Average Error: 0.4 → 0.2
Time: 15.2s
Precision: 64
Internal Precision: 128
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[e + \left(\left(c + b\right) + \left(d + a\right)\right)\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Bits error versus e

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 0.4

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

  2. Initial simplification0.2

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

  4. Applied associate-+l+0.3

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

  6. Applied associate-+r+0.2

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

  7. Final simplification0.2

    \[\leadsto e + \left(\left(c + b\right) + \left(d + a\right)\right)\]

Runtime

Time bar (total: 15.2s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes0.20.20.00.20%
herbie shell --seed 2018354 
(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))