Details

sample240.0ms

Algorithm

intervals

Results

78.0ms	198×	body	80	valid
75.0ms	67×	body	1280	valid
42.0ms	53×	body	640	valid
14.0ms	24×	body	320	valid
5.0ms	13×	body	160	valid

simplify1.0s

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize36.0ms

Local error

Found 4 expressions with local error:

3.4b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
4.1b	(* (/ (pow t 3.0) (* l l)) (sin k))
14.0b	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
16.9b	(/ (pow t 3.0) (* l l))

rewrite894.0ms

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:

111.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
60.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
695.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
13.0ms	(/ (pow t 3.0) (* l l))

series1.9s

Counts

4 → 12

Calls

4 calls:

452.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
306.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
824.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
272.0ms	(/ (pow t 3.0) (* l l))

simplify461.0ms

Counts

156 → 156

Iterations

Useful iterations: done (455.0ms)

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

prune811.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 17.8b

localize41.0ms

Local error

Found 4 expressions with local error:

3.4b	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.8b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
8.0b	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
14.0b	(* (* (* (/ (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))

rewrite1.4s

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:

207.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
37.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
14.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
1.1s	(* (* (* (/ (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))

series2.3s

Counts

4 → 12

Calls

4 calls:

587.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
327.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
287.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
1.1s	(* (* (* (/ (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))

simplify845.0ms

Counts

241 → 241

Iterations

Useful iterations: done (828.0ms)

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

prune1.8s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 12.3b

localize35.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow (cbrt t) 3.0)
3.4b	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.8b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
14.0b	(* (* (* (/ (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))

rewrite2.3s

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:

7.0ms	(pow (cbrt t) 3.0)
399.0ms	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
32.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.8s	(* (* (* (/ (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))

series2.8s

Counts

4 → 12

Calls

4 calls:

448.0ms	(pow (cbrt t) 3.0)
510.0ms	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
387.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.5s	(* (* (* (/ (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))

simplify949.0ms

Counts

310 → 310

Iterations

Useful iterations: done (936.0ms)

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

prune1.6s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 9.0b

localize58.0ms

Local error

Found 4 expressions with local error:

2.9b	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
3.8b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
7.2b	(/ (* (* (* (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)))
11.1b	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite2.2s

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:

182.0ms	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
49.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
824.0ms	(/ (* (* (* (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)))
1.1s	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.5s

Counts

4 → 12

Calls

4 calls:

368.0ms	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
365.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.0s	(/ (* (* (* (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)))
779.0ms	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify833.0ms

Counts

276 → 276

Iterations

Useful iterations: done (817.0ms)

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

prune1.5s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 7.0b

regimes1.2s

Accuracy

53.2% (3.7b remaining)

Error of 10.7b against oracle of 7.0b and baseline of 14.9b

bsearch472.0ms

Steps

Iters	Range		Point
8	5.064835482675284e+41	4.157834906481639e+44	5.130930139981709e+41
6	-1.0292899679065174e-84	-1.0287841356724107e-85	-2.3776106513571675e-85

simplify19.0ms

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	63	163
1	84	161
done	84	161

end0.0ms

sample11.1s

Algorithm

intervals

Results

5.0s	2077×	body	1280	valid
2.3s	1754×	body	640	valid
1.7s	5844×	body	80	valid
1.3s	843×	body	320	valid
198.0ms	439×	body	160	valid