Details

sample718.0ms

Algorithm

intervals

Results

219.0ms	148×	body	80	valid
197.0ms	57×	body	1280	valid
168.0ms	21×	body	2560	valid
25.0ms	32×	body	640	valid
11.0ms	12×	body	320	valid
2.0ms	5×	body	160	valid

simplify250.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	14
1	19	14
2	41	14
3	82	14
4	126	14
5	152	14
6	162	14
7	164	14
done	164	14

prune38.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(/ 1.0 (* F F))
6.0b	(* (/ 1.0 (* F F)) (tan (* PI l)))
29.6b	(tan (* PI l))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-cbrt-cube`
17×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
8×	`pow1`
7×	`times-frac`
6×	`associate-r` `prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`tan-quot` `associate-/l*` `unswap-sqr`
2×	`pow-prod-down` `*-commutative` `div-inv`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `associate-/r*`

Counts

4 → 85

Calls

4 calls:

17.0ms	(* PI l)
18.0ms	(/ 1.0 (* F F))
110.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
45.0ms	(tan (* PI l))

series465.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* PI l)
53.0ms	(/ 1.0 (* F F))
226.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
147.0ms	(tan (* PI l))

simplify1.2s

Counts

97 → 97

Iterations

Useful iterations: 2 (359.0ms)

Iter	Nodes	Cost
0	143	924
1	350	903
2	1911	789
done	5001	789

prune497.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(* PI l)
0.3b	(* (/ 1.0 F) (tan (* PI l)))
29.6b	(tan (* PI l))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
19×	`associate-l`
16×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log` `add-cbrt-cube`
10×	`pow1` `times-frac`
9×	`associate-r`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`tan-quot` `pow-prod-down` `*-commutative`
1×	`cbrt-undiv` `frac-times` `associate-r/` `div-exp` `associate-l/` `div-inv`

Counts

4 → 86

Calls

4 calls:

7.0ms	(* PI l)
11.0ms	(* PI l)
40.0ms	(* (/ 1.0 F) (tan (* PI l)))
8.0ms	(tan (* PI l))

series325.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* PI l)
37.0ms	(* PI l)
154.0ms	(* (/ 1.0 F) (tan (* PI l)))
97.0ms	(tan (* PI l))

simplify883.0ms

Counts

98 → 98

Iterations

Useful iterations: done (880.0ms)

Iter	Nodes	Cost
0	131	780
1	298	758
2	1230	692
done	5001	680

prune391.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(* PI l)
29.4b	(sin (* PI l))
29.5b	(cos (* PI l))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

14.0ms	(* PI l)
11.0ms	(* PI l)
7.0ms	(sin (* PI l))
8.0ms	(cos (* PI l))

series139.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* PI l)
35.0ms	(* PI l)
51.0ms	(sin (* PI l))
32.0ms	(cos (* PI l))

simplify522.0ms

Counts

70 → 70

Iterations

Useful iterations: done (520.0ms)

Iter	Nodes	Cost
0	80	402
1	170	386
2	719	357
done	5000	356

prune345.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.5b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt l)
0.6b	(cbrt l)
29.4b	(sin (* PI l))
29.4b	(cos (* (* PI (* (cbrt l) (cbrt l))) (cbrt l)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3`

Counts

4 → 44

Calls

4 calls:

2.0ms	(cbrt l)
2.0ms	(cbrt l)
15.0ms	(sin (* PI l))
62.0ms	(cos (* (* PI (* (cbrt l) (cbrt l))) (cbrt l)))

series621.0ms

Counts

4 → 12

Calls

4 calls:

280.0ms	(cbrt l)
268.0ms	(cbrt l)
39.0ms	(sin (* PI l))
34.0ms	(cos (* (* PI (* (cbrt l) (cbrt l))) (cbrt l)))

simplify4.2s

Counts

56 → 56

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	79	406
1	163	396
2	633	313
3	3983	276
done	5000	276

prune273.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.5b

regimes623.0ms

Accuracy

83.6% (0.8b remaining)

Error of 8.5b against oracle of 7.7b and baseline of 12.5b

bsearch3.0ms

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	41	112
1	56	81
done	56	81

end0.0ms

sample9.2s

Algorithm

intervals

Results

3.8s	800×	body	2560	valid
3.4s	1679×	body	1280	valid
657.0ms	4591×	body	80	valid
630.0ms	929×	body	640	valid
263.0ms	406×	body	320	valid
68.0ms	2×	body	10240	exit
55.0ms	192×	body	160	valid