Details

sample467.0ms

Algorithm

intervals

Results

158.0ms	30×	body	2560	valid
77.0ms	47×	body	1280	valid
63.0ms	150×	body	80	valid
40.0ms	40×	body	640	valid
4.0ms	6×	body	320	valid
3.0ms	5×	body	160	valid

simplify5.2s

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

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.6b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(* PI l)
3.5b	(/ (tan (* PI l)) (* F F))
30.3b	(tan (* PI l))

rewrite70.0ms

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:

5.0ms	(* PI l)
9.0ms	(* PI l)
28.0ms	(/ (tan (* PI l)) (* F F))
26.0ms	(tan (* PI l))

series331.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* PI l)
27.0ms	(* PI l)
149.0ms	(/ (tan (* PI l)) (* F F))
112.0ms	(tan (* PI l))

simplify1.8s

Counts

82 → 82

Iterations

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

prune346.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 9.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (tan (* PI l)) F)
0.3b	(* PI l)
0.3b	(* PI l)
30.3b	(tan (* PI l))

rewrite46.0ms

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:

23.0ms	(/ (tan (* PI l)) F)
8.0ms	(* PI l)
5.0ms	(* PI l)
8.0ms	(tan (* PI l))

series328.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(/ (tan (* PI l)) F)
38.0ms	(* PI l)
24.0ms	(* PI l)
96.0ms	(tan (* PI l))

simplify2.3s

Counts

88 → 88

Iterations

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

prune367.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (tan (* PI l)) F)
0.3b	(* PI l)
0.3b	(* PI l)
30.3b	(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:

14.0ms	(/ (tan (* PI l)) F)
6.0ms	(* PI l)
5.0ms	(* PI l)
14.0ms	(tan (* PI l))

series326.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(/ (tan (* PI l)) F)
23.0ms	(* PI l)
36.0ms	(* PI l)
101.0ms	(tan (* PI l))

simplify2.0s

Counts

88 → 88

Iterations

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

prune349.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.3b

localize39.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt PI)
1.0b	(cbrt PI)
1.0b	(cbrt PI)
30.4b	(tan (* (* (cbrt PI) (cbrt PI)) (* (cbrt PI) l)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 45

Calls

4 calls:

1.0ms	(cbrt PI)
1.0ms	(cbrt PI)
1.0ms	(cbrt PI)
61.0ms	(tan (* (* (cbrt PI) (cbrt PI)) (* (cbrt PI) l)))

series121.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt PI)
0.0ms	(cbrt PI)
0.0ms	(cbrt PI)
121.0ms	(tan (* (* (cbrt PI) (cbrt PI)) (* (cbrt PI) l)))

simplify1.8s

Counts

51 → 51

Iterations

Iter	Nodes
done	5000
4	1798
3	536
2	201
1	88
0	47

prune262.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.3b

regimes431.0ms

Accuracy

59.2% (2.5b remaining)

Error of 9.1b against oracle of 6.6b and baseline of 12.8b

bsearch2.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	31
1	31
0	24

end0.0ms

sample12.2s

Algorithm

intervals

Results

4.9s	854×	body	2560	valid
3.4s	1638×	body	1280	valid
1.6s	4634×	body	80	valid
1.3s	938×	body	640	valid
387.0ms	407×	body	320	valid
219.0ms	6×	body	10240	exit
93.0ms	188×	body	160	valid