Average Error: 0.0 → 0.0
Time: 29.8s
Precision: 64
Internal Precision: 384
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[(c \cdot i + \left(x \cdot y\right))_* + (b \cdot a + \left(t \cdot z\right))_*\]

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. Taylor expanded around inf 0.0

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

  3. Applied simplify0.0

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

Runtime

Time bar (total: 29.8s)Debug logProfile

herbie shell --seed '#(1070100504 930361288 1279167582 284574201 1450237281 2578255382)' +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)))