Details

analyze2.0s (8.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	81.1%	18.9%	7
0%	68.6%	31.4%	8
0%	59.2%	40.8%	9
0%	59.2%	40.8%	10
0%	59.2%	40.8%	11
0.4%	49.5%	50.1%	12
0.8%	44.4%	54.8%	13
1.4%	39.9%	58.7%	14

sample158.0ms (0.7%)

Algorithm

1×

intervals

Results

50.0ms	256×	body	80	valid
39.0ms	263×	body	80	nan
34.0ms	182×	body	80	invalid

simplify20.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5401	35

prune18.0ms (0.1%)

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: 22.6b

Counts

2 → 2

localize35.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.6b	(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
10.1b	(pow (/ d h) (/ 1.0 2.0))
10.4b	(pow (/ d l) (/ 1.0 2.0))
12.6b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite46.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

205×	`add-exp-log`
107×	`prod-exp`
55×	`div-exp`
45×	`times-frac`
40×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `pow-exp`
30×	`add-cbrt-cube`
26×	`unpow-prod-down` `pow-unpow`
16×	`associate-r`
14×	`pow-to-exp`
13×	`cbrt-unprod`
10×	`pow1`
5×	`cbrt-undiv` `div-inv`
4×	`add-log-exp`
3×	`associate-r/` `associate-l/`
2×	`sub-neg` `pow-pow` `associate-l` `pow-prod-down` `*-commutative` `sqr-pow`
1×	`distribute-rgt-in` `frac-times` `flip3--` `distribute-lft-in` `flip--`

Counts

4 → 174

Calls

4 calls:

15.0ms	(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
12.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
5.0ms	(pow (/ d h) (/ 1.0 2.0))
5.0ms	(pow (/ d l) (/ 1.0 2.0))

series525.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

270.0ms	(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
228.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
14.0ms	(pow (/ d h) (/ 1.0 2.0))
13.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify54.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5441	3690

prune847.0ms (3.6%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	164	22	186
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	166	22	188

Merged error: 10.6b

Counts

188 → 22

localize43.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.2b	(pow (/ (cbrt d) h) (/ 1.0 2.0))
6.6b	(* (* (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
10.4b	(pow (/ d l) (/ 1.0 2.0))
12.6b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite64.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

425×	`add-exp-log`
291×	`prod-exp`
122×	`pow-exp`
80×	`div-exp`
55×	`pow-to-exp`
54×	`times-frac`
46×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
35×	`unpow-prod-down`
34×	`add-cbrt-cube`
26×	`pow-unpow`
16×	`associate-r` `cbrt-unprod`
10×	`pow1`
9×	`cbrt-prod`
5×	`cbrt-undiv` `div-inv`
4×	`add-log-exp`
3×	`associate-r/` `associate-l/`
2×	`sub-neg` `pow-pow` `associate-l` `pow-prod-down` `*-commutative` `sqr-pow`
1×	`distribute-rgt-in` `frac-times` `flip3--` `distribute-lft-in` `flip--`

Counts

4 → 236

Calls

4 calls:

23.0ms	(* (* (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
14.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
7.0ms	(pow (/ (cbrt d) h) (/ 1.0 2.0))
5.0ms	(pow (/ d l) (/ 1.0 2.0))

series599.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

321.0ms	(* (* (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
229.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
35.0ms	(pow (/ (cbrt d) h) (/ 1.0 2.0))
14.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify87.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5028	6482

prune1.4s (6%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	238	10	248
Fresh	3	18	21
Picked	1	0	1
Done	0	0	0
Total	242	28	270

Merged error: 10.0b

Counts

270 → 28

localize59.0ms (0.3%)

Local error

Found 4 expressions with local error:

3.2b	(pow (/ (cbrt d) h) (/ 1.0 2.0))
3.3b	(pow (/ d (cbrt l)) (/ 1.0 2.0))
6.6b	(* (* (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
12.6b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite197.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

3520×	`add-exp-log`
2889×	`prod-exp`
1398×	`pow-exp`
620×	`div-exp`
523×	`pow-to-exp`
136×	`rec-exp` `1-exp`
63×	`times-frac`
52×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
44×	`unpow-prod-down`
43×	`add-cbrt-cube`
26×	`pow-unpow`
23×	`cbrt-unprod`
18×	`cbrt-prod`
16×	`associate-r`
13×	`pow1`
5×	`cbrt-undiv` `div-inv`
4×	`pow-prod-down` `add-log-exp`
3×	`associate-r/` `associate-l/`
2×	`sub-neg` `pow-pow` `associate-l` `*-commutative` `sqr-pow`
1×	`distribute-rgt-in` `frac-times` `flip3--` `distribute-lft-in` `flip--`

Counts

4 → 809

Calls

4 calls:

57.0ms	(* (* (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
12.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
7.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
7.0ms	(pow (/ (cbrt d) h) (/ 1.0 2.0))

series590.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

285.0ms	(* (* (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
233.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
37.0ms	(pow (/ (cbrt d) h) (/ 1.0 2.0))
35.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))

simplify240.0ms (1%)

Algorithm

1×	egg-herbie

Counts

821 → 821

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	5004	34585

prune5.1s (21.8%)

Pruning

32 alts after pruning (32 fresh and 0 done)

	Pruned	Kept	Total
New	814	7	821
Fresh	2	25	27
Picked	1	0	1
Done	0	0	0
Total	817	32	849

Merged error: 9.3b

Counts

849 → 32

localize60.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.9b	(/ (* M D) (* 2.0 d))
3.2b	(pow (/ (cbrt d) h) (/ 1.0 2.0))
6.6b	(* (* (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
12.6b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite171.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

3061×	`add-exp-log`
2393×	`prod-exp`
1064×	`pow-exp`
557×	`div-exp`
424×	`pow-to-exp`
55×	`add-cbrt-cube`
37×	`times-frac`
32×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
27×	`cbrt-unprod`
22×	`unpow-prod-down`
16×	`associate-r`
13×	`pow-unpow`
12×	`pow1`
9×	`cbrt-undiv` `cbrt-prod`
4×	`pow-prod-down` `div-inv` `add-log-exp`
3×	`associate-r/` `associate-l/`
2×	`sub-neg` `associate-l` `*-commutative`
1×	`distribute-rgt-in` `frac-times` `flip3--` `pow-pow` `frac-2neg` `distribute-lft-in` `clear-num` `associate-/r` `flip--` `associate-/l` `sqr-pow`

Counts

4 → 647

Calls

4 calls:

53.0ms	(* (* (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
12.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
7.0ms	(pow (/ (cbrt d) h) (/ 1.0 2.0))
5.0ms	(/ (* M D) (* 2.0 d))

series821.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

449.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
328.0ms	(* (* (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
35.0ms	(pow (/ (cbrt d) h) (/ 1.0 2.0))
8.0ms	(/ (* M D) (* 2.0 d))

simplify192.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

659 → 659

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	5140	26184

prune3.2s (13.7%)

Pruning

33 alts after pruning (32 fresh and 1 done)

	Pruned	Kept	Total
New	657	2	659
Fresh	1	30	31
Picked	0	1	1
Done	0	0	0
Total	658	33	691

Merged error: 9.3b

Counts

691 → 33

regimes2.1s (9%)

Accuracy

Total 6.0b remaining (38.4%)

Threshold costs 0b (0%)

bsearch286.0ms (1.2%)

Steps

Iters	Range		Point
7	4.581554567918593e-51	1.9584742320092106e-49	1.2357718989279625e-49
6	-1.3393951792766152e+31	-1.2486150746478509e+30	-1.5282400649379168e+30

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	153	137
1	153	137

end0.0ms (0%)

sample4.5s (19.3%)

Algorithm

1×

intervals

Results

1.5s	8000×	body	80	valid
1.3s	8455×	body	80	nan
927.0ms	4900×	body	80	invalid

Details

analyze2.0s (8.4%)

sample158.0ms (0.7%)

simplify20.0ms (0.1%)

prune18.0ms (0.1%)

localize35.0ms (0.1%)

rewrite46.0ms (0.2%)

series525.0ms (2.2%)

simplify54.0ms (0.2%)

prune847.0ms (3.6%)

localize43.0ms (0.2%)

rewrite64.0ms (0.3%)

series599.0ms (2.5%)

simplify87.0ms (0.4%)

prune1.4s (6%)

localize59.0ms (0.3%)

rewrite197.0ms (0.8%)

series590.0ms (2.5%)

simplify240.0ms (1%)

prune5.1s (21.8%)

localize60.0ms (0.3%)

rewrite171.0ms (0.7%)

series821.0ms (3.5%)

simplify192.0ms (0.8%)

prune3.2s (13.7%)

regimes2.1s (9%)

bsearch286.0ms (1.2%)

simplify3.0ms (0%)

end0.0ms (0%)

sample4.5s (19.3%)

Profiling