdot \left(\frac{3}{-1 - x1 \cdot x1} - 2 \cdot \frac{-1}{t_0}\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	2.7
Cost	4552

\[\begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := \left(x1 + \left(t_0 \cdot \left(-6 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{x2 + \left(x2 + x1 \cdot \left(-1 + x1 \cdot 3\right)\right)}{1 + x1 \cdot x1} - 6\right)\right) + x1 \cdot \left(x1 \cdot x1 + x1 \cdot 9\right)\right)\right) + \left(x1 + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{t_0}\right)\\ \mathbf{if}\;x1 \leq -3.1:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq 0.41:\\ \;\;\;\;x1 + \left(4 \cdot \left(\left(x2 \cdot 2 - 3\right) \cdot \left(x2 \cdot x1\right)\right) + \left(x1 + 3 \cdot \left(\left(\left(x2 + x2\right) + \left(x1 + x1 \cdot \left(x1 \cdot -3\right)\right)\right) \cdot \left(\frac{3}{-1 - x1 \cdot x1} - 2 \cdot \frac{-1}{t_0}\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	3.5
Cost	3908

\[\begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot -3\right)\\ t_1 := x1 \cdot 6 - 4\\ t_2 := -1 - x1 \cdot x1\\ t_3 := x1 \cdot x1 + 1\\ \mathbf{if}\;x1 \leq -3.1:\\ \;\;\;\;x1 + \left(3 \cdot \left(\frac{x1 + \left(2 \cdot x2 + t_0\right)}{t_2} + \left(x1 \cdot x1\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{t_3}\right) + t_3 \cdot \left(x1 + x1 \cdot t_1\right)\right)\\ \mathbf{elif}\;x1 \leq 3.95:\\ \;\;\;\;x1 + \left(4 \cdot \left(\left(x2 \cdot 2 - 3\right) \cdot \left(x2 \cdot x1\right)\right) + \left(x1 + 3 \cdot \left(\left(\left(x2 + x2\right) + \left(x1 + t_0\right)\right) \cdot \left(\frac{3}{t_2} - 2 \cdot \frac{-1}{t_3}\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x1 \cdot x1 + t_3 \cdot t_1\right) + \left(x1 + 3 \cdot \frac{x1 + \left(2 \cdot x2 - 3 \cdot \left(x1 \cdot x1\right)\right)}{t_2}\right)\right)\\ \end{array} \]

Alternative 14
Error	3.5
Cost	3272

\[\begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := -1 - x1 \cdot x1\\ t_2 := x1 + \left(x1 \cdot \left(x1 \cdot x1 + t_0 \cdot \left(x1 \cdot 6 - 4\right)\right) + \left(x1 + 3 \cdot \frac{x1 + \left(2 \cdot x2 - 3 \cdot \left(x1 \cdot x1\right)\right)}{t_1}\right)\right)\\ \mathbf{if}\;x1 \leq -1.5:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x1 \leq 3.5:\\ \;\;\;\;x1 + \left(4 \cdot \left(\left(x2 \cdot 2 - 3\right) \cdot \left(x2 \cdot x1\right)\right) + \left(x1 + 3 \cdot \left(\left(\left(x2 + x2\right) + \left(x1 + x1 \cdot \left(x1 \cdot -3\right)\right)\right) \cdot \left(\frac{3}{t_1} - 2 \cdot \frac{-1}{t_0}\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Error	3.5
Cost	2888

\[\begin{array}{l} t_0 := -1 - x1 \cdot x1\\ t_1 := x1 + \left(x1 \cdot \left(x1 \cdot x1 + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot 6 - 4\right)\right) + \left(x1 + 3 \cdot \frac{x1 + \left(2 \cdot x2 - 3 \cdot \left(x1 \cdot x1\right)\right)}{t_0}\right)\right)\\ \mathbf{if}\;x1 \leq -0.96:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq 2.7:\\ \;\;\;\;x1 + \left(4 \cdot \left(\left(x2 \cdot 2 - 3\right) \cdot \left(x2 \cdot x1\right)\right) + \left(x1 + \left(\left(x2 + x2\right) + \left(x1 + x1 \cdot \left(-3 \cdot x1\right)\right)\right) \cdot \frac{3}{t_0}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	11.4
Cost	2240

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

Alternative 17
Error	11.4
Cost	2240

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

Alternative 18
Error	11.7
Cost	1536

\[x1 + \left(4 \cdot \left(\left(x2 \cdot 2 - 3\right) \cdot \left(x2 \cdot x1\right)\right) + \left(x1 + 3 \cdot \left(x2 \cdot -2 + \left(-x1\right)\right)\right)\right) \]

Alternative 19
Error	12.0
Cost	1352

\[\begin{array}{l} t_0 := x1 + \left(4 \cdot \left(\left(x2 \cdot 2 - 3\right) \cdot \left(x2 \cdot x1\right)\right) + x2 \cdot -6\right)\\ \mathbf{if}\;x2 \leq -3.6 \cdot 10^{+65}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x2 \leq 6.8 \cdot 10^{-46}:\\ \;\;\;\;x1 + \left(-2 \cdot x1 + -6 \cdot x2\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 20
Error	20.2
Cost	1092

\[\begin{array}{l} \mathbf{if}\;x1 \leq 5.8 \cdot 10^{-38}:\\ \;\;\;\;x1 + \left(-2 \cdot x1 + -6 \cdot x2\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(4 \cdot \left(\left(x2 \cdot 2 - 3\right) \cdot \left(x2 \cdot x1\right)\right) + x1\right)\\ \end{array} \]

Alternative 21
Error	19.5
Cost	576

\[x1 + \left(-2 \cdot x1 + -6 \cdot x2\right) \]

Alternative 22
Error	32.3
Cost	448

\[x2 \cdot -6 + x1 \cdot -5 \]

Alternative 23
Error	56.8
Cost	192

\[-10 \cdot x2 \]

Alternative 24
Error	34.1
Cost	192

\[x2 \cdot -6 \]

Alternative 25
Error	61.8
Cost	64

\[x1 \]

Reproduce

herbie shell --seed 2023096 
(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))))))