Average Error: 0.0 → 0
Time: 805.0ms
Precision: 64
Internal Precision: 128
\[x + x \cdot x\]
↓
\[(x \cdot x + x)_*\]

Error

Bits error versus x

Target

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

Derivation

  1. Initial program 0.0

    \[x + x \cdot x\]

  2. Simplified0

    \[\leadsto \color{blue}{(x \cdot x + x)_*}\]

  3. Final simplification0

    \[\leadsto (x \cdot x + x)_*\]

Reproduce

herbie shell --seed 2019004 +o rules:numerics
(FPCore (x)
  :name "Expression 2, p15"
  :pre (<= 0 x 2)

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

  (+ x (* x x)))

Details

Time bar (total: 567.0ms)Debug log

sample14.0ms

Algorithm
intervals

simplify7.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

7.0ms
(+ x (* x x))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize4.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

Algorithm
rewrite-expression-head
Counts
0 → 0
Calls

0 calls. Slowest were:

series0.0ms

Counts
0 → 0
Calls

0 calls. Slowest were:

simplify0.0ms

Counts
0 → 0
Calls

0 calls. Slowest were:

prune2.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample535.0ms

Algorithm
intervals