Details

analyze1.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

sample28.0ms (1.5%)

Algorithm

1×

intervals

Results

14.0ms	91×	body	1280	valid
5.0ms	140×	body	80	valid
2.0ms	13×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	4×	body	160	valid

simplify5.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune5.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 11.5b

Counts

2 → 1

localize10.0ms (0.5%)

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.0b	(- (atan (+ N 1.0)) (atan N))

rewrite5.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `diff-atan` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 21

Calls

2 calls:

3.0ms	(- (atan (+ N 1.0)) (atan N))
1.0ms	(atan (+ N 1.0))

series4.0ms (0.2%)

Counts

2 → 6

Calls

2 calls:

3.0ms	(- (atan (+ N 1.0)) (atan N))
1.0ms	(atan (+ N 1.0))

simplify81.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	5349	236

prune48.0ms (2.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	25	2	27
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	2	28

Merged error: 0.1b

Counts

28 → 2

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(* N (+ N 1.0))
0.1b	(atan2 1.0 (+ 1 (* N (+ N 1.0))))

rewrite7.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-r` `add-cbrt-cube`
3×	`associate-l`
2×	`associate-*r/` `add-log-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

2 → 30

Calls

2 calls:

6.0ms	(* N (+ N 1.0))
1.0ms	(atan2 1.0 (+ 1 (* N (+ N 1.0))))

series7.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

4.0ms	(* N (+ N 1.0))
2.0ms	(atan2 1.0 (+ 1 (* N (+ N 1.0))))

simplify70.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4907	272
1	4907	272

prune69.0ms (3.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	33	3	36
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	33	5	38

Merged error: 0.1b

Counts

38 → 5

localize10.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* N (+ 1.0 N))) (cbrt (* N (+ 1.0 N))))
16.2b	(cbrt (* N (+ 1.0 N)))
16.2b	(cbrt (* N (+ 1.0 N)))
16.2b	(cbrt (* N (+ 1.0 N)))

rewrite22.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`associate-*r/`
18×	`cbrt-div`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`flip3-+` `pow1/3` `flip-+`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`frac-times` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `associate-*l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

6.0ms	(* (cbrt (* N (+ 1.0 N))) (cbrt (* N (+ 1.0 N))))
5.0ms	(cbrt (* N (+ 1.0 N)))
4.0ms	(cbrt (* N (+ 1.0 N)))
4.0ms	(cbrt (* N (+ 1.0 N)))

series41.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (cbrt (* N (+ 1.0 N))) (cbrt (* N (+ 1.0 N))))
12.0ms	(cbrt (* N (+ 1.0 N)))
9.0ms	(cbrt (* N (+ 1.0 N)))
9.0ms	(cbrt (* N (+ 1.0 N)))

simplify55.0ms (3%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4950	1066
1	4950	1066

prune228.0ms (12.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	84	5	89

Merged error: 0.1b

Counts

89 → 5

localize9.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
0.6b	(* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))
15.7b	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
15.7b	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

rewrite13.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 82

Calls

4 calls:

6.0ms	(* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
1.0ms	(atan2 1.0 (+ 1 (* N (+ 1.0 N))))

series17.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
6.0ms	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
2.0ms	(* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))
2.0ms	(atan2 1.0 (+ 1 (* N (+ 1.0 N))))

simplify45.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5253	989

prune204.0ms (10.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	91	8	99

Merged error: 0.1b

Counts

99 → 8

regimes47.0ms (2.5%)

Accuracy

Total 0.0b remaining (13.1%)

Threshold costs 0.0b (13.1%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	9
1	11	9

end0.0ms (0%)

sample830.0ms (44.4%)

Algorithm

1×

intervals

Results

457.0ms	2851×	body	1280	valid
140.0ms	4039×	body	80	valid
82.0ms	654×	body	640	valid
30.0ms	312×	body	320	valid
10.0ms	144×	body	160	valid

Details

analyze1.0ms (0.1%)

sample28.0ms (1.5%)

simplify5.0ms (0.3%)

prune5.0ms (0.2%)

localize10.0ms (0.5%)

rewrite5.0ms (0.3%)

series4.0ms (0.2%)

simplify81.0ms (4.3%)

prune48.0ms (2.6%)

localize6.0ms (0.3%)

rewrite7.0ms (0.4%)

series7.0ms (0.3%)

simplify70.0ms (3.8%)

prune69.0ms (3.7%)

localize10.0ms (0.5%)

rewrite22.0ms (1.2%)

series41.0ms (2.2%)

simplify55.0ms (3%)

prune228.0ms (12.2%)

localize9.0ms (0.5%)

rewrite13.0ms (0.7%)

series17.0ms (0.9%)

simplify45.0ms (2.4%)

prune204.0ms (10.9%)

regimes47.0ms (2.5%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample830.0ms (44.4%)

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