Error

Derivation

1. Initial program 0.0

   \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]

2. Initial simplification0.0

   \[\leadsto (b \cdot a + \left(z \cdot t\right))_* + (i \cdot c + \left(x \cdot y\right))_*\]
3. Using strategy rm

4. Applied add-cbrt-cube27.6

   \[\leadsto \color{blue}{\sqrt[3]{\left((b \cdot a + \left(z \cdot t\right))_* \cdot (b \cdot a + \left(z \cdot t\right))_*\right) \cdot (b \cdot a + \left(z \cdot t\right))_*}} + (i \cdot c + \left(x \cdot y\right))_*\]
5. Using strategy rm

6. Applied *-un-lft-identity27.6

   \[\leadsto \sqrt[3]{\left((b \cdot a + \left(z \cdot t\right))_* \cdot (b \cdot a + \left(z \cdot t\right))_*\right) \cdot (b \cdot a + \left(z \cdot t\right))_*} + \color{blue}{1 \cdot (i \cdot c + \left(x \cdot y\right))_*}\]

7. Applied *-un-lft-identity27.6

   \[\leadsto \color{blue}{1 \cdot \sqrt[3]{\left((b \cdot a + \left(z \cdot t\right))_* \cdot (b \cdot a + \left(z \cdot t\right))_*\right) \cdot (b \cdot a + \left(z \cdot t\right))_*}} + 1 \cdot (i \cdot c + \left(x \cdot y\right))_*\]

8. Applied distribute-lft-out27.6

   \[\leadsto \color{blue}{1 \cdot \left(\sqrt[3]{\left((b \cdot a + \left(z \cdot t\right))_* \cdot (b \cdot a + \left(z \cdot t\right))_*\right) \cdot (b \cdot a + \left(z \cdot t\right))_*} + (i \cdot c + \left(x \cdot y\right))_*\right)}\]

9. Simplified0.0

   \[\leadsto 1 \cdot \color{blue}{\left((t \cdot z + \left(b \cdot a\right))_* + (c \cdot i + \left(x \cdot y\right))_*\right)}\]

10. Final simplification0.0

    \[\leadsto (c \cdot i + \left(x \cdot y\right))_* + (t \cdot z + \left(b \cdot a\right))_*\]

Runtime

Time bar (total: 31.1s)Debug logProfile

herbie shell --seed 2018235 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3"
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))