Details

analyze618.0ms (9.3%)

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
49.9%	49.9%	0.2%	3
49.9%	49.9%	0.2%	4
49.9%	49.9%	0.2%	5
49.9%	49.9%	0.2%	6
74.9%	25%	0.2%	7
74.9%	25%	0.2%	8
74.9%	25%	0.2%	9
74.9%	25%	0.2%	10
87.3%	12.5%	0.2%	11
87.3%	12.5%	0.2%	12
87.3%	12.5%	0.2%	13
87.3%	12.5%	0.2%	14

sample104.0ms (1.6%)

Algorithm

1×

intervals

Results

35.0ms	199×	body	80	valid
31.0ms	25×	body	1280	valid
15.0ms	19×	body	640	valid
5.0ms	8×	body	320	valid
2.0ms	5×	body	160	valid

simplify57.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4882	29
1	4882	29

prune12.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 1.3b

Counts

2 → 1

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(pow (sin ky) 2.0)
0.4b	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
2.2b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.2b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
26×	`add-cube-cbrt`
21×	`times-frac`
19×	`add-exp-log`
15×	`sqrt-prod`
13×	`unpow-prod-down`
11×	`associate-l`
8×	`add-cbrt-cube`
6×	`pow1` `prod-exp` `associate-/r*`
5×	`associate-r`
4×	`sqrt-div` `pow-exp` `add-log-exp`
3×	`pow-unpow` `flip3-+` `div-exp` `flip-+` `associate-/l*` `unswap-sqr` `sqr-pow`
2×	`pow-to-exp` `associate-*r/` `associate-/r/` `div-inv` `distribute-lft-out`
1×	`cbrt-undiv` `distribute-rgt-in` `rem-sqrt-square` `pow-pow` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `clear-num` `*-commutative` `cbrt-unprod`

Counts

4 → 110

Calls

4 calls:

14.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
6.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
6.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.0ms	(pow (sin ky) 2.0)

series418.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

162.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
130.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
108.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
18.0ms	(pow (sin ky) 2.0)

simplify60.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4958	2674
1	4958	2674

prune465.0ms (7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	121	2	123

Merged error: 1.0b

Counts

123 → 2

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(pow (* (/ 2.0 Om) l) 2.0)
0.2b	(pow (sin ky) 2.0)
1.4b	(log (pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
2.0b	(pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity`
13×	`unpow-prod-down`
12×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt`
11×	`pow-unpow`
9×	`pow1` `pow-pow`
8×	`log-prod`
6×	`pow-exp`
5×	`exp-prod` `sqr-pow`
4×	`pow-to-exp` `add-cbrt-cube` `add-log-exp`
3×	`rem-log-exp`
2×	`unpow-prod-up` `prod-exp` `distribute-lft-out`
1×	`div-exp` `pow-prod-down` `log-pow`

Counts

4 → 79

Calls

4 calls:

11.0ms	(pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
6.0ms	(pow (* (/ 2.0 Om) l) 2.0)
5.0ms	(log (pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.0ms	(pow (sin ky) 2.0)

series156.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

62.0ms	(log (pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
60.0ms	(pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
20.0ms	(pow (sin ky) 2.0)
14.0ms	(pow (* (/ 2.0 Om) l) 2.0)

simplify41.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4953	1342
1	4953	1342

prune345.0ms (5.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	91	2	93

Merged error: 1.0b

Counts

93 → 2

regimes1.3s (18.8%)

Accuracy

Total 0.4b remaining (34.2%)

Threshold costs 0.4b (34.2%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	29
1	28	29

end0.0ms (0%)

sample3.0s (45.5%)

Algorithm

1×

intervals

Results

1.1s	6219×	body	80	valid
837.0ms	589×	body	1280	valid
525.0ms	626×	body	640	valid
229.0ms	376×	body	320	valid
76.0ms	190×	body	160	valid

Details

analyze618.0ms (9.3%)

sample104.0ms (1.6%)

simplify57.0ms (0.9%)

prune12.0ms (0.2%)

localize25.0ms (0.4%)

rewrite33.0ms (0.5%)

series418.0ms (6.3%)

simplify60.0ms (0.9%)

prune465.0ms (7%)

localize27.0ms (0.4%)

rewrite27.0ms (0.4%)

series156.0ms (2.3%)

simplify41.0ms (0.6%)

prune345.0ms (5.2%)

regimes1.3s (18.8%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample3.0s (45.5%)

Profiling