Details

sample316.0ms

Algorithm

intervals

Results

106.0ms	58×	body	640	valid
105.0ms	65×	body	1280	valid
46.0ms	192×	body	80	valid
21.0ms	27×	body	320	valid
5.0ms	8×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	25
1	48	25
2	157	25
3	881	25
done	5001	25

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize44.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
2.7b	(* (/ (pow t 3.0) (* l l)) (sin k))
13.5b	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
14.6b	(/ (pow t 3.0) (* l l))

rewrite976.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-exp-log`
58×	`prod-exp`
52×	`add-cbrt-cube`
26×	`cbrt-unprod`
24×	`div-exp`
21×	`add-sqr-sqrt`
20×	`pow1`
19×	`*-un-lft-identity`
17×	`times-frac`
16×	`associate-*l/`
14×	`add-cube-cbrt`
13×	`associate-l`
11×	`associate-r`
10×	`frac-times` `unpow-prod-down` `pow-prod-down`
8×	`tan-quot` `cbrt-undiv` `pow-to-exp` `pow-exp`
7×	`associate-/l*`
6×	`associate-*r/`
4×	`flip3-+` `flip-+` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`*-commutative` `distribute-lft-out`
2×	`div-inv`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `associate-/r*`

Counts

4 → 144

Calls

4 calls:

110.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
33.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
797.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
25.0ms	(/ (pow t 3.0) (* l l))

series2.0s

Counts

4 → 12

Calls

4 calls:

474.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
317.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
953.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
238.0ms	(/ (pow t 3.0) (* l l))

simplify625.0ms

Counts

156 → 156

Iterations

Useful iterations: done (620.0ms)

Iter	Nodes	Cost
0	255	3209
1	825	3073
done	5000	2625

prune868.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 16.0b

localize45.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.7b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
7.8b	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
13.5b	(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

304×	`add-exp-log`
184×	`prod-exp`
78×	`add-cbrt-cube`
77×	`div-exp`
50×	`add-sqr-sqrt`
49×	`times-frac`
44×	`associate-*l/` `cbrt-unprod`
42×	`*-un-lft-identity`
37×	`add-cube-cbrt`
36×	`associate-l`
34×	`frac-times`
33×	`pow-exp`
29×	`pow1`
24×	`unpow-prod-down`
22×	`pow-to-exp`
17×	`pow-prod-down`
16×	`tan-quot`
14×	`associate-*r/`
12×	`cbrt-undiv`
11×	`associate-r`
10×	`cbrt-prod`
8×	`flip3-+` `flip-+` `sqr-pow`
5×	`associate-/l*` `unswap-sqr`
4×	`add-log-exp`
3×	`associate-/r` `-commutative` `distribute-lft-out`
2×	`div-inv`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num`

Counts

4 → 229

Calls

4 calls:

257.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
60.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
9.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
1.2s	(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.2s

Counts

4 → 12

Calls

4 calls:

586.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
340.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
271.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
1.0s	(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify798.0ms

Counts

241 → 241

Iterations

Useful iterations: done (781.0ms)

Iter	Nodes	Cost
0	429	6958
1	1362	6586
done	5000	5737

prune1.6s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 9.2b

localize68.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (cbrt t) 3.0)
1.7b	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.7b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
13.5b	(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite2.6s

Algorithm

rewrite-expression-head

Rules

773×	`add-exp-log`
437×	`prod-exp`
291×	`div-exp`
115×	`add-cbrt-cube`
98×	`pow-to-exp` `pow-exp`
63×	`cbrt-unprod`
44×	`associate-*l/`
43×	`add-sqr-sqrt`
36×	`associate-l`
35×	`*-un-lft-identity`
34×	`frac-times` `times-frac`
30×	`pow1` `add-cube-cbrt`
26×	`unpow-prod-down`
25×	`cbrt-undiv`
17×	`pow-prod-down`
16×	`tan-quot`
14×	`associate-*r/`
13×	`cbrt-prod`
11×	`associate-r`
8×	`flip3-+` `flip-+`
5×	`unswap-sqr` `sqr-pow`
4×	`add-log-exp`
3×	`pow-unpow` `*-commutative` `distribute-lft-out`
2×	`pow-pow`
1×	`distribute-rgt-in` `distribute-lft-in` `pow1/3` `div-inv`

Counts

4 → 298

Calls

4 calls:

6.0ms	(pow (cbrt t) 3.0)
401.0ms	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
51.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
2.1s	(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.5s

Counts

4 → 12

Calls

4 calls:

423.0ms	(pow (cbrt t) 3.0)
533.0ms	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
412.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.1s	(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify937.0ms

Counts

310 → 310

Iterations

Useful iterations: done (912.0ms)

Iter	Nodes	Cost
0	458	10217
1	1620	9879
done	5001	8196

prune1.5s

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 8.5b

localize50.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
3.7b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
5.3b	(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k)))
10.6b	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite2.1s

Algorithm

rewrite-expression-head

Rules

745×	`add-exp-log`
479×	`prod-exp`
210×	`div-exp`
142×	`add-cbrt-cube`
79×	`cbrt-unprod`
75×	`pow-to-exp` `pow-exp`
40×	`add-sqr-sqrt`
36×	`associate-l`
35×	`times-frac`
32×	`*-un-lft-identity`
30×	`cbrt-undiv`
27×	`add-cube-cbrt`
20×	`unpow-prod-down`
18×	`associate-*l/`
13×	`pow1`
11×	`associate-r/` `associate-r*`
10×	`cbrt-prod`
5×	`pow-prod-down` `associate-/l/` `unswap-sqr`
4×	`frac-times` `flip3-+` `flip-+` `add-log-exp` `sqr-pow`
3×	`*-commutative` `distribute-lft-out`
2×	`div-inv`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `associate-/r` `associate-/r/` `associate-/l`

Counts

4 → 264

Calls

4 calls:

203.0ms	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
64.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
835.0ms	(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k)))
978.0ms	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.7s

Counts

4 → 12

Calls

4 calls:

384.0ms	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
338.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.2s	(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k)))
771.0ms	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify801.0ms

Counts

276 → 276

Iterations

Useful iterations: done (786.0ms)

Iter	Nodes	Cost
0	401	10294
1	1390	9243
done	5000	7662

prune1.4s

Pruning

24 alts after pruning (22 fresh and 2 done)

Merged error: 6.8b

regimes1.7s

Accuracy

53.3% (3.6b remaining)

Error of 10.6b against oracle of 7.0b and baseline of 14.7b

bsearch705.0ms

Steps

Iters	Range		Point
9	6.545218941452655e-68	7.815403578573561e-63	1.7172356299695205e-64
10	-2.917217971092476e+62	-1.1182076422269923e+52	-1.82032386021601e+57

simplify18.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	57	138
1	73	138
done	73	138

end0.0ms

sample11.4s

Algorithm

intervals

Results

4.7s	2138×	body	1280	valid
2.4s	5949×	body	80	valid
2.2s	1708×	body	640	valid
1.2s	830×	body	320	valid
238.0ms	398×	body	160	valid