Details

sample1.3s

Algorithm

intervals

Results

623.0ms	67×	body	2560	valid
241.0ms	36×	body	5120	valid
184.0ms	133×	body	1280	valid
79.0ms	76×	body	640	valid
69.0ms	35×	body	320	valid
14.0ms	72×	body	80	valid
8.0ms	16×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Useful iterations: 4 (1.4s)

Iter	Nodes	Cost
0	19	25
1	44	25
2	146	25
3	798	23
4	4467	21
done	5000	21

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.3b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (pow t 3.0) (* l l)) (sin k))
0.6b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
14.0b	(/ (pow t 3.0) (* l l))
26.9b	(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

rewrite342.0ms

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:

40.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
96.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
14.0ms	(/ (pow t 3.0) (* l l))
166.0ms	(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

series1.8s

Counts

4 → 12

Calls

4 calls:

355.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
466.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
241.0ms	(/ (pow t 3.0) (* l l))
756.0ms	(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify1.1s

Counts

366 → 366

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	662	10242
1	1504	9739
done	5001	9233

prune2.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.9b

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
4.9b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.5b	(* (pow k 2.0) (pow t 1.0))
15.3b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite317.0ms

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:

8.0ms	(pow (sin k) 2)
34.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
35.0ms	(* (pow k 2.0) (pow t 1.0))
128.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.8s

Counts

4 → 12

Calls

4 calls:

35.0ms	(pow (sin k) 2)
141.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
612.0ms	(* (pow k 2.0) (pow t 1.0))
996.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.6s

Counts

579 → 579

Iterations

Useful iterations: 2 (697.0ms)

Iter	Nodes	Cost
0	438	14412
1	949	12754
2	2545	12085
done	5000	12085

prune963.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 11.6b

localize39.0ms

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)
4.9b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
15.3b	(* (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)))

rewrite630.0ms

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))))
6.0ms	(pow (sin k) 2)
35.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
219.0ms	(* (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)))

series1.8s

Counts

4 → 12

Calls

4 calls:

546.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
29.0ms	(pow (sin k) 2)
134.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
1.1s	(* (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)))

simplify1.8s

Counts

1472 → 1472

Iterations

Useful iterations: 2 (913.0ms)

Iter	Nodes	Cost
0	597	50343
1	1262	33112
2	2940	31574
done	5001	31574

prune1.0s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 11.1b

localize63.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
4.9b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
4.9b	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0)))
9.8b	(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

rewrite2.7s

Algorithm

rewrite-expression-head

Rules

25023×	`add-exp-log`
19197×	`prod-exp`
16899×	`pow-exp`
11140×	`div-exp`
7959×	`pow-to-exp`
2990×	`rec-exp` `1-exp`
51×	`unpow-prod-down`
43×	`times-frac`
41×	`associate-l`
37×	`add-cbrt-cube`
36×	`add-sqr-sqrt`
31×	`add-cube-cbrt` `*-un-lft-identity`
14×	`cbrt-unprod`
12×	`associate-r`
9×	`associate-/r*` `sqr-pow`
8×	`cbrt-undiv`
5×	`pow1` `div-inv`
4×	`associate-/l*` `add-log-exp`
3×	`unpow2` `unswap-sqr`
2×	`frac-2neg` `associate-l/` `clear-num` `-commutative`
1×	`pow-flip` `associate-*r/` `inv-pow`

Counts

4 → 5762

Calls

4 calls:

24.0ms	(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
19.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
362.0ms	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0)))
152.0ms	(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

series1.8s

Counts

4 → 12

Calls

4 calls:

545.0ms	(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
105.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
578.0ms	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0)))
616.0ms	(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

simplify3.8s

Counts

5774 → 5774

Iterations

Useful iterations: 2 (2.0s)

Iter	Nodes	Cost
0	1477	226017
1	2411	201321
2	4560	190075
done	5002	190075

prune1.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.1b

regimes715.0ms

Accuracy

31.9% (3.8b remaining)

Error of 15.8b against oracle of 12.0b and baseline of 17.6b

bsearch3.0ms

simplify12.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	43	74
1	53	74
done	53	74

end0.0ms

sample32.2s

Algorithm

intervals

Results

8.9s	3994×	body	1280	valid
8.6s	961×	body	5120	valid
8.3s	2247×	body	2560	valid
3.2s	2502×	body	640	valid
1.3s	1008×	body	320	valid
706.0ms	2040×	body	80	valid
213.0ms	441×	body	160	valid