Details

analyze685.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
50%	50%	0%	6
50%	50%	0%	7
50%	50%	0%	8
50%	50%	0%	9
50%	50%	0%	10
50%	50%	0%	11
50%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0.1%	14

sample219.0ms

Algorithm

intervals

Results

84.0ms	54×	body	5120	exit
52.0ms	103×	body	1280	valid
29.0ms	85×	body	640	valid
16.0ms	42×	body	1280	nan
10.0ms	37×	body	640	nan
7.0ms	33×	body	320	valid
3.0ms	17×	body	320	nan
3.0ms	18×	body	160	valid
1.0ms	17×	body	80	valid
1.0ms	6×	body	160	nan
1.0ms	9×	body	80	nan

simplify80.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4797	9
1	4797	9

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 60.2b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (cos x))
0.5b	(/ (fmod (exp x) (sqrt (cos x))) (exp x))
4.7b	(fmod (exp x) (sqrt (cos x)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
5×	`add-cbrt-cube`
4×	`pow1` `add-exp-log`
3×	`associate-/r` `sqrt-prod` `associate-/l` `add-log-exp`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

3 → 47

Calls

3 calls:

1.0ms	(sqrt (cos x))
4.0ms	(/ (fmod (exp x) (sqrt (cos x))) (exp x))
1.0ms	(fmod (exp x) (sqrt (cos x)))

series12.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(sqrt (cos x))
6.0ms	(/ (fmod (exp x) (sqrt (cos x))) (exp x))
2.0ms	(fmod (exp x) (sqrt (cos x)))

simplify54.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5687	564

prune75.0ms

Filtered

41 candidates to 56 candidates (-36.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	52	4	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	4	57

Merged error: 60.2b

Counts

57 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (sqrt (cos x)) 3)
0.1b	(cbrt (pow (sqrt (cos x)) 3))
0.5b	(/ (fmod (exp x) (cbrt (pow (sqrt (cos x)) 3))) (exp x))
4.7b	(fmod (exp x) (cbrt (pow (sqrt (cos x)) 3)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`cbrt-prod`
12×	`unpow-prod-down` `cube-prod` `sqrt-prod`
9×	`times-frac`
7×	`add-cbrt-cube`
6×	`pow1` `add-exp-log`
4×	`add-log-exp`
3×	`pow-unpow` `pow-pow` `associate-/r` `associate-/l`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `sqrt-pow1` `pow1/2` `pow1/3` `div-exp` `pow-exp` `clear-num` `sqrt-pow2` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 93

Calls

4 calls:

3.0ms	(pow (sqrt (cos x)) 3)
3.0ms	(cbrt (pow (sqrt (cos x)) 3))
4.0ms	(/ (fmod (exp x) (cbrt (pow (sqrt (cos x)) 3))) (exp x))
1.0ms	(fmod (exp x) (cbrt (pow (sqrt (cos x)) 3)))

series17.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(pow (sqrt (cos x)) 3)
3.0ms	(cbrt (pow (sqrt (cos x)) 3))
6.0ms	(/ (fmod (exp x) (cbrt (pow (sqrt (cos x)) 3))) (exp x))
2.0ms	(fmod (exp x) (cbrt (pow (sqrt (cos x)) 3)))

simplify89.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4914	867
1	4914	867

prune104.0ms

Filtered

57 candidates to 105 candidates (-84.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	105	4	109

Merged error: 60.1b

Counts

109 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (exp x) (cbrt (fmod (exp x) (sqrt (cos x)))))
4.7b	(fmod (exp x) (cbrt (pow (sqrt (cos x)) 3)))
4.7b	(fmod (exp x) (cbrt (pow (sqrt (cos x)) 3)))
4.7b	(fmod (exp x) (sqrt (cos x)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
12×	`cbrt-prod`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 60

Calls

4 calls:

5.0ms	(/ (exp x) (cbrt (fmod (exp x) (sqrt (cos x)))))
1.0ms	(fmod (exp x) (cbrt (pow (sqrt (cos x)) 3)))
1.0ms	(fmod (exp x) (cbrt (pow (sqrt (cos x)) 3)))
1.0ms	(fmod (exp x) (sqrt (cos x)))

series36.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (exp x) (cbrt (fmod (exp x) (sqrt (cos x)))))
1.0ms	(fmod (exp x) (cbrt (pow (sqrt (cos x)) 3)))
1.0ms	(fmod (exp x) (cbrt (pow (sqrt (cos x)) 3)))
1.0ms	(fmod (exp x) (sqrt (cos x)))

simplify48.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4921	948
1	4921	948

prune201.0ms

Filtered

59 candidates to 72 candidates (-22.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	71	5	76

Merged error: 60.1b

Counts

76 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (pow (exp x) 3) (fmod (exp x) (sqrt (cos x))))
4.7b	(fmod (exp x) (sqrt (cos x)))
4.7b	(fmod (exp x) (cbrt (pow (sqrt (cos x)) 3)))
4.7b	(fmod (exp x) (cbrt (pow (sqrt (cos x)) 3)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
29×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down` `cube-prod` `associate-/l*`
8×	`add-exp-log`
6×	`add-cbrt-cube`
4×	`pow1` `cube-mult` `unpow3` `add-log-exp` `sqr-pow`
3×	`div-exp` `associate-/r*`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv`

Counts

4 → 86

Calls

4 calls:

6.0ms	(/ (pow (exp x) 3) (fmod (exp x) (sqrt (cos x))))
1.0ms	(fmod (exp x) (sqrt (cos x)))
1.0ms	(fmod (exp x) (cbrt (pow (sqrt (cos x)) 3)))
1.0ms	(fmod (exp x) (cbrt (pow (sqrt (cos x)) 3)))

series20.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ (pow (exp x) 3) (fmod (exp x) (sqrt (cos x))))
1.0ms	(fmod (exp x) (sqrt (cos x)))
1.0ms	(fmod (exp x) (cbrt (pow (sqrt (cos x)) 3)))
2.0ms	(fmod (exp x) (cbrt (pow (sqrt (cos x)) 3)))

simplify67.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5106	1432

prune222.0ms

Filtered

61 candidates to 98 candidates (-60.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	100	3	103

Merged error: 60.1b

Counts

103 → 3

regimes35.0ms

Accuracy

0% (0.0b remaining)

Error of 59.5b against oracle of 59.5b and baseline of 59.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	35
1	28	35

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.2s	1511×	body	5120	exit
1.6s	3152×	body	1280	valid
821.0ms	2465×	body	640	valid
461.0ms	1191×	body	1280	nan
281.0ms	1238×	body	320	valid
266.0ms	973×	body	640	nan
106.0ms	525×	body	320	nan
100.0ms	635×	body	160	valid
45.0ms	510×	body	80	valid
32.0ms	248×	body	160	nan
21.0ms	226×	body	80	nan

Details

analyze685.0ms

sample219.0ms

simplify80.0ms

prune7.0ms

localize8.0ms

rewrite7.0ms

series12.0ms

simplify54.0ms

prune75.0ms

localize11.0ms

rewrite13.0ms

series17.0ms

simplify89.0ms

prune104.0ms

localize18.0ms

rewrite8.0ms

series36.0ms

simplify48.0ms

prune201.0ms

localize20.0ms

rewrite10.0ms

series20.0ms

simplify67.0ms

prune222.0ms

regimes35.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample6.2s

Profiling