Details

analyze1.0ms (0.1%)

Algorithm

1×

Search

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

sample33.0ms (1.7%)

Algorithm

1×

intervals

Results

15.0ms	96×	body	1280	valid
8.0ms	127×	body	80	valid
1.0ms	12×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	11×	body	160	valid

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune5.0ms (0.3%)

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: 15.2b

Counts

2 → 1

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
2.2b	(- (atan (+ N 1.0)) (atan N))

rewrite5.0ms (0.2%)

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))

simplify66.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5349	236

prune46.0ms (2.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Merged error: 0.3b

Counts

28 → 2

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(* N (+ N 1.0))
0.3b	(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 (0.4%)

Counts

2 → 6

Calls

2 calls:

5.0ms	(* N (+ N 1.0))
2.0ms	(atan2 1.0 (+ 1 (* N (+ N 1.0))))

simplify60.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4907	272
1	4907	272

prune67.0ms (3.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

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

Merged error: 0.3b

Counts

38 → 5

localize8.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b	(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))))))
14.9b	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
14.9b	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

rewrite11.0ms (0.6%)

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))))

series19.0ms (1%)

Counts

4 → 12

Calls

4 calls:

8.0ms	(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))))

simplify46.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5253	989

prune216.0ms (11.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	94	5	99

Merged error: 0.3b

Counts

99 → 5

localize12.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.6b	(* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))))
14.9b	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
14.9b	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
14.9b	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

rewrite22.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`sqrt-pow1`
45×	`pow1`
30×	`pow1/2` `pow-prod-up`
16×	`add-sqr-sqrt`
14×	`sqrt-prod`
9×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
7×	`pow-prod-down`
6×	`associate-l` `pow-sqr`
4×	`add-log-exp`
3×	`rem-sqrt-square` `prod-exp` `cbrt-unprod`
2×	`sqrt-unprod` `swap-sqr` `unswap-sqr`
1×	`associate-r` `*-commutative`

Counts

4 → 85

Calls

4 calls:

15.0ms	(* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (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	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

series21.0ms (1.1%)

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)))))
6.0ms	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
3.0ms	(* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))))

simplify55.0ms (3%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4775	929
1	4775	929

prune268.0ms (14.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	0	1	1
Picked	0	1	1
Done	1	2	3
Total	97	5	102

Merged error: 0.2b

Counts

102 → 5

regimes80.0ms (4.2%)

Accuracy

Total 0.0b remaining (10.5%)

Threshold costs 0.0b (10.5%)

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%)

sample801.0ms (42.6%)

Algorithm

1×

intervals

Results

434.0ms	2826×	body	1280	valid
143.0ms	4078×	body	80	valid
79.0ms	631×	body	640	valid
30.0ms	310×	body	320	valid
11.0ms	155×	body	160	valid

Details

analyze1.0ms (0.1%)

sample33.0ms (1.7%)

simplify4.0ms (0.2%)

prune5.0ms (0.3%)

localize6.0ms (0.3%)

rewrite5.0ms (0.2%)

series4.0ms (0.2%)

simplify66.0ms (3.5%)

prune46.0ms (2.4%)

localize6.0ms (0.3%)

rewrite7.0ms (0.4%)

series7.0ms (0.4%)

simplify60.0ms (3.2%)

prune67.0ms (3.6%)

localize8.0ms (0.5%)

rewrite11.0ms (0.6%)

series19.0ms (1%)

simplify46.0ms (2.4%)

prune216.0ms (11.5%)

localize12.0ms (0.6%)

rewrite22.0ms (1.2%)

series21.0ms (1.1%)

simplify55.0ms (3%)

prune268.0ms (14.3%)

regimes80.0ms (4.2%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample801.0ms (42.6%)

Profiling