Average Error: 0.0 → 0.0
Time: 1.5m
Precision: 64
Internal Precision: 576
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[z \cdot t + (i \cdot c + \left((b \cdot a + \left(x \cdot y\right))_*\right))_*\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Try it out

  1. Inputs

  2. Original Output:

    Herbie Output:

Derivation

  1. Initial program 0.0

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

  2. Applied simplify0.0

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

  4. Applied fma-udef0.0

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

  5. Applied associate-+l+0.0

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

  6. Applied simplify0.0

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

Runtime

Time bar (total: 1.5m)Debug logProfile

herbie shell --seed '#(1072361757 3390613284 2339397988 1175251238 145061547 3101881848)' +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)))