Details

sample862.0ms

Algorithm

intervals

Results

298.0ms	90×	body	2560	valid
233.0ms	32×	body	5120	valid
172.0ms	120×	body	1280	valid
79.0ms	76×	body	640	valid
24.0ms	35×	body	320	valid
13.0ms	65×	body	80	valid
5.0ms	12×	body	160	valid

simplify872.0ms

Counts

1 → 1

Iterations

Useful iterations: done (872.0ms)

Iter	Nodes	Cost
0	19	25
1	44	25
2	146	25
3	848	23
done	5001	21

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 39.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (pow t 3.0) (* l l)) (sin k))
0.8b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
13.5b	(/ (pow t 3.0) (* l l))
29.0b	(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

rewrite401.0ms

Algorithm

rewrite-expression-head

Rules

340×	`times-frac`
272×	`add-exp-log`
153×	`unpow-prod-down`
144×	`add-sqr-sqrt`
137×	`add-cube-cbrt` `*-un-lft-identity`
128×	`div-exp`
103×	`prod-exp`
59×	`add-cbrt-cube`
58×	`associate-*l/`
54×	`associate-/r/`
38×	`tan-quot`
34×	`pow-exp`
32×	`div-inv`
24×	`pow-to-exp`
21×	`cbrt-unprod`
19×	`cbrt-undiv` `frac-times` `associate-*r/`
18×	`associate-/r*`
17×	`associate-/l*`
15×	`sqr-pow`
12×	`associate-l`
11×	`pow1`
6×	`associate-r`
4×	`pow-prod-down` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`associate-/l/`

Counts

4 → 354

Calls

4 calls:

47.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
128.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
24.0ms	(/ (pow t 3.0) (* l l))
180.0ms	(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

series2.3s

Counts

4 → 12

Calls

4 calls:

357.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
485.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
271.0ms	(/ (pow t 3.0) (* l l))
1.2s	(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify967.0ms

Counts

366 → 366

Iterations

Useful iterations: done (946.0ms)

Iter	Nodes	Cost
0	662	10242
1	1764	9771
done	5000	9289

prune2.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
5.2b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.1b	(* (pow k 2.0) (pow t 1.0))
16.6b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite224.0ms

Algorithm

rewrite-expression-head

Rules

1597×	`add-exp-log`
1095×	`prod-exp`
882×	`pow-exp`
668×	`div-exp`
492×	`pow-to-exp`
130×	`rec-exp` `1-exp`
37×	`add-sqr-sqrt`
32×	`unpow-prod-down`
20×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
19×	`times-frac` `associate-r`
18×	`associate-l`
14×	`sqr-pow`
12×	`unswap-sqr`
8×	`associate-/r*`
6×	`cbrt-unprod`
5×	`pow1`
4×	`cbrt-undiv` `unpow2` `add-log-exp`
3×	`pow-unpow` `div-inv`
2×	`*-commutative`
1×	`pow-pow` `frac-2neg` `associate-r/` `clear-num` `associate-/l`

Counts

4 → 567

Calls

4 calls:

4.0ms	(pow (sin k) 2)
20.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
26.0ms	(* (pow k 2.0) (pow t 1.0))
104.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.4s

Counts

4 → 12

Calls

4 calls:

28.0ms	(pow (sin k) 2)
117.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
447.0ms	(* (pow k 2.0) (pow t 1.0))
830.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify630.0ms

Counts

579 → 579

Iterations

Useful iterations: done (599.0ms)

Iter	Nodes	Cost
0	438	14412
1	1228	13310
done	5000	12377

prune834.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
0.4b	(pow (sin k) 2)
5.2b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.6b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite563.0ms

Algorithm

rewrite-expression-head

Rules

5603×	`add-exp-log`
4515×	`prod-exp`
3078×	`pow-exp`
2032×	`div-exp`
1869×	`pow-to-exp`
434×	`rec-exp` `1-exp`
27×	`add-cbrt-cube`
23×	`add-sqr-sqrt`
22×	`times-frac`
20×	`unpow-prod-down`
18×	`add-cube-cbrt` `*-un-lft-identity`
12×	`associate-r`
11×	`associate-l`
9×	`associate-/r*`
8×	`cbrt-unprod`
7×	`cbrt-undiv`
6×	`pow1` `sqr-pow`
4×	`div-inv` `associate-/l*` `unpow2` `add-log-exp`
3×	`pow-unpow` `unswap-sqr`
2×	`frac-2neg` `clear-num`
1×	`pow-flip` `pow-pow` `associate-r/` `-commutative` `inv-pow`

Counts

4 → 1460

Calls

4 calls:

68.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
5.0ms	(pow (sin k) 2)
18.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
191.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.5s

Counts

4 → 12

Calls

4 calls:

477.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
21.0ms	(pow (sin k) 2)
165.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
871.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify865.0ms

Counts

1472 → 1472

Iterations

Useful iterations: done (798.0ms)

Iter	Nodes	Cost
0	597	50343
1	1808	34674
done	5000	32849

prune839.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 12.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
2.2b	(/ (pow l 2) (sin k))
2.7b	(* (/ (cos k) (sin k)) (/ (pow l 2) (sin k)))
16.6b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ (pow l 2) (sin k))))

rewrite481.0ms

Algorithm

rewrite-expression-head

Rules

4561×	`add-exp-log`
3350×	`prod-exp`
1881×	`pow-exp`
1593×	`div-exp`
1044×	`pow-to-exp`
310×	`rec-exp` `1-exp`
77×	`add-sqr-sqrt`
76×	`times-frac`
48×	`add-cube-cbrt` `*-un-lft-identity`
45×	`add-cbrt-cube`
30×	`unpow-prod-down`
29×	`associate-r`
24×	`associate-l`
16×	`cbrt-unprod`
12×	`cbrt-undiv`
11×	`associate-/l*`
10×	`unswap-sqr` `sqr-pow`
9×	`unpow2`
7×	`pow1`
5×	`associate-*r/` `div-inv`
4×	`associate-/r*` `add-log-exp`
2×	`frac-times` `frac-2neg` `associate-l/` `clear-num` `-commutative`
1×	`pow-flip` `pow-prod-down` `inv-pow`

Counts

4 → 1131

Calls

4 calls:

47.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
10.0ms	(/ (pow l 2) (sin k))
46.0ms	(* (/ (cos k) (sin k)) (/ (pow l 2) (sin k)))
191.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ (pow l 2) (sin k))))

series1.4s

Counts

4 → 12

Calls

4 calls:

446.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
77.0ms	(/ (pow l 2) (sin k))
126.0ms	(* (/ (cos k) (sin k)) (/ (pow l 2) (sin k)))
799.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ (pow l 2) (sin k))))

simplify1.0s

Counts

1143 → 1143

Iterations

Useful iterations: done (958.0ms)

Iter	Nodes	Cost
0	675	38489
1	2056	25721
done	5001	25246

prune1.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.9b

regimes508.0ms

Accuracy

51.6% (3.5b remaining)

Error of 12.9b against oracle of 9.4b and baseline of 16.6b

bsearch4.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	114
1	69	114
done	69	114

end0.0ms

sample31.4s

Algorithm

intervals

Results

9.0s	2303×	body	2560	valid
7.8s	3994×	body	1280	valid
7.0s	939×	body	5120	valid
4.3s	2569×	body	640	valid
896.0ms	2048×	body	80	valid
786.0ms	1007×	body	320	valid
655.0ms	432×	body	160	valid