Average Error: 0.4 → 0.3
Time: 1.3m
Precision: 64
Internal Precision: 320
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(b + \left(a + c\right)\right) + \left(d + e\right)\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Bits error versus e

Try it out

  1. Inputs

  2. Original Output:

    Herbie Output:

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 add-cbrt-cube0.7

    \[\leadsto \left(\color{blue}{\sqrt[3]{\left(\left(\left(e + d\right) + c\right) \cdot \left(\left(e + d\right) + c\right)\right) \cdot \left(\left(e + d\right) + c\right)}} + b\right) + a\]

  4. Applied simplify0.6

    \[\leadsto \left(\sqrt[3]{\color{blue}{{\left(\left(e + c\right) + d\right)}^{3}}} + b\right) + a\]

  5. Taylor expanded around 0 0.7

    \[\leadsto \left(\sqrt[3]{{\color{blue}{\left(c + \left(d + e\right)\right)}}^{3}} + b\right) + a\]

  6. Applied simplify0.3

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

Runtime

Time bar (total: 1.3m)Debug logProfile

herbie shell --seed '#(1072361757 3390613284 2339397988 1175251238 145061547 3101881848)' 
(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))