Error

Target

Derivation

1. Initial program 0.0

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

2. Initial simplification0.0

   \[\leadsto (\left(x \cdot x\right) \cdot x + \left(x \cdot x\right))_*\]
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 pow10.0

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

7. Applied pow10.0

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

8. Applied pow-prod-down0.0

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

9. Simplified0.0

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

10. Final simplification0.0

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

Runtime

Time bar (total: 10.4s)Debug logProfile

herbie shell --seed 2018225 +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)))