Average Error: 0.5 → 0.7
Time: 5.4m
Precision: 64
Internal precision: 128
\[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]
⬇
\[\left(\frac{3}{x1 \cdot x1 + 1} \cdot \left(3 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 + x2\right) + x2\right)\right) + \left(x1 + x1\right)\right) + \left(\left({x1}^3 + \left(3 \cdot \left(x1 \cdot x1\right)\right) \cdot \frac{\left(x2 - \left(x1 - x2\right)\right) + 3 \cdot \left(x1 \cdot x1\right)}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1 + 1\right) \cdot {\left(\sqrt[3]{\left(\left(x1 + x1\right) \cdot \frac{\left(x2 - \left(x1 - x2\right)\right) + 3 \cdot \left(x1 \cdot x1\right)}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x2 - \left(x1 - x2\right)\right) + 3 \cdot \left(x1 \cdot x1\right)}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x2 - \left(x1 - x2\right)\right) + 3 \cdot \left(x1 \cdot x1\right)}{\frac{x1 \cdot x1 + 1}{4}} - 6\right)}\right)}^3\right)\]

Error

Bits error versus x1

Bits error versus x2

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. Applied simplify 0.4

    \[\leadsto \color{blue}{\left(\frac{3}{x1 \cdot x1 + 1} \cdot \left(3 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 + x2\right) + x2\right)\right) + \left(x1 + x1\right)\right) + \left(\left({x1}^3 + \left(3 \cdot \left(x1 \cdot x1\right)\right) \cdot \frac{\left(x2 - \left(x1 - x2\right)\right) + 3 \cdot \left(x1 \cdot x1\right)}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 + x1\right) \cdot \frac{\left(x2 - \left(x1 - x2\right)\right) + 3 \cdot \left(x1 \cdot x1\right)}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x2 - \left(x1 - x2\right)\right) + 3 \cdot \left(x1 \cdot x1\right)}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x2 - \left(x1 - x2\right)\right) + 3 \cdot \left(x1 \cdot x1\right)}{\frac{x1 \cdot x1 + 1}{4}} - 6\right)\right)\right)}\]
  3. Using strategy rm

  4. Applied add-cube-cbrt 0.7

    \[\leadsto \left(\frac{3}{x1 \cdot x1 + 1} \cdot \left(3 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 + x2\right) + x2\right)\right) + \left(x1 + x1\right)\right) + \left(\left({x1}^3 + \left(3 \cdot \left(x1 \cdot x1\right)\right) \cdot \frac{\left(x2 - \left(x1 - x2\right)\right) + 3 \cdot \left(x1 \cdot x1\right)}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1 + 1\right) \cdot \color{blue}{{\left(\sqrt[3]{\left(\left(x1 + x1\right) \cdot \frac{\left(x2 - \left(x1 - x2\right)\right) + 3 \cdot \left(x1 \cdot x1\right)}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x2 - \left(x1 - x2\right)\right) + 3 \cdot \left(x1 \cdot x1\right)}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x2 - \left(x1 - x2\right)\right) + 3 \cdot \left(x1 \cdot x1\right)}{\frac{x1 \cdot x1 + 1}{4}} - 6\right)}\right)}^3}\right)\]
  5. Removed slow pow expressions

Runtime

Time bar (total: 5.4m) Debug log

Please include this information when filing a bug report:

herbie --seed '#(2372288293 1959800816 1650479543 3512282057 2131781342 3398936133)'
(FPCore (x1 x2)
  :name "Rosa's FloatVsDoubleBenchmark"
  (+ x1 (+ (+ (+ (+ (* (+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)) (* (* x1 x1) (- (* 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) 6))) (+ (* x1 x1) 1)) (* (* (* 3 x1) x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)))) (* (* x1 x1) x1)) x1) (* 3 (/ (- (- (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))))))