Details

sample425.0ms

Algorithm

intervals

Results

93.0ms	30×	body	2560	valid
47.0ms	57×	body	1280	valid
11.0ms	35×	body	640	valid
10.0ms	148×	body	80	valid
2.0ms	7×	body	320	valid
1.0ms	6×	body	160	valid

simplify84.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	14
1	18	14
2	38	14
3	73	14
4	109	14
5	130	14
6	137	14
done	137	14

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.3b	(/ 1.0 (* F F))
4.6b	(* (/ 1.0 (* F F)) (tan (* PI l)))
32.4b	(tan (* PI l))

rewrite28.0ms

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` `div-exp` `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 → 77

Calls

4 calls:

3.0ms	(* PI l)
3.0ms	(/ 1.0 (* F F))
15.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
3.0ms	(tan (* PI l))

series262.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* PI l)
25.0ms	(/ 1.0 (* F F))
135.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
78.0ms	(tan (* PI l))

simplify525.0ms

Counts

89 → 89

Iterations

Useful iterations: 2 (119.0ms)

Iter	Nodes	Cost
0	135	872
1	318	854
2	1207	722
done	5000	722

prune225.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 16.0b

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)))
32.4b	(tan (* PI l))

rewrite28.0ms

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×	`prod-exp` `cbrt-unprod` `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 → 88

Calls

4 calls:

3.0ms	(* PI l)
3.0ms	(* PI l)
18.0ms	(* (/ (sqrt 1.0) F) (tan (* PI l)))
2.0ms	(tan (* PI l))

series276.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* PI l)
23.0ms	(* PI l)
166.0ms	(* (/ (sqrt 1.0) F) (tan (* PI l)))
66.0ms	(tan (* PI l))

simplify1.3s

Counts

100 → 100

Iterations

Useful iterations: 2 (98.0ms)

Iter	Nodes	Cost
0	134	900
1	299	877
2	880	797
3	3080	797
done	5000	797

prune315.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 15.9b

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))
31.8b	(cos (* PI l))
32.1b	(sin (* PI l))

rewrite15.0ms

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` `div-exp` `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 → 53

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))

series262.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* PI l)
198.0ms	(/ (* (sin (* PI l)) (sqrt 1.0)) (* (cos (* PI l)) F))
17.0ms	(cos (* PI l))
26.0ms	(sin (* PI l))

simplify487.0ms

Counts

65 → 65

Iterations

Useful iterations: 2 (120.0ms)

Iter	Nodes	Cost
0	131	794
1	338	763
2	1485	611
done	5001	611

prune250.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 10.5b

localize22.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt PI)
1.0b	(* (cbrt PI) (cbrt PI))
31.4b	(cos (* (* (cbrt PI) (cbrt PI)) (* (cbrt PI) l)))
32.1b	(sin (* PI l))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`cbrt-prod`
13×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
7×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 65

Calls

4 calls:

0.0ms	(cbrt PI)
6.0ms	(* (cbrt PI) (cbrt PI))
7.0ms	(cos (* (* (cbrt PI) (cbrt PI)) (* (cbrt PI) l)))
2.0ms	(sin (* PI l))

series45.0ms

Counts

4 → 8

Calls

4 calls:

0.0ms	(cbrt PI)
0.0ms	(* (cbrt PI) (cbrt PI))
21.0ms	(cos (* (* (cbrt PI) (cbrt PI)) (* (cbrt PI) l)))
24.0ms	(sin (* PI l))

simplify1.7s

Counts

73 → 73

Iterations

Useful iterations: 3 (466.0ms)

Iter	Nodes	Cost
0	92	598
1	178	547
2	582	463
3	2890	425
done	5001	425

prune235.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 10.4b

regimes533.0ms

Accuracy

85.7% (0.6b remaining)

Error of 8.7b against oracle of 8.0b and baseline of 12.5b

bsearch3.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	112
1	71	112
done	71	112

end0.0ms

sample4.7s

Algorithm

intervals

Results

2.5s	823×	body	2560	valid
1.2s	1659×	body	1280	valid
325.0ms	959×	body	640	valid
300.0ms	4589×	body	80	valid
93.0ms	4×	body	10240	exit
92.0ms	398×	body	320	valid
36.0ms	213×	body	160	valid