Error

Derivation

1. Initial program 0.0

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

2. Simplified0.0

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

4. Applied add-cube-cbrt0.7

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

5. Applied fma-def0.7

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

6. Final simplification0.7

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

Reproduce

herbie shell --seed 2019008 +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)))

Details

Time bar (total: 17.6s)Debug log