Details

sample511.0ms

Algorithm

intervals

Results

104.0ms	32×	body	2560	valid
67.0ms	58×	body	1280	valid
10.0ms	28×	body	640	valid
9.0ms	142×	body	80	valid
4.0ms	15×	body	320	valid
0.0ms	1×	body	160	valid

simplify17.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	39	7
2	76	7
3	114	7
4	137	7
5	144	7
6	144	7
done	144	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.4b	(/ 1.0 (* F F))
3.9b	(* (/ 1.0 (* F F)) (tan (* PI l)))
31.1b	(tan (* PI l))

rewrite73.0ms

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:

6.0ms	(* PI l)
7.0ms	(/ 1.0 (* F F))
47.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
9.0ms	(tan (* PI l))

series251.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* PI l)
24.0ms	(/ 1.0 (* F F))
130.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
74.0ms	(tan (* PI l))

simplify41.0ms

Counts

89 → 89

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	323	443
1	1416	374
2	5001	374
done	5001	374

prune213.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 15.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
0.3b	(* (/ (cbrt 1.0) F) (tan (* PI l)))
31.1b	(tan (* PI l))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
28×	`associate-l`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
13×	`add-exp-log`
12×	`add-cbrt-cube`
10×	`pow1` `cbrt-prod`
9×	`associate-r`
5×	`unswap-sqr`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`tan-quot` `pow-prod-down` `*-commutative`
1×	`cbrt-undiv` `frac-times` `associate-r/` `div-exp` `associate-l/` `div-inv`

Counts

4 → 88

Calls

4 calls:

6.0ms	(* PI l)
6.0ms	(* PI l)
36.0ms	(* (/ (cbrt 1.0) F) (tan (* PI l)))
8.0ms	(tan (* PI l))

series269.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* PI l)
23.0ms	(* PI l)
162.0ms	(* (/ (cbrt 1.0) F) (tan (* PI l)))
64.0ms	(tan (* PI l))

simplify92.0ms

Counts

100 → 100

Iterations

Useful iterations: 3 (86.0ms)

Iter	Nodes	Cost
0	294	496
1	1023	455
2	3911	454
3	5001	451
done	5001	451

prune320.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 15.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt PI) l)
1.0b	(sqrt PI)
1.0b	(sqrt PI)
31.0b	(tan (* (sqrt PI) (* (sqrt PI) l)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
10×	`sqrt-prod`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`add-exp-log` `associate-l` `add-cbrt-cube`
4×	`add-log-exp`
3×	`associate-r`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `unswap-sqr`
1×	`tan-quot` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 56

Calls

4 calls:

9.0ms	(* (sqrt PI) l)
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
23.0ms	(tan (* (sqrt PI) (* (sqrt PI) l)))

series114.0ms

Counts

4 → 8

Calls

4 calls:

50.0ms	(* (sqrt PI) l)
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
64.0ms	(tan (* (sqrt PI) (* (sqrt PI) l)))

simplify44.0ms

Counts

64 → 64

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	128	226
1	418	212
2	1234	210
3	5001	210
done	5001	210

prune241.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 15.4b

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.0b	(sqrt PI)
1.0b	(sqrt PI)
31.0b	(tan (* (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (* (sqrt PI) l)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`tan-quot`

Counts

4 → 47

Calls

4 calls:

1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
43.0ms	(tan (* (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (* (sqrt PI) l)))

series67.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
67.0ms	(tan (* (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (* (sqrt PI) l)))

simplify37.0ms

Counts

53 → 53

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	89	218
1	244	199
2	874	199
3	5001	199
done	5001	199

prune197.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 15.4b

regimes412.0ms

Accuracy

0% (0.3b remaining)

Error of 12.5b against oracle of 12.2b and baseline of 12.5b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	23
1	23	23
done	23	23

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.6s	847×	body	2560	valid
1.2s	1729×	body	1280	valid
300.0ms	4493×	body	80	valid
291.0ms	877×	body	640	valid
102.0ms	443×	body	320	valid
70.0ms	3×	body	10240	exit
31.0ms	208×	body	160	valid