Details

sample134.0ms

Algorithm

intervals

Results

56.0ms	72×	body	1280	valid
26.0ms	50×	body	640	valid
21.0ms	179×	body	80	valid
10.0ms	27×	body	320	valid
3.0ms	11×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 34.2b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

3.0b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
4.1b	(* (/ (pow t 3.0) (* l l)) (sin k))
10.9b	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
20.2b	(/ (pow t 3.0) (* l l))

rewrite58.0ms

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:

12.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
9.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
24.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
6.0ms	(/ (pow t 3.0) (* l l))

series1.4s

Counts

4 → 12

Calls

4 calls:

321.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
256.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
632.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
184.0ms	(/ (pow t 3.0) (* l l))

simplify125.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 1 (22.0ms)

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

prune500.0ms

Filtered

156 candidates to 93 candidates (59.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	143	13	156
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	144	13	157

Merged error: 20.1b

Counts

157 → 13

localize28.0ms

Local error

Found 4 expressions with local error:

3.0b	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.2b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
10.9b	(* (* (* (/ (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))
12.5b	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)

rewrite88.0ms

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:

18.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
11.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
36.0ms	(* (* (* (/ (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))
5.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)

series1.5s

Counts

4 → 12

Calls

4 calls:

359.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
241.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
739.0ms	(* (* (* (/ (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))
202.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)

simplify62.0ms

Algorithm

egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1347	3795
1	5001	3312

prune1.0s

Filtered

241 candidates to 150 candidates (62.2%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	229	12	241
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	232	22	254

Merged error: 11.3b

Counts

254 → 22

localize24.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
3.0b	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.2b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
10.9b	(* (* (* (* (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))

rewrite144.0ms

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:

25.0ms	(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
25.0ms	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
12.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
46.0ms	(* (* (* (* (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))

series1.7s

Counts

4 → 12

Calls

4 calls:

292.0ms	(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
369.0ms	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
243.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
751.0ms	(* (* (* (* (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))

simplify83.0ms

Algorithm

egg-herbie

Counts

378 → 378

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1479	6579
1	5001	5389

prune1.1s

Filtered

378 candidates to 138 candidates (36.5%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	368	10	378
Fresh	8	13	21
Picked	1	0	1
Done	0	0	0
Total	377	23	400

Merged error: 10.5b

Counts

400 → 23

localize28.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (cbrt t) 3.0)
1.3b	(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
4.2b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
13.1b	(* (* (* (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)))

rewrite115.0ms

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)
19.0ms	(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
11.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
41.0ms	(* (* (* (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)))

series1.6s

Counts

4 → 12

Calls

4 calls:

303.0ms	(pow (cbrt t) 3.0)
291.0ms	(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
243.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
749.0ms	(* (* (* (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)))

simplify84.0ms

Algorithm

egg-herbie

Counts

375 → 375

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1515	6755
1	5001	5848

prune781.0ms

Filtered

375 candidates to 134 candidates (35.7%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	366	9	375
Fresh	6	16	22
Picked	1	0	1
Done	0	0	0
Total	373	25	398

Merged error: 10.2b

Counts

398 → 25

regimes621.0ms

Accuracy

15.9% (6.4b remaining)

Error of 16.4b against oracle of 10.1b and baseline of 17.7b

bsearch304.0ms

Steps

Iters	Range		Point
10	2.148817561883343e-143	3.720390315671067e-124	8.702284512568455e-134
7	-1.173924602192883e+22	-4.390657834609298e+20	-9.786333064001067e+20

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	40
1	49	40

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.6s	2070×	body	1280	valid
960.0ms	1775×	body	640	valid
702.0ms	5850×	body	80	valid
327.0ms	837×	body	320	valid
115.0ms	431×	body	160	valid

Details

sample134.0ms

simplify29.0ms

prune4.0ms

localize25.0ms

rewrite58.0ms

series1.4s

simplify125.0ms

prune500.0ms

localize28.0ms

rewrite88.0ms

series1.5s

simplify62.0ms

prune1.0s

localize24.0ms

rewrite144.0ms

series1.7s

simplify83.0ms

prune1.1s

localize28.0ms

rewrite115.0ms

series1.6s

simplify84.0ms

prune781.0ms

regimes621.0ms

bsearch304.0ms

simplify2.0ms

end0.0ms

sample4.0s

Profiling