Details

Time bar (total: 16.1s)

sample72.0ms

Algorithm
intervals
Results
44.0ms650×body80valid

simplify2.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
1147
2297
3697
42007
56117
629167
done50007

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 1 expressions with local error:

0.0b
(- (pow x 4.0) (pow y 4.0))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×difference-of-squares
8×unpow-prod-down
6×sqr-pow
5×*-un-lft-identity
3×add-log-exp
2×distribute-lft-out--
1×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- diff-log add-cbrt-cube flip--
Counts
1 → 23
Calls
1 calls:
25.0ms
(- (pow x 4.0) (pow y 4.0))

series81.0ms

Counts
1 → 3
Calls
1 calls:
81.0ms
(- (pow x 4.0) (pow y 4.0))

simplify4.7s

Counts
26 → 26
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
061356
1127345
2305331
3995331
44931331
done5001331

prune89.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (pow x 4.0) (pow y 4.0))
0.1b
(* (sqrt (- (pow x 4.0) (pow y 4.0))) (sqrt (- (pow x 4.0) (pow y 4.0))))
17.6b
(sqrt (- (pow x 4.0) (pow y 4.0)))
17.6b
(sqrt (- (pow x 4.0) (pow y 4.0)))

rewrite302.0ms

Algorithm
rewrite-expression-head
Rules
112×add-sqr-sqrt
94×sqrt-prod
63×difference-of-squares
56×unpow-prod-down
48×*-un-lft-identity
42×sqr-pow
21×pow1 swap-sqr
17×associate-*r* associate-*l*
16×sqrt-div distribute-lft-out--
14×add-cube-cbrt
10×sqrt-pow1 pow1/2
9×flip3-- flip--
6×add-exp-log add-cbrt-cube add-log-exp
5×pow-prod-up
4×frac-times unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square associate-*r/ associate-*l/
1×pow2 sub-neg pow-plus sqrt-unprod diff-log prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 167
Calls
4 calls:
42.0ms
(- (pow x 4.0) (pow y 4.0))
179.0ms
(* (sqrt (- (pow x 4.0) (pow y 4.0))) (sqrt (- (pow x 4.0) (pow y 4.0))))
27.0ms
(sqrt (- (pow x 4.0) (pow y 4.0)))
41.0ms
(sqrt (- (pow x 4.0) (pow y 4.0)))

series324.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(- (pow x 4.0) (pow y 4.0))
54.0ms
(* (sqrt (- (pow x 4.0) (pow y 4.0))) (sqrt (- (pow x 4.0) (pow y 4.0))))
99.0ms
(sqrt (- (pow x 4.0) (pow y 4.0)))
98.0ms
(sqrt (- (pow x 4.0) (pow y 4.0)))

simplify2.1s

Counts
179 → 179
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01843514
13062563
28512463
321902424
done50002398

prune717.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

3.7b
(sqrt (sqrt (- (pow x 4.0) (pow y 4.0))))
17.6b
(sqrt (- (pow x 4.0) (pow y 4.0)))
17.6b
(sqrt (- (pow x 4.0) (pow y 4.0)))
17.6b
(sqrt (- (pow x 4.0) (pow y 4.0)))

rewrite172.0ms

Algorithm
rewrite-expression-head
Rules
74×sqrt-prod
62×add-sqr-sqrt
36×difference-of-squares
32×unpow-prod-down
25×*-un-lft-identity
24×sqr-pow
10×sqrt-div
9×pow1 add-cube-cbrt
8×distribute-lft-out--
7×sqrt-pow1
5×rem-sqrt-square pow1/2
4×add-exp-log flip3-- add-cbrt-cube flip-- add-log-exp
Counts
4 → 110
Calls
4 calls:
37.0ms
(sqrt (sqrt (- (pow x 4.0) (pow y 4.0))))
53.0ms
(sqrt (- (pow x 4.0) (pow y 4.0)))
48.0ms
(sqrt (- (pow x 4.0) (pow y 4.0)))
28.0ms
(sqrt (- (pow x 4.0) (pow y 4.0)))

series434.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(sqrt (sqrt (- (pow x 4.0) (pow y 4.0))))
107.0ms
(sqrt (- (pow x 4.0) (pow y 4.0)))
108.0ms
(sqrt (- (pow x 4.0) (pow y 4.0)))
101.0ms
(sqrt (- (pow x 4.0) (pow y 4.0)))

simplify3.6s

Counts
122 → 122
Iterations

Useful iterations: 3 (331.0ms)

IterNodesCost
01361849
12261683
24221658
310531653
441031653
done50011653

prune680.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes1.0ms