Average Error: 0.0 → 0.0
Time: 44.8s
Precision: 64
Internal Precision: 384
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[\left(b \cdot a + z \cdot t\right) + \left(y \cdot x + c \cdot i\right)\]

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. Using strategy rm

  3. Applied add-cbrt-cube43.1

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

  4. Applied simplify43.1

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

  6. Applied rem-cbrt-cube0.0

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

Runtime

Time bar (total: 44.8s)Debug logProfile

herbie shell --seed '#(1070227846 1561819246 480764335 4016816270 2602869839 2117310382)' 
(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)))