Details

sample135.0ms

Algorithm

intervals

Results

51.0ms	67×	body	1280	valid
33.0ms	64×	body	640	valid
20.0ms	172×	body	80	valid
9.0ms	25×	body	320	valid
5.0ms	18×	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

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: 31.2b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
3.6b	(* (/ (pow t 3.0) (* l l)) (sin k))
12.3b	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
16.5b	(/ (pow t 3.0) (* l l))

rewrite56.0ms

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:

11.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
9.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
23.0ms	(* (* (* (/ (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:

313.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
246.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
625.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
180.0ms	(/ (pow t 3.0) (* l l))

simplify123.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 1 (22.0ms)

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

prune465.0ms

Filtered

156 candidates to 93 candidates (59.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	145	11	156
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	146	11	157

Merged error: 15.8b

Counts

157 → 11

localize27.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (* (/ (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))
8.1b	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
12.3b	(* (* (* (/ (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))

rewrite83.0ms

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:

17.0ms	(* (* (/ (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))
5.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
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))

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))
236.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
194.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
720.0ms	(* (* (* (/ (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))

simplify62.0ms

Algorithm

egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1347	3795
1	5001	3312

prune925.0ms

Filtered

241 candidates to 150 candidates (62.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	231	10	241
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	235	17	252

Merged error: 9.7b

Counts

252 → 17

localize26.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
1.6b	(* (* (/ (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))
12.3b	(* (* (* (/ (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))

rewrite254.0ms

Algorithm

rewrite-expression-head

Rules

1050×	`add-exp-log`
674×	`times-frac`
554×	`prod-exp`
435×	`div-exp`
404×	`unpow-prod-down`
381×	`associate-l`
343×	`add-sqr-sqrt`
335×	`*-un-lft-identity`
330×	`add-cube-cbrt`
202×	`cbrt-prod`
151×	`add-cbrt-cube`
145×	`pow-to-exp` `pow-exp`
78×	`cbrt-unprod`
68×	`sqr-pow`
47×	`associate-*l/`
37×	`cbrt-undiv`
35×	`frac-times`
34×	`pow1`
20×	`pow-prod-down`
16×	`tan-quot`
15×	`associate-*r/`
12×	`associate-r` `div-inv`
8×	`flip3-+` `flip-+`
5×	`unswap-sqr`
4×	`*-commutative` `add-log-exp`
3×	`distribute-lft-out`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-/r/`

Counts

4 → 710

Calls

4 calls:

62.0ms	(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
47.0ms	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
11.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
60.0ms	(* (* (* (/ (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))

series1.8s

Counts

4 → 12

Calls

4 calls:

284.0ms	(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
352.0ms	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
226.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
925.0ms	(* (* (* (/ (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))

simplify147.0ms

Algorithm

egg-herbie

Counts

722 → 722

Iterations

Useful iterations: 1 (49.0ms)

Iter	Nodes	Cost
0	2727	11417
1	5001	10598

prune3.0s

Filtered

722 candidates to 479 candidates (66.3%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	708	14	722
Fresh	7	9	16
Picked	1	0	1
Done	0	0	0
Total	716	23	739

Merged error: 7.0b

Counts

739 → 23

localize25.0ms

Local error

Found 4 expressions with local error:

3.0b	(* (* (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))
5.9b	(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (/ l (pow (cbrt t) 3.0)))
9.0b	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

576×	`add-exp-log`
347×	`prod-exp`
183×	`div-exp`
128×	`times-frac`
103×	`add-cbrt-cube`
80×	`add-sqr-sqrt`
72×	`*-un-lft-identity`
67×	`pow-to-exp` `add-cube-cbrt` `pow-exp`
56×	`unpow-prod-down`
53×	`cbrt-unprod`
36×	`associate-l`
34×	`associate-/r*`
28×	`cbrt-prod` `associate-*l/`
25×	`associate-*r/`
23×	`cbrt-undiv`
19×	`frac-times`
14×	`tan-quot`
13×	`pow1`
11×	`associate-r` `associate-/l/`
10×	`sqr-pow`
8×	`flip3-+` `flip-+`
5×	`pow-prod-down` `unswap-sqr`
4×	`div-inv` `add-log-exp`
3×	`*-commutative` `distribute-lft-out`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `associate-/r/` `associate-/l*`

Counts

4 → 320

Calls

4 calls:

15.0ms	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
11.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
41.0ms	(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (/ l (pow (cbrt t) 3.0)))
28.0ms	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.1s

Counts

4 → 12

Calls

4 calls:

347.0ms	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
230.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
723.0ms	(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (/ l (pow (cbrt t) 3.0)))
814.0ms	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify91.0ms

Algorithm

egg-herbie

Counts

332 → 332

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1740	6179
1	5001	5668

prune1.1s

Filtered

332 candidates to 191 candidates (57.5%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	321	11	332
Fresh	9	13	22
Picked	1	0	1
Done	0	0	0
Total	331	24	355

Merged error: 5.9b

Counts

355 → 24

regimes501.0ms

Accuracy

52.9% (3.5b remaining)

Error of 10.3b against oracle of 6.8b and baseline of 14.3b

bsearch304.0ms

Steps

Iters	Range		Point
9	4.551365472929582e-09	14.716166499582775	6.442870362593039e-06
7	-1.4827304130402651e-151	-1.3532601870290134e-153	-1.4624216300770186e-151

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	77
1	76	77

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.5s	2042×	body	1280	valid
937.0ms	1781×	body	640	valid
717.0ms	5965×	body	80	valid
304.0ms	821×	body	320	valid
110.0ms	417×	body	160	valid