Details

sample119.0ms

Algorithm

intervals

Results

40.0ms	59×	body	1280	valid
31.0ms	70×	body	640	valid
19.0ms	164×	body	80	valid
9.0ms	29×	body	320	valid
4.0ms	16×	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: 33.3b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
3.6b	(* (/ (pow t 3.0) (* l l)) (sin k))
15.6b	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
16.8b	(/ (pow t 3.0) (* l l))

rewrite59.0ms

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))
12.0ms	(* (/ (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:

317.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
239.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
621.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
179.0ms	(/ (pow t 3.0) (* l l))

simplify118.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 1 (22.0ms)

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

prune476.0ms

Filtered

156 candidates to 93 candidates (59.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	142	14	156
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	143	14	157

Merged error: 17.7b

Counts

157 → 14

localize26.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
2.8b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
9.5b	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
15.6b	(* (* (* (/ (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))

rewrite80.0ms

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))
14.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
5.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
31.0ms	(* (* (* (/ (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:

354.0ms	(* (* (/ (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))
191.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
711.0ms	(* (* (* (/ (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

prune916.0ms

Filtered

241 candidates to 150 candidates (62.2%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	231	10	241
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	236	19	255

Merged error: 12.1b

Counts

255 → 19

localize23.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow (cbrt t) 3.0)
1.8b	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
2.8b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
15.6b	(* (* (* (* (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))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

773×	`add-exp-log`
557×	`prod-exp`
171×	`div-exp`
115×	`add-cbrt-cube`
98×	`pow-to-exp` `pow-exp`
75×	`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` `associate-*r/`
26×	`unpow-prod-down`
17×	`pow-prod-down`
16×	`tan-quot`
13×	`cbrt-undiv` `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:

3.0ms	(pow (cbrt t) 3.0)
24.0ms	(* (* (* (pow (cbrt t) 3.0) (/ (pow (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))
42.0ms	(* (* (* (* (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))

series1.8s

Counts

4 → 12

Calls

4 calls:

291.0ms	(pow (cbrt t) 3.0)
552.0ms	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
230.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
719.0ms	(* (* (* (* (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

310 → 310

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1512	5297
1	5002	4431

prune853.0ms

Filtered

310 candidates to 138 candidates (44.5%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	299	11	310
Fresh	5	13	18
Picked	1	0	1
Done	0	0	0
Total	305	24	329

Merged error: 11.0b

Counts

329 → 24

localize24.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow (cbrt t) 3.0)
0.8b	(pow (cbrt t) 3.0)
2.8b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
17.0b	(* (* (* (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)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

772×	`add-exp-log`
556×	`prod-exp`
171×	`div-exp`
113×	`add-cbrt-cube`
99×	`pow-to-exp` `pow-exp`
74×	`cbrt-unprod`
44×	`add-sqr-sqrt`
35×	`associate-l`
34×	`times-frac`
32×	`unpow-prod-down`
31×	`add-cube-cbrt` `-un-lft-identity` `associate-r/`
29×	`pow1` `frac-times`
26×	`associate-*l/`
16×	`cbrt-prod` `pow-prod-down`
13×	`cbrt-undiv`
12×	`tan-quot`
8×	`flip3-+` `flip-+`
6×	`pow-unpow` `sqr-pow`
5×	`unswap-sqr`
4×	`distribute-rgt-in` `pow-pow` `distribute-lft-in` `associate-r` `add-log-exp`
2×	`pow1/3` `*-commutative`
1×	`div-inv`

Counts

4 → 295

Calls

4 calls:

3.0ms	(pow (cbrt t) 3.0)
3.0ms	(pow (cbrt t) 3.0)
14.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
36.0ms	(* (* (* (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:

298.0ms	(pow (cbrt t) 3.0)
290.0ms	(pow (cbrt t) 3.0)
229.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
698.0ms	(* (* (* (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)))

simplify81.0ms

Algorithm

egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1463	5473
1	5001	4750

prune703.0ms

Filtered

307 candidates to 134 candidates (43.6%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	303	4	307
Fresh	3	20	23
Picked	1	0	1
Done	0	0	0
Total	307	24	331

Merged error: 11.0b

Counts

331 → 24

regimes653.0ms

Accuracy

11.9% (6.7b remaining)

Error of 16.8b against oracle of 10.1b and baseline of 17.7b

bsearch545.0ms

Steps

Iters	Range		Point
9	4.8339210116458816e+117	1.7315093612803965e+123	3.3590285888199126e+118
9	6.0165772449486556e-89	4.331923767059982e-84	4.9174063856139084e-88
6	-1.167033680025666e-160	-1.840183851440567e-161	-1.0367076514937989e-160
8	-1.497668790369623e+132	-2.2942039375383668e+129	-2.5232769949611197e+129

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	109	118
1	109	118

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.4s	2066×	body	1280	valid
778.0ms	1690×	body	640	valid
593.0ms	5869×	body	80	valid
288.0ms	894×	body	320	valid
91.0ms	416×	body	160	valid