Details

sample55.0ms

Algorithm

intervals

Results

21.0ms	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

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

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

localize10.0ms

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))

rewrite66.0ms

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×	`add-log-exp`

Counts

3 → 260

Calls

3 calls:

18.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
9.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
24.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series180.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
38.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
82.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify57.0ms

Algorithm

egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	991	3221
1	5001	2760

prune554.0ms

Filtered

269 candidates to 213 candidates (20.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	259	10	269
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	260	10	270

Merged error: 0b

Counts

270 → 10

localize12.0ms

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)))))

rewrite257.0ms

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×	`pow-prod-down` `add-log-exp`
3×	`*-commutative`
2×	`un-div-inv`

Counts

4 → 1057

Calls

4 calls:

11.0ms	(* (sin (* x 0.5)) (sqrt (/ 8.0 3.0)))
16.0ms	(/ (sqrt (/ 8.0 3.0)) (/ (sin x) (sin (* x 0.5))))
6.0ms	(/ (sin x) (sin (* x 0.5)))
132.0ms	(* (* (sin (* x 0.5)) (sqrt (/ 8.0 3.0))) (/ (sqrt (/ 8.0 3.0)) (/ (sin x) (sin (* x 0.5)))))

series399.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (sin (* x 0.5)) (sqrt (/ 8.0 3.0)))
108.0ms	(/ (sqrt (/ 8.0 3.0)) (/ (sin x) (sin (* x 0.5))))
47.0ms	(/ (sin x) (sin (* x 0.5)))
172.0ms	(* (* (sin (* x 0.5)) (sqrt (/ 8.0 3.0))) (/ (sqrt (/ 8.0 3.0)) (/ (sin x) (sin (* x 0.5)))))

simplify252.0ms

Algorithm

egg-herbie

Counts

1069 → 1069

Iterations

Useful iterations: 1 (96.0ms)

Iter	Nodes	Cost
0	4658	18147
1	5001	17694

prune2.8s

Filtered

1069 candidates to 755 candidates (29.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	1065	4	1069
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	1071	8	1079

Merged error: 0b

Counts

1079 → 8

localize10.0ms

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)))

rewrite97.0ms

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×	`add-log-exp`
1×	`pow-prod-down`

Counts

3 → 538

Calls

3 calls:

15.0ms	(/ (sin x) (* (/ 8.0 3.0) (sin (* x 0.5))))
34.0ms	(/ (sin (* x 0.5)) (/ (sin x) (* (/ 8.0 3.0) (sin (* x 0.5)))))
9.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series194.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(/ (sin x) (* (/ 8.0 3.0) (sin (* x 0.5))))
87.0ms	(/ (sin (* x 0.5)) (/ (sin x) (* (/ 8.0 3.0) (sin (* x 0.5)))))
40.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify128.0ms

Algorithm

egg-herbie

Counts

547 → 547

Iterations

Useful iterations: 1 (53.0ms)

Iter	Nodes	Cost
0	1961	8015
1	5001	7845

prune1.2s

Filtered

547 candidates to 450 candidates (17.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	547	0	547
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	547	8	555

Merged error: 0b

Counts

555 → 8

localize28.0ms

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)))

rewrite382.0ms

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×	`prod-exp` `un-div-inv` `add-log-exp`
1×	`pow-prod-down`

Counts

4 → 1639

Calls

4 calls:

172.0ms	(* (sqrt (cbrt 3.0)) (/ (/ (sin x) (sin (* x 0.5))) (sqrt (/ (sqrt 8.0) (cbrt 3.0)))))
28.0ms	(/ (/ (sin x) (sin (* x 0.5))) (sqrt (/ (sqrt 8.0) (cbrt 3.0))))
5.0ms	(/ (sqrt 8.0) (cbrt 3.0))
14.0ms	(/ (sqrt 8.0) (* (cbrt 3.0) (cbrt 3.0)))

series426.0ms

Counts

4 → 8

Calls

4 calls:

234.0ms	(* (sqrt (cbrt 3.0)) (/ (/ (sin x) (sin (* x 0.5))) (sqrt (/ (sqrt 8.0) (cbrt 3.0)))))
192.0ms	(/ (/ (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)))

simplify331.0ms

Algorithm

egg-herbie

Counts

1647 → 1647

Iterations

Useful iterations: 1 (97.0ms)

Iter	Nodes	Cost
0	4138	29024
1	5002	28378

prune6.5s

Filtered

1647 candidates to 987 candidates (40.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	1647	0	1647
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	1647	8	1655

Merged error: 0b

Counts

1655 → 8

regimes38.0ms

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

718.0ms	1491×	body	1280	valid
386.0ms	1295×	body	640	valid
267.0ms	4303×	body	80	valid
119.0ms	593×	body	320	valid
46.0ms	318×	body	160	valid