Details

sample617.0ms

Algorithm

intervals

Results

196.0ms	31×	body	2560	valid
71.0ms	47×	body	1280	valid
28.0ms	151×	body	80	valid
23.0ms	26×	body	640	valid
10.0ms	13×	body	320	valid
2.0ms	6×	body	160	valid

simplify5.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
8	4695
7	2334
6	817
5	388
4	156
3	86
2	43
1	20
0	10

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
4.6b	(/ (tan (* PI l)) (* F F))
28.3b	(tan (* PI l))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
6×	`associate-r` `associate-l`
4×	`insert-posit16` `add-log-exp`
3×	`times-frac` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `tan-quot` `*-commutative` `unswap-sqr`
1×	`clear-num` `associate-/r*` `frac-2neg` `div-inv` `associate-/l/`

Counts

4 → 70

Calls

4 calls:

7.0ms	(* PI l)
6.0ms	(* PI l)
16.0ms	(/ (tan (* PI l)) (* F F))
9.0ms	(tan (* PI l))

series304.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* PI l)
29.0ms	(* PI l)
168.0ms	(/ (tan (* PI l)) (* F F))
85.0ms	(tan (* PI l))

simplify1.7s

Counts

82 → 82

Iterations

Iter	Nodes
done	5040
3	3132
2	709
1	230
0	102

prune459.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (tan (* PI l)) F)
0.2b	(* PI l)
0.2b	(* PI l)
28.3b	(tan (* PI l))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
10×	`add-cbrt-cube` `add-exp-log`
9×	`times-frac`
8×	`pow1`
6×	`associate-r` `associate-l`
4×	`insert-posit16` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow-prod-down` `prod-exp` `tan-quot` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv` `associate-/l/`

Counts

4 → 76

Calls

4 calls:

12.0ms	(/ (tan (* PI l)) F)
7.0ms	(* PI l)
7.0ms	(* PI l)
9.0ms	(tan (* PI l))

series367.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ (tan (* PI l)) F)
41.0ms	(* PI l)
45.0ms	(* PI l)
123.0ms	(tan (* PI l))

simplify1.9s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
3	1729
2	583
1	221
0	108

prune521.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (tan (* PI l)) F)
0.2b	(* PI l)
0.2b	(* PI l)
28.3b	(tan (* PI l))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
10×	`add-cbrt-cube` `add-exp-log`
9×	`times-frac`
8×	`pow1`
6×	`associate-r` `associate-l`
4×	`insert-posit16` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow-prod-down` `prod-exp` `tan-quot` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv` `associate-/l/`

Counts

4 → 76

Calls

4 calls:

25.0ms	(/ (tan (* PI l)) F)
6.0ms	(* PI l)
7.0ms	(* PI l)
8.0ms	(tan (* PI l))

series331.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (tan (* PI l)) F)
27.0ms	(* PI l)
44.0ms	(* PI l)
123.0ms	(tan (* PI l))

simplify1.9s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
3	1729
2	583
1	221
0	108

prune392.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
0.8b	(/ 1 (/ F (tan (* PI l))))
28.3b	(tan (* PI l))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
55×	`add-sqr-sqrt`
51×	`*-un-lft-identity` `add-cube-cbrt`
19×	`add-exp-log`
14×	`associate-/r*`
13×	`add-cbrt-cube`
9×	`pow1`
7×	`div-exp`
6×	`associate-r` `associate-l`
5×	`tan-quot` `associate-/r/` `div-inv`
4×	`insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `1-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`clear-num` `frac-2neg` `pow-flip` `inv-pow`

Counts

4 → 128

Calls

4 calls:

8.0ms	(* PI l)
7.0ms	(* PI l)
22.0ms	(/ 1 (/ F (tan (* PI l))))
8.0ms	(tan (* PI l))

series303.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* PI l)
24.0ms	(* PI l)
160.0ms	(/ 1 (/ F (tan (* PI l))))
93.0ms	(tan (* PI l))

simplify2.6s

Counts

140 → 140

Iterations

Iter	Nodes
done	5311
3	3600
2	1085
1	464
0	201

prune522.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 8.1b

regimes611.0ms

Accuracy

62% (2.3b remaining)

Error of 9.1b against oracle of 6.7b and baseline of 12.9b

bsearch2.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	33
1	33
0	25

end0.0ms

sample9.6s

Algorithm

intervals

Results

4.1s	851×	body	2560	valid
2.8s	1658×	body	1280	valid
845.0ms	4479×	body	80	valid
706.0ms	943×	body	640	valid
665.0ms	401×	body	320	valid
103.0ms	3×	body	10240	exit
65.0ms	204×	body	160	valid