Average Error: 0.0 → 0.0
Time: 1.5s
Precision: 64
Internal Precision: 128
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[x \cdot \left(x \cdot x + x\right)\]

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. Using strategy rm

  3. Applied distribute-lft-out0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019008 
(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: 1.2s)Debug log

sample35.0ms

Algorithm
intervals

simplify48.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

48.0ms
(+ (* x (* x x)) (* x x))

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b
(* x (* x x))
0.0b
(+ (* x (* x x)) (* x x))

rewrite4.0ms

Algorithm
rewrite-expression-head
Counts
2 → 23
Calls

2 calls. Slowest were:

3.0ms
(+ (* x (* x x)) (* x x))
1.0ms
(* x (* x x))

series71.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

49.0ms
(+ (* x (* x x)) (* x x))
22.0ms
(* x (* x x))

simplify91.0ms

Counts
9 → 29
Calls

9 calls. Slowest were:

52.0ms
(* (exp (* x (* x x))) (exp (* x x)))
12.0ms
(+ (pow x 3) (pow x 2))
10.0ms
(+ (pow x 3) (pow x 2))

prune185.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize10.0ms

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:

prune5.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample748.0ms

Algorithm
intervals