Details

sample1.0s

Algorithm

intervals

Results

611.0ms	61×	body	1280	valid
133.0ms	25×	body	2560	valid
60.0ms	2×	body	10240	exit
31.0ms	31×	body	640	valid
29.0ms	139×	body	80	valid
10.0ms	12×	body	320	valid
2.0ms	5×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	2002
7	2002
6	817
5	388
4	156
3	86
2	43
1	20
0	10

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.9b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(* PI l)
4.5b	(/ (tan (* PI l)) (* F F))
31.5b	(tan (* PI l))

rewrite72.0ms

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:

6.0ms	(* PI l)
16.0ms	(* PI l)
28.0ms	(/ (tan (* PI l)) (* F F))
19.0ms	(tan (* PI l))

series324.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* PI l)
28.0ms	(* PI l)
162.0ms	(/ (tan (* PI l)) (* F F))
109.0ms	(tan (* PI l))

simplify882.0ms

Counts

82 → 82

Iterations

Iter	Nodes
done	2000
3	2000
2	709
1	230
0	102

prune894.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.8b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (tan (* PI l)) F)
0.3b	(* PI l)
0.3b	(* PI l)
31.5b	(tan (* PI l))

rewrite40.0ms

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:

16.0ms	(/ (tan (* PI l)) F)
5.0ms	(* PI l)
5.0ms	(* PI l)
12.0ms	(tan (* PI l))

series329.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(/ (tan (* PI l)) F)
40.0ms	(* PI l)
28.0ms	(* PI l)
79.0ms	(tan (* PI l))

simplify1.3s

Counts

88 → 88

Iterations

Iter	Nodes
done	2029
4	2029
3	1729
2	583
1	221
0	108

prune876.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(* PI l)
0.7b	(/ 1 (/ F (tan (* PI l))))
31.5b	(tan (* PI l))

rewrite56.0ms

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:

11.0ms	(* PI l)
11.0ms	(* PI l)
19.0ms	(/ 1 (/ F (tan (* PI l))))
11.0ms	(tan (* PI l))

series345.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* PI l)
34.0ms	(* PI l)
162.0ms	(/ 1 (/ F (tan (* PI l))))
123.0ms	(tan (* PI l))

simplify1.0s

Counts

140 → 140

Iterations

Iter	Nodes
done	2006
3	2006
2	1085
1	464
0	201

prune1.4s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(* PI l)
0.3b	(* (/ 1 F) (tan (* PI l)))
31.5b	(tan (* PI l))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
19×	`associate-l`
17×	`*-un-lft-identity` `add-exp-log`
16×	`add-cube-cbrt`
13×	`add-cbrt-cube`
11×	`times-frac`
10×	`pow1`
9×	`associate-r`
6×	`prod-exp`
5×	`unswap-sqr`
4×	`cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`pow-prod-down` `tan-quot` `*-commutative`
2×	`div-exp`
1×	`frac-times` `cbrt-undiv` `rec-exp` `1-exp` `associate-l/` `associate-r/` `div-inv`

Counts

4 → 85

Calls

4 calls:

16.0ms	(* PI l)
11.0ms	(* PI l)
28.0ms	(* (/ 1 F) (tan (* PI l)))
8.0ms	(tan (* PI l))

series324.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* PI l)
24.0ms	(* PI l)
184.0ms	(* (/ 1 F) (tan (* PI l)))
92.0ms	(tan (* PI l))

simplify1.4s

Counts

97 → 97

Iterations

Iter	Nodes
done	2004
4	2004
3	1980
2	768
1	290
0	127

prune1.1s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 6.0b

regimes694.0ms

Accuracy

69% (1.8b remaining)

Error of 8.3b against oracle of 6.5b and baseline of 12.4b

bsearch2.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	32
1	32
0	29

end0.0ms

sample12.3s

Algorithm

intervals

Results

4.7s	837×	body	2560	valid
4.4s	1646×	body	1280	valid
1.2s	932×	body	640	valid
1.1s	4495×	body	80	valid
373.0ms	440×	body	320	valid
218.0ms	6×	body	10240	exit
113.0ms	227×	body	160	valid