Details

analyze665.0ms

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

sample195.0ms

Algorithm

intervals

Results

70.0ms	48×	body	5120	exit
51.0ms	109×	body	1280	valid
21.0ms	68×	body	640	valid
14.0ms	30×	body	1280	nan
10.0ms	49×	body	320	valid
8.0ms	32×	body	640	nan
3.0ms	19×	body	320	nan
2.0ms	15×	body	160	valid
1.0ms	11×	body	160	nan
1.0ms	15×	body	80	valid
1.0ms	10×	body	80	nan

simplify79.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4797	9
1	4797	9

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 59.5b

Counts

2 → 2

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (fmod (exp x) (sqrt (cos x))) (exp x))
0.1b	(sqrt (cos x))
4.6b	(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:

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

series10.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(/ (fmod (exp x) (sqrt (cos x))) (exp x))
3.0ms	(sqrt (cos x))
1.0ms	(fmod (exp x) (sqrt (cos x)))

simplify53.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5687	564

prune73.0ms

Filtered

40 candidates to 56 candidates (-40.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	51	5	56
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	53	5	58

Merged error: 59.5b

Counts

58 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (cos x))
0.1b	(cbrt (pow (sqrt (cos x)) 3))
0.2b	(pow (sqrt (cos x)) 3)
4.6b	(fmod (exp x) (cbrt (pow (sqrt (cos x)) 3)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
12×	`unpow-prod-down` `cube-prod`
7×	`pow1`
5×	`add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-unpow` `pow-pow`
2×	`cube-mult` `sqrt-pow1` `pow1/2` `unpow3` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `pow1/3` `pow-exp` `sqrt-pow2` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 79

Calls

4 calls:

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

series14.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify67.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4909	521
1	4909	521

prune91.0ms

Filtered

46 candidates to 91 candidates (-97.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	91	5	96

Merged error: 59.5b

Counts

96 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (fmod (exp x) (sqrt (cos x))) (exp x))
0.1b	(sqrt (cos x))
3.6b	(log (exp (/ (fmod (exp x) (sqrt (cos x))) (exp x))))
4.6b	(fmod (exp x) (sqrt (cos x)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

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

series16.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ (fmod (exp x) (sqrt (cos x))) (exp x))
3.0ms	(sqrt (cos x))
6.0ms	(log (exp (/ (fmod (exp x) (sqrt (cos x))) (exp x))))
1.0ms	(fmod (exp x) (sqrt (cos x)))

simplify72.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4843	892
1	4843	892

prune100.0ms

Filtered

63 candidates to 84 candidates (-33.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	3	3
Picked	0	1	1
Done	1	0	1
Total	84	5	89

Merged error: 59.5b

Counts

89 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (- (log (fmod (exp x) (sqrt (cos x)))) x))
1.0b	(log (fmod (exp x) (sqrt (cos x))))
1.7b	(- (log (fmod (exp x) (sqrt (cos x)))) x)
4.6b	(fmod (exp x) (sqrt (cos x)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
9×	`log-prod`
8×	`add-cube-cbrt`
7×	`pow1` `add-log-exp`
6×	`exp-prod` `associate--l+`
5×	`add-exp-log`
4×	`exp-sum` `add-cbrt-cube` `distribute-lft-out--`
3×	`log-pow`
2×	`sub-neg` `diff-log` `rem-exp-log` `difference-of-squares`
1×	`flip3--` `exp-diff` `rem-log-exp` `flip--`

Counts

4 → 56

Calls

4 calls:

5.0ms	(exp (- (log (fmod (exp x) (sqrt (cos x)))) x))
1.0ms	(log (fmod (exp x) (sqrt (cos x))))
4.0ms	(- (log (fmod (exp x) (sqrt (cos x)))) x)
1.0ms	(fmod (exp x) (sqrt (cos x)))

series42.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(exp (- (log (fmod (exp x) (sqrt (cos x)))) x))
17.0ms	(log (fmod (exp x) (sqrt (cos x))))
19.0ms	(- (log (fmod (exp x) (sqrt (cos x)))) x)
1.0ms	(fmod (exp x) (sqrt (cos x)))

simplify57.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4902	681
1	4902	681

prune63.0ms

Filtered

45 candidates to 68 candidates (-51.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	68	5	73

Merged error: 59.5b

Counts

73 → 5

regimes37.0ms

Accuracy

0% (0.0b remaining)

Error of 59.7b against oracle of 59.6b and baseline of 59.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	8	11

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.3s	1556×	body	5120	exit
1.5s	3104×	body	1280	valid
819.0ms	2537×	body	640	valid
436.0ms	1144×	body	1280	nan
272.0ms	1253×	body	320	valid
247.0ms	958×	body	640	nan
95.0ms	643×	body	160	valid
88.0ms	480×	body	320	nan
40.0ms	463×	body	80	valid
32.0ms	256×	body	160	nan
19.0ms	254×	body	80	nan

Details

analyze665.0ms

sample195.0ms

simplify79.0ms

prune9.0ms

localize8.0ms

rewrite7.0ms

series10.0ms

simplify53.0ms

prune73.0ms

localize10.0ms

rewrite10.0ms

series14.0ms

simplify67.0ms

prune91.0ms

localize10.0ms

rewrite12.0ms

series16.0ms

simplify72.0ms

prune100.0ms

localize10.0ms

rewrite12.0ms

series42.0ms

simplify57.0ms

prune63.0ms

regimes37.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample6.1s

Profiling