Details

analyze274.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	25%	0%	5
75%	25%	0%	6
78.1%	21.9%	0%	7
78.1%	21.9%	0%	8
78.1%	21.9%	0%	9
78.1%	21.9%	0%	10
78.1%	21.9%	0%	11
78.1%	21.9%	0%	12
78.1%	21.9%	0%	13
78.1%	21.8%	0%	14

sample62.0ms

Algorithm

intervals

Results

29.0ms	44×	body	2560	valid
12.0ms	44×	body	1280	valid
8.0ms	49×	body	640	valid
3.0ms	93×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	8×	body	160	valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	8
1	16	8

prune2.0ms

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: 27.8b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.3b	(- 1.0 (cos x))
13.8b	(/ (- 1.0 (cos x)) (* x x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 41

Calls

2 calls:

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

series9.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify30.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5871	438

prune84.0ms

Filtered

34 candidates to 47 candidates (-38.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	38	9	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	9	48

Merged error: 0.1b

Counts

48 → 9

localize6.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
1.3b	(- 1.0 (cos x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 146

Calls

3 calls:

8.0ms	(/ (/ (- 1.0 (cos x)) x) x)
6.0ms	(/ (- 1.0 (cos x)) x)
3.0ms	(- 1.0 (cos x))

series13.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(/ (/ (- 1.0 (cos x)) x) x)
5.0ms	(/ (- 1.0 (cos x)) x)
3.0ms	(- 1.0 (cos x))

simplify47.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5245	1987

prune151.0ms

Filtered

101 candidates to 155 candidates (-53.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	152	3	155
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	156	8	164

Merged error: 0.1b

Counts

164 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (exp (log (- 1.0 (cos x)))) x)
0.2b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.3b	(- 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:

9.0ms	(/ (exp (log (- 1.0 (cos x)))) x)
4.0ms	(exp (log (- 1.0 (cos x))))
3.0ms	(log (- 1.0 (cos x)))
4.0ms	(- 1.0 (cos x))

series24.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ (exp (log (- 1.0 (cos x)))) x)
3.0ms	(exp (log (- 1.0 (cos x))))
13.0ms	(log (- 1.0 (cos x)))
3.0ms	(- 1.0 (cos x))

simplify60.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5047	1013

prune129.0ms

Filtered

72 candidates to 109 candidates (-51.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	109	8	117

Merged error: 0.1b

Counts

117 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (log (exp (- 1.0 (cos x)))) x)
0.1b	(exp (- 1.0 (cos x)))
1.3b	(- 1.0 (cos x))
1.4b	(log (exp (- 1.0 (cos x))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

7.0ms	(/ (log (exp (- 1.0 (cos x)))) x)
6.0ms	(exp (- 1.0 (cos x)))
4.0ms	(- 1.0 (cos x))
5.0ms	(log (exp (- 1.0 (cos x))))

series19.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify60.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4953	976
1	4953	976

prune113.0ms

Filtered

79 candidates to 112 candidates (-41.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	112	8	120

Merged error: 0.1b

Counts

120 → 8

regimes100.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.4b

bsearch48.0ms

Steps

Iters	Range		Point
10	2.1339584213351845e-15	0.04035150785030129	0.03564219456903279
9	-185188.55234176936	-4.4891869641656926e-05	-0.03662840477444983

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	32
1	31	32

end0.0ms

analyze229.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	25%	0%	5
75%	25%	0%	6
78.1%	21.9%	0%	7
78.1%	21.9%	0%	8
78.1%	21.9%	0%	9
78.1%	21.9%	0%	10
78.1%	21.9%	0%	11
78.1%	21.9%	0%	12
78.1%	21.9%	0%	13
78.1%	21.8%	0%	14

sample1.8s

Algorithm

intervals

Results

827.0ms	1598×	body	2560	valid
333.0ms	1222×	body	1280	valid
269.0ms	1526×	body	640	valid
115.0ms	914×	body	320	valid
82.0ms	2282×	body	80	valid
48.0ms	458×	body	160	valid

Details

analyze274.0ms

sample62.0ms

simplify2.0ms

prune2.0ms

localize6.0ms

rewrite11.0ms

series9.0ms

simplify30.0ms

prune84.0ms

localize6.0ms

rewrite24.0ms

series13.0ms

simplify47.0ms

prune151.0ms

localize10.0ms

rewrite24.0ms

series24.0ms

simplify60.0ms

prune129.0ms

localize9.0ms

rewrite25.0ms

series19.0ms

simplify60.0ms

prune113.0ms

regimes100.0ms

bsearch48.0ms

simplify1.0ms

end0.0ms

analyze229.0ms

sample1.8s

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