Details

analyze222.0ms

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

sample63.0ms

Algorithm

intervals

Results

31.0ms	52×	body	2560	valid
11.0ms	40×	body	1280	valid
7.0ms	47×	body	640	valid
4.0ms	32×	body	320	valid
2.0ms	69×	body	80	valid
1.0ms	16×	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: 32.9b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

2.3b	(- 1.0 (cos x))
14.8b	(/ (- 1.0 (cos x)) (* x x))

rewrite20.0ms

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:

6.0ms	(- 1.0 (cos x))
12.0ms	(/ (- 1.0 (cos x)) (* x x))

series15.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(- 1.0 (cos x))
11.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify47.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5871	438

prune99.0ms

Filtered

34 candidates to 47 candidates (-38.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	39	8	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	8	48

Merged error: 0.0b

Counts

48 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (pow x 4) 1/720)
0.1b	(* x (* x 1/24))
0.3b	(* x 1/24)
11.6b	(+ (* (pow x 4) 1/720) (- 1/2 (* x (* x 1/24))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`add-exp-log`
13×	`associate-l` `add-cbrt-cube`
11×	`pow1`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-log-exp`
7×	`associate-r` `prod-exp`
5×	`cbrt-unprod`
4×	`unpow-prod-down` `pow-prod-down` `unswap-sqr`
3×	`*-commutative`
2×	`sum-log` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r-` `sub-neg` `associate-+r+` `flip3-+` `diff-log` `pow-exp` `flip-+`

Counts

4 → 75

Calls

4 calls:

4.0ms	(* (pow x 4) 1/720)
4.0ms	(* x (* x 1/24))
3.0ms	(* x 1/24)
5.0ms	(+ (* (pow x 4) 1/720) (- 1/2 (* x (* x 1/24))))

series13.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (pow x 4) 1/720)
3.0ms	(* x (* x 1/24))
2.0ms	(* x 1/24)
5.0ms	(+ (* (pow x 4) 1/720) (- 1/2 (* x (* x 1/24))))

simplify29.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5078	653

prune108.0ms

Filtered

54 candidates to 87 candidates (-61.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	87	8	95

Merged error: 0.0b

Counts

95 → 8

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)
2.3b	(- 1.0 (cos x))

rewrite25.0ms

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:

10.0ms	(/ (/ (- 1.0 (cos x)) x) x)
5.0ms	(/ (- 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))

simplify46.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5245	1987

prune154.0ms

Filtered

102 candidates to 155 candidates (-52.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	153	2	155
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	154	9	163

Merged error: 0.0b

Counts

163 → 9

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- 1.0 (cos x))) x)
0.2b	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
2.3b	(- 1.0 (cos x))
2.3b	(- 1.0 (cos x))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

167×	`add-sqr-sqrt`
156×	`times-frac`
143×	`*-un-lft-identity`
104×	`sqrt-prod`
89×	`add-cube-cbrt`
40×	`swap-sqr`
28×	`associate-r` `associate-l`
24×	`distribute-lft-out--`
18×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
11×	`pow1`
9×	`unswap-sqr`
8×	`associate-/l*` `add-log-exp`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`prod-exp` `cbrt-unprod`
3×	`flip3--` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`pow2` `frac-times` `frac-2neg` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 204

Calls

4 calls:

6.0ms	(/ (sqrt (- 1.0 (cos x))) x)
24.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))

series22.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ (sqrt (- 1.0 (cos x))) x)
5.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
3.0ms	(- 1.0 (cos x))
6.0ms	(- 1.0 (cos x))

simplify66.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4980	2689
1	4980	2689

prune236.0ms

Filtered

123 candidates to 216 candidates (-75.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	213	3	216
Fresh	3	3	6
Picked	0	1	1
Done	0	2	2
Total	216	9	225

Merged error: 0.0b

Counts

225 → 9

regimes64.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 32.0b

bsearch45.0ms

Steps

Iters	Range		Point
10	5.855821036270785e-07	120031312.1677242	0.034041023082368414
9	-1.7525930748559126	-4.830644338133403e-06	-0.0311513612479286

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	30
1	29	30

end0.0ms

analyze223.0ms

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

815.0ms	1584×	body	2560	valid
342.0ms	1274×	body	1280	valid
236.0ms	1451×	body	640	valid
120.0ms	938×	body	320	valid
93.0ms	2292×	body	80	valid
38.0ms	461×	body	160	valid

Details

analyze222.0ms

sample63.0ms

simplify2.0ms

prune2.0ms

localize8.0ms

rewrite20.0ms

series15.0ms

simplify47.0ms

prune99.0ms

localize9.0ms

rewrite19.0ms

series13.0ms

simplify29.0ms

prune108.0ms

localize6.0ms

rewrite25.0ms

series13.0ms

simplify46.0ms

prune154.0ms

localize7.0ms

rewrite47.0ms

series22.0ms

simplify66.0ms

prune236.0ms

regimes64.0ms

bsearch45.0ms

simplify1.0ms

end0.0ms

analyze223.0ms

sample1.8s

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