Rosa's FloatVsDoubleBenchmark

Average Error: 0.5 → 0.3

Time: 40.5s

Precision: binary64

Cost: 94848

Math

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

↓

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

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

C

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

↓

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

Julia

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

↓

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

Wolfram

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

↓

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision] + N[(2.0 * x2 + (-x1)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, N[(x1 + N[(3.0 * N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2 + x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * N[(3.0 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1 + 1.0), $MachinePrecision] * N[(x1 + N[(N[(x1 * N[(x1 * -6.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(N[(x1 * N[(-6.0 + N[(2.0 / N[(N[(x1 * x1 + 1.0), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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. Simplified 0.3

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

   [Start] 0.5

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

   +-commutative [=>] 0.5

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

3. Final simplification 0.3

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

Alternatives

Alternative 1
Error	0.5
Cost	53376

\[\begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 1 + {x1}^{2}\\ t_2 := 1 + x1 \cdot x1\\ t_3 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_2}\\ x1 + \left(\left(x1 + \left(\left(t_2 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_3\right) \cdot \left(t_3 + -3\right) + \left({x1}^{2} \cdot \left(-6 + 4 \cdot \left(3 \cdot \frac{{x1}^{2}}{t_1} - \frac{x1}{t_1}\right)\right) + 8 \cdot \frac{x2 \cdot \left(x1 \cdot x1\right)}{t_1}\right)\right) + \left(3 \cdot \frac{x1 \cdot x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) \cdot \left(\mathsf{fma}\left(x1 \cdot 3, x1, 2 \cdot x2\right) - x1\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(t_0 + x2 \cdot -2\right) - x1}{t_2}\right) \end{array} \]

Alternative 2
Error	0.5
Cost	40832

\[\begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 1 + x1 \cdot x1\\ t_2 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_1}\\ t_3 := 1 + {x1}^{2}\\ x1 + \left(3 \cdot \frac{\left(t_0 + x2 \cdot -2\right) - x1}{t_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(t_2 + -3\right) + \left({x1}^{2} \cdot \left(-6 + 4 \cdot \left(3 \cdot \frac{{x1}^{2}}{t_3} - \frac{x1}{t_3}\right)\right) + 8 \cdot \frac{x2 \cdot \left(x1 \cdot x1\right)}{t_3}\right)\right) + t_0 \cdot t_2\right)\right)\right)\right) \end{array} \]

Alternative 3
Error	0.5
Cost	8128

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

Alternative 4
Error	1.3
Cost	6976

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

Alternative 5
Error	2.8
Cost	6848

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

Alternative 6
Error	2.8
Cost	6848

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

Alternative 7
Error	2.9
Cost	5320

\[\begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 6 + -4\right)\\ t_1 := 1 + x1 \cdot x1\\ t_2 := 4 \cdot \left(2 \cdot x2\right) + -18\\ t_3 := x1 \cdot \left(x1 \cdot x1\right)\\ t_4 := x1 \cdot \left(x1 \cdot 3\right)\\ t_5 := 3 \cdot \frac{\left(t_4 + x2 \cdot -2\right) - x1}{t_1}\\ t_6 := t_4 \cdot \frac{\left(t_4 + 2 \cdot x2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -8400000000:\\ \;\;\;\;x1 + \left(t_5 + \left(x1 + \left(t_3 + \left(t_6 + t_1 \cdot \left(t_0 + t_2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 35:\\ \;\;\;\;x1 + \left(t_5 + \left(x1 + \left(t_3 + \left(t_1 \cdot \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 + -3\right)\right)\right)\right) + x2 \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(t_5 + \left(x1 + \left(t_3 + \left(t_6 + t_1 \cdot \left(t_0 + \left(t_2 + \frac{-12}{x1}\right)\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 8
Error	2.9
Cost	5065

\[\begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 1 + x1 \cdot x1\\ t_2 := x1 \cdot \left(x1 \cdot x1\right)\\ t_3 := 3 \cdot \frac{\left(t_0 + x2 \cdot -2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -8400000000 \lor \neg \left(x1 \leq 35\right):\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + \left(t_2 + \left(t_0 \cdot \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_1} + t_1 \cdot \left(x1 \cdot \left(x1 \cdot 6 + -4\right) + \left(4 \cdot \left(2 \cdot x2\right) + -18\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + \left(t_2 + \left(t_1 \cdot \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 + -3\right)\right)\right)\right) + x2 \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 9
Error	3.8
Cost	4552

\[\begin{array}{l} t_0 := 1 + x1 \cdot x1\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := x2 \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := 3 \cdot \frac{\left(t_3 + x2 \cdot -2\right) - x1}{t_0}\\ \mathbf{if}\;x1 \leq -8400000000:\\ \;\;\;\;x1 + \left(t_4 + \left(x1 + \left(t_1 + \left(t_2 + t_0 \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 35:\\ \;\;\;\;x1 + \left(t_4 + \left(x1 + \left(t_1 + \left(t_0 \cdot \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 + -3\right)\right)\right)\right) + t_2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(t_4 + \left(x1 + \left(t_1 + \left(t_3 \cdot \frac{\left(t_3 + 2 \cdot x2\right) - x1}{t_0} + t_0 \cdot \left(x1 \cdot \left(x1 \cdot 6 + -4\right)\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 10
Error	3.9
Cost	3785

\[\begin{array}{l} t_0 := 1 + x1 \cdot x1\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{t_0}\\ t_3 := x2 \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right)\\ \mathbf{if}\;x1 \leq -8400000000 \lor \neg \left(x1 \leq 35\right):\\ \;\;\;\;x1 + \left(t_2 + \left(x1 + \left(t_1 + \left(t_3 + t_0 \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(t_2 + \left(x1 + \left(t_1 + \left(t_0 \cdot \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 + -3\right)\right)\right)\right) + t_3\right)\right)\right)\right)\\ \end{array} \]

Alternative 11
Error	8.3
Cost	3664

\[\begin{array}{l} t_0 := 1 + x1 \cdot x1\\ t_1 := x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{t_0} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(x2 \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right) + t_0 \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ t_2 := x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 + -3\right)\right) + -2\right) + x2 \cdot -6\right)\\ \mathbf{if}\;x1 \leq -1.05 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq -4.9 \cdot 10^{-136}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{-174}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 0.195:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	4.4
Cost	3657

\[\begin{array}{l} t_0 := 1 + x1 \cdot x1\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{t_0}\\ \mathbf{if}\;x1 \leq -1.05 \cdot 10^{-14} \lor \neg \left(x1 \leq 35\right):\\ \;\;\;\;x1 + \left(t_2 + \left(x1 + \left(t_1 + \left(x2 \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right) + t_0 \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(t_2 + \left(x1 + \left(t_1 + \left(x1 \cdot \left(x1 \cdot 9\right) + t_0 \cdot \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 + -3\right)\right)\right)\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 13
Error	8.2
Cost	3536

\[\begin{array}{l} t_0 := 1 + x1 \cdot x1\\ t_1 := x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{t_0} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(x1 \cdot \left(x1 \cdot 9\right) + t_0 \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ t_2 := x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 + -3\right)\right) + -2\right) + x2 \cdot -6\right)\\ \mathbf{if}\;x1 \leq -8400000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq -5 \cdot 10^{-136}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{-169}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 0.185:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	16.4
Cost	1481

\[\begin{array}{l} \mathbf{if}\;x1 \leq -5.3 \cdot 10^{-136} \lor \neg \left(x1 \leq 10^{-169}\right):\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 + -3\right)\right) + -2\right) + x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \end{array} \]

Alternative 15
Error	20.2
Cost	576

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

Alternative 16
Error	32.3
Cost	448

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

Alternative 17
Error	34.1
Cost	192

\[x2 \cdot -6 \]

Alternative 18
Error	61.8
Cost	64

\[x1 \]

Reproduce

herbie shell --seed 2023083 
(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))))))