Details

analyze2.6s (10%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	98.1%	1.9%	7
0%	98.1%	1.9%	8
0%	97.8%	2.2%	9
0%	96.8%	3.2%	10
0%	96.3%	3.7%	11
0%	94.3%	5.7%	12
0.4%	92.1%	7.5%	13
0.6%	90.8%	8.6%	14

sample109.0ms (0.4%)

Algorithm

1×

intervals

Results

48.0ms	473×	body	80	nan
24.0ms	256×	body	80	valid
4.0ms	39×	body	80	invalid

simplify46.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5186	28

prune11.0ms (0%)

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: 35.1b

Counts

2 → 1

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.5b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.0b	(/ (* l l) Om)
10.1b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.2b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite46.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log`
25×	`pow1`
23×	`add-cbrt-cube`
22×	`associate-*r/`
16×	`prod-exp`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`add-sqr-sqrt` `*-un-lft-identity` `cbrt-unprod`
8×	`add-cube-cbrt` `associate-r` `frac-sub`
6×	`sub-neg` `sqrt-div`
4×	`sqrt-pow1` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `times-frac` `div-exp` `associate-/r*`
2×	`cbrt-undiv` `associate-l` `pow-exp` `associate--l+` `*-commutative`
1×	`pow-to-exp` `frac-2neg` `pow1/2` `clear-num` `sqrt-prod` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 97

Calls

4 calls:

14.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
13.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
11.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
5.0ms	(/ (* l l) Om)

series2.4s (9.3%)

Counts

4 → 12

Calls

4 calls:

1.9s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
376.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
128.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
3.0ms	(/ (* l l) Om)

simplify41.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5140	2554

prune353.0ms (1.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	97	12	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	12	110

Merged error: 21.6b

Counts

110 → 12

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.6b	(* n (pow (/ l Om) 2.0))
6.5b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.1b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.2b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite50.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-exp-log`
25×	`pow1` `add-sqr-sqrt` `associate-r`
22×	`associate-*r/`
20×	`add-cbrt-cube`
19×	`prod-exp`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt` `unpow-prod-down`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`times-frac` `cbrt-unprod`
8×	`frac-sub`
6×	`sub-neg` `sqrt-div`
5×	`associate-l`
4×	`sqrt-pow1` `pow-exp` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
2×	`pow-to-exp` `div-exp` `associate--l+` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 113

Calls

4 calls:

13.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
13.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
10.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.0ms	(* n (pow (/ l Om) 2.0))

series2.4s (9.5%)

Counts

4 → 12

Calls

4 calls:

1.9s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
351.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
125.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
41.0ms	(* n (pow (/ l Om) 2.0))

simplify46.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5291	2823

prune364.0ms (1.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	118	7	125
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	127	10	137

Merged error: 19.9b

Counts

137 → 10

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.2b	(* n (pow (/ l Om) (/ 2.0 2)))
6.5b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
10.1b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
19.2b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite60.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

99×	`add-exp-log`
67×	`prod-exp`
25×	`pow1` `add-sqr-sqrt` `associate-r`
24×	`add-cbrt-cube`
22×	`associate-*r/`
20×	`pow-exp`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt` `unpow-prod-down`
13×	`pow-prod-down` `cbrt-unprod`
11×	`flip3--` `flip--`
10×	`pow-to-exp` `times-frac` `div-exp`
8×	`frac-sub`
6×	`sub-neg` `sqrt-div`
5×	`associate-l`
4×	`sqrt-pow1` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
2×	`associate--l+` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 130

Calls

4 calls:

18.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
15.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
13.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
9.0ms	(* n (pow (/ l Om) (/ 2.0 2)))

series2.5s (9.6%)

Counts

4 → 12

Calls

4 calls:

2.0s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
350.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
128.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
47.0ms	(* n (pow (/ l Om) (/ 2.0 2)))

simplify55.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5045	3520

prune456.0ms (1.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	142	10	152

Merged error: 19.9b

Counts

152 → 10

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

12.7b	(cbrt (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
12.7b	(cbrt (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
12.7b	(cbrt (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.2b	(sqrt (* (* (* (* 2.0 n) U) (* (cbrt (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U)))) (cbrt (- (- t ( 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U)))))) (cbrt (- (- t ( 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite167.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

984×	`associate-*r/`
900×	`cbrt-div`
750×	`flip3--` `flip--`
600×	`frac-sub`
540×	`frac-times`
342×	`sqrt-div`
90×	`associate-*l/`
34×	`pow1`
22×	`pow-prod-down`
9×	`cbrt-prod`
8×	`sqrt-pow1`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
1×	`pow1/2` `sqrt-prod`

Counts

4 → 410

Calls

4 calls:

54.0ms	(sqrt (* (* (* (* 2.0 n) U) (* (cbrt (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U)))) (cbrt (- (- t ( 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U)))))) (cbrt (- (- t ( 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
7.0ms	(cbrt (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.0ms	(cbrt (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.0ms	(cbrt (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))

series2.8s (10.7%)

Counts

4 → 12

Calls

4 calls:

1.9s	(sqrt (* (* (* (* 2.0 n) U) (* (cbrt (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U)))) (cbrt (- (- t ( 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U)))))) (cbrt (- (- t ( 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
272.0ms	(cbrt (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
272.0ms	(cbrt (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
270.0ms	(cbrt (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))

simplify315.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

422 → 422

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5387	76297

prune6.7s (26%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	421	1	422
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	421	11	432

Merged error: 19.9b

Counts

432 → 11

regimes1.2s (4.8%)

Accuracy

Total 5.9b remaining (21.4%)

Threshold costs 0b (0%)

bsearch1.0ms (0%)

simplify18.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	791	155
1	791	155

end0.0ms (0%)

sample3.0s (11.5%)

Algorithm

1×

intervals

Results

1.3s	12970×	body	80	nan
779.0ms	8000×	body	80	valid
113.0ms	1151×	body	80	invalid

Details

analyze2.6s (10%)

sample109.0ms (0.4%)

simplify46.0ms (0.2%)

prune11.0ms (0%)

localize20.0ms (0.1%)

rewrite46.0ms (0.2%)

series2.4s (9.3%)

simplify41.0ms (0.2%)

prune353.0ms (1.4%)

localize19.0ms (0.1%)

rewrite50.0ms (0.2%)

series2.4s (9.5%)

simplify46.0ms (0.2%)

prune364.0ms (1.4%)

localize21.0ms (0.1%)

rewrite60.0ms (0.2%)

series2.5s (9.6%)

simplify55.0ms (0.2%)

prune456.0ms (1.8%)

localize25.0ms (0.1%)

rewrite167.0ms (0.6%)

series2.8s (10.7%)

simplify315.0ms (1.2%)

prune6.7s (26%)

regimes1.2s (4.8%)

bsearch1.0ms (0%)

simplify18.0ms (0.1%)

end0.0ms (0%)

sample3.0s (11.5%)

Profiling