Details

sample388.0ms

Algorithm

intervals

Results

61.0ms	19×	body	2560	valid
38.0ms	54×	body	1280	valid
12.0ms	37×	body	640	valid
9.0ms	143×	body	80	valid
3.0ms	14×	body	320	valid
1.0ms	6×	body	160	valid

simplify99.0ms

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)
0.5b	(/ 1.0 (* F F))
4.2b	(* (/ 1.0 (* F F)) (tan (* PI l)))
29.7b	(tan (* PI l))

rewrite28.0ms

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:

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

series262.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* PI l)
28.0ms	(/ 1.0 (* F F))
133.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
80.0ms	(tan (* PI l))

simplify1.0s

Counts

89 → 89

Iterations

Useful iterations: 2 (143.0ms)

Iter	Nodes	Cost
0	135	872
1	320	854
2	1194	722
done	5000	722

prune214.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
0.3b	(* (/ (sqrt 1.0) F) (tan (* PI l)))
29.7b	(tan (* PI l))

rewrite26.0ms

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:

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

series278.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* PI l)
20.0ms	(* PI l)
171.0ms	(* (/ (sqrt 1.0) F) (tan (* PI l)))
67.0ms	(tan (* PI l))

simplify2.0s

Counts

100 → 100

Iterations

Useful iterations: 2 (108.0ms)

Iter	Nodes	Cost
0	134	900
1	299	877
2	875	797
3	3036	797
done	5000	797

prune291.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(/ (* (sqrt 1.0) (sin (* PI l))) (* F (cos (* PI l))))
29.5b	(sin (* PI l))
29.8b	(cos (* PI l))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

3.0ms	(* PI l)
8.0ms	(/ (* (sqrt 1.0) (sin (* PI l))) (* F (cos (* PI l))))
2.0ms	(sin (* PI l))
2.0ms	(cos (* PI l))

series261.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* PI l)
197.0ms	(/ (* (sqrt 1.0) (sin (* PI l))) (* F (cos (* PI l))))
23.0ms	(sin (* PI l))
20.0ms	(cos (* PI l))

simplify940.0ms

Counts

65 → 65

Iterations

Useful iterations: 2 (130.0ms)

Iter	Nodes	Cost
0	134	793
1	342	762
2	1491	610
done	5001	610

prune232.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt PI) (* (sqrt PI) l))
1.0b	(sqrt PI)
1.0b	(sqrt PI)
29.8b	(tan (* (sqrt PI) (* (sqrt PI) l)))

rewrite19.0ms

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:

11.0ms	(* (sqrt PI) (* (sqrt PI) l))
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
6.0ms	(tan (* (sqrt PI) (* (sqrt PI) l)))

series92.0ms

Counts

4 → 8

Calls

4 calls:

22.0ms	(* (sqrt PI) (* (sqrt PI) l))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
69.0ms	(tan (* (sqrt PI) (* (sqrt PI) l)))

simplify2.7s

Counts

63 → 63

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	70	478
1	153	321
2	417	287
3	985	287
4	3065	287
done	5001	287

prune164.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.4b

regimes366.0ms

Accuracy

84.3% (0.8b remaining)

Error of 8.5b against oracle of 7.7b and baseline of 12.6b

bsearch3.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	52	114
1	71	114
done	71	114

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.6s	823×	body	2560	valid
1.3s	1741×	body	1280	valid
325.0ms	920×	body	640	valid
314.0ms	4487×	body	80	valid
89.0ms	396×	body	320	valid
46.0ms	2×	body	10240	exit
30.0ms	191×	body	160	valid