Details

sample968.0ms

Algorithm

intervals

Results

294.0ms	32×	body	5120	valid
243.0ms	71×	body	2560	valid
195.0ms	125×	body	1280	valid
82.0ms	79×	body	640	valid
73.0ms	38×	body	320	valid
17.0ms	72×	body	80	valid
9.0ms	18×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	856
2	149
1	44
0	19

prune38.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 37.6b

localize43.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 2.0 (* (pow t 3.0) (/ (sin k) l)))
3.4b	(* (pow t 3.0) (/ (sin k) l))
3.7b	(* (/ (/ 2.0 (* (pow t 3.0) (/ (sin k) l))) (pow (/ k t) 2.0)) (/ l (tan k)))
32.3b	(/ (/ 2.0 (* (pow t 3.0) (/ (sin k) l))) (pow (/ k t) 2.0))

rewrite249.0ms

Algorithm

rewrite-expression-head

Rules

569×	`times-frac`
499×	`add-exp-log`
286×	`div-exp`
275×	`add-sqr-sqrt`
230×	`unpow-prod-down`
229×	`*-un-lft-identity` `add-cube-cbrt`
150×	`prod-exp`
147×	`associate-l`
77×	`add-cbrt-cube`
76×	`pow-exp`
57×	`div-inv`
52×	`pow-to-exp`
38×	`associate-*r/`
37×	`associate-/r/`
34×	`cbrt-undiv`
27×	`associate-r`
22×	`sqr-pow`
20×	`cbrt-unprod`
18×	`associate-/r*`
16×	`unswap-sqr`
11×	`associate-/l*`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`frac-times` `pow-prod-down` `associate-*l/` `tan-quot` `associate-/l/`

Counts

4 → 539

Calls

4 calls:

18.0ms	(/ 2.0 (* (pow t 3.0) (/ (sin k) l)))
23.0ms	(* (pow t 3.0) (/ (sin k) l))
124.0ms	(* (/ (/ 2.0 (* (pow t 3.0) (/ (sin k) l))) (pow (/ k t) 2.0)) (/ l (tan k)))
34.0ms	(/ (/ 2.0 (* (pow t 3.0) (/ (sin k) l))) (pow (/ k t) 2.0))

series2.6s

Counts

4 → 12

Calls

4 calls:

520.0ms	(/ 2.0 (* (pow t 3.0) (/ (sin k) l)))
326.0ms	(* (pow t 3.0) (/ (sin k) l))
1.1s	(* (/ (/ 2.0 (* (pow t 3.0) (/ (sin k) l))) (pow (/ k t) 2.0)) (/ l (tan k)))
612.0ms	(/ (/ 2.0 (* (pow t 3.0) (/ (sin k) l))) (pow (/ k t) 2.0))

simplify2.4s

Counts

551 → 551

Iterations

Iter	Nodes
done	5000
1	2527
0	795

prune4.9s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.3b

localize47.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (* (pow t 1.0) (pow k 2.0)))
3.7b	(* (* 2.0 (* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ l (sin k)))) (/ l (tan k)))
6.4b	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ l (sin k)))
8.4b	(* (pow t 1.0) (pow k 2.0))

rewrite336.0ms

Algorithm

rewrite-expression-head

Rules

1010×	`add-exp-log`
666×	`prod-exp`
318×	`pow-exp`
307×	`div-exp`
138×	`pow-to-exp`
70×	`rec-exp` `1-exp`
52×	`add-sqr-sqrt`
48×	`add-cbrt-cube`
34×	`associate-r`
27×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
22×	`cbrt-unprod`
21×	`unpow-prod-down`
19×	`associate-l`
15×	`unswap-sqr`
11×	`sqr-pow`
10×	`pow1`
9×	`cbrt-undiv`
6×	`associate-*r/`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-prod-down` `-commutative` `associate-/l`
1×	`frac-times` `clear-num` `associate-/r` `frac-2neg` `associate-l/` `tan-quot` `associate-/r/` `pow-flip` `inv-pow`

Counts

4 → 379

Calls

4 calls:

15.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
212.0ms	(* (* 2.0 (* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ l (sin k)))) (/ l (tan k)))
59.0ms	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ l (sin k)))
19.0ms	(* (pow t 1.0) (pow k 2.0))

series2.7s

Counts

4 → 12

Calls

4 calls:

426.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
1.2s	(* (* 2.0 (* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ l (sin k)))) (/ l (tan k)))
646.0ms	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ l (sin k)))
478.0ms	(* (pow t 1.0) (pow k 2.0))

simplify6.1s

Counts

391 → 391

Iterations

Iter	Nodes
done	5000
1	1582
0	504

prune1.6s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.6b

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ l (tan k))
0.4b	(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
3.7b	(* (* 2.0 (* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) (/ l (sin k)))) (/ l (tan k)))
6.4b	(* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) (/ l (sin k)))

rewrite781.0ms

Algorithm

rewrite-expression-head

Rules

3331×	`add-exp-log`
2547×	`prod-exp`
1152×	`pow-exp`
917×	`div-exp`
594×	`pow-to-exp`
217×	`rec-exp` `1-exp`
52×	`add-cbrt-cube`
44×	`add-sqr-sqrt`
36×	`times-frac`
31×	`*-un-lft-identity` `add-cube-cbrt`
27×	`associate-r`
23×	`cbrt-unprod`
12×	`associate-l`
11×	`cbrt-undiv`
10×	`pow1`
9×	`unpow-prod-down`
6×	`associate-r/` `associate-/l` `unswap-sqr`
5×	`div-inv`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `sqr-pow`
2×	`clear-num` `frac-2neg` `tan-quot` `associate-/r/` `*-commutative`
1×	`frac-times` `associate-*l/` `pow-flip` `inv-pow`

Counts

4 → 808

Calls

4 calls:

10.0ms	(/ l (tan k))
60.0ms	(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
421.0ms	(* (* 2.0 (* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) (/ l (sin k)))) (/ l (tan k)))
116.0ms	(* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) (/ l (sin k)))

series2.5s

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ l (tan k))
490.0ms	(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
1.2s	(* (* 2.0 (* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) (/ l (sin k)))) (/ l (tan k)))
690.0ms	(* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) (/ l (sin k)))

simplify5.4s

Counts

820 → 820

Iterations

Iter	Nodes
done	5000
1	2219
0	664

prune1.7s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 3.1b

localize64.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* (pow t 1.0) (pow k (/ 2.0 2))))
0.6b	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ l (sin k)))
1.9b	(* (pow (/ 1 (* (pow t 1.0) (pow k (/ 2.0 2)))) 1.0) (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ l (sin k))))
3.7b	(* (* 2.0 (* (pow (/ 1 (* (pow t 1.0) (pow k (/ 2.0 2)))) 1.0) (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ l (sin k))))) (/ l (tan k)))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

13914×	`add-exp-log`
10233×	`prod-exp`
6293×	`pow-exp`
4747×	`div-exp`
2243×	`pow-to-exp`
1360×	`rec-exp` `1-exp`
83×	`add-sqr-sqrt`
68×	`add-cbrt-cube`
66×	`times-frac`
59×	`unpow-prod-down`
44×	`*-un-lft-identity`
41×	`associate-l`
38×	`add-cube-cbrt`
36×	`cbrt-unprod`
28×	`associate-r`
18×	`unswap-sqr`
11×	`cbrt-undiv` `sqr-pow`
10×	`pow1` `associate-*r/`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `-commutative` `associate-/l`
1×	`frac-times` `clear-num` `associate-/r` `frac-2neg` `associate-l/` `tan-quot` `associate-/r/` `pow-flip` `inv-pow`

Counts

4 → 2695

Calls

4 calls:

18.0ms	(/ 1 (* (pow t 1.0) (pow k (/ 2.0 2))))
80.0ms	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ l (sin k)))
145.0ms	(* (pow (/ 1 (* (pow t 1.0) (pow k (/ 2.0 2)))) 1.0) (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ l (sin k))))
940.0ms	(* (* 2.0 (* (pow (/ 1 (* (pow t 1.0) (pow k (/ 2.0 2)))) 1.0) (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ l (sin k))))) (/ l (tan k)))

series3.1s

Counts

4 → 12

Calls

4 calls:

471.0ms	(/ 1 (* (pow t 1.0) (pow k (/ 2.0 2))))
399.0ms	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ l (sin k)))
595.0ms	(* (pow (/ 1 (* (pow t 1.0) (pow k (/ 2.0 2)))) 1.0) (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ l (sin k))))
1.7s	(* (* 2.0 (* (pow (/ 1 (* (pow t 1.0) (pow k (/ 2.0 2)))) 1.0) (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ l (sin k))))) (/ l (tan k)))

simplify9.4s

Counts

2707 → 2707

Iterations

Iter	Nodes
done	5000
0	1600

prune3.1s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 2.6b

regimes899.0ms

Accuracy

0% (2.7b remaining)

Error of 5.3b against oracle of 2.6b and baseline of 5.3b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	30
1	30
0	23

end0.0ms

sample31.5s

Algorithm

intervals

Results

9.1s	4025×	body	1280	valid
8.2s	2196×	body	2560	valid
7.4s	952×	body	5120	valid
3.8s	2527×	body	640	valid
811.0ms	947×	body	320	valid
666.0ms	437×	body	160	valid
585.0ms	2009×	body	80	valid