Details

sample188.0ms

Algorithm

intervals

Results

70.0ms	68×	body	1280	valid
40.0ms	52×	body	640	valid
37.0ms	220×	body	80	valid
12.0ms	25×	body	320	valid
7.0ms	21×	body	160	valid

simplify30.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	13
1	158	13
2	903	13
3	5001	13

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize20.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (/ (pow t 3.0) (* l l)) (sin k))
2.2b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
13.5b	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
16.3b	(/ (pow t 3.0) (* l l))

rewrite350.0ms

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:

15.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
35.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
289.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
5.0ms	(/ (pow t 3.0) (* l l))

series1.4s

Counts

4 → 12

Calls

4 calls:

251.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
333.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
651.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
186.0ms	(/ (pow t 3.0) (* l l))

simplify122.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	801	1619
1	4646	1348
2	5002	1348

prune517.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.5b

localize27.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.5b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
7.2b	(/ (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))

rewrite555.0ms

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:

76.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
18.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
3.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
443.0ms	(* (* (* (/ (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))

series1.6s

Counts

4 → 12

Calls

4 calls:

374.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
249.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
216.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
759.0ms	(* (* (* (/ (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))

simplify61.0ms

Algorithm

egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1347	3795
1	5001	3312

prune1.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (cbrt t) 3.0)
2.2b	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.5b	(* (/ (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))

rewrite1.0s

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:

2.0ms	(pow (cbrt t) 3.0)
168.0ms	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
18.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
801.0ms	(* (* (* (/ (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))

series1.9s

Counts

4 → 12

Calls

4 calls:

300.0ms	(pow (cbrt t) 3.0)
359.0ms	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
234.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.0s	(* (* (* (/ (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))

simplify79.0ms

Algorithm

egg-herbie

Counts

310 → 310

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1552	5337
1	5001	4698

prune953.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.8b

localize27.0ms

Local error

Found 4 expressions with local error:

2.3b	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
3.5b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
7.7b	(/ (* (* (* (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)))
10.4b	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite897.0ms

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:

70.0ms	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
18.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
358.0ms	(/ (* (* (* (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)))
424.0ms	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.8s

Counts

4 → 12

Calls

4 calls:

258.0ms	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
246.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
724.0ms	(/ (* (* (* (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)))
547.0ms	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify70.0ms

Algorithm

egg-herbie

Counts

276 → 276

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1356	5415
1	5002	4747

prune819.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 7.3b

regimes528.0ms

Accuracy

57% (3.3b remaining)

Error of 10.3b against oracle of 7.0b and baseline of 14.7b

bsearch359.0ms

Steps

Iters	Range		Point
9	2.8057318983993542e-92	8.852536544814759e-86	1.4716678417993841e-86
6	-2.499758669720196e-37	-2.8595103141703443e-38	-5.933928029743507e-38

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	118
1	78	118

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.2s	2091×	body	1280	valid
1.3s	1761×	body	640	valid
1.0s	5941×	body	80	valid
431.0ms	820×	body	320	valid
154.0ms	429×	body	160	valid