Average Error: 0.0 → 0.0
Time: 13.8s
Precision: 64
Internal Precision: 576
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[(i \cdot c + \left((t \cdot z + \left(a \cdot b\right))_*\right))_* + x \cdot y\]

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

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 fma-udef0.0

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

  5. Applied associate-+r+0.0

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

  6. Taylor expanded around inf 0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Runtime

Time bar (total: 13.8s)Debug logProfile

herbie shell --seed 2018227 +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)))