Details

sample511.0ms

Algorithm

intervals

Results

118.0ms	37×	body	2560	valid
54.0ms	49×	body	1280	valid
11.0ms	150×	body	80	valid
8.0ms	23×	body	640	valid
3.0ms	12×	body	320	valid
2.0ms	11×	body	160	valid

simplify109.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	14
1	18	14
2	39	14
3	76	14
4	114	14
5	136	14
6	142	14
done	142	14

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(/ 1.0 (* F F))
2.8b	(* (/ 1.0 (* F F)) (tan (* PI l)))
30.6b	(tan (* PI l))

rewrite76.0ms

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:

9.0ms	(* PI l)
8.0ms	(/ 1.0 (* F F))
43.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
13.0ms	(tan (* PI l))

series251.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* PI l)
25.0ms	(/ 1.0 (* F F))
135.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
71.0ms	(tan (* PI l))

simplify1.9s

Counts

89 → 89

Iterations

Useful iterations: 2 (164.0ms)

Iter	Nodes	Cost
0	135	872
1	305	854
2	1001	722
3	3970	722
done	5001	722

prune220.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(* PI l)
0.3b	(* (/ (sqrt 1.0) F) (tan (* PI l)))
30.6b	(tan (* PI l))

rewrite63.0ms

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` `add-cbrt-cube`
10×	`pow1` `sqrt-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:

7.0ms	(* PI l)
7.0ms	(* PI l)
38.0ms	(* (/ (sqrt 1.0) F) (tan (* PI l)))
8.0ms	(tan (* PI l))

series260.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* PI l)
22.0ms	(* PI l)
155.0ms	(* (/ (sqrt 1.0) F) (tan (* PI l)))
62.0ms	(tan (* PI l))

simplify1.6s

Counts

100 → 100

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	134	900
1	297	877
2	822	797
3	2714	797
done	5000	792

prune310.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 13.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt PI) l)
1.0b	(sqrt PI)
1.0b	(sqrt PI)
30.8b	(tan (* (sqrt PI) (* (sqrt PI) l)))

rewrite39.0ms

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:

10.0ms	(* (sqrt PI) l)
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
24.0ms	(tan (* (sqrt PI) (* (sqrt PI) l)))

series112.0ms

Counts

4 → 8

Calls

4 calls:

50.0ms	(* (sqrt PI) l)
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
61.0ms	(tan (* (sqrt PI) (* (sqrt PI) l)))

simplify2.0s

Counts

64 → 64

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	70	414
1	130	333
2	323	319
3	826	319
4	2795	319
done	5000	317

prune232.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 13.7b

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.0b	(sqrt PI)
1.0b	(sqrt PI)
31.1b	(tan (* (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (* (sqrt PI) l)))

rewrite49.0ms

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)
3.0ms	(sqrt PI)
1.0ms	(sqrt PI)
42.0ms	(tan (* (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (* (sqrt PI) l)))

series64.0ms

Counts

4 → 6

Calls

4 calls:

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

simplify1.4s

Counts

53 → 53

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	49	381
1	90	243
2	203	235
3	568	235
4	2253	235
done	5001	233

prune174.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 13.7b

regimes441.0ms

Accuracy

0% (0.3b remaining)

Error of 12.2b against oracle of 11.9b and baseline of 12.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	32
1	21	32
done	21	32

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.5s	815×	body	2560	valid
1.2s	1665×	body	1280	valid
320.0ms	908×	body	640	valid
296.0ms	4622×	body	80	valid
140.0ms	6×	body	10240	exit
90.0ms	380×	body	320	valid
40.0ms	239×	body	160	valid