Rosa's FloatVsDoubleBenchmark

Average Error: 0.5 → 0.5

Time: 46.8s

Precision: binary64

Cost: 8128

Math

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

↓

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

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 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (+
    x1
    (+
     (+
      (+
       (+
        (*
         (+
          (* (* (* 2.0 x1) t_2) (- t_2 3.0))
          (* (* x1 x1) (- (* 4.0 t_2) 6.0)))
         t_1)
        (* t_0 t_2))
       (* (* x1 x1) x1))
      x1)
     (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))))))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 0.5

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

2. Final simplification 0.5

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

Alternatives

Alternative 1
Error	0.5
Cost	8000

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

Alternative 2
Error	1.1
Cost	6984

\[\begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := t_0 + \left(x2 + \left(x2 - x1\right)\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{t_1}{t_2}\\ t_4 := \left(t_2 \cdot \left(x1 \cdot \left(x1 \cdot \left(t_3 \cdot 4 + -6\right) + \frac{2 \cdot \left(t_3 + -3\right)}{\frac{t_2}{t_1}}\right)\right) + x1 \cdot \left(x1 \cdot x1 + x1 \cdot 9\right)\right) + \left(\left(x1 + 3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_2}\right) + x1\right)\\ \mathbf{if}\;x1 \leq -8 \cdot 10^{-5}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x1 \leq 0.000182:\\ \;\;\;\;4 \cdot \left(\left(x2 \cdot 2 - 3\right) \cdot \left(x2 \cdot x1\right)\right) + \left(3 \cdot \frac{\left(t_0 - x1\right) - 2 \cdot x2}{t_2} + \left(x1 + x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 3
Error	1.4
Cost	6848

\[\begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_0}\\ \left(t_0 \cdot \left(t_2 \cdot \left(\left(x1 \cdot 2\right) \cdot \left(t_2 - 3\right)\right) + \left(x1 \cdot x1\right) \cdot \left(t_2 \cdot 4 - 6\right)\right) + x1 \cdot \left(x1 \cdot x1 + x1 \cdot 9\right)\right) + \left(\left(x1 + 3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_0}\right) + x1\right) \end{array} \]

Alternative 4
Error	1.4
Cost	6848

\[\begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ \left(t_0 \cdot \left(\frac{x1 - \left(t_1 + \left(x2 + x2\right)\right)}{\frac{-1 - x1 \cdot x1}{x1 \cdot \left(2 \cdot \left(\frac{t_1 + \left(\left(x2 + x2\right) - x1\right)}{t_0} + -3\right)\right)}} + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_0} \cdot 4 - 6\right)\right) + x1 \cdot \left(x1 \cdot x1 + x1 \cdot 9\right)\right) + \left(\left(x1 + 3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_0}\right) + x1\right) \end{array} \]

Alternative 5
Error	1.1
Cost	6792

\[\begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{t_1 + \left(2 \cdot x2 - x1\right)}{t_0}\\ t_3 := x1 \cdot \left(x1 \cdot \left(x1 + 3 \cdot t_2\right) + t_0 \cdot \left(x1 \cdot \left(t_2 \cdot 4 - 6\right) + \left(t_2 - 3\right) \cdot \left(2 \cdot t_2\right)\right)\right)\\ \mathbf{if}\;x1 \leq -8.2 \cdot 10^{-5}:\\ \;\;\;\;t_3 + x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 0.00012:\\ \;\;\;\;4 \cdot \left(\left(x2 \cdot 2 - 3\right) \cdot \left(x2 \cdot x1\right)\right) + \left(3 \cdot \frac{\left(t_1 - x1\right) - 2 \cdot x2}{t_0} + \left(x1 + x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3 + \left(x2 \cdot -6 + \left(-x1\right)\right)\\ \end{array} \]

Alternative 6
Error	1.1
Cost	6600

\[\begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{t_1 + \left(2 \cdot x2 - x1\right)}{t_0}\\ t_3 := x1 \cdot \left(x1 \cdot \left(x1 + 3 \cdot t_2\right) + t_0 \cdot \left(x1 \cdot \left(t_2 \cdot 4 - 6\right) + \left(t_2 - 3\right) \cdot \left(2 \cdot t_2\right)\right)\right) + x2 \cdot -6\\ \mathbf{if}\;x1 \leq -8.2 \cdot 10^{-5}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x1 \leq 0.007:\\ \;\;\;\;4 \cdot \left(\left(x2 \cdot 2 - 3\right) \cdot \left(x2 \cdot x1\right)\right) + \left(3 \cdot \frac{\left(t_1 - x1\right) - 2 \cdot x2}{t_0} + \left(x1 + x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 7
Error	4.3
Cost	6084

\[\begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := 3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -26500000000:\\ \;\;\;\;\left(t_1 \cdot \left(x1 \cdot \left(x1 \cdot 6 + \left(-4 - \frac{6 + \left(x2 \cdot 2 - 3\right) \cdot -4}{x1}\right)\right)\right) + x1 \cdot \left(x1 \cdot x1 + x1 \cdot \left(3 \cdot \frac{t_0 + \left(2 \cdot x2 - x1\right)}{t_1}\right)\right)\right) + \left(t_2 + \left(x1 + x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t_1 \cdot \left(\left(x1 \cdot \left(x2 + \left(x2 + -3\right)\right)\right) \cdot \left(\frac{2}{-1 - x1 \cdot x1} \cdot \left(x1 - \left(t_0 + \left(x2 + x2\right)\right)\right)\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_1} \cdot 4 - 6\right)\right) + x1 \cdot \left(x1 \cdot x1 + x1 \cdot 9\right)\right) + \left(\left(x1 + t_2\right) + x1\right)\\ \end{array} \]

Alternative 8
Error	3.3
Cost	5060

\[\begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x2 \cdot 2 - 3\\ t_2 := x1 \cdot x1 + 1\\ t_3 := x1 \cdot 6 + \left(-4 - \frac{6 + t_1 \cdot -4}{x1}\right)\\ t_4 := 3 \cdot \frac{t_0 + \left(2 \cdot x2 - x1\right)}{t_2}\\ \mathbf{if}\;x1 \leq -26500000000:\\ \;\;\;\;\left(t_2 \cdot \left(x1 \cdot t_3\right) + x1 \cdot \left(x1 \cdot x1 + x1 \cdot t_4\right)\right) + \left(3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_2} + \left(x1 + x1\right)\right)\\ \mathbf{elif}\;x1 \leq 2.15:\\ \;\;\;\;4 \cdot \left(t_1 \cdot \left(x2 \cdot x1\right)\right) + \left(3 \cdot \frac{\left(t_0 - x1\right) - 2 \cdot x2}{t_2} + \left(x1 + x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot \left(x1 + t_4\right) + t_2 \cdot t_3\right) + \left(x1 + x1\right)\\ \end{array} \]

Alternative 9
Error	3.3
Cost	3656

\[\begin{array}{l} t_0 := x2 \cdot 2 - 3\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := x1 \cdot \left(x1 \cdot \left(x1 + 3 \cdot \frac{t_2 + \left(2 \cdot x2 - x1\right)}{t_1}\right) + t_1 \cdot \left(x1 \cdot 6 + \left(-4 - \frac{6 + t_0 \cdot -4}{x1}\right)\right)\right) + \left(x1 + x1\right)\\ \mathbf{if}\;x1 \leq -26500000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x1 \leq 2.5:\\ \;\;\;\;4 \cdot \left(t_0 \cdot \left(x2 \cdot x1\right)\right) + \left(3 \cdot \frac{\left(t_2 - x1\right) - 2 \cdot x2}{t_1} + \left(x1 + x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 10
Error	3.3
Cost	3272

\[\begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \left(t_1 \cdot \left(-6 + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_1} \cdot 4 - 6\right)\right) + x1 \cdot \left(x1 \cdot x1 + x1 \cdot 9\right)\right) + \left(x1 + x1\right)\\ \mathbf{if}\;x1 \leq -26500000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x1 \leq 2:\\ \;\;\;\;4 \cdot \left(\left(x2 \cdot 2 - 3\right) \cdot \left(x2 \cdot x1\right)\right) + \left(3 \cdot \frac{\left(t_0 - x1\right) - 2 \cdot x2}{t_1} + \left(x1 + x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	12.7
Cost	3008

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

Alternative 12
Error	12.7
Cost	2624

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

Alternative 13
Error	12.7
Cost	2240

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

Alternative 14
Error	12.8
Cost	1152

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

Alternative 15
Error	26.9
Cost	960

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

Alternative 16
Error	48.8
Cost	320

\[-18 + x2 \cdot -6 \]

Alternative 17
Error	61.8
Cost	192

\[x1 + x1 \]

Alternative 18
Error	61.8
Cost	64

\[-18 \]

Reproduce

herbie shell --seed 2023074 
(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))))))