Details

sample1.0s

Algorithm

intervals

Results

333.0ms	80×	body	2560	valid
295.0ms	42×	body	5120	valid
234.0ms	125×	body	1280	valid
79.0ms	83×	body	640	valid
22.0ms	34×	body	320	valid
13.0ms	60×	body	80	valid
6.0ms	14×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

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

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 2.0 (* (pow t 3.0) (/ (sin k) l)))
3.6b	(* (/ (/ 2.0 (* (pow t 3.0) (/ (sin k) l))) (pow (/ k t) 2.0)) (/ l (tan k)))
4.9b	(* (pow t 3.0) (/ (sin k) l))
33.9b	(/ (/ 2.0 (* (pow t 3.0) (/ (sin k) l))) (pow (/ k t) 2.0))

rewrite302.0ms

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:

9.0ms	(/ 2.0 (* (pow t 3.0) (/ (sin k) l)))
159.0ms	(* (/ (/ 2.0 (* (pow t 3.0) (/ (sin k) l))) (pow (/ k t) 2.0)) (/ l (tan k)))
32.0ms	(* (pow t 3.0) (/ (sin k) l))
46.0ms	(/ (/ 2.0 (* (pow t 3.0) (/ (sin k) l))) (pow (/ k t) 2.0))

series2.6s

Counts

4 → 12

Calls

4 calls:

476.0ms	(/ 2.0 (* (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)))
324.0ms	(* (pow t 3.0) (/ (sin k) l))
665.0ms	(/ (/ 2.0 (* (pow t 3.0) (/ (sin k) l))) (pow (/ k t) 2.0))

simplify2.3s

Counts

551 → 551

Iterations

Iter	Nodes
done	5001
1	2527
0	795

prune4.5s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.1b

localize72.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ 1 (* (pow t 1.0) (pow k 2.0)))
3.6b	(* (* 2.0 (* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ l (sin k)))) (/ l (tan k)))
6.7b	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ l (sin k)))
7.7b	(* (pow t 1.0) (pow k 2.0))

rewrite404.0ms

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:

17.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
264.0ms	(* (* 2.0 (* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ l (sin k)))) (/ l (tan k)))
52.0ms	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ l (sin k)))
36.0ms	(* (pow t 1.0) (pow k 2.0))

series2.5s

Counts

4 → 12

Calls

4 calls:

473.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
923.0ms	(* (* 2.0 (* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ l (sin k)))) (/ l (tan k)))
675.0ms	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ l (sin k)))
429.0ms	(* (pow t 1.0) (pow k 2.0))

simplify5.6s

Counts

391 → 391

Iterations

Iter	Nodes
done	5000
1	1582
0	504

prune1.4s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 4.1b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ l (tan k))
0.7b	(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
3.6b	(* (* 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)))
6.7b	(* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) (/ l (sin k)))

rewrite772.0ms

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:

4.0ms	(/ l (tan k))
75.0ms	(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
450.0ms	(* (* 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)))
120.0ms	(* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) (/ l (sin k)))

series2.8s

Counts

4 → 12

Calls

4 calls:

181.0ms	(/ l (tan k))
464.0ms	(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
1.1s	(* (* 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)))
1.0s	(* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) (/ l (sin k)))

simplify5.3s

Counts

820 → 820

Iterations

Iter	Nodes
done	5000
1	2219
0	664

prune1.6s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 2.8b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ l (sin k)))
0.6b	(/ 1 (* (pow t 1.0) (pow k (/ 2.0 2))))
2.8b	(* (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))))
3.6b	(* (* 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)))

rewrite1.7s

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:

67.0ms	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ l (sin k)))
29.0ms	(/ 1 (* (pow t 1.0) (pow k (/ 2.0 2))))
115.0ms	(* (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))))
851.0ms	(* (* 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)))

series2.7s

Counts

4 → 12

Calls

4 calls:

347.0ms	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ l (sin k)))
511.0ms	(/ 1 (* (pow t 1.0) (pow k (/ 2.0 2))))
650.0ms	(* (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))))
1.2s	(* (* 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)))

simplify9.7s

Counts

2707 → 2707

Iterations

Iter	Nodes
done	5000
0	1600

prune2.6s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 2.3b

regimes653.0ms

Accuracy

0% (2.6b 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

sample30.9s

Algorithm

intervals

Results

9.5s	2317×	body	2560	valid
8.6s	3989×	body	1280	valid
7.0s	932×	body	5120	valid
3.5s	2554×	body	640	valid
716.0ms	977×	body	320	valid
683.0ms	1985×	body	80	valid
232.0ms	421×	body	160	valid