Details

sample132.0ms

Algorithm

intervals

Results

44.0ms	54×	body	1280	valid
34.0ms	65×	body	640	valid
19.0ms	178×	body	80	valid
10.0ms	27×	body	320	valid
5.0ms	20×	body	160	valid

simplify29.0ms

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: 34.0b

localize26.0ms

Local error

Found 4 expressions with local error:

3.6b	(* (/ (pow t 3.0) (* l l)) (sin k))
4.5b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
12.9b	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
16.1b	(/ (pow t 3.0) (* l l))

rewrite607.0ms

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:

31.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
74.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
485.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
11.0ms	(/ (pow t 3.0) (* l l))

series1.3s

Counts

4 → 12

Calls

4 calls:

229.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
298.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
597.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
172.0ms	(/ (pow t 3.0) (* l l))

simplify124.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 1 (22.0ms)

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

prune485.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 19.4b

localize28.0ms

Local error

Found 4 expressions with local error:

4.5b	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.7b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
7.5b	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
12.9b	(* (* (* (/ (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))

rewrite890.0ms

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:

138.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
29.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
9.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
701.0ms	(* (* (* (/ (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))

series1.4s

Counts

4 → 12

Calls

4 calls:

342.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
222.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
189.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
696.0ms	(* (* (* (/ (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))

simplify60.0ms

Algorithm

egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1347	3795
1	5001	3312

prune1.2s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 12.5b

localize24.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
4.5b	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.7b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
12.9b	(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

1050×	`add-exp-log`
734×	`prod-exp`
255×	`div-exp`
151×	`add-cbrt-cube`
145×	`pow-to-exp` `pow-exp`
96×	`cbrt-unprod`
47×	`associate-*l/`
40×	`add-sqr-sqrt`
37×	`associate-l`
35×	`frac-times`
34×	`pow1` `times-frac`
33×	`associate-*r/`
32×	`*-un-lft-identity`
27×	`add-cube-cbrt`
20×	`unpow-prod-down` `pow-prod-down`
19×	`cbrt-undiv`
16×	`tan-quot`
12×	`associate-r`
10×	`cbrt-prod`
8×	`flip3-+` `flip-+`
5×	`unswap-sqr`
4×	`*-commutative` `add-log-exp` `sqr-pow`
3×	`distribute-lft-out`
1×	`distribute-rgt-in` `distribute-lft-in` `div-inv`

Counts

4 → 366

Calls

4 calls:

85.0ms	(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
261.0ms	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
29.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.1s	(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

260.0ms	(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
324.0ms	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
212.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
688.0ms	(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (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

378 → 378

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1479	6579
1	5001	5389

prune911.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 11.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow (cbrt t) 3.0)
1.0b	(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
4.7b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
16.9b	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

rewrite646.0ms

Algorithm

rewrite-expression-head

Rules

1049×	`add-exp-log`
733×	`prod-exp`
255×	`div-exp`
149×	`add-cbrt-cube`
146×	`pow-to-exp` `pow-exp`
95×	`cbrt-unprod`
41×	`add-sqr-sqrt`
36×	`associate-l`
34×	`times-frac` `associate-*r/`
33×	`pow1`
30×	`frac-times`
29×	`associate-*l/`
28×	`add-cube-cbrt` `*-un-lft-identity`
26×	`unpow-prod-down`
19×	`cbrt-undiv` `pow-prod-down`
13×	`cbrt-prod`
12×	`tan-quot`
8×	`flip3-+` `flip-+`
5×	`associate-r` `unswap-sqr` `sqr-pow`
4×	`distribute-rgt-in` `distribute-lft-in` `add-log-exp`
3×	`pow-unpow` `*-commutative`
2×	`pow-pow`
1×	`pow1/3` `div-inv`

Counts

4 → 363

Calls

4 calls:

3.0ms	(pow (cbrt t) 3.0)
76.0ms	(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
29.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
507.0ms	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

series1.5s

Counts

4 → 12

Calls

4 calls:

292.0ms	(pow (cbrt t) 3.0)
264.0ms	(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
217.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
682.0ms	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

simplify82.0ms

Algorithm

egg-herbie

Counts

375 → 375

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1515	6755
1	5001	5848

prune832.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 11.7b

regimes640.0ms

Accuracy

22.5% (5.8b remaining)

Error of 16.2b against oracle of 10.3b and baseline of 17.9b

bsearch169.0ms

Steps

Iters	Range		Point
4	2.2550830235690177e-146	4.133308837495724e-146	3.5586471885166657e-146
8	-1.5293855688601356e-212	-2.910689807272824e-215	-1.5084231617352398e-212

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	40
1	49	40

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.7s	2043×	body	1280	valid
932.0ms	1700×	body	640	valid
683.0ms	5869×	body	80	valid
317.0ms	858×	body	320	valid
123.0ms	473×	body	160	valid