Details

sample2.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 14.260864%

Guaranteed chance to sample good point: 71.201281%

Results

16.0ms	185×	body	80	valid
13.0ms	26×	body	1280	valid
8.0ms	22×	body	640	valid
4.0ms	14×	body	320	valid
3.0ms	40×	body	80	invalid
2.0ms	5×	body	640	invalid
2.0ms	9×	body	160	valid
1.0ms	6×	body	320	invalid
0.0ms	1×	body	1280	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: 26.2b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
2.9b	(* (* x (pow s 2.0)) x)
7.9b	(* x (pow s 2.0))
18.4b	(* (pow c 2.0) (* (* x (pow s 2.0)) x))

rewrite39.0ms

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:

14.0ms	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
5.0ms	(* (* x (pow s 2.0)) x)
5.0ms	(* x (pow s 2.0))
9.0ms	(* (pow c 2.0) (* (* x (pow s 2.0)) x))

series226.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
32.0ms	(* (* x (pow s 2.0)) x)
34.0ms	(* x (pow s 2.0))
80.0ms	(* (pow c 2.0) (* (* x (pow s 2.0)) x))

simplify68.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (57.0ms)

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

prune257.0ms

Filtered

70 candidates to 127 candidates (-81.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	116	11	127
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	11	128

Merged error: 14.2b

Counts

128 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))
0.4b	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
2.9b	(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
18.4b	(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

rewrite56.0ms

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)
13.0ms	(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

series225.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))
77.0ms	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
32.0ms	(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
85.0ms	(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

simplify100.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (76.0ms)

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

prune242.0ms

Filtered

68 candidates to 198 candidates (-191.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	192	6	198
Fresh	6	4	10
Picked	0	1	1
Done	0	0	0
Total	198	11	209

Merged error: 2.2b

Counts

209 → 11

localize15.0ms

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))))))
0.4b	(/ (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)))))))
3.5b	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
3.5b	(* (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))))

series198.0ms

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))))
69.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

simplify52.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (38.0ms)

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

prune372.0ms

Filtered

69 candidates to 118 candidates (-71.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	107	11	118
Fresh	7	2	9
Picked	1	0	1
Done	1	0	1
Total	116	13	129

Merged error: 0.0b

Counts

129 → 13

localize16.0ms

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))))))
0.5b	(/ (cos (* 2.0 x)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
3.5b	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
3.5b	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

rewrite30.0ms

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))))

series212.0ms

Counts

4 → 12

Calls

4 calls:

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))))))
28.0ms	(/ (cos (* 2.0 x)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
69.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
70.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

simplify74.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (45.0ms)

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

prune599.0ms

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	3	9	12
Picked	0	1	1
Done	0	0	0
Total	168	14	182

Merged error: 0.0b

Counts

182 → 14

regimes590.0ms

Accuracy

10.2% (2.4b remaining)

Error of 2.5b against oracle of 0.1b and baseline of 2.8b

bsearch261.0ms

Steps

Iters	Range		Point
10	2.8468494353131904e-307	5.836887450709904e-294	2.2844956518282255e-294
8	-4.710045750942875e-147	-2.3486676994832678e-150	-2.374825666918312e-150

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	28
1	38	28

end0.0ms

sample4.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 14.260864%

Guaranteed chance to sample good point: 71.201281%

Results

538.0ms	5951×	body	80	valid
323.0ms	678×	body	1280	valid
257.0ms	737×	body	640	valid
117.0ms	1322×	body	80	invalid
110.0ms	419×	body	320	valid
79.0ms	244×	body	640	invalid
51.0ms	112×	body	1280	invalid
43.0ms	187×	body	320	invalid
38.0ms	215×	body	160	valid
21.0ms	130×	body	160	invalid

Details

sample2.8s

simplify41.0ms

prune4.0ms

localize14.0ms

rewrite39.0ms

series226.0ms

simplify68.0ms

prune257.0ms

localize18.0ms

rewrite56.0ms

series225.0ms

simplify100.0ms

prune242.0ms

localize15.0ms

rewrite26.0ms

series198.0ms

simplify52.0ms

prune372.0ms

localize16.0ms

rewrite30.0ms

series212.0ms

simplify74.0ms

prune599.0ms

regimes590.0ms

bsearch261.0ms

simplify2.0ms

end0.0ms

sample4.5s

Profiling