Average Error: 0.0 → 0.0
Time: 38.8s
Precision: 64
Internal Precision: 384
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[i \cdot c + (b \cdot a + \left((z \cdot t + \left(y \cdot x\right))_*\right))_*\]

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

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

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

  5. Applied associate-+r+0.0

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

  6. Applied simplify0.0

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

  8. Applied fma-udef0.0

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

  9. Applied associate-+l+0.0

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

  10. Applied simplify0.0

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

Runtime

Time bar (total: 38.8s)Debug logProfile

herbie shell --seed '#(1070960995 739739648 2531964651 3069671617 351857262 3877178482)' +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)))