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-sqr-sqrt0.0

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

6. Applied pow1/20.0

   \[\leadsto \sqrt{(\left(x \cdot x\right) \cdot x + \left(x \cdot x\right))_*} \cdot \color{blue}{{\left((\left(x \cdot x\right) \cdot x + \left(x \cdot x\right))_*\right)}^{\frac{1}{2}}}\]

7. Applied pow1/20.0

   \[\leadsto \color{blue}{{\left((\left(x \cdot x\right) \cdot x + \left(x \cdot x\right))_*\right)}^{\frac{1}{2}}} \cdot {\left((\left(x \cdot x\right) \cdot x + \left(x \cdot x\right))_*\right)}^{\frac{1}{2}}\]

8. Applied pow-prod-up0.0

   \[\leadsto \color{blue}{{\left((\left(x \cdot x\right) \cdot x + \left(x \cdot x\right))_*\right)}^{\left(\frac{1}{2} + \frac{1}{2}\right)}}\]

9. Simplified0.0

   \[\leadsto {\color{blue}{\left((x \cdot x + x)_* \cdot x\right)}}^{\left(\frac{1}{2} + \frac{1}{2}\right)}\]

10. Simplified0.0

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

11. Final simplification0.0

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

Reproduce

herbie shell --seed 2019007 +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: 3.4s)Debug log