Details

sample66.0ms

Algorithm

intervals

Results

25.0ms	49×	body	1280	valid
11.0ms	36×	body	640	valid
11.0ms	144×	body	80	valid
4.0ms	20×	body	320	valid
1.0ms	7×	body	160	valid

simplify47.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	13
1	75	13
2	139	13
3	207	13
4	375	13
5	1364	13
6	5002	13

prune3.0ms

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: 18.7b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* -2.0 J) (cos (/ K 2.0)))
0.2b	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
5.9b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
11.5b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

126×	`add-sqr-sqrt`
97×	`associate-l`
74×	`unpow-prod-down`
69×	`times-frac`
59×	`*-un-lft-identity`
55×	`add-cube-cbrt`
37×	`associate-r`
35×	`unswap-sqr`
28×	`add-exp-log`
20×	`pow1`
18×	`add-cbrt-cube`
12×	`prod-exp`
11×	`sqrt-prod` `*-commutative`
9×	`pow-prod-down` `cbrt-unprod`
6×	`hypot-def`
4×	`expm1-log1p-u` `sqrt-div` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `div-exp`
2×	`flip3-+` `associate-*r/` `flip-+` `distribute-lft-out` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `div-inv`

Counts

4 → 202

Calls

4 calls:

8.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
17.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
44.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
30.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series541.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
135.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
201.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
152.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify101.0ms

Algorithm

egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	1161	2449
1	4205	2339
2	5002	2338

prune592.0ms

Filtered

214 candidates to 158 candidates (73.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	205	9	214
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	206	9	215

Merged error: 6.2b

Counts

215 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.1b	(* (* 2.0 J) (cos (/ K 2.0)))
0.1b	(* (* -2.0 J) (cos (/ K 2.0)))
5.9b	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

127×	`associate-l`
119×	`add-sqr-sqrt`
66×	`times-frac`
61×	`add-cube-cbrt` `*-un-lft-identity`
45×	`associate-r`
34×	`unswap-sqr`
32×	`add-exp-log` `add-cbrt-cube`
23×	`pow1`
22×	`associate-/r*`
15×	`prod-exp` `*-commutative` `cbrt-unprod`
12×	`pow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
1×	`frac-2neg` `clear-num` `div-inv`

Counts

4 → 222

Calls

4 calls:

17.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
9.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
8.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
14.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series708.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
53.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
48.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
516.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify103.0ms

Algorithm

egg-herbie

Counts

234 → 234

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	891	2326
1	3897	2103
2	5002	2103

prune868.0ms

Filtered

234 candidates to 175 candidates (74.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	226	8	234
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	233	10	243

Merged error: 6.1b

Counts

243 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.1b	(* (* 2.0 J) (cos (/ K 2.0)))
0.1b	(* (cos (/ K 2.0)) (* (* -2.0 J) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
5.9b	(* (* -2.0 J) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

119×	`add-sqr-sqrt`
108×	`associate-l`
66×	`times-frac`
64×	`associate-r`
61×	`add-cube-cbrt` `*-un-lft-identity`
34×	`unswap-sqr`
32×	`add-exp-log` `add-cbrt-cube`
23×	`pow1`
22×	`associate-/r*`
15×	`prod-exp` `*-commutative` `cbrt-unprod`
12×	`pow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
1×	`frac-2neg` `clear-num` `div-inv`

Counts

4 → 222

Calls

4 calls:

14.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
9.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
15.0ms	(* (cos (/ K 2.0)) (* (* -2.0 J) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
8.0ms	(* (* -2.0 J) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series1.2s

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
51.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
597.0ms	(* (cos (/ K 2.0)) (* (* -2.0 J) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
464.0ms	(* (* -2.0 J) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify122.0ms

Algorithm

egg-herbie

Counts

234 → 234

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	982	2524
1	4796	2259
2	5001	2259

prune671.0ms

Filtered

234 candidates to 174 candidates (74.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	228	6	234
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	231	13	244

Merged error: 6.1b

Counts

244 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ U (cos (/ K 2.0))) (* 2.0 J))
0.1b	(* (cos (/ K 2.0)) (* (* -2.0 J) (hypot (sqrt 1.0) (pow (/ (/ U (cos (/ K 2.0))) (* 2.0 J)) (/ 2.0 2)))))
0.1b	(/ U (cos (/ K 2.0)))
5.9b	(* (* -2.0 J) (hypot (sqrt 1.0) (pow (/ (/ U (cos (/ K 2.0))) (* 2.0 J)) (/ 2.0 2))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

282×	`times-frac`
208×	`add-sqr-sqrt`
157×	`add-cube-cbrt` `*-un-lft-identity`
76×	`associate-r`
75×	`associate-l`
32×	`add-exp-log` `add-cbrt-cube`
28×	`unswap-sqr`
19×	`-commutative` `associate-/l`
18×	`pow1` `associate-/r*`
15×	`div-inv`
11×	`prod-exp` `cbrt-unprod`
9×	`pow-prod-down` `associate-/l/`
7×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`

Counts

4 → 319

Calls

4 calls:

14.0ms	(/ (/ U (cos (/ K 2.0))) (* 2.0 J))
15.0ms	(* (cos (/ K 2.0)) (* (* -2.0 J) (hypot (sqrt 1.0) (pow (/ (/ U (cos (/ K 2.0))) (* 2.0 J)) (/ 2.0 2)))))
5.0ms	(/ U (cos (/ K 2.0)))
9.0ms	(* (* -2.0 J) (hypot (sqrt 1.0) (pow (/ (/ U (cos (/ K 2.0))) (* 2.0 J)) (/ 2.0 2))))

series1.2s

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ (/ U (cos (/ K 2.0))) (* 2.0 J))
584.0ms	(* (cos (/ K 2.0)) (* (* -2.0 J) (hypot (sqrt 1.0) (pow (/ (/ U (cos (/ K 2.0))) (* 2.0 J)) (/ 2.0 2)))))
66.0ms	(/ U (cos (/ K 2.0)))
457.0ms	(* (* -2.0 J) (hypot (sqrt 1.0) (pow (/ (/ U (cos (/ K 2.0))) (* 2.0 J)) (/ 2.0 2))))

simplify77.0ms

Algorithm

egg-herbie

Counts

331 → 331

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1471	4015
1	5002	3741

prune922.0ms

Filtered

331 candidates to 246 candidates (74.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	328	3	331
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	332	12	344

Merged error: 6.1b

Counts

344 → 12

regimes291.0ms

Accuracy

0% (0.4b remaining)

Error of 7.9b against oracle of 7.5b and baseline of 7.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	26
1	27	26

end0.0ms

sample1.8s

Algorithm

intervals

Results

668.0ms	1474×	body	1280	valid
379.0ms	1201×	body	640	valid
329.0ms	4391×	body	80	valid
144.0ms	628×	body	320	valid
47.0ms	308×	body	160	valid