Details

sample52.0ms

Algorithm

intervals

Results

18.0ms	40×	body	1280	valid
12.0ms	41×	body	640	valid
9.0ms	151×	body	80	valid
4.0ms	18×	body	320	valid
1.0ms	6×	body	160	valid

simplify26.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	9
1	43	9
2	93	9
3	174	9
4	269	9
5	288	9
6	288	9

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 15.1b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))
14.9b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

193×	`associate-l`
181×	`add-sqr-sqrt`
167×	`times-frac`
106×	`add-cube-cbrt` `*-un-lft-identity`
45×	`associate-*l/`
43×	`associate-/l*`
37×	`unswap-sqr`
33×	`associate-r`
31×	`add-exp-log` `add-cbrt-cube`
12×	`prod-exp` `associate-/r*` `cbrt-unprod`
11×	`*-commutative`
10×	`pow1`
9×	`associate-/l/`
7×	`cbrt-undiv` `div-exp` `div-inv`
4×	`frac-2neg` `pow-prod-down` `clear-num`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`

Counts

3 → 266

Calls

3 calls:

19.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
11.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
32.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series203.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
47.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
94.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify75.0ms

Algorithm

egg-herbie

Counts

275 → 275

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1001	3265
1	5001	2802

prune627.0ms

Filtered

275 candidates to 219 candidates (20.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	265	10	275
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	266	10	276

Merged error: 0b

Counts

276 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin (* x 0.5)) (sqrt (/ 8.0 3.0)))
0.1b	(/ (sqrt (/ 8.0 3.0)) (/ (sin x) (sin (* x 0.5))))
0.2b	(/ (sin x) (sin (* x 0.5)))
0.3b	(* (* (sin (* x 0.5)) (sqrt (/ 8.0 3.0))) (/ (sqrt (/ 8.0 3.0)) (/ (sin x) (sin (* x 0.5)))))

rewrite308.0ms

Algorithm

rewrite-expression-head

Rules

1216×	`times-frac`
883×	`add-sqr-sqrt`
742×	`*-un-lft-identity`
741×	`add-cube-cbrt`
541×	`sqrt-prod`
486×	`sqrt-div`
428×	`associate-*r/`
369×	`frac-times`
348×	`associate-/l*`
314×	`associate-/r*`
253×	`associate-r`
99×	`associate-/l/`
85×	`div-inv`
69×	`clear-num`
68×	`frac-2neg`
55×	`unswap-sqr`
34×	`add-exp-log` `add-cbrt-cube`
33×	`associate-l`
18×	`associate-/r/`
11×	`pow1`
10×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
9×	`associate-*l/`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`un-div-inv`

Counts

4 → 1065

Calls

4 calls:

13.0ms	(* (sin (* x 0.5)) (sqrt (/ 8.0 3.0)))
19.0ms	(/ (sqrt (/ 8.0 3.0)) (/ (sin x) (sin (* x 0.5))))
6.0ms	(/ (sin x) (sin (* x 0.5)))
154.0ms	(* (* (sin (* x 0.5)) (sqrt (/ 8.0 3.0))) (/ (sqrt (/ 8.0 3.0)) (/ (sin x) (sin (* x 0.5)))))

series435.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (sin (* x 0.5)) (sqrt (/ 8.0 3.0)))
117.0ms	(/ (sqrt (/ 8.0 3.0)) (/ (sin x) (sin (* x 0.5))))
52.0ms	(/ (sin x) (sin (* x 0.5)))
189.0ms	(* (* (sin (* x 0.5)) (sqrt (/ 8.0 3.0))) (/ (sqrt (/ 8.0 3.0)) (/ (sin x) (sin (* x 0.5)))))

simplify286.0ms

Algorithm

egg-herbie

Counts

1077 → 1077

Iterations

Useful iterations: 1 (121.0ms)

Iter	Nodes	Cost
0	4672	18209
1	5001	17754

prune3.3s

Filtered

1077 candidates to 763 candidates (29.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	1073	4	1077
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	1079	8	1087

Merged error: 0b

Counts

1087 → 8

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (sin x) (* (/ 8.0 3.0) (sin (* x 0.5))))
0.2b	(/ (sin (* x 0.5)) (/ (sin x) (* (/ 8.0 3.0) (sin (* x 0.5)))))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

771×	`times-frac`
470×	`add-sqr-sqrt`
380×	`add-cube-cbrt` `*-un-lft-identity`
234×	`associate-l`
146×	`associate-/r*`
74×	`associate-/r/`
54×	`associate-r` `associate-*l/`
36×	`unswap-sqr`
31×	`add-exp-log` `add-cbrt-cube`
27×	`associate-/l*`
24×	`div-inv`
18×	`*-commutative`
13×	`cbrt-undiv` `div-exp`
9×	`frac-2neg` `clear-num`
6×	`prod-exp` `cbrt-unprod`
5×	`pow1`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`pow-prod-down`

Counts

3 → 544

Calls

3 calls:

17.0ms	(/ (sin x) (* (/ 8.0 3.0) (sin (* x 0.5))))
38.0ms	(/ (sin (* x 0.5)) (/ (sin x) (* (/ 8.0 3.0) (sin (* x 0.5)))))
11.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series200.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(/ (sin x) (* (/ 8.0 3.0) (sin (* x 0.5))))
89.0ms	(/ (sin (* x 0.5)) (/ (sin x) (* (/ 8.0 3.0) (sin (* x 0.5)))))
43.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify140.0ms

Algorithm

egg-herbie

Counts

553 → 553

Iterations

Useful iterations: 1 (64.0ms)

Iter	Nodes	Cost
0	1971	8057
1	5001	7885

prune1.3s

Filtered

553 candidates to 456 candidates (17.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	553	0	553
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	553	8	561

Merged error: 0b

Counts

561 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (sqrt (cbrt 3.0)) (/ (/ (sin x) (sin (* x 0.5))) (sqrt (/ (sqrt 8.0) (cbrt 3.0)))))
0.7b	(/ (/ (sin x) (sin (* x 0.5))) (sqrt (/ (sqrt 8.0) (cbrt 3.0))))
1.0b	(/ (sqrt 8.0) (cbrt 3.0))
1.0b	(/ (sqrt 8.0) (* (cbrt 3.0) (cbrt 3.0)))

rewrite458.0ms

Algorithm

rewrite-expression-head

Rules

3194×	`times-frac`
1809×	`sqrt-prod`
1723×	`add-sqr-sqrt`
1513×	`*-un-lft-identity`
1511×	`add-cube-cbrt`
671×	`cbrt-prod`
620×	`associate-r`
137×	`associate-/r*`
120×	`div-inv`
68×	`associate-*r/`
67×	`unswap-sqr`
58×	`associate-/l*`
51×	`associate-l`
42×	`swap-sqr`
31×	`add-cbrt-cube`
30×	`sqrt-div` `associate-/r/`
25×	`add-exp-log`
20×	`associate-/l/`
13×	`cbrt-undiv`
10×	`clear-num`
9×	`div-exp`
8×	`frac-2neg` `*-commutative`
7×	`cbrt-unprod`
6×	`pow1`
4×	`expm1-log1p-u` `prod-exp` `un-div-inv` `log1p-expm1-u` `add-log-exp`
1×	`pow-prod-down`

Counts

4 → 1647

Calls

4 calls:

197.0ms	(* (sqrt (cbrt 3.0)) (/ (/ (sin x) (sin (* x 0.5))) (sqrt (/ (sqrt 8.0) (cbrt 3.0)))))
37.0ms	(/ (/ (sin x) (sin (* x 0.5))) (sqrt (/ (sqrt 8.0) (cbrt 3.0))))
6.0ms	(/ (sqrt 8.0) (cbrt 3.0))
16.0ms	(/ (sqrt 8.0) (* (cbrt 3.0) (cbrt 3.0)))

series438.0ms

Counts

4 → 8

Calls

4 calls:

233.0ms	(* (sqrt (cbrt 3.0)) (/ (/ (sin x) (sin (* x 0.5))) (sqrt (/ (sqrt 8.0) (cbrt 3.0)))))
204.0ms	(/ (/ (sin x) (sin (* x 0.5))) (sqrt (/ (sqrt 8.0) (cbrt 3.0))))
0.0ms	(/ (sqrt 8.0) (cbrt 3.0))
0.0ms	(/ (sqrt 8.0) (* (cbrt 3.0) (cbrt 3.0)))

simplify351.0ms

Algorithm

egg-herbie

Counts

1655 → 1655

Iterations

Useful iterations: 1 (103.0ms)

Iter	Nodes	Cost
0	4148	29090
1	5001	28442

prune6.9s

Filtered

1655 candidates to 995 candidates (39.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	1655	0	1655
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	1655	8	1663

Merged error: 0b

Counts

1663 → 8

regimes44.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	9
1	13	9

end0.0ms

sample1.7s

Algorithm

intervals

Results

711.0ms	1491×	body	1280	valid
391.0ms	1295×	body	640	valid
273.0ms	4303×	body	80	valid
117.0ms	593×	body	320	valid
44.0ms	318×	body	160	valid