Details

sample62.0ms

Algorithm

intervals

Results

21.0ms	291×	body	80	valid
12.0ms	23×	body	1280	valid
9.0ms	30×	body	640	valid
3.0ms	12×	body	320	valid
2.0ms	13×	body	160	valid

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

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 26.9b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.6b	(* (* x (pow sin 2.0)) x)
6.9b	(* x (pow sin 2.0))
18.2b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

424×	`add-sqr-sqrt`
243×	`unswap-sqr`
217×	`associate-r`
171×	`times-frac`
164×	`associate-l`
122×	`add-exp-log`
114×	`add-cube-cbrt` `*-un-lft-identity`
89×	`unpow-prod-down`
82×	`prod-exp`
65×	`sqr-pow`
57×	`associate-/r*`
34×	`add-cbrt-cube`
20×	`pow1`
18×	`pow-to-exp` `pow-exp` `*-commutative`
16×	`div-exp` `cbrt-unprod`
10×	`pow-prod-down`
4×	`cbrt-undiv` `add-log-exp`
3×	`associate-/l*`
1×	`frac-2neg` `clear-num` `div-inv`

Counts

4 → 409

Calls

4 calls:

34.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
13.0ms	(* (* x (pow sin 2.0)) x)
6.0ms	(* x (pow sin 2.0))
22.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series838.0ms

Counts

4 → 12

Calls

4 calls:

297.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
145.0ms	(* (* x (pow sin 2.0)) x)
134.0ms	(* x (pow sin 2.0))
262.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify73.0ms

Algorithm

egg-herbie

Counts

421 → 421

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1396	5063
1	5001	4907

prune1.3s

Filtered

421 candidates to 309 candidates (73.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	407	14	421
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	408	14	422

Merged error: 7.6b

Counts

422 → 14

localize16.0ms

Local error

Found 3 expressions with local error:

0.3b

(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))

6.8b

(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))

12.1b

(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

1327×	`add-sqr-sqrt`
1034×	`unswap-sqr`
455×	`add-exp-log`
371×	`prod-exp`
351×	`times-frac`
309×	`unpow-prod-down`
305×	`associate-l`
275×	`sqr-pow`
255×	`associate-r`
186×	`add-cube-cbrt` `*-un-lft-identity`
117×	`associate-/r*`
89×	`pow-to-exp` `pow-exp`
58×	`add-cbrt-cube`
53×	`div-exp`
33×	`cbrt-unprod`
29×	`pow1`
22×	`*-commutative`
18×	`pow-prod-down`
7×	`cbrt-undiv`
3×	`associate-/l*` `add-log-exp`
1×	`frac-2neg` `clear-num` `div-inv`

Counts

3 → 786

Calls

3 calls:

68.0ms

(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))

45.0ms

(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))

18.0ms

(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

series777.0ms

Counts

3 → 9

Calls

3 calls:

299.0ms

(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))

266.0ms

(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))

212.0ms

(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

simplify186.0ms

Algorithm

egg-herbie

Counts

795 → 795

Iterations

Useful iterations: 1 (49.0ms)

Iter	Nodes	Cost
0	2881	15600
1	5002	15239

prune2.9s

Filtered

795 candidates to 602 candidates (75.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	782	13	795
Fresh	11	2	13
Picked	1	0	1
Done	0	0	0
Total	794	15	809

Merged error: 1.5b

Counts

809 → 15

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
1.1b	(/ 1 (* x (pow sin (/ 2.0 2))))
4.7b	(* (/ 1 (pow cos (/ 2.0 2))) (/ 1 (* x (pow sin (/ 2.0 2)))))
5.5b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

757×	`add-sqr-sqrt`
487×	`associate-/r*`
452×	`add-exp-log`
365×	`times-frac`
362×	`*-un-lft-identity`
330×	`associate-r`
312×	`frac-times`
306×	`add-cube-cbrt`
288×	`unswap-sqr`
271×	`prod-exp`
270×	`unpow-prod-down`
179×	`div-exp`
152×	`sqr-pow`
138×	`associate-l`
124×	`associate-/l*`
86×	`pow-to-exp` `pow-exp`
83×	`rec-exp` `1-exp`
44×	`add-cbrt-cube`
42×	`clear-num`
41×	`frac-2neg`
32×	`*-commutative`
24×	`associate-*r/`
19×	`pow1`
15×	`cbrt-unprod`
13×	`associate-*l/`
12×	`cbrt-undiv`
9×	`pow-prod-down`
6×	`pow-flip`
4×	`div-inv` `add-log-exp`
3×	`un-div-inv` `inv-pow`

Counts

4 → 1006

Calls

4 calls:

30.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
17.0ms	(/ 1 (* x (pow sin (/ 2.0 2))))
64.0ms	(* (/ 1 (pow cos (/ 2.0 2))) (/ 1 (* x (pow sin (/ 2.0 2)))))
21.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series853.0ms

Counts

4 → 12

Calls

4 calls:

258.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
202.0ms	(/ 1 (* x (pow sin (/ 2.0 2))))
172.0ms	(* (/ 1 (pow cos (/ 2.0 2))) (/ 1 (* x (pow sin (/ 2.0 2)))))
222.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify184.0ms

Algorithm

egg-herbie

Counts

1018 → 1018

Iterations

Useful iterations: 1 (62.0ms)

Iter	Nodes	Cost
0	3502	12356
1	5001	11915

prune2.9s

Filtered

1018 candidates to 535 candidates (52.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	1014	4	1018
Fresh	4	10	14
Picked	1	0	1
Done	0	0	0
Total	1019	14	1033

Merged error: 1.5b

Counts

1033 → 14

localize25.0ms

Local error

Found 4 expressions with local error:

5.5b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
15.7b	(cbrt (* (/ 1 (pow cos (/ 2.0 2))) (/ 1 (* x (pow sin (/ 2.0 2))))))
15.7b	(cbrt (* (/ 1 (pow cos (/ 2.0 2))) (/ 1 (* x (pow sin (/ 2.0 2))))))
15.7b	(cbrt (* (/ 1 (pow cos (/ 2.0 2))) (/ 1 (* x (pow sin (/ 2.0 2))))))

rewrite400.0ms

Algorithm

rewrite-expression-head

Rules

1442×	`add-sqr-sqrt`
1281×	`associate-/r*`
1056×	`cbrt-div`
936×	`frac-times`
751×	`*-un-lft-identity`
583×	`add-cube-cbrt`
566×	`unpow-prod-down`
556×	`associate-r`
555×	`times-frac`
492×	`unswap-sqr`
453×	`cbrt-prod`
354×	`associate-/l*`
292×	`sqr-pow`
238×	`associate-l`
120×	`clear-num`
117×	`frac-2neg`
72×	`associate-*r/`
56×	`*-commutative`
39×	`associate-*l/`
30×	`add-exp-log`
21×	`prod-exp`
9×	`pow1` `un-div-inv` `add-cbrt-cube`
7×	`pow-to-exp` `pow-exp`
6×	`div-inv`
4×	`add-log-exp`
3×	`pow1/3` `pow-prod-down` `cbrt-unprod`

Counts

4 → 1594

Calls

4 calls:

20.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
82.0ms	(cbrt (* (/ 1 (pow cos (/ 2.0 2))) (/ 1 (* x (pow sin (/ 2.0 2))))))
79.0ms	(cbrt (* (/ 1 (pow cos (/ 2.0 2))) (/ 1 (* x (pow sin (/ 2.0 2))))))
77.0ms	(cbrt (* (/ 1 (pow cos (/ 2.0 2))) (/ 1 (* x (pow sin (/ 2.0 2))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

216.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
348.0ms	(cbrt (* (/ 1 (pow cos (/ 2.0 2))) (/ 1 (* x (pow sin (/ 2.0 2))))))
348.0ms	(cbrt (* (/ 1 (pow cos (/ 2.0 2))) (/ 1 (* x (pow sin (/ 2.0 2))))))
350.0ms	(cbrt (* (/ 1 (pow cos (/ 2.0 2))) (/ 1 (* x (pow sin (/ 2.0 2))))))

simplify311.0ms

Algorithm

egg-herbie

Counts

1606 → 1606

Iterations

Useful iterations: 1 (55.0ms)

Iter	Nodes	Cost
0	3169	25947
1	5001	25007

prune5.2s

Filtered

1606 candidates to 757 candidates (47.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	1604	2	1606
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	1607	13	1620

Merged error: 1.5b

Counts

1620 → 13

regimes323.0ms

Accuracy

0% (1.2b remaining)

Error of 2.9b against oracle of 1.7b and baseline of 2.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	45
1	38	45

end0.0ms

sample1.9s

Algorithm

intervals

Results

717.0ms	9166×	body	80	valid
370.0ms	865×	body	1280	valid
292.0ms	982×	body	640	valid
139.0ms	590×	body	320	valid
48.0ms	308×	body	160	valid