Average Error: 0.4 → 0.3
Time: 36.2s
Precision: 64
Internal Precision: 384
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\log \left(e^{\left(e + c\right) + \left(a + \left(b + d\right)\right)}\right)\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Bits error versus e

Target

Original0.4
Target0.2
Herbie0.3
\[\left(d + \left(c + \left(a + b\right)\right)\right) + e\]

Derivation

  1. Initial program 0.4

    \[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
  2. Using strategy rm

  3. Applied associate-+l+0.3

    \[\leadsto \color{blue}{\left(\left(e + d\right) + c\right) + \left(b + a\right)}\]
  4. Using strategy rm

  5. Applied add-log-exp0.3

    \[\leadsto \left(\left(e + d\right) + c\right) + \color{blue}{\log \left(e^{b + a}\right)}\]

  6. Applied add-log-exp0.3

    \[\leadsto \color{blue}{\log \left(e^{\left(e + d\right) + c}\right)} + \log \left(e^{b + a}\right)\]

  7. Applied sum-log0.3

    \[\leadsto \color{blue}{\log \left(e^{\left(e + d\right) + c} \cdot e^{b + a}\right)}\]

  8. Applied simplify0.3

    \[\leadsto \log \color{blue}{\left(e^{\left(e + c\right) + \left(a + \left(b + d\right)\right)}\right)}\]

Runtime

Time bar (total: 36.2s)Debug logProfile

herbie shell --seed '#(1064173506 2580572819 2847706409 4129882574 1125180799 1845288547)' +o rules:numerics
(FPCore (a b c d e)
  :name "Expression 1, p15"
  :pre (<= 1 a 2 b 4 c 8 d 16 e 32)

  :herbie-target
  (+ (+ d (+ c (+ a b))) e)

  (+ (+ (+ (+ e d) c) b) a))