Details

sample111.0ms

Algorithm

intervals

Results

29.0ms	66×	body	1280	valid
22.0ms	315×	body	80	valid
22.0ms	68×	body	640	valid
10.0ms	44×	body	320	valid
3.0ms	18×	body	160	valid

simplify13.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	15	7
2	32	7
3	69	7
4	144	7
5	272	7
6	482	7
7	1052	7
8	2094	7
9	3638	7
10	4858	7
done	5000	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(sinh y)
0.1b	(* (sin x) (sinh y))
13.7b	(/ (* (sin x) (sinh y)) x)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
3×	`sinh-def` `times-frac` `associate-r` `associate-l` `associate-/r*` `add-log-exp`
2×	`cbrt-undiv` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l/` `associate-/l` `unswap-sqr`

Counts

3 → 49

Calls

3 calls:

1.0ms	(sinh y)
12.0ms	(* (sin x) (sinh y))
23.0ms	(/ (* (sin x) (sinh y)) x)

series259.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(sinh y)
90.0ms	(* (sin x) (sinh y))
101.0ms	(/ (* (sin x) (sinh y)) x)

simplify3.2s

Counts

58 → 58

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	117	538
1	270	516
2	984	445
3	4845	419
done	5000	419

prune143.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (sinh y) x)
0.0b	(sinh y)
0.1b	(* (/ (sinh y) x) (sin x))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-l`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`associate-r` `associate-/r` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `sinh-def` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `associate-/l/`

Counts

3 → 68

Calls

3 calls:

7.0ms	(/ (sinh y) x)
1.0ms	(sinh y)
22.0ms	(* (/ (sinh y) x) (sin x))

series236.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(/ (sinh y) x)
64.0ms	(sinh y)
91.0ms	(* (/ (sinh y) x) (sin x))

simplify1.9s

Counts

77 → 77

Iterations

Useful iterations: 3 (977.0ms)

Iter	Nodes	Cost
0	141	721
1	324	694
2	900	622
3	2873	620
done	5000	620

prune277.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(sinh y)
0.1b	(* (sinh y) (/ (sin x) x))
0.1b	(/ (sin x) x)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`sinh-def` `associate-l` `associate-/r` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 69

Calls

3 calls:

2.0ms	(sinh y)
24.0ms	(* (sinh y) (/ (sin x) x))
12.0ms	(/ (sin x) x)

series238.0ms

Counts

3 → 9

Calls

3 calls:

85.0ms	(sinh y)
109.0ms	(* (sinh y) (/ (sin x) x))
44.0ms	(/ (sin x) x)

simplify2.2s

Counts

78 → 78

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	134	733
1	299	700
2	999	631
3	3632	629
done	5000	629

prune230.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt (sin x))
0.6b	(cbrt (sin x))
0.6b	(cbrt (sin x))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp`

Counts

4 → 44

Calls

4 calls:

1.0ms	(cbrt x)
2.0ms	(cbrt (sin x))
2.0ms	(cbrt (sin x))
2.0ms	(cbrt (sin x))

series644.0ms

Counts

4 → 12

Calls

4 calls:

273.0ms	(cbrt x)
133.0ms	(cbrt (sin x))
126.0ms	(cbrt (sin x))
112.0ms	(cbrt (sin x))

simplify2.7s

Counts

56 → 56

Iterations

Useful iterations: 3 (108.0ms)

Iter	Nodes	Cost
0	49	341
1	91	319
2	189	286
3	411	274
4	1084	274
5	3847	274
done	5000	274

prune181.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes83.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	23
1	14	23
done	14	23

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.6s	10312×	body	80	valid
896.0ms	1835×	body	1280	valid
671.0ms	1879×	body	640	valid
447.0ms	1175×	body	320	valid
134.0ms	572×	body	160	valid