Details

sample2.9s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 14.199829%

Guaranteed chance to sample good point: 71.150631%

Results

18.0ms	201×	body	80	valid
10.0ms	21×	body	1280	valid
7.0ms	19×	body	640	valid
5.0ms	16×	body	640	invalid
5.0ms	56×	body	80	invalid
3.0ms	10×	body	320	valid
2.0ms	9×	body	320	invalid
2.0ms	5×	body	1280	invalid
1.0ms	5×	body	160	valid
0.0ms	3×	body	160	invalid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	8
1	68	8
2	243	8
3	1266	8
4	5001	8

prune4.0ms

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: 27.7b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
2.2b	(* (* x (pow s 2.0)) x)
7.8b	(* x (pow s 2.0))
18.7b	(* (pow c 2.0) (* (* x (pow s 2.0)) x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

122×	`add-exp-log`
82×	`prod-exp`
34×	`add-cbrt-cube`
18×	`pow-to-exp` `pow-exp`
17×	`add-sqr-sqrt`
16×	`div-exp` `cbrt-unprod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`associate-r` `associate-l`
7×	`unpow-prod-down`
6×	`pow1`
4×	`cbrt-undiv` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l` `unswap-sqr` `sqr-pow`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 115

Calls

4 calls:

11.0ms	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
5.0ms	(* (* x (pow s 2.0)) x)
8.0ms	(* x (pow s 2.0))
9.0ms	(* (pow c 2.0) (* (* x (pow s 2.0)) x))

series222.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
31.0ms	(* (* x (pow s 2.0)) x)
30.0ms	(* x (pow s 2.0))
82.0ms	(* (pow c 2.0) (* (* x (pow s 2.0)) x))

simplify64.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	571	1041
1	2506	875
2	5001	871

prune261.0ms

Filtered

70 candidates to 127 candidates (-81.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	115	12	127
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	12	128

Merged error: 13.7b

Counts

128 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))
0.3b	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
2.2b	(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
18.7b	(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

416×	`add-exp-log`
343×	`prod-exp`
84×	`pow-to-exp` `pow-exp`
52×	`add-cbrt-cube`
43×	`div-exp`
29×	`cbrt-unprod`
11×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-r*`
9×	`associate-l`
6×	`pow1` `unpow-prod-down`
5×	`cbrt-undiv`
4×	`add-log-exp`
3×	`times-frac` `-commutative` `associate-/l`
2×	`sqr-pow`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 186

Calls

4 calls:

7.0ms	(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))
15.0ms	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
9.0ms	(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
12.0ms	(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

series225.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))
76.0ms	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
34.0ms	(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
82.0ms	(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

simplify99.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	721	2340
1	3234	1837
2	5001	1781

prune272.0ms

Filtered

69 candidates to 198 candidates (-187.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	192	6	198
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	198	12	210

Merged error: 2.9b

Counts

210 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
0.3b	(/ (cos (* 2.0 x)) (* (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2)))))))
5.6b	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
5.6b	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-exp-log`
44×	`prod-exp`
21×	`add-cbrt-cube`
17×	`associate-l`
16×	`add-sqr-sqrt`
14×	`pow-to-exp` `add-cube-cbrt` `*-un-lft-identity` `pow-exp`
11×	`pow1`
8×	`cbrt-unprod`
6×	`unpow-prod-down`
5×	`associate-r`
4×	`add-log-exp`
3×	`times-frac` `swap-sqr` `-commutative` `associate-/l`
2×	`cbrt-undiv` `div-exp` `sqr-pow`
1×	`pow2` `frac-2neg` `pow-plus` `pow-prod-down` `clear-num` `associate-/r*` `pow-sqr` `pow-prod-up` `div-inv` `unswap-sqr`

Counts

4 → 106

Calls

4 calls:

3.0ms	(* (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
5.0ms	(/ (cos (* 2.0 x)) (* (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2)))))))
7.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
7.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

series196.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
45.0ms	(/ (cos (* 2.0 x)) (* (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2)))))))
68.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
66.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

simplify50.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	402	1518
1	1482	1245
2	5002	1172

prune388.0ms

Filtered

69 candidates to 118 candidates (-71.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	108	10	118
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	116	14	130

Merged error: 0.2b

Counts

130 → 14

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (cos (* 2.0 x)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2)))))) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
0.8b	(/ (cos (* 2.0 x)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
5.6b	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
5.6b	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
63×	`add-exp-log`
58×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
42×	`prod-exp`
21×	`add-cbrt-cube`
16×	`associate-/l*`
14×	`pow-to-exp` `associate-l` `pow-exp`
6×	`unpow-prod-down` `associate-/r*` `cbrt-unprod` `div-inv`
4×	`pow1` `cbrt-undiv` `div-exp` `add-log-exp`
2×	`frac-2neg` `associate-r` `clear-num` `*-commutative` `sqr-pow`
1×	`associate-/l/`

Counts

4 → 157

Calls

4 calls:

6.0ms	(/ (/ (cos (* 2.0 x)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2)))))) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
4.0ms	(/ (cos (* 2.0 x)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
7.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
7.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

series208.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ (/ (cos (* 2.0 x)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2)))))) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
29.0ms	(/ (cos (* 2.0 x)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
66.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
70.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

simplify70.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	595	3343
1	2082	3048
2	5001	2963

prune648.0ms

Filtered

111 candidates to 169 candidates (-52.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	165	4	169
Fresh	4	9	13
Picked	0	1	1
Done	0	0	0
Total	169	14	183

Merged error: 0.2b

Counts

183 → 14

regimes668.0ms

Accuracy

0% (2.4b remaining)

Error of 2.6b against oracle of 0.2b and baseline of 2.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	18
1	18	18

end0.0ms

sample4.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 14.199829%

Guaranteed chance to sample good point: 71.150631%

Results

535.0ms	5936×	body	80	valid
351.0ms	725×	body	1280	valid
254.0ms	738×	body	640	valid
120.0ms	1314×	body	80	invalid
111.0ms	423×	body	320	valid
75.0ms	221×	body	640	invalid
66.0ms	144×	body	1280	invalid
43.0ms	185×	body	320	invalid
32.0ms	178×	body	160	valid
17.0ms	106×	body	160	invalid

Details

sample2.9s

simplify40.0ms

prune4.0ms

localize13.0ms

rewrite38.0ms

series222.0ms

simplify64.0ms

prune261.0ms

localize15.0ms

rewrite55.0ms

series225.0ms

simplify99.0ms

prune272.0ms

localize17.0ms

rewrite26.0ms

series196.0ms

simplify50.0ms

prune388.0ms

localize17.0ms

rewrite29.0ms

series208.0ms

simplify70.0ms

prune648.0ms

regimes668.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample4.6s

Profiling