Details

sample417.0ms

Algorithm

intervals

Results

84.0ms	27×	body	2560	valid
48.0ms	63×	body	1280	valid
11.0ms	28×	body	640	valid
9.0ms	136×	body	80	valid
2.0ms	14×	body	160	valid
2.0ms	7×	body	320	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.3b	(/ 1.0 (* F F))
3.9b	(* (/ 1.0 (* F F)) (tan (* PI l)))
32.1b	(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))

series269.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* PI l)
30.0ms	(/ 1.0 (* F F))
137.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
82.0ms	(tan (* PI l))

simplify879.0ms

Counts

89 → 89

Iterations

Useful iterations: 2 (136.0ms)

Iter	Nodes	Cost
0	135	872
1	318	854
2	1191	722
done	5001	722

prune248.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
0.3b	(* (/ 1.0 F) (tan (* PI l)))
32.1b	(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)
11.0ms	(* (/ 1.0 F) (tan (* PI l)))
2.0ms	(tan (* PI l))

series242.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* PI l)
20.0ms	(* PI l)
134.0ms	(* (/ 1.0 F) (tan (* PI l)))
66.0ms	(tan (* PI l))

simplify1.3s

Counts

90 → 90

Iterations

Useful iterations: 2 (102.0ms)

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

prune283.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 14.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.3b	(/ (* 1.0 (sin (* PI l))) (* F (cos (* PI l))))
31.2b	(cos (* PI l))
31.9b	(sin (* PI l))

rewrite17.0ms

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)
7.0ms	(/ (* 1.0 (sin (* PI l))) (* F (cos (* PI l))))
2.0ms	(cos (* PI l))
2.0ms	(sin (* PI l))

series182.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* PI l)
117.0ms	(/ (* 1.0 (sin (* PI l))) (* F (cos (* PI l))))
18.0ms	(cos (* PI l))
24.0ms	(sin (* PI l))

simplify754.0ms

Counts

65 → 65

Iterations

Useful iterations: 2 (125.0ms)

Iter	Nodes	Cost
0	131	754
1	333	739
2	1466	601
done	5000	601

prune234.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* PI l))
0.6b	(cbrt (* PI l))
31.0b	(cos (* (* (cbrt (* PI l)) (cbrt (* PI l))) (cbrt (* PI l))))
31.9b	(sin (* PI l))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
2×	`cbrt-prod` `pow1/3`

Counts

4 → 32

Calls

4 calls:

1.0ms	(cbrt (* PI l))
1.0ms	(cbrt (* PI l))
13.0ms	(cos (* (* (cbrt (* PI l)) (cbrt (* PI l))) (cbrt (* PI l))))
2.0ms	(sin (* PI l))

series490.0ms

Counts

4 → 12

Calls

4 calls:

218.0ms	(cbrt (* PI l))
216.0ms	(cbrt (* PI l))
29.0ms	(cos (* (* (cbrt (* PI l)) (cbrt (* PI l))) (cbrt (* PI l))))
27.0ms	(sin (* PI l))

simplify1.3s

Counts

44 → 44

Iterations

Useful iterations: 3 (246.0ms)

Iter	Nodes	Cost
0	78	440
1	162	438
2	420	318
3	1783	282
done	5000	282

prune170.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.8b

regimes493.0ms

Accuracy

84.4% (0.7b remaining)

Error of 8.6b against oracle of 7.8b and baseline of 12.5b

bsearch3.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	58	110
1	77	110
done	77	110

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.5s	800×	body	2560	valid
1.2s	1714×	body	1280	valid
338.0ms	962×	body	640	valid
306.0ms	4526×	body	80	valid
140.0ms	6×	body	10240	exit
92.0ms	387×	body	320	valid
30.0ms	194×	body	160	valid