Details

sample383.0ms

Algorithm

intervals

Results

61.0ms	20×	body	2560	valid
37.0ms	51×	body	1280	valid
11.0ms	33×	body	640	valid
9.0ms	141×	body	80	valid
4.0ms	17×	body	320	valid
1.0ms	7×	body	160	valid

simplify96.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	14
1	18	14
2	38	14
3	73	14
4	109	14
5	130	14
6	137	14
done	137	14

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
4.9b	(* (/ 1.0 (* F F)) (tan (* PI l)))
29.8b	(tan (* PI l))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

3.0ms	(* PI l)
3.0ms	(* PI l)
16.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
3.0ms	(tan (* PI l))

series256.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* PI l)
23.0ms	(* PI l)
133.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
78.0ms	(tan (* PI l))

simplify858.0ms

Counts

86 → 86

Iterations

Useful iterations: 2 (125.0ms)

Iter	Nodes	Cost
0	124	790
1	301	768
2	1162	658
done	5000	658

prune232.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
0.4b	(* (/ 1.0 F) (tan (* PI l)))
29.8b	(tan (* PI l))

rewrite24.0ms

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×	`prod-exp` `cbrt-unprod` `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 → 78

Calls

4 calls:

3.0ms	(* PI l)
3.0ms	(* PI l)
15.0ms	(* (/ 1.0 F) (tan (* PI l)))
2.0ms	(tan (* PI l))

series245.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* PI l)
21.0ms	(* PI l)
138.0ms	(* (/ 1.0 F) (tan (* PI l)))
66.0ms	(tan (* PI l))

simplify1.3s

Counts

90 → 90

Iterations

Useful iterations: 2 (107.0ms)

Iter	Nodes	Cost
0	125	736
1	279	717
2	836	639
3	2699	639
done	5000	639

prune256.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 10.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt PI) (* (sqrt PI) l))
1.0b	(sqrt PI)
1.0b	(sqrt PI)
29.7b	(tan (* (sqrt PI) (* (sqrt PI) l)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

13.0ms	(* (sqrt PI) (* (sqrt PI) l))
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
5.0ms	(tan (* (sqrt PI) (* (sqrt PI) l)))

series92.0ms

Counts

4 → 8

Calls

4 calls:

26.0ms	(* (sqrt PI) (* (sqrt PI) l))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
65.0ms	(tan (* (sqrt PI) (* (sqrt PI) l)))

simplify2.5s

Counts

63 → 63

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	70	478
1	153	321
2	413	287
3	986	287
4	3123	287
done	5000	287

prune200.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 10.2b

localize19.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.0b	(sqrt PI)
1.0b	(sqrt PI)
29.8b	(tan (* (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (* (sqrt PI) l)))

rewrite13.0ms

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

series72.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
72.0ms	(tan (* (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (* (sqrt PI) l)))

simplify2.3s

Counts

53 → 53

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	49	381
1	92	291
2	219	235
3	735	235
4	3813	235
done	5000	235

prune171.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 10.2b

regimes348.0ms

Accuracy

0% (0.3b remaining)

Error of 12.1b against oracle of 11.8b and baseline of 12.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	30
1	24	30
done	24	30

end0.0ms

sample4.6s

Algorithm

intervals

Results

2.4s	773×	body	2560	valid
1.2s	1713×	body	1280	valid
336.0ms	940×	body	640	valid
298.0ms	4532×	body	80	valid
115.0ms	5×	body	10240	exit
94.0ms	387×	body	320	valid
32.0ms	209×	body	160	valid