Details

analyze504.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
37.5%	62.5%	0%	4
43.7%	56.2%	0%	5
46.9%	53.1%	0%	6
48.4%	51.5%	0%	7
49.2%	50.8%	0%	8
49.6%	50.4%	0%	9
49.8%	50.2%	0%	10
49.9%	50.1%	0%	11
49.9%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

sample138.0ms

Algorithm

intervals

Results

65.0ms	47×	body	2560	valid
37.0ms	80×	body	1280	valid
15.0ms	59×	body	640	valid
7.0ms	40×	body	320	valid
2.0ms	16×	body	160	valid
1.0ms	14×	body	80	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	229	7
1	229	7

prune3.0ms

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: 27.3b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.8b	(- 1.0 (cos x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 51

Calls

2 calls:

6.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

series12.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

simplify36.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5058	605

prune135.0ms

Filtered

42 candidates to 57 candidates (-35.7%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	39	18	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	18	58

Merged error: 0.3b

Counts

58 → 18

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.3b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.8b	(- 1.0 (cos x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`log-prod`
25×	`exp-sum`
24×	`add-cube-cbrt` `times-frac`
8×	`associate-/l*`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `add-exp-log` `log-div` `add-cbrt-cube` `add-log-exp`
4×	`exp-prod` `flip3--` `exp-diff` `flip--`
3×	`associate-/r*`
2×	`log-pow` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `div-inv` `rem-exp-log`

Counts

4 → 97

Calls

4 calls:

7.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
4.0ms	(exp (log (- 1.0 (cos x))))
3.0ms	(log (- 1.0 (cos x)))
5.0ms	(- 1.0 (cos x))

series26.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
3.0ms	(exp (log (- 1.0 (cos x))))
12.0ms	(log (- 1.0 (cos x)))
3.0ms	(- 1.0 (cos x))

simplify63.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4878	1087
1	4878	1087

prune164.0ms

Filtered

60 candidates to 109 candidates (-81.7%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	98	11	109
Fresh	8	9	17
Picked	1	0	1
Done	0	0	0
Total	107	20	127

Merged error: 0.2b

Counts

127 → 20

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.3b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.3b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.8b	(- 1.0 (cos x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
38×	`exp-prod`
33×	`add-cube-cbrt`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
3×	`log-prod` `div-sub` `associate-/r*` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 111

Calls

4 calls:

6.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
7.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
4.0ms	(- 1.0 (cos x))

series32.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
13.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
8.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms	(- 1.0 (cos x))

simplify46.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5525	1215

prune216.0ms

Filtered

88 candidates to 123 candidates (-39.8%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	115	8	123
Fresh	7	12	19
Picked	0	1	1
Done	0	0	0
Total	122	21	143

Merged error: 0.2b

Counts

143 → 21

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sin x))
0.2b	(/ (cos x) (sin x))
1.9b	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
28×	`times-frac`
21×	`add-cube-cbrt`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
5×	`add-log-exp`
4×	`div-inv` `distribute-lft-out--` `difference-of-squares`
3×	`pow1`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `diff-log` `frac-sub` `flip--` `sub-div`

Counts

3 → 76

Calls

3 calls:

3.0ms	(/ 1.0 (sin x))
4.0ms	(/ (cos x) (sin x))
13.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

series26.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(/ 1.0 (sin x))
6.0ms	(/ (cos x) (sin x))
15.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

simplify77.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4880	864
1	4880	864

prune83.0ms

Filtered

66 candidates to 85 candidates (-28.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	82	3	85
Fresh	8	11	19
Picked	1	0	1
Done	0	1	1
Total	91	15	106

Merged error: 0.1b

Counts

106 → 15

regimes228.0ms

Accuracy

98.3% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 30.4b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	45
1	44	45

end0.0ms

sample4.6s

Algorithm

intervals

Results

2.3s	1623×	body	2560	valid
1.3s	2736×	body	1280	valid
491.0ms	1848×	body	640	valid
176.0ms	918×	body	320	valid
61.0ms	488×	body	160	valid
28.0ms	380×	body	80	valid
24.0ms	7×	body	5120	valid

Details

analyze504.0ms

sample138.0ms

simplify11.0ms

prune3.0ms

localize7.0ms

rewrite11.0ms

series12.0ms

simplify36.0ms

prune135.0ms

localize11.0ms

rewrite24.0ms

series26.0ms

simplify63.0ms

prune164.0ms

localize11.0ms

rewrite26.0ms

series32.0ms

simplify46.0ms

prune216.0ms

localize10.0ms

rewrite22.0ms

series26.0ms

simplify77.0ms

prune83.0ms

regimes228.0ms

bsearch1.0ms

simplify1.0ms

end0.0ms

sample4.6s

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