Details

analyze500.0ms

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

sample141.0ms

Algorithm

intervals

Results

67.0ms	48×	body	2560	valid
40.0ms	87×	body	1280	valid
19.0ms	63×	body	640	valid
5.0ms	28×	body	320	valid
2.0ms	18×	body	160	valid
1.0ms	12×	body	80	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

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: 28.2b

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))

series10.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

simplify36.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5058	605

prune126.0ms

Filtered

42 candidates to 57 candidates (-35.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	43	14	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	14	58

Merged error: 0.2b

Counts

58 → 14

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.4b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.1b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.8b	(- 1.0 (cos x))

rewrite27.0ms

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))

series29.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
11.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
7.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms	(- 1.0 (cos x))

simplify49.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5525	1215

prune194.0ms

Filtered

89 candidates to 123 candidates (-38.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	118	5	123
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	124	13	137

Merged error: 0.2b

Counts

137 → 13

localize9.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin x) (- 1.0 (cos x)))
0.2b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
1.8b	(- 1.0 (cos x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
105×	`add-sqr-sqrt` `*-un-lft-identity`
71×	`add-cube-cbrt`
26×	`associate-/r*`
17×	`distribute-lft-out--` `difference-of-squares`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`flip3--` `flip--` `div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`sub-neg` `pow-flip` `diff-log` `inv-pow`

Counts

3 → 158

Calls

3 calls:

6.0ms	(/ (sin x) (- 1.0 (cos x)))
8.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
4.0ms	(- 1.0 (cos x))

series21.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(/ (sin x) (- 1.0 (cos x)))
7.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
3.0ms	(- 1.0 (cos x))

simplify57.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5093	2252

prune194.0ms

Filtered

99 candidates to 167 candidates (-68.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	164	3	167
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	166	14	180

Merged error: 0.1b

Counts

180 → 14

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

44×	`log-pow`
42×	`add-sqr-sqrt` `*-un-lft-identity`
40×	`sqrt-pow1`
38×	`exp-prod`
30×	`times-frac`
26×	`add-cube-cbrt`
12×	`log-prod`
8×	`pow1` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
6×	`add-exp-log` `sqrt-prod`
4×	`add-cbrt-cube`
2×	`sub-neg` `log-div` `flip3--` `pow1/2` `exp-diff` `sqrt-div` `diff-log` `div-sub` `rem-log-exp` `flip--` `div-inv`

Counts

4 → 100

Calls

4 calls:

8.0ms	(log (sqrt (exp (/ (- 1.0 (cos x)) (sin x)))))
8.0ms	(log (sqrt (exp (/ (- 1.0 (cos x)) (sin x)))))
4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))

series57.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(log (sqrt (exp (/ (- 1.0 (cos x)) (sin x)))))
26.0ms	(log (sqrt (exp (/ (- 1.0 (cos x)) (sin x)))))
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))

simplify49.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5180	1116

prune213.0ms

Filtered

82 candidates to 112 candidates (-36.6%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	107	5	112
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	109	17	126

Merged error: 0.1b

Counts

126 → 17

regimes256.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.9b

bsearch41.0ms

Steps

Iters	Range		Point
9	1.106345144933365e-05	1.958212435825927	0.02149337157003914
10	-25.507993624504685	-1.5289413834786174e-12	-0.017330074816333453

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	73	71
1	73	71

end0.0ms

sample4.7s

Algorithm

intervals

Results

2.4s	1650×	body	2560	valid
1.4s	2764×	body	1280	valid
482.0ms	1850×	body	640	valid
166.0ms	928×	body	320	valid
58.0ms	458×	body	160	valid
26.0ms	348×	body	80	valid
6.0ms	2×	body	5120	valid

Details

analyze500.0ms

sample141.0ms

simplify10.0ms

prune3.0ms

localize7.0ms

rewrite11.0ms

series10.0ms

simplify36.0ms

prune126.0ms

localize10.0ms

rewrite27.0ms

series29.0ms

simplify49.0ms

prune194.0ms

localize9.0ms

rewrite25.0ms

series21.0ms

simplify57.0ms

prune194.0ms

localize13.0ms

rewrite30.0ms

series57.0ms

simplify49.0ms

prune213.0ms

regimes256.0ms

bsearch41.0ms

simplify2.0ms

end0.0ms

sample4.7s

Profiling