Details

sample67.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 73.520795%

Results

28.0ms	47×	body	2560	valid
12.0ms	45×	body	1280	valid
9.0ms	53×	body	640	valid
4.0ms	38×	body	320	valid
2.0ms	64×	body	80	valid
1.0ms	9×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	4
1	21	4
2	26	4
3	28	4
4	28	4

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: 31.8b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.2b	(- 1.0 (cos x))
13.9b	(/ (- 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 → 42

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))

simplify59.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	221	271
1	735	239
2	2396	239
3	5002	239

prune90.0ms

Filtered

34 candidates to 48 candidates (-41.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	38	10	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	10	49

Merged error: 0.1b

Counts

49 → 10

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.2b	(/ (- 1.0 (cos x)) x)
2.2b	(- 1.0 (cos x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
46×	`times-frac`
29×	`add-cube-cbrt`
27×	`add-exp-log`
19×	`associate-r`
17×	`add-cbrt-cube`
13×	`associate-l`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`cbrt-unprod`
3×	`associate-/r*` `div-inv`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 114

Calls

3 calls:

13.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
5.0ms	(/ (- 1.0 (cos x)) x)
4.0ms	(- 1.0 (cos x))

series13.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
5.0ms	(/ (- 1.0 (cos x)) x)
3.0ms	(- 1.0 (cos x))

simplify61.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	521	814
1	2334	726
2	5001	690

prune147.0ms

Filtered

81 candidates to 123 candidates (-51.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	116	7	123
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	120	13	133

Merged error: 0.0b

Counts

133 → 13

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cbrt (pow (- 1.0 (cos x)) 3)) x)
0.3b	(cbrt (pow (- 1.0 (cos x)) 3))
0.4b	(pow (- 1.0 (cos x)) 3)
2.2b	(- 1.0 (cos x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

80×	`cbrt-prod`
72×	`add-sqr-sqrt` `*-un-lft-identity`
57×	`times-frac`
46×	`add-cube-cbrt`
30×	`unpow-prod-down` `cube-prod`
19×	`associate-/l*`
13×	`distribute-lft-out--` `difference-of-squares`
7×	`add-exp-log`
6×	`cube-div` `cube-mult` `unpow3` `add-cbrt-cube` `add-log-exp` `sqr-pow`
5×	`pow1`
4×	`cbrt-div` `flip3--` `flip--`
3×	`pow-unpow` `associate-/r*`
2×	`associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `div-exp` `pow-exp` `clear-num` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 163

Calls

4 calls:

9.0ms	(/ (cbrt (pow (- 1.0 (cos x)) 3)) x)
5.0ms	(cbrt (pow (- 1.0 (cos x)) 3))
5.0ms	(pow (- 1.0 (cos x)) 3)
4.0ms	(- 1.0 (cos x))

series23.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ (cbrt (pow (- 1.0 (cos x)) 3)) x)
7.0ms	(cbrt (pow (- 1.0 (cos x)) 3))
7.0ms	(pow (- 1.0 (cos x)) 3)
3.0ms	(- 1.0 (cos x))

simplify56.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	409	1242
1	1611	1149
2	5002	1118

prune175.0ms

Filtered

86 candidates to 175 candidates (-103.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	174	1	175
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	176	12	188

Merged error: 0.0b

Counts

188 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (pow (pow (- 1.0 (cos x)) (sqrt 3)) (sqrt 3)))
0.6b	(pow (- 1.0 (cos x)) (sqrt 3))
0.8b	(pow (pow (- 1.0 (cos x)) (sqrt 3)) (sqrt 3))
2.2b	(- 1.0 (cos x))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

33×	`unpow-prod-down`
22×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`add-cube-cbrt`
13×	`cbrt-prod`
12×	`pow-unpow`
7×	`add-exp-log`
6×	`sqrt-prod` `add-log-exp`
5×	`pow1` `pow-exp` `sqr-pow`
4×	`add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
3×	`pow-to-exp`
2×	`pow-pow`
1×	`sub-neg` `flip3--` `pow1/3` `diff-log` `flip--`

Counts

4 → 85

Calls

4 calls:

5.0ms	(cbrt (pow (pow (- 1.0 (cos x)) (sqrt 3)) (sqrt 3)))
5.0ms	(pow (- 1.0 (cos x)) (sqrt 3))
6.0ms	(pow (pow (- 1.0 (cos x)) (sqrt 3)) (sqrt 3))
4.0ms	(- 1.0 (cos x))

series144.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(cbrt (pow (pow (- 1.0 (cos x)) (sqrt 3)) (sqrt 3)))
21.0ms	(pow (- 1.0 (cos x)) (sqrt 3))
48.0ms	(pow (pow (- 1.0 (cos x)) (sqrt 3)) (sqrt 3))
3.0ms	(- 1.0 (cos x))

simplify49.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	413	933
1	1557	868
2	5001	804

prune190.0ms

Filtered

63 candidates to 97 candidates (-54.0%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	95	14	109

Merged error: 0.0b

Counts

109 → 14

regimes161.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.9b

bsearch34.0ms

Steps

Iters	Range		Point
10	0.00031157581617804726	87511408.73844521	0.031765462474626915
9	-871263.1049503816	-0.0065084385888304844	-0.03062086483746403

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	27
1	49	27

end0.0ms

sample1.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 73.520795%

Results

799.0ms	1558×	body	2560	valid
343.0ms	1259×	body	1280	valid
263.0ms	1549×	body	640	valid
128.0ms	990×	body	320	valid
77.0ms	2183×	body	80	valid
47.0ms	461×	body	160	valid

Details

sample67.0ms

simplify6.0ms

prune3.0ms

localize6.0ms

rewrite11.0ms

series9.0ms

simplify59.0ms

prune90.0ms

localize7.0ms

rewrite26.0ms

series13.0ms

simplify61.0ms

prune147.0ms

localize10.0ms

rewrite29.0ms

series23.0ms

simplify56.0ms

prune175.0ms

localize15.0ms

rewrite22.0ms

series144.0ms

simplify49.0ms

prune190.0ms

regimes161.0ms

bsearch34.0ms

simplify1.0ms

end0.0ms

sample1.8s

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