Error

Target

Derivation

1. Initial program 0.0

   \[x \cdot \left(x \cdot x\right) + x \cdot x\]

2. Simplified0.0

   \[\leadsto \color{blue}{(\left(x \cdot x\right) \cdot x + \left(x \cdot x\right))_*}\]
3. Using strategy rm

4. Applied add-cbrt-cube20.4

   \[\leadsto \color{blue}{\sqrt[3]{\left((\left(x \cdot x\right) \cdot x + \left(x \cdot x\right))_* \cdot (\left(x \cdot x\right) \cdot x + \left(x \cdot x\right))_*\right) \cdot (\left(x \cdot x\right) \cdot x + \left(x \cdot x\right))_*}}\]
5. Using strategy rm

6. Applied pow120.4

   \[\leadsto \sqrt[3]{\left((\left(x \cdot x\right) \cdot x + \left(x \cdot x\right))_* \cdot (\left(x \cdot x\right) \cdot x + \left(x \cdot x\right))_*\right) \cdot \color{blue}{{\left((\left(x \cdot x\right) \cdot x + \left(x \cdot x\right))_*\right)}^{1}}}\]

7. Applied pow120.4

   \[\leadsto \sqrt[3]{\left((\left(x \cdot x\right) \cdot x + \left(x \cdot x\right))_* \cdot \color{blue}{{\left((\left(x \cdot x\right) \cdot x + \left(x \cdot x\right))_*\right)}^{1}}\right) \cdot {\left((\left(x \cdot x\right) \cdot x + \left(x \cdot x\right))_*\right)}^{1}}\]

8. Applied pow120.4

   \[\leadsto \sqrt[3]{\left(\color{blue}{{\left((\left(x \cdot x\right) \cdot x + \left(x \cdot x\right))_*\right)}^{1}} \cdot {\left((\left(x \cdot x\right) \cdot x + \left(x \cdot x\right))_*\right)}^{1}\right) \cdot {\left((\left(x \cdot x\right) \cdot x + \left(x \cdot x\right))_*\right)}^{1}}\]

9. Applied pow-prod-up20.4

   \[\leadsto \sqrt[3]{\color{blue}{{\left((\left(x \cdot x\right) \cdot x + \left(x \cdot x\right))_*\right)}^{\left(1 + 1\right)}} \cdot {\left((\left(x \cdot x\right) \cdot x + \left(x \cdot x\right))_*\right)}^{1}}\]

10. Applied pow-prod-up20.4

    \[\leadsto \sqrt[3]{\color{blue}{{\left((\left(x \cdot x\right) \cdot x + \left(x \cdot x\right))_*\right)}^{\left(\left(1 + 1\right) + 1\right)}}}\]

11. Simplified20.4

    \[\leadsto \sqrt[3]{{\color{blue}{\left((x \cdot x + x)_* \cdot x\right)}}^{\left(\left(1 + 1\right) + 1\right)}}\]

12. Simplified20.4

    \[\leadsto \sqrt[3]{{\left((x \cdot x + x)_* \cdot x\right)}^{\color{blue}{3}}}\]
13. Using strategy rm

14. Applied rem-cbrt-cube0.0

    \[\leadsto \color{blue}{(x \cdot x + x)_* \cdot x}\]

15. Final simplification0.0

    \[\leadsto x \cdot (x \cdot x + x)_*\]

Reproduce

herbie shell --seed 2019002 +o rules:numerics
(FPCore (x)
  :name "Expression 3, p15"
  :pre (<= 0 x 2)

  :herbie-target
  (* (* (+ 1.0 x) x) x)

  (+ (* x (* x x)) (* x x)))

Details

Time bar (total: 8.5s)Debug log