Details

sample1.1s

Algorithm

intervals

Results

721.0ms	57×	body	1280	valid
168.0ms	22×	body	2560	valid
69.0ms	1×	body	10240	exit
68.0ms	27×	body	640	valid
36.0ms	156×	body	80	valid
7.0ms	10×	body	320	valid
6.0ms	11×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
7	2001
6	880
5	396
4	166
3	91
2	45
1	21
0	10

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
4.7b	(/ (tan (* PI l)) (* F F))
30.4b	(tan (* PI l))

rewrite63.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `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 → 78

Calls

4 calls:

11.0ms	(* PI l)
11.0ms	(* PI l)
19.0ms	(/ (tan (* PI l)) (* F F))
10.0ms	(tan (* PI l))

series372.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* PI l)
33.0ms	(* PI l)
202.0ms	(/ (tan (* PI l)) (* F F))
110.0ms	(tan (* PI l))

simplify1.0s

Counts

90 → 90

Iterations

Iter	Nodes
done	2014
3	2014
2	719
1	240
0	108

prune982.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (tan (* PI l)) F)
0.2b	(* PI l)
0.2b	(* PI l)
30.4b	(tan (* PI l))

rewrite50.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `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 → 84

Calls

4 calls:

17.0ms	(/ (tan (* PI l)) F)
11.0ms	(* PI l)
11.0ms	(* PI l)
10.0ms	(tan (* PI l))

series277.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(/ (tan (* PI l)) F)
39.0ms	(* PI l)
24.0ms	(* PI l)
92.0ms	(tan (* PI l))

simplify1.2s

Counts

96 → 96

Iterations

Iter	Nodes
done	2029
4	2029
3	1667
2	588
1	227
0	114

prune979.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 6.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
0.8b	(/ 1 (/ F (tan (* PI l))))
30.4b	(tan (* PI l))

rewrite73.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `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 → 136

Calls

4 calls:

11.0ms	(* PI l)
11.0ms	(* PI l)
30.0ms	(/ 1 (/ F (tan (* PI l))))
17.0ms	(tan (* PI l))

series333.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* PI l)
31.0ms	(* PI l)
177.0ms	(/ 1 (/ F (tan (* PI l))))
93.0ms	(tan (* PI l))

simplify1.1s

Counts

148 → 148

Iterations

Iter	Nodes
done	2003
3	2003
2	1065
1	473
0	207

prune1.6s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.5b

localize53.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt F)
0.6b	(cbrt F)
0.6b	(cbrt F)
30.4b	(tan (* PI l))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`tan-quot`

Counts

4 → 53

Calls

4 calls:

1.0ms	(cbrt F)
1.0ms	(cbrt F)
1.0ms	(cbrt F)
8.0ms	(tan (* PI l))

series1.0s

Counts

4 → 12

Calls

4 calls:

293.0ms	(cbrt F)
327.0ms	(cbrt F)
300.0ms	(cbrt F)
95.0ms	(tan (* PI l))

simplify959.0ms

Counts

65 → 65

Iterations

Iter	Nodes
done	2148
4	2148
3	769
2	274
1	111
0	57

prune772.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 6.5b

regimes652.0ms

Accuracy

61.7% (2.3b remaining)

Error of 8.2b against oracle of 6.0b and baseline of 11.9b

bsearch4.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	31
1	31
0	24

end0.0ms

sample11.2s

Algorithm

intervals

Results

4.2s	750×	body	2560	valid
3.3s	1659×	body	1280	valid
1.8s	937×	body	640	valid
1.1s	4590×	body	80	valid
339.0ms	465×	body	320	valid
136.0ms	4×	body	10240	exit
127.0ms	218×	body	160	valid