Details

analyze6.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.7%	50.3%	0
0%	49.7%	50.3%	1
0%	49.7%	50.3%	2
24.8%	24.8%	50.3%	3
37.3%	12.4%	50.3%	4
43.5%	6.2%	50.3%	5
46.6%	3.1%	50.3%	6
48.1%	1.6%	50.3%	7
48.9%	0.8%	50.3%	8
49.3%	0.4%	50.3%	9
49.5%	0.2%	50.3%	10
49.6%	0.1%	50.3%	11
49.6%	0%	50.3%	12
49.7%	0%	50.3%	13
49.7%	0%	50.3%	14

sample232.0ms (2.4%)

Algorithm

1×

intervals

Results

162.0ms	102×	body	2560	valid
48.0ms	82×	body	1280	valid
7.0ms	38×	body	640	valid
4.0ms	256×	pre	80	true
2.0ms	18×	body	320	valid
1.0ms	14×	body	160	valid
0.0ms	2×	body	80	valid

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	220	8
1	220	8

prune5.0ms (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: 59.9b

Counts

2 → 1

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
3.4b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
19×	`times-frac`
12×	`add-cube-cbrt`
5×	`distribute-lft-out--`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
3×	`associate-/r` `div-inv` `associate-/l`
2×	`pow1`
1×	`tan-quot` `cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `associate-/r/` `frac-sub` `flip--`

Counts

2 → 49

Calls

2 calls:

13.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))
3.0ms	(/ 1.0 (tan x))

series30.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

20.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))
11.0ms	(/ 1.0 (tan x))

simplify50.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4916	556
1	4916	556

prune98.0ms (1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	1	56

Merged error: 0.3b

Counts

56 → 1

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))
0.0b	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
0.1b	(* 0.0021164021164021165 (pow x 5))
0.1b	(* 0.022222222222222223 (pow x 3))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`associate-r`
14×	`add-exp-log`
11×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `cube-prod` `sum-log` `sqr-pow`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`cube-mult` `associate-+r+` `unpow3`

Counts

4 → 80

Calls

4 calls:

8.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
8.0ms	(* 0.022222222222222223 (pow x 3))
5.0ms	(* 0.0021164021164021165 (pow x 5))
4.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))

series26.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))
6.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
4.0ms	(* 0.0021164021164021165 (pow x 5))
4.0ms	(* 0.022222222222222223 (pow x 3))

simplify60.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4959	885
1	4959	885

prune203.0ms (2.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	88	4	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	88	5	93

Merged error: 0.2b

Counts

93 → 5

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
0.7b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
0.7b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
0.7b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

12.0ms	(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
4.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
4.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
4.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))

series230.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
58.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
56.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
55.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))

simplify48.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4987	2218
1	4987	2218

prune567.0ms (5.9%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	91	8	99
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	91	13	104

Merged error: 0.1b

Counts

104 → 13

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
0.7b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
0.7b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
0.7b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

5.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
4.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
4.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
4.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))

series228.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

57.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
57.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
57.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
56.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))

simplify40.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5236	1372

prune462.0ms (4.8%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	63	14	77

Merged error: 0.1b

Counts

77 → 14

regimes107.0ms (1.1%)

Accuracy

Total 0.2b remaining (58.9%)

Threshold costs 0.2b (58.9%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	15
1	18	15

end0.0ms (0%)

sample7.1s (73.7%)

Algorithm

1×

intervals

Results

5.2s	3225×	body	2560	valid
1.3s	2504×	body	1280	valid
241.0ms	1265×	body	640	valid
131.0ms	8000×	pre	80	true
77.0ms	643×	body	320	valid
27.0ms	316×	body	160	valid
2.0ms	47×	body	80	valid

Details

analyze6.0ms (0.1%)

sample232.0ms (2.4%)

simplify10.0ms (0.1%)

prune5.0ms (0.1%)

localize6.0ms (0.1%)

rewrite18.0ms (0.2%)

series30.0ms (0.3%)

simplify50.0ms (0.5%)

prune98.0ms (1%)

localize10.0ms (0.1%)

rewrite28.0ms (0.3%)

series26.0ms (0.3%)

simplify60.0ms (0.6%)

prune203.0ms (2.1%)

localize15.0ms (0.2%)

rewrite27.0ms (0.3%)

series230.0ms (2.4%)

simplify48.0ms (0.5%)

prune567.0ms (5.9%)

localize21.0ms (0.2%)

rewrite19.0ms (0.2%)

series228.0ms (2.4%)

simplify40.0ms (0.4%)

prune462.0ms (4.8%)

regimes107.0ms (1.1%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample7.1s (73.7%)

Profiling