Details

sample480.0ms

Algorithm

intervals

Results

81.0ms	27×	body	2560	valid
42.0ms	59×	body	1280	valid
34.0ms	142×	body	80	valid
10.0ms	28×	body	640	valid
2.0ms	11×	body	320	valid
1.0ms	5×	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: 15.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.6b	(/ 1.0 (* F F))
2.9b	(* (/ 1.0 (* F F)) (tan (* PI l)))
29.5b	(tan (* PI l))

rewrite77.0ms

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:

7.0ms	(* PI l)
8.0ms	(/ 1.0 (* F F))
50.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
9.0ms	(tan (* PI l))

series256.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* PI l)
25.0ms	(/ 1.0 (* F F))
132.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
77.0ms	(tan (* PI l))

simplify40.0ms

Counts

89 → 89

Iterations

Useful iterations: 1 (9.0ms)

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

prune220.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.2b

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)))
29.5b	(tan (* PI l))

rewrite64.0ms

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)
39.0ms	(* (/ (sqrt 1.0) F) (tan (* PI l)))
8.0ms	(tan (* PI l))

series274.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* PI l)
25.0ms	(* PI l)
164.0ms	(* (/ (sqrt 1.0) F) (tan (* PI l)))
64.0ms	(tan (* PI l))

simplify94.0ms

Counts

100 → 100

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	297	498
1	1061	455
2	4012	454
3	5002	454
done	5002	454

prune302.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 12.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.3b	(/ (* (sqrt 1.0) (sin (* PI l))) (* F (cos (* PI l))))
29.2b	(cos (* PI l))
29.3b	(sin (* PI l))

rewrite53.0ms

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:

7.0ms	(* PI l)
28.0ms	(/ (* (sqrt 1.0) (sin (* PI l))) (* F (cos (* PI l))))
10.0ms	(cos (* PI l))
7.0ms	(sin (* PI l))

series259.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* PI l)
195.0ms	(/ (* (sqrt 1.0) (sin (* PI l))) (* F (cos (* PI l))))
21.0ms	(cos (* PI l))
23.0ms	(sin (* PI l))

simplify44.0ms

Counts

65 → 65

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	345	428
1	1721	341
2	5001	341
done	5001	341

prune237.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.6b	(/ 1 (/ (* F (cos (* PI l))) (* (sqrt 1.0) (sin (* PI l)))))
29.2b	(cos (* PI l))
29.3b	(sin (* PI l))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log`
24×	`add-cbrt-cube`
22×	`div-exp`
19×	`times-frac`
18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
13×	`prod-exp`
9×	`cbrt-undiv`
7×	`pow1`
5×	`rec-exp` `1-exp` `associate-/r*` `cbrt-unprod` `div-inv`
4×	`add-log-exp`
3×	`associate-r` `associate-l` `associate-/l*`
1×	`pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r/` `*-commutative` `inv-pow` `unswap-sqr`

Counts

4 → 88

Calls

4 calls:

7.0ms	(* PI l)
35.0ms	(/ 1 (/ (* F (cos (* PI l))) (* (sqrt 1.0) (sin (* PI l)))))
7.0ms	(cos (* PI l))
7.0ms	(sin (* PI l))

series264.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* PI l)
199.0ms	(/ 1 (/ (* F (cos (* PI l))) (* (sqrt 1.0) (sin (* PI l)))))
21.0ms	(cos (* PI l))
23.0ms	(sin (* PI l))

simplify64.0ms

Counts

100 → 100

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	472	894
1	2517	771
2	5003	740
done	5003	740

prune221.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.5b

regimes421.0ms

Accuracy

69.7% (1.4b remaining)

Error of 9.2b against oracle of 7.8b and baseline of 12.3b

bsearch3.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	54
1	68	54
done	68	54

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.6s	834×	body	2560	valid
1.2s	1643×	body	1280	valid
343.0ms	976×	body	640	valid
302.0ms	4550×	body	80	valid
89.0ms	377×	body	320	valid
47.0ms	2×	body	10240	exit
28.0ms	181×	body	160	valid