Details

analyze2.7s

Algorithm

sampling

Space saved by range analysis: 0.146413%

Space saved by search: 14.386397%

Guaranteed chance to sample good point: 71.201281%

sample60.0ms

Algorithm

intervals

Results

17.0ms	193×	body	80	valid
12.0ms	25×	body	1280	valid
6.0ms	17×	body	640	valid
3.0ms	36×	body	80	invalid
3.0ms	12×	body	320	valid
2.0ms	5×	body	1280	invalid
2.0ms	5×	body	640	invalid
2.0ms	9×	body	160	valid
1.0ms	6×	body	320	invalid
0.0ms	3×	body	160	invalid

simplify41.0ms

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: 26.4b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
3.9b	(* (* x (pow s 2.0)) x)
8.8b	(* x (pow s 2.0))
16.2b	(* (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)))
6.0ms	(* (* 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))

series221.0ms

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))

simplify66.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (53.0ms)

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

prune235.0ms

Filtered

70 candidates to 127 candidates (-81.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	117	10	127
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	10	128

Merged error: 14.6b

Counts

128 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(cos (* 2.0 x))
0.7b	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
3.9b	(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
16.2b	(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

390×	`add-exp-log`
322×	`prod-exp`
77×	`pow-to-exp` `pow-exp`
47×	`add-cbrt-cube`
43×	`div-exp`
26×	`cbrt-unprod`
9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`associate-l`
6×	`pow1`
5×	`cbrt-undiv`
4×	`associate-r` `add-log-exp`
3×	`unpow-prod-down` `times-frac` `associate-/l*`
2×	`*-commutative`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv` `sqr-pow`

Counts

4 → 163

Calls

4 calls:

2.0ms	(cos (* 2.0 x))
14.0ms	(/ (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))

series188.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(cos (* 2.0 x))
74.0ms	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
31.0ms	(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
81.0ms	(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

simplify87.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	681	2125
1	2956	1680
2	5001	1624

prune220.0ms

Filtered

61 candidates to 175 candidates (-186.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	169	6	175
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	175	10	185

Merged error: 2.8b

Counts

185 → 10

localize16.0ms

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))))))
0.7b	(/ (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)))))))
5.4b	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
5.4b	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

rewrite28.0ms

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))))
9.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

series194.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
42.0ms	(/ (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)))))))
67.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
67.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

simplify51.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (36.0ms)

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

prune354.0ms

Filtered

69 candidates to 118 candidates (-71.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	109	9	118
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	115	13	128

Merged error: 0.4b

Counts

128 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(cos (* 2.0 x))
0.4b	(/ (cos (* 2.0 x)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
5.4b	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
5.4b	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

2.0ms	(cos (* 2.0 x))
4.0ms	(/ (cos (* 2.0 x)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
9.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
7.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

series161.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(cos (* 2.0 x))
27.0ms	(/ (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))))
65.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

simplify46.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	374	1085
1	1246	972
2	5002	972

prune290.0ms

Filtered

68 candidates to 106 candidates (-55.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	99	7	106
Fresh	8	4	12
Picked	1	0	1
Done	0	0	0
Total	108	11	119

Merged error: 0.4b

Counts

119 → 11

Details

analyze2.7s

sample60.0ms

simplify41.0ms

prune4.0ms

localize14.0ms

rewrite38.0ms

series221.0ms

simplify66.0ms

prune235.0ms

localize18.0ms

rewrite48.0ms

series188.0ms

simplify87.0ms

prune220.0ms

localize16.0ms

rewrite28.0ms

series194.0ms

simplify51.0ms

prune354.0ms

localize16.0ms

rewrite24.0ms

series161.0ms

simplify46.0ms

prune290.0ms

regimes416.0ms

bsearch1.0ms

Profiling