Average Error: 0.0 → 0.0
Time: 2.2s
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 2019004 +o rules:numerics
(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: 1.9s)Debug log

sample31.0ms

Algorithm
intervals

simplify90.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

90.0ms
(+ (* x (* x x)) (* x x))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

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 → 28
Calls

2 calls. Slowest were:

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

series59.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

41.0ms
(+ (* x (* x x)) (* x x))
18.0ms
(* x (* x x))

simplify86.0ms

Counts
9 → 34
Calls

9 calls. Slowest were:

49.0ms
(* (exp (* x (* x x))) (exp (* x x)))
12.0ms
(+ (pow x 3) (pow x 2))
7.0ms
(+ (* x x) x)

prune176.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 1 expressions with local error:

0.0b
(* x (fma x x x))

rewrite2.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

2.0ms
(* x (fma x x x))

series64.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

64.0ms
(* x (fma x x x))

simplify50.0ms

Counts
8 → 18
Calls

8 calls. Slowest were:

13.0ms
(+ (pow x 3) (pow x 2))
13.0ms
(+ (pow x 3) (pow x 2))
12.0ms
(+ (pow x 3) (pow x 2))

prune96.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes58.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch1.0ms

end0.0ms

sample1.1s

Algorithm
intervals