Details

sample487.0ms

Algorithm

intervals

Results

169.0ms	36×	body	5120	valid
132.0ms	69×	body	2560	valid
101.0ms	126×	body	1280	valid
40.0ms	79×	body	640	valid
11.0ms	30×	body	320	valid
7.0ms	62×	body	80	valid
2.0ms	7×	body	160	valid

simplify28.0ms

Counts

1 → 1

Iterations

Useful iterations: 3 (26.0ms)

Iter	Nodes	Cost
0	44	13
1	149	13
2	869	12
3	5001	11
done	5001	11

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
0.8b	(* (pow t 3.0) (tan k))
20.2b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
31.7b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

337×	`add-exp-log`
220×	`prod-exp`
71×	`div-exp`
65×	`add-cbrt-cube`
51×	`pow-exp`
34×	`pow-to-exp` `cbrt-unprod`
30×	`unpow-prod-down`
28×	`add-sqr-sqrt`
24×	`associate-l`
23×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
12×	`cbrt-undiv`
5×	`pow1` `associate-*r/`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`tan-quot` `pow-unpow` `div-inv` `unswap-sqr`
2×	`*-commutative`
1×	`pow-pow` `frac-2neg` `associate-l/` `clear-num` `associate-/r` `associate-/r/` `associate-/l*`

Counts

4 → 187

Calls

4 calls:

6.0ms	(pow (/ k t) 2.0)
14.0ms	(* (pow t 3.0) (tan k))
92.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
48.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series960.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(pow (/ k t) 2.0)
252.0ms	(* (pow t 3.0) (tan k))
384.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
256.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify39.0ms

Counts

199 → 199

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	991	2005
1	5001	1672
done	5001	1672

prune480.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sin k) (cos k))
0.4b	(* (pow (* (pow k 2.0) (pow t 1.0)) 1.0) (/ (sin k) (cos k)))
8.6b	(* (pow k 2.0) (pow t 1.0))
20.2b	(/ (* 2.0 (* l l)) (* (* (pow (* (pow k 2.0) (pow t 1.0)) 1.0) (/ (sin k) (cos k))) (sin k)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

511×	`add-exp-log`
330×	`prod-exp`
134×	`pow-exp`
127×	`div-exp`
67×	`add-cbrt-cube`
62×	`pow-to-exp`
44×	`add-sqr-sqrt`
30×	`cbrt-unprod`
24×	`add-cube-cbrt` `*-un-lft-identity`
21×	`times-frac`
20×	`associate-r`
17×	`cbrt-undiv`
13×	`unpow-prod-down` `unswap-sqr`
12×	`associate-l`
11×	`sqr-pow`
4×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`div-inv`
2×	`frac-2neg` `associate-r/` `clear-num` `-commutative`
1×	`quot-tan` `associate-*l/` `associate-/r/`

Counts

4 → 238

Calls

4 calls:

8.0ms	(/ (sin k) (cos k))
29.0ms	(* (pow (* (pow k 2.0) (pow t 1.0)) 1.0) (/ (sin k) (cos k)))
17.0ms	(* (pow k 2.0) (pow t 1.0))
63.0ms	(/ (* 2.0 (* l l)) (* (* (pow (* (pow k 2.0) (pow t 1.0)) 1.0) (/ (sin k) (cos k))) (sin k)))

series987.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ (sin k) (cos k))
251.0ms	(* (pow (* (pow k 2.0) (pow t 1.0)) 1.0) (/ (sin k) (cos k)))
347.0ms	(* (pow k 2.0) (pow t 1.0))
369.0ms	(/ (* 2.0 (* l l)) (* (* (pow (* (pow k 2.0) (pow t 1.0)) 1.0) (/ (sin k) (cos k))) (sin k)))

simplify55.0ms

Counts

250 → 250

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1144	2986
1	5001	2604
done	5001	2604

prune549.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 19.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (pow (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (sin k) (cos k))) (sin k))
0.3b	(/ (sin k) (cos k))
0.4b	(* (pow (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (sin k) (cos k)))
20.2b	(/ (* 2.0 (* l l)) (* (* (pow (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (sin k) (cos k))) (sin k)))

rewrite291.0ms

Algorithm

rewrite-expression-head

Rules

1794×	`add-exp-log`
1372×	`prod-exp`
590×	`pow-exp`
370×	`div-exp`
290×	`pow-to-exp`
74×	`add-cbrt-cube`
34×	`cbrt-unprod`
29×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
18×	`cbrt-undiv`
16×	`associate-r`
6×	`pow1` `associate-l`
4×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp` `unswap-sqr`
3×	`associate-*r/` `div-inv` `sqr-pow`
2×	`frac-2neg` `associate-l/` `clear-num` `-commutative`
1×	`unpow-prod-down` `quot-tan` `pow-prod-down` `associate-/r/`

Counts

4 → 449

Calls

4 calls:

91.0ms	(* (* (pow (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (sin k) (cos k))) (sin k))
8.0ms	(/ (sin k) (cos k))
49.0ms	(* (pow (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (sin k) (cos k)))
92.0ms	(/ (* 2.0 (* l l)) (* (* (pow (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (sin k) (cos k))) (sin k)))

series909.0ms

Counts

4 → 12

Calls

4 calls:

262.0ms	(* (* (pow (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (sin k) (cos k))) (sin k))
19.0ms	(/ (sin k) (cos k))
260.0ms	(* (pow (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (sin k) (cos k)))
367.0ms	(/ (* 2.0 (* l l)) (* (* (pow (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (sin k) (cos k))) (sin k)))

simplify80.0ms

Counts

461 → 461

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	1285	7620
1	5001	5452
done	5001	5452

prune511.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.0b

localize29.0ms

Local error

Found 4 expressions with local error:

2.8b	(/ l (pow (sin k) 2))
3.2b	(* (/ (* 2.0 l) (pow (* (pow k 2.0) (pow t 1.0)) 1.0)) (/ l (pow (sin k) 2)))
6.6b	(/ (* 2.0 l) (pow (* (pow k 2.0) (pow t 1.0)) 1.0))
8.6b	(* (pow k 2.0) (pow t 1.0))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

495×	`add-exp-log`
259×	`prod-exp`
198×	`div-exp`
192×	`pow-exp`
102×	`pow-to-exp`
68×	`add-sqr-sqrt`
62×	`times-frac`
44×	`add-cube-cbrt` `*-un-lft-identity`
37×	`unpow-prod-down`
35×	`associate-r`
34×	`add-cbrt-cube`
19×	`sqr-pow`
16×	`associate-l`
14×	`unswap-sqr`
13×	`associate-/r*`
10×	`cbrt-undiv` `cbrt-unprod`
8×	`unpow2`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/`

Counts

4 → 305

Calls

4 calls:

8.0ms	(/ l (pow (sin k) 2))
58.0ms	(* (/ (* 2.0 l) (pow (* (pow k 2.0) (pow t 1.0)) 1.0)) (/ l (pow (sin k) 2)))
15.0ms	(/ (* 2.0 l) (pow (* (pow k 2.0) (pow t 1.0)) 1.0))
17.0ms	(* (pow k 2.0) (pow t 1.0))

series966.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ l (pow (sin k) 2))
335.0ms	(* (/ (* 2.0 l) (pow (* (pow k 2.0) (pow t 1.0)) 1.0)) (/ l (pow (sin k) 2)))
209.0ms	(/ (* 2.0 l) (pow (* (pow k 2.0) (pow t 1.0)) 1.0))
346.0ms	(* (pow k 2.0) (pow t 1.0))

simplify127.0ms

Counts

317 → 317

Iterations

Useful iterations: 2 (102.0ms)

Iter	Nodes	Cost
0	1105	3051
1	4795	2827
2	5001	2826
done	5001	2826

prune916.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.4b

regimes404.0ms

Accuracy

72.2% (1.2b remaining)

Error of 9.2b against oracle of 8.0b and baseline of 12.2b

bsearch245.0ms

Steps

Iters	Range		Point
8	5.202175949629937e+144	1.6197547301821798e+147	1.5960164217416833e+147
5	-2.519337225575135e+155	-6.95915484922881e+154	-7.116427264207922e+154

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	29
1	43	29
done	43	29

end0.0ms

sample14.2s

Algorithm

intervals

Results

4.2s	947×	body	5120	valid
4.0s	2169×	body	2560	valid
3.4s	4138×	body	1280	valid
1.3s	2505×	body	640	valid
358.0ms	976×	body	320	valid
250.0ms	2045×	body	80	valid
103.0ms	431×	body	160	valid