Average Error: 48.8 → 0
Time: 3.3s
Precision: 64
Internal Precision: 384
\[e^{\log a + \log b}\]
↓
\[a \cdot b\]

Error

Bits error versus a

Bits error versus b

Target

Original48.8
Target0
Herbie0
\[a \cdot b\]

Derivation

  1. Initial program 48.8

    \[e^{\log a + \log b}\]

  2. Applied simplify0

    \[\leadsto \color{blue}{a \cdot b}\]
  3. Removed slow pow expressions.

Runtime

Time bar (total: 3.3s)Debug log

herbie shell --seed '#(1567391828 2030694642 2833800258 828025724 3004380912 3532991858)' +o setup:early-exit +o reduce:binary-search
(FPCore (a b)
  :name "Exp of sum of logs"

  :herbie-target
  (* a b)

  (exp (+ (log a) (log b))))