Details

analyze710.0ms

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

sample214.0ms

Algorithm

intervals

Results

74.0ms	49×	body	5120	exit
51.0ms	102×	body	1280	valid
29.0ms	87×	body	640	valid
16.0ms	41×	body	1280	nan
13.0ms	33×	body	640	nan
8.0ms	32×	body	320	valid
4.0ms	19×	body	320	nan
3.0ms	19×	body	160	valid
2.0ms	14×	body	160	nan
2.0ms	16×	body	80	valid
0.0ms	6×	body	80	nan

simplify81.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4797	9
1	4797	9

prune11.0ms

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: 59.3b

Counts

2 → 2

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (cos x))
0.3b	(/ (fmod (exp x) (sqrt (cos x))) (exp x))
4.8b	(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)))

series10.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify55.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5687	564

prune76.0ms

Filtered

40 candidates to 56 candidates (-40.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	52	4	56
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	53	5	58

Merged error: 59.2b

Counts

58 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (- (log (fmod (exp x) (sqrt (cos x)))) x))
2.2b	(- (log (fmod (exp x) (sqrt (cos x)))) x)
3.2b	(log (fmod (exp x) (sqrt (cos x))))
4.8b	(fmod (exp x) (sqrt (cos x)))

rewrite13.0ms

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

series41.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(exp (- (log (fmod (exp x) (sqrt (cos x)))) x))
20.0ms	(- (log (fmod (exp x) (sqrt (cos x)))) x)
16.0ms	(log (fmod (exp x) (sqrt (cos x))))
1.0ms	(fmod (exp x) (sqrt (cos x)))

simplify60.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4902	681
1	4902	681

prune76.0ms

Filtered

44 candidates to 68 candidates (-54.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	68	5	73

Merged error: 59.2b

Counts

73 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (cos x)))
0.1b	(* (sqrt (sqrt (cos x))) (sqrt (sqrt (cos x))))
0.3b	(/ (fmod (exp x) (* (sqrt (sqrt (cos x))) (sqrt (sqrt (cos x))))) (exp x))
4.8b	(fmod (exp x) (* (sqrt (sqrt (cos x))) (sqrt (sqrt (cos x)))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

76×	`sqrt-prod`
58×	`add-sqr-sqrt`
36×	`sqrt-pow1`
29×	`pow1`
26×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1/2`
15×	`swap-sqr`
9×	`times-frac` `associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
8×	`add-cbrt-cube`
7×	`add-exp-log`
5×	`pow-prod-down` `pow-sqr`
4×	`add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`rem-sqrt-square`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 128

Calls

4 calls:

2.0ms	(sqrt (sqrt (cos x)))
11.0ms	(* (sqrt (sqrt (cos x))) (sqrt (sqrt (cos x))))
4.0ms	(/ (fmod (exp x) (* (sqrt (sqrt (cos x))) (sqrt (sqrt (cos x))))) (exp x))
1.0ms	(fmod (exp x) (* (sqrt (sqrt (cos x))) (sqrt (sqrt (cos x)))))

series28.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(sqrt (sqrt (cos x)))
3.0ms	(* (sqrt (sqrt (cos x))) (sqrt (sqrt (cos x))))
6.0ms	(/ (fmod (exp x) (* (sqrt (sqrt (cos x))) (sqrt (sqrt (cos x))))) (exp x))
2.0ms	(fmod (exp x) (* (sqrt (sqrt (cos x))) (sqrt (sqrt (cos x)))))

simplify68.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4880	996
1	4880	996

prune98.0ms

Filtered

67 candidates to 140 candidates (-109.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	140	5	145

Merged error: 59.2b

Counts

145 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (cos x))
0.3b	(/ (fmod (exp x) (sqrt (cos x))) (exp x))
2.6b	(log (exp (/ (fmod (exp x) (sqrt (cos x))) (exp x))))
4.8b	(fmod (exp x) (sqrt (cos x)))

rewrite13.0ms

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:

2.0ms	(sqrt (cos x))
4.0ms	(/ (fmod (exp x) (sqrt (cos x))) (exp x))
5.0ms	(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:

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

simplify78.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4843	892
1	4843	892

prune88.0ms

Filtered

63 candidates to 84 candidates (-33.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	83	6	89

Merged error: 59.2b

Counts

89 → 6

regimes102.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10

end0.0ms

sample6.5s

Algorithm

intervals

Results

2.4s	1560×	body	5120	exit
1.7s	3167×	body	1280	valid
857.0ms	2540×	body	640	valid
467.0ms	1121×	body	1280	nan
293.0ms	1226×	body	320	valid
292.0ms	996×	body	640	nan
105.0ms	528×	body	320	nan
94.0ms	577×	body	160	valid
45.0ms	490×	body	80	valid
33.0ms	244×	body	160	nan
18.0ms	228×	body	80	nan

Details

analyze710.0ms

sample214.0ms

simplify81.0ms

prune11.0ms

localize8.0ms

rewrite7.0ms

series10.0ms

simplify55.0ms

prune76.0ms

localize11.0ms

rewrite13.0ms

series41.0ms

simplify60.0ms

prune76.0ms

localize11.0ms

rewrite22.0ms

series28.0ms

simplify68.0ms

prune98.0ms

localize11.0ms

rewrite13.0ms

series16.0ms

simplify78.0ms

prune88.0ms

regimes102.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample6.5s

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