Details

sample416.0ms

Algorithm

intervals

Results

84.0ms	27×	body	2560	valid
49.0ms	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

simplify125.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	14
1	19	14
2	40	14
3	79	14
4	116	14
5	138	14
6	147	14
7	149	14
done	149	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))

rewrite33.0ms

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:

3.0ms	(* PI l)
3.0ms	(/ 1.0 (* F F))
16.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
7.0ms	(tan (* PI l))

series254.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* PI l)
24.0ms	(/ 1.0 (* F F))
130.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
77.0ms	(tan (* PI l))

simplify902.0ms

Counts

97 → 97

Iterations

Useful iterations: 2 (135.0ms)

Iter	Nodes	Cost
0	143	924
1	330	903
2	1217	771
done	5001	771

prune255.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.3b

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)))
32.1b	(tan (* PI l))

rewrite30.0ms

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:

3.0ms	(* PI l)
3.0ms	(* PI l)
19.0ms	(* (/ (sqrt 1.0) F) (tan (* PI l)))
2.0ms	(tan (* PI l))

series270.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* PI l)
26.0ms	(* PI l)
160.0ms	(* (/ (sqrt 1.0) F) (tan (* PI l)))
65.0ms	(tan (* PI l))

simplify1.4s

Counts

108 → 108

Iterations

Useful iterations: 2 (109.0ms)

Iter	Nodes	Cost
0	140	946
1	307	921
2	893	840
3	3091	840
done	5000	840

prune345.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 14.2b

localize15.0ms

Local error

Found 4 expressions with local error:

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

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

series263.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* PI l)
197.0ms	(/ (* (sin (* PI l)) (sqrt 1.0)) (* (cos (* PI l)) F))
22.0ms	(cos (* PI l))
25.0ms	(sin (* PI l))

simplify741.0ms

Counts

73 → 73

Iterations

Useful iterations: 2 (134.0ms)

Iter	Nodes	Cost
0	139	852
1	349	818
2	1491	665
done	5000	665

prune276.0ms

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))

rewrite19.0ms

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:

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))

series485.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(cbrt (* PI l))
218.0ms	(cbrt (* PI l))
33.0ms	(cos (* (* (cbrt (* PI l)) (cbrt (* PI l))) (cbrt (* PI l))))
23.0ms	(sin (* PI l))

simplify1.2s

Counts

52 → 52

Iterations

Useful iterations: 3 (261.0ms)

Iter	Nodes	Cost
0	84	502
1	170	498
2	444	361
3	1853	318
done	5000	318

prune212.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.8b

regimes499.0ms

Accuracy

84.3% (0.7b remaining)

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

bsearch3.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	114
1	73	114
done	73	114

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.5s	800×	body	2560	valid
1.2s	1714×	body	1280	valid
350.0ms	962×	body	640	valid
309.0ms	4526×	body	80	valid
140.0ms	6×	body	10240	exit
87.0ms	387×	body	320	valid
31.0ms	194×	body	160	valid