Average Error: 39.3 → 0.0
Time: 1.7s
Precision: 64
Internal Precision: 128
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[\left(x + 2\right) \cdot x\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 39.3

    \[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(2 + x\right) \cdot x}\]

  3. Final simplification0.0

    \[\leadsto \left(x + 2\right) \cdot x\]

Reproduce

herbie shell --seed 2019022 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))

Details

Time bar (total: 1.6s)Debug log

sample104.0ms

Algorithm
intervals
Results
11.0ms80×body1280valid
5.0ms170×body80valid
5.0ms50×body640valid
2.0ms25×body320valid
1.0ms11×body160valid

simplify424.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
423.0ms
(- (* (+ x 1) (+ x 1)) 1)

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize7.0ms

Local error

Found 0 expressions with local error:

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0
Calls
0 calls:
Slowest

series0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

simplify0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

prune2.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample1.0s

Algorithm
intervals
Results
420.0ms2264×body1280valid
211.0ms5430×body80valid
177.0ms1685×body640valid
96.0ms887×body320valid
46.0ms386×body160valid