Details

sample362.0ms

Algorithm

intervals

Results

119.0ms	24×	body	2560	valid
67.0ms	143×	body	80	valid
62.0ms	50×	body	1280	valid
24.0ms	33×	body	640	valid
8.0ms	16×	body	320	valid
3.0ms	8×	body	160	valid

simplify5.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
8	4695
7	2334
6	817
5	388
4	156
3	86
2	43
1	20
0	10

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
4.7b	(/ (tan (* PI l)) (* F F))
30.7b	(tan (* PI l))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
6×	`associate-r` `associate-l`
4×	`insert-posit16` `add-log-exp`
3×	`times-frac` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `tan-quot` `*-commutative` `unswap-sqr`
1×	`clear-num` `associate-/r*` `frac-2neg` `div-inv` `associate-/l/`

Counts

4 → 70

Calls

4 calls:

12.0ms	(* PI l)
14.0ms	(* PI l)
33.0ms	(/ (tan (* PI l)) (* F F))
26.0ms	(tan (* PI l))

series360.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* PI l)
42.0ms	(* PI l)
183.0ms	(/ (tan (* PI l)) (* F F))
96.0ms	(tan (* PI l))

simplify2.0s

Counts

82 → 82

Iterations

Iter	Nodes
done	5040
3	3132
2	709
1	230
0	102

prune407.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (tan (* PI l)) F)
0.2b	(* PI l)
0.2b	(* PI l)
30.7b	(tan (* PI l))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
10×	`add-cbrt-cube` `add-exp-log`
9×	`times-frac`
8×	`pow1`
6×	`associate-r` `associate-l`
4×	`insert-posit16` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow-prod-down` `prod-exp` `tan-quot` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv` `associate-/l/`

Counts

4 → 76

Calls

4 calls:

24.0ms	(/ (tan (* PI l)) F)
14.0ms	(* PI l)
13.0ms	(* PI l)
22.0ms	(tan (* PI l))

series316.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(/ (tan (* PI l)) F)
30.0ms	(* PI l)
27.0ms	(* PI l)
93.0ms	(tan (* PI l))

simplify1.9s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
3	1729
2	583
1	221
0	108

prune457.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.3b

localize32.0ms

Local error

Found 4 expressions with local error:

7.4b	(cbrt (/ (tan (* PI l)) F))
30.7b	(tan (* PI l))
30.7b	(tan (* PI l))
30.7b	(tan (* PI l))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

13×	`cbrt-prod`
11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`tan-quot`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 50

Calls

4 calls:

2.0ms	(cbrt (/ (tan (* PI l)) F))
12.0ms	(tan (* PI l))
11.0ms	(tan (* PI l))
9.0ms	(tan (* PI l))

series616.0ms

Counts

4 → 12

Calls

4 calls:

329.0ms	(cbrt (/ (tan (* PI l)) F))
83.0ms	(tan (* PI l))
97.0ms	(tan (* PI l))
106.0ms	(tan (* PI l))

simplify1.9s

Counts

62 → 62

Iterations

Iter	Nodes
done	5000
3	1431
2	468
1	203
0	110

prune508.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.3b

localize45.0ms

Local error

Found 4 expressions with local error:

7.4b	(cbrt (/ (tan (* PI l)) F))
30.7b	(tan (* PI l))
30.7b	(tan (* PI l))
30.7b	(tan (* PI l))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

13×	`cbrt-prod`
11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`tan-quot`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 50

Calls

4 calls:

5.0ms	(cbrt (/ (tan (* PI l)) F))
16.0ms	(tan (* PI l))
16.0ms	(tan (* PI l))
14.0ms	(tan (* PI l))

series539.0ms

Counts

4 → 12

Calls

4 calls:

255.0ms	(cbrt (/ (tan (* PI l)) F))
89.0ms	(tan (* PI l))
94.0ms	(tan (* PI l))
101.0ms	(tan (* PI l))

simplify1.9s

Counts

62 → 62

Iterations

Iter	Nodes
done	5000
3	1431
2	468
1	203
0	110

prune435.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 6.3b

regimes522.0ms

Accuracy

75.2% (1.5b remaining)

Error of 7.9b against oracle of 6.4b and baseline of 12.3b

bsearch4.0ms

simplify16.0ms

Iterations

Iter	Nodes
done	40
1	40
0	31

end0.0ms

sample9.8s

Algorithm

intervals

Results

3.9s	814×	body	2560	valid
2.9s	1632×	body	1280	valid
1.3s	923×	body	640	valid
1.2s	4670×	body	80	valid
166.0ms	367×	body	320	valid
77.0ms	2×	body	10240	exit
64.0ms	210×	body	160	valid