Details

sample478.0ms

Algorithm

intervals

Results

97.0ms	23×	body	2560	valid
28.0ms	39×	body	1280	valid
16.0ms	45×	body	640	valid
11.0ms	141×	body	80	valid
3.0ms	14×	body	320	valid
1.0ms	7×	body	160	valid

simplify19.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	7
1	41	7
2	82	7
3	122	7
4	147	7
5	157	7
6	159	7
7	159	7
done	159	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.7b	(/ 1.0 (* F F))
3.9b	(* (/ 1.0 (* F F)) (tan (* PI l)))
30.2b	(tan (* PI l))

rewrite79.0ms

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` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `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 → 85

Calls

4 calls:

7.0ms	(* PI l)
8.0ms	(/ 1.0 (* F F))
51.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
9.0ms	(tan (* PI l))

series268.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* PI l)
26.0ms	(/ 1.0 (* F F))
138.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
78.0ms	(tan (* PI l))

simplify43.0ms

Counts

97 → 97

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	334	468
1	1442	399
2	5001	398
done	5001	398

prune238.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 10.3b

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)))
30.2b	(tan (* PI l))

rewrite67.0ms

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×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `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 → 96

Calls

4 calls:

7.0ms	(* PI l)
7.0ms	(* PI l)
41.0ms	(* (/ (sqrt 1.0) F) (tan (* PI l)))
8.0ms	(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)))
66.0ms	(tan (* PI l))

simplify100.0ms

Counts

108 → 108

Iterations

Useful iterations: 3 (94.0ms)

Iter	Nodes	Cost
0	305	522
1	1082	478
2	4101	476
3	5001	475
done	5001	475

prune320.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.3b	(/ (* (sin (* PI l)) (sqrt 1.0)) (* (cos (* PI l)) F))
29.6b	(cos (* PI l))
29.9b	(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` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `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 → 61

Calls

4 calls:

7.0ms	(* PI l)
30.0ms	(/ (* (sin (* PI l)) (sqrt 1.0)) (* (cos (* PI l)) F))
7.0ms	(cos (* PI l))
7.0ms	(sin (* PI l))

series269.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* PI l)
201.0ms	(/ (* (sin (* PI l)) (sqrt 1.0)) (* (cos (* PI l)) F))
18.0ms	(cos (* PI l))
24.0ms	(sin (* PI l))

simplify44.0ms

Counts

73 → 73

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	350	462
1	1685	373
2	5001	371
done	5001	371

prune253.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt l)
0.5b	(cbrt l)
29.8b	(cos (* (* PI (* (cbrt l) (cbrt l))) (cbrt l)))
29.9b	(sin (* PI l))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3`

Counts

4 → 44

Calls

4 calls:

1.0ms	(cbrt l)
1.0ms	(cbrt l)
44.0ms	(cos (* (* PI (* (cbrt l) (cbrt l))) (cbrt l)))
7.0ms	(sin (* PI l))

series425.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(cbrt l)
188.0ms	(cbrt l)
33.0ms	(cos (* (* PI (* (cbrt l) (cbrt l))) (cbrt l)))
23.0ms	(sin (* PI l))

simplify83.0ms

Counts

56 → 56

Iterations

Useful iterations: 3 (79.0ms)

Iter	Nodes	Cost
0	156	247
1	513	219
2	2269	215
3	5001	210
done	5001	210

prune226.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.0b

regimes368.0ms

Accuracy

86.8% (0.6b remaining)

Error of 8.1b against oracle of 7.5b and baseline of 12.2b

bsearch3.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	50
1	65	50
done	65	50

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.5s	807×	body	2560	valid
1.2s	1663×	body	1280	valid
346.0ms	983×	body	640	valid
301.0ms	4537×	body	80	valid
140.0ms	6×	body	10240	exit
90.0ms	404×	body	320	valid
29.0ms	190×	body	160	valid