Details

sample65.0ms

Algorithm

intervals

Results

26.0ms	46×	body	1280	valid
14.0ms	47×	body	640	valid
9.0ms	135×	body	80	valid
3.0ms	14×	body	320	valid
2.0ms	14×	body	160	valid

simplify29.0ms

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 (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: 15.2b

Counts

2 → 1

localize13.0ms

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)))
15.0b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite79.0ms

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:

26.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
10.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
29.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series212.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
43.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
98.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify70.0ms

Algorithm

egg-herbie

Counts

275 → 275

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	1001	3265
1	5001	2802

prune640.0ms

Filtered

275 candidates to 219 candidates (79.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	260	15	275
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	261	15	276

Merged error: 0.0b

Counts

276 → 15

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)))))

rewrite287.0ms

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)))
18.0ms	(/ (sqrt (/ 8.0 3.0)) (/ (sin x) (sin (* x 0.5))))
7.0ms	(/ (sin x) (sin (* x 0.5)))
151.0ms	(* (* (sin (* x 0.5)) (sqrt (/ 8.0 3.0))) (/ (sqrt (/ 8.0 3.0)) (/ (sin x) (sin (* x 0.5)))))

series455.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (sin (* x 0.5)) (sqrt (/ 8.0 3.0)))
130.0ms	(/ (sqrt (/ 8.0 3.0)) (/ (sin x) (sin (* x 0.5))))
47.0ms	(/ (sin x) (sin (* x 0.5)))
197.0ms	(* (* (sin (* x 0.5)) (sqrt (/ 8.0 3.0))) (/ (sqrt (/ 8.0 3.0)) (/ (sin x) (sin (* x 0.5)))))

simplify284.0ms

Algorithm

egg-herbie

Counts

1077 → 1077

Iterations

Useful iterations: 1 (119.0ms)

Iter	Nodes	Cost
0	4672	18209
1	5001	17754

prune3.1s

Filtered

1077 candidates to 763 candidates (70.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	1068	9	1077
Fresh	14	0	14
Picked	1	0	1
Done	0	0	0
Total	1083	9	1092

Merged error: 0b

Counts

1092 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite395.0ms

Algorithm

rewrite-expression-head

Rules

1704×	`times-frac`
1131×	`add-sqr-sqrt`
982×	`*-un-lft-identity`
971×	`add-cube-cbrt`
712×	`sqrt-prod`
678×	`associate-r`
504×	`sqrt-div`
494×	`associate-*r/`
387×	`frac-times`
383×	`associate-/l*`
336×	`associate-/r*`
116×	`div-inv`
108×	`associate-/l/`
83×	`clear-num`
72×	`frac-2neg`
59×	`unswap-sqr`
34×	`add-exp-log` `add-cbrt-cube`
27×	`associate-/r/`
22×	`associate-l` `un-div-inv`
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`

Counts

4 → 1326

Calls

4 calls:

18.0ms	(/ (sqrt (/ 8.0 3.0)) (/ (sin x) (sin (* x 0.5))))
7.0ms	(/ (sin x) (sin (* x 0.5)))
70.0ms	(* (sin (* x 0.5)) (/ (sqrt (/ 8.0 3.0)) (/ (sin x) (sin (* x 0.5)))))
165.0ms	(* (sqrt (/ 8.0 3.0)) (* (sin (* x 0.5)) (/ (sqrt (/ 8.0 3.0)) (/ (sin x) (sin (* x 0.5))))))

series515.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(/ (sqrt (/ 8.0 3.0)) (/ (sin x) (sin (* x 0.5))))
55.0ms	(/ (sin x) (sin (* x 0.5)))
141.0ms	(* (sin (* x 0.5)) (/ (sqrt (/ 8.0 3.0)) (/ (sin x) (sin (* x 0.5)))))
195.0ms	(* (sqrt (/ 8.0 3.0)) (* (sin (* x 0.5)) (/ (sqrt (/ 8.0 3.0)) (/ (sin x) (sin (* x 0.5))))))

simplify313.0ms

Algorithm

egg-herbie

Counts

1338 → 1338

Iterations

Useful iterations: 1 (107.0ms)

Iter	Nodes	Cost
0	4395	21785
1	5002	21241

prune3.7s

Filtered

1338 candidates to 919 candidates (68.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	1335	3	1338
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	1338	9	1347

Merged error: 0b

Counts

1347 → 9

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sqrt (/ 8.0 (cbrt 3.0))) (/ 1 (sin (* x 0.5))))
0.4b	(* (* (sin (* x 0.5)) (/ (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sin x))) (/ (sqrt (/ 8.0 (cbrt 3.0))) (/ 1 (sin (* x 0.5)))))
0.5b	(/ (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sin x))
1.0b	(/ 8.0 (cbrt 3.0))

rewrite2.8s

Algorithm

rewrite-expression-head

Rules

11875×	`add-sqr-sqrt`
11696×	`times-frac`
9103×	`sqrt-prod`
8737×	`associate-/l*`
8351×	`*-un-lft-identity`
8082×	`add-cube-cbrt`
6911×	`associate-*r/`
6837×	`frac-times`
5860×	`cbrt-prod`
4151×	`associate-/r*`
3387×	`sqrt-div` `associate-/l/`
2034×	`associate-r`
1728×	`associate-l`
1644×	`unswap-sqr`
1484×	`swap-sqr`
430×	`clear-num`
404×	`div-inv`
375×	`frac-2neg`
268×	`*-commutative`
129×	`associate-*l/`
110×	`un-div-inv`
77×	`add-exp-log`
50×	`add-cbrt-cube`
31×	`div-exp`
25×	`prod-exp`
18×	`cbrt-undiv` `associate-/r/`
15×	`cbrt-unprod`
9×	`pow1`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down`

Counts

4 → 8824

Calls

4 calls:

24.0ms	(/ (sqrt (/ 8.0 (cbrt 3.0))) (/ 1 (sin (* x 0.5))))
1.4s	(* (* (sin (* x 0.5)) (/ (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sin x))) (/ (sqrt (/ 8.0 (cbrt 3.0))) (/ 1 (sin (* x 0.5)))))
36.0ms	(/ (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sin x))
5.0ms	(/ 8.0 (cbrt 3.0))

series647.0ms

Counts

4 → 10

Calls

4 calls:

223.0ms	(/ (sqrt (/ 8.0 (cbrt 3.0))) (/ 1 (sin (* x 0.5))))
307.0ms	(* (* (sin (* x 0.5)) (/ (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sin x))) (/ (sqrt (/ 8.0 (cbrt 3.0))) (/ 1 (sin (* x 0.5)))))
116.0ms	(/ (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sin x))
0.0ms	(/ 8.0 (cbrt 3.0))

simplify2.5s

Algorithm

egg-herbie

Counts

8834 → 8834

Iterations

Useful iterations: 0 (175.0ms)

Iter	Nodes	Cost
0	8531	256113

prune50.2s

Filtered

8834 candidates to 6927 candidates (78.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	8834	0	8834
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	8834	9	8843

Merged error: 0b

Counts

8843 → 9

regimes51.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	13
1	16	13

end0.0ms

sample1.7s

Algorithm

intervals

Results

733.0ms	1479×	body	1280	valid
377.0ms	1181×	body	640	valid
329.0ms	4435×	body	80	valid
127.0ms	607×	body	320	valid
44.0ms	298×	body	160	valid