Average Error: 0.0 → 0.0
Time: 1.8s
Precision: 64
Internal Precision: 128
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[x \cdot x + x \cdot \left(x \cdot x\right)\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[\left(\left(1.0 + x\right) \cdot x\right) \cdot x\]

Derivation

  1. Initial program 0.0

    \[x \cdot \left(x \cdot x\right) + x \cdot x\]

  2. Final simplification0.0

    \[\leadsto x \cdot x + x \cdot \left(x \cdot x\right)\]

Reproduce

herbie shell --seed 2018365 
(FPCore (x)
  :name "Expression 3, p15"
  :pre (<= 0 x 2)

  :herbie-target
  (* (* (+ 1.0 x) x) x)

  (+ (* x (* x x)) (* x x)))

Details

Time bar (total: 300.0ms)Debug log

start40.0ms

Algorithm
intervals

setup78.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 1 expressions with local error:

0.1b
(* x (* x x))

rewrite2.0ms

Algorithm
rewrite-expression-head
Counts
1 → 10
Calls

1 calls. Slowest were:

2.0ms
(* x (* x x))

series24.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

24.0ms
(* x (* x x))

simplify5.0ms

Counts
3 → 13
Calls

3 calls. Slowest were:

2.0ms
(pow x 3)
1.0ms
(pow x 3)
1.0ms
(pow x 3)

prune134.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b