Details

sample404.0ms

Algorithm

intervals

Results

225.0ms	37×	body	2560	valid
59.0ms	49×	body	1280	valid
20.0ms	149×	body	80	valid
16.0ms	26×	body	640	valid
4.0ms	11×	body	320	valid
1.0ms	4×	body	160	valid

simplify281.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	14
1	19	14
2	41	14
3	82	14
4	126	14
5	152	14
6	162	14
7	164	14
done	164	14

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.5b	(/ 1.0 (* F F))
2.8b	(* (/ 1.0 (* F F)) (tan (* PI l)))
29.5b	(tan (* PI l))

rewrite100.0ms

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)
11.0ms	(/ 1.0 (* F F))
68.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
11.0ms	(tan (* PI l))

series385.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* PI l)
38.0ms	(/ 1.0 (* F F))
204.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
117.0ms	(tan (* PI l))

simplify1.3s

Counts

97 → 97

Iterations

Useful iterations: 2 (317.0ms)

Iter	Nodes	Cost
0	143	924
1	350	903
2	1911	789
done	5001	789

prune417.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.9b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite112.0ms

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:

14.0ms	(* PI l)
14.0ms	(* PI l)
60.0ms	(* (/ (sqrt 1.0) F) (tan (* PI l)))
17.0ms	(tan (* PI l))

series428.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* PI l)
38.0ms	(* PI l)
228.0ms	(* (/ (sqrt 1.0) F) (tan (* PI l)))
129.0ms	(tan (* PI l))

simplify1.0s

Counts

108 → 108

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	140	946
1	317	921
2	1306	854
done	5001	840

prune477.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 14.8b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(/ (* (sin (* PI l)) (sqrt 1.0)) (* (cos (* PI l)) F))
28.7b	(cos (* PI l))
29.3b	(sin (* PI l))

rewrite81.0ms

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:

15.0ms	(* PI l)
40.0ms	(/ (* (sin (* PI l)) (sqrt 1.0)) (* (cos (* PI l)) F))
9.0ms	(cos (* PI l))
16.0ms	(sin (* PI l))

series365.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* PI l)
276.0ms	(/ (* (sin (* PI l)) (sqrt 1.0)) (* (cos (* PI l)) F))
29.0ms	(cos (* PI l))
24.0ms	(sin (* PI l))

simplify1.2s

Counts

73 → 73

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	139	852
1	355	818
2	1799	679
done	5000	669

prune408.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.5b

localize62.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* PI l))
0.6b	(cbrt (* PI l))
28.5b	(cos (* (* (cbrt (* PI l)) (cbrt (* PI l))) (cbrt (* PI l))))
29.3b	(sin (* PI l))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

7.0ms	(cbrt (* PI l))
6.0ms	(cbrt (* PI l))
97.0ms	(cos (* (* (cbrt (* PI l)) (cbrt (* PI l))) (cbrt (* PI l))))
15.0ms	(sin (* PI l))

series731.0ms

Counts

4 → 12

Calls

4 calls:

340.0ms	(cbrt (* PI l))
309.0ms	(cbrt (* PI l))
50.0ms	(cos (* (* (cbrt (* PI l)) (cbrt (* PI l))) (cbrt (* PI l))))
32.0ms	(sin (* PI l))

simplify4.2s

Counts

52 → 52

Iterations

Useful iterations: done (4.2s)

Iter	Nodes	Cost
0	84	502
1	170	498
2	587	361
3	3551	318
done	5001	300

prune356.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.5b

regimes673.0ms

Accuracy

77.8% (1.0b remaining)

Error of 8.7b against oracle of 7.7b and baseline of 12.3b

bsearch5.0ms

simplify11.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	46	117
1	59	117
done	59	117

end0.0ms

sample9.4s

Algorithm

intervals

Results

4.4s	773×	body	2560	valid
2.8s	1745×	body	1280	valid
780.0ms	4502×	body	80	valid
588.0ms	942×	body	640	valid
204.0ms	399×	body	320	valid
173.0ms	5×	body	10240	exit
66.0ms	228×	body	160	valid