Average Error: 0.0 → 0.0
Time: 13.0s
Precision: 64
Internal Precision: 320
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[\left(b + \left(c + d\right)\right) \cdot a\]

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

Original0.0
Target0.0
Herbie0.0
\[a \cdot b + a \cdot \left(c + d\right)\]

Derivation

  1. Initial program 0.0

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

  3. Applied distribute-lft-in0.0

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

  4. Taylor expanded around -inf 0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Runtime

Time bar (total: 13.0s)Debug logProfile

herbie shell --seed 2018255 
(FPCore (a b c d)
  :name "Expression, p14"
  :pre (and (<= 56789 a 98765) (<= 0 b 1) (<= 0 c 0.0016773) (<= 0 d 0.0016773))

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

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