Average Error: 3.7 → 0
Time: 44.6s
Precision: 64
Internal Precision: 320
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\left(\left(a + d\right) + \left(c + b\right)\right) \cdot 2\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original3.7
Target3.9
Herbie0
\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

Derivation

  1. Initial program 3.7

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

  3. Applied associate-+r+2.8

    \[\leadsto \left(a + \color{blue}{\left(\left(b + c\right) + d\right)}\right) \cdot 2\]
  4. Using strategy rm

  5. Applied add-log-exp3.0

    \[\leadsto \color{blue}{\log \left(e^{a + \left(\left(b + c\right) + d\right)}\right)} \cdot 2\]

  6. Taylor expanded around inf 0.9

    \[\leadsto \log \color{blue}{\left(e^{b + \left(c + \left(d + a\right)\right)}\right)} \cdot 2\]

  7. Applied simplify0

    \[\leadsto \color{blue}{\left(\left(a + d\right) + \left(c + b\right)\right) \cdot 2}\]

Runtime

Time bar (total: 44.6s)Debug logProfile

herbie shell --seed '#(1072936661 1621281212 3440817831 3219514234 460296804 1258167384)' +o rules:numerics
(FPCore (a b c d)
  :name "Expression, p6"
  :pre (and (<= -14 a -13) (<= -3 b -2) (<= 3 c 3.5) (<= 12.5 d 13.5))

  :herbie-target
  (+ (* (+ a b) 2) (* (+ c d) 2))

  (* (+ a (+ b (+ c d))) 2))