Details

sample402.0ms

Algorithm

intervals

Results

92.0ms	15×	body	2560	valid
92.0ms	55×	body	1280	valid
91.0ms	145×	body	80	valid
30.0ms	35×	body	640	valid
8.0ms	14×	body	320	valid
4.0ms	11×	body	160	valid

simplify180.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	14
1	18	14
2	39	14
3	76	14
4	118	14
5	141	14
6	148	14
done	148	14

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.7b	(/ 1.0 (* F F))
4.4b	(* (/ 1.0 (* F F)) (tan (* PI l)))
29.9b	(tan (* PI l))

rewrite117.0ms

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` `div-exp` `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 → 77

Calls

4 calls:

13.0ms	(* PI l)
23.0ms	(/ 1.0 (* F F))
64.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
13.0ms	(tan (* PI l))

series353.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* PI l)
44.0ms	(/ 1.0 (* F F))
175.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
109.0ms	(tan (* PI l))

simplify1.3s

Counts

89 → 89

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	135	872
1	339	854
2	1966	740
done	5001	726

prune370.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
0.2b	(/ (tan (* PI l)) F)
29.9b	(tan (* PI l))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

14.0ms	(* PI l)
14.0ms	(* PI l)
19.0ms	(/ (tan (* PI l)) F)
8.0ms	(tan (* PI l))

series293.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* PI l)
28.0ms	(* PI l)
133.0ms	(/ (tan (* PI l)) F)
107.0ms	(tan (* PI l))

simplify2.1s

Counts

84 → 84

Iterations

Useful iterations: 3 (819.0ms)

Iter	Nodes	Cost
0	106	669
1	216	646
2	672	604
3	3213	594
done	5001	594

prune394.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 10.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
0.5b	(/ 1 (/ F (tan (* PI l))))
29.9b	(tan (* PI l))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
55×	`add-sqr-sqrt`
51×	`add-cube-cbrt` `*-un-lft-identity`
19×	`add-exp-log`
14×	`associate-/r*`
13×	`add-cbrt-cube`
9×	`pow1`
7×	`div-exp`
6×	`associate-r` `associate-l`
5×	`tan-quot` `associate-/r/` `div-inv`
4×	`add-log-exp`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `1-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`pow-flip` `frac-2neg` `clear-num` `inv-pow`

Counts

4 → 124

Calls

4 calls:

13.0ms	(* PI l)
13.0ms	(* PI l)
39.0ms	(/ 1 (/ F (tan (* PI l))))
9.0ms	(tan (* PI l))

series350.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* PI l)
23.0ms	(* PI l)
188.0ms	(/ 1 (/ F (tan (* PI l))))
94.0ms	(tan (* PI l))

simplify1.5s

Counts

136 → 136

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	198	1637
1	471	1411
2	2529	1353
done	5000	1343

prune546.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 10.5b

localize43.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt F)
0.6b	(cbrt F)
0.6b	(cbrt F)
29.9b	(tan (* PI l))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
1×	`tan-quot`

Counts

4 → 41

Calls

4 calls:

2.0ms	(cbrt F)
2.0ms	(cbrt F)
2.0ms	(cbrt F)
30.0ms	(tan (* PI l))

series1.0s

Counts

4 → 12

Calls

4 calls:

300.0ms	(cbrt F)
304.0ms	(cbrt F)
284.0ms	(cbrt F)
119.0ms	(tan (* PI l))

simplify2.5s

Counts

53 → 53

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	51	294
1	104	282
2	276	256
3	935	247
4	3483	247
done	5001	245

prune346.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 10.5b

regimes618.0ms

Accuracy

0% (0.4b remaining)

Error of 12.7b against oracle of 12.3b and baseline of 12.7b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	23
1	19	23
done	19	23

end0.0ms

sample9.2s

Algorithm

intervals

Results

4.2s	787×	body	2560	valid
2.3s	1745×	body	1280	valid
1.2s	4558×	body	80	valid
684.0ms	922×	body	640	valid
192.0ms	5×	body	10240	exit
158.0ms	394×	body	320	valid
127.0ms	217×	body	160	valid