Average Error: 0.4 → 0.5
Time: 51.7s
Precision: 64
Internal Precision: 384
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left((\left(\sqrt{e + d}\right) \cdot \left(\sqrt{e + d}\right) + c)_* + b\right) + a\]

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
Herbie0.5
\[\left(d + \left(c + \left(a + b\right)\right)\right) + e\]

Derivation

  1. Initial program 0.4

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

  3. Applied add-sqr-sqrt0.6

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

  4. Applied fma-def0.5

    \[\leadsto \left(\color{blue}{(\left(\sqrt{e + d}\right) \cdot \left(\sqrt{e + d}\right) + c)_*} + b\right) + a\]

Runtime

Time bar (total: 51.7s)Debug logProfile

herbie shell --seed '#(1070864556 424010669 783715395 1203517814 4070606583 4107618214)' +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))