Details

sample65.0ms

Algorithm

intervals

Results

22.0ms	49×	body	1280	valid
12.0ms	36×	body	640	valid
11.0ms	144×	body	80	valid
5.0ms	20×	body	320	valid
1.0ms	7×	body	160	valid

simplify48.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	13
1	74	13
2	138	13
3	203	13
4	368	13
5	1352	13
6	5001	13

prune8.0ms

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

localize17.0ms

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)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

109×	`add-sqr-sqrt`
97×	`associate-l`
70×	`unpow-prod-down`
66×	`times-frac`
59×	`*-un-lft-identity`
55×	`add-cube-cbrt`
37×	`associate-r`
32×	`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`
4×	`sqrt-div` `pow-exp` `add-log-exp`
3×	`pow-unpow` `div-exp`
2×	`flip3-+` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `div-inv` `sqr-pow`

Counts

4 → 188

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)
46.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
28.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series560.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
146.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
202.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
156.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify104.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1150	2379
1	4183	2271
2	5001	2271

prune569.0ms

Filtered

200 candidates to 144 candidates (72.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	191	9	200
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	191	10	201

Merged error: 13.6b

Counts

201 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

6.0b	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
6.0b	(sqrt (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)))
11.5b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

32×	`sqrt-prod`
18×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
12×	`sqrt-div`
10×	`pow1` `add-cube-cbrt` `sqrt-pow1`
6×	`rem-sqrt-square` `pow1/2`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`

Counts

4 → 76

Calls

4 calls:

30.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
31.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
28.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
29.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series789.0ms

Counts

4 → 12

Calls

4 calls:

240.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
232.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
158.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
158.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify59.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	187	1016
1	456	986
2	1671	986
3	5001	962

prune512.0ms

Filtered

88 candidates to 62 candidates (70.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	88	10	98

Merged error: 13.6b

Counts

98 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))
6.0b	(* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (* (cbrt (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)))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

538×	`add-sqr-sqrt`
390×	`unswap-sqr`
137×	`cbrt-prod`
126×	`add-cbrt-cube`
124×	`cbrt-unprod`
89×	`associate-l`
65×	`associate-r`
48×	`sqrt-prod`
46×	`pow1`
45×	`add-exp-log`
31×	`pow-prod-down` `prod-exp`
30×	`swap-sqr`
29×	`*-un-lft-identity`
25×	`add-cube-cbrt`
17×	`*-commutative`
4×	`sqrt-div` `associate-*r/` `add-log-exp`
2×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 280

Calls

4 calls:

2.0ms	(cbrt (cos (/ K 2.0)))
2.0ms	(cbrt (cos (/ K 2.0)))
86.0ms	(* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (* (cbrt (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
28.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series648.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(cbrt (cos (/ K 2.0)))
148.0ms	(cbrt (cos (/ K 2.0)))
205.0ms	(* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (* (cbrt (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
150.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify102.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1143	8977
1	5001	7684

prune685.0ms

Filtered

292 candidates to 156 candidates (53.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	288	4	292
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	290	12	302

Merged error: 13.6b

Counts

302 → 12

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))))
0.3b	(cbrt (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))))
6.0b	(* (* (* -2.0 J) (* (cbrt (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))))) (* (* (cbrt (cbrt (cos (/ K 2.0)))) (cbrt (cbrt (cos (/ K 2.0))))) (* (cbrt (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)))

rewrite7.6s

Algorithm

rewrite-expression-head

Rules

140714×	`add-sqr-sqrt`
118643×	`unswap-sqr`
90541×	`cbrt-prod`
13583×	`swap-sqr`
7210×	`sqrt-prod`
5085×	`*-commutative`
951×	`cbrt-unprod`
816×	`add-cbrt-cube`
597×	`associate-l`
453×	`associate-r`
135×	`pow1`
134×	`add-exp-log`
105×	`pow-prod-down` `prod-exp`
95×	`*-un-lft-identity`
87×	`add-cube-cbrt`
6×	`associate-*r/`
4×	`sqrt-div` `add-log-exp`
2×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 19087

Calls

4 calls:

9.0ms	(cbrt (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))))
9.0ms	(cbrt (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))))
1.2s	(* (* (* -2.0 J) (* (cbrt (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))))) (* (* (cbrt (cbrt (cos (/ K 2.0)))) (cbrt (cbrt (cos (/ K 2.0))))) (* (cbrt (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
31.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series719.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(cbrt (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))))
176.0ms	(cbrt (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))))
207.0ms	(* (* (* -2.0 J) (* (cbrt (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))))) (* (* (cbrt (cbrt (cos (/ K 2.0)))) (cbrt (cbrt (cos (/ K 2.0))))) (* (cbrt (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
160.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify12.5s

Algorithm

egg-herbie

Counts

19099 → 19099

Iterations

Useful iterations: 0 (156.0ms)

Iter	Nodes	Cost
0	5001	1632145

prune21.2s

Filtered

19099 candidates to 2853 candidates (14.9%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	19097	2	19099
Fresh	0	9	9
Picked	1	0	1
Done	0	2	2
Total	19098	13	19111

Merged error: 13.6b

Counts

19111 → 13

regimes449.0ms

Accuracy

81.7% (1.0b remaining)

Error of 13.3b against oracle of 12.3b and baseline of 17.8b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	50
1	45	50

end0.0ms

sample1.8s

Algorithm

intervals

Results

684.0ms	1474×	body	1280	valid
397.0ms	1201×	body	640	valid
333.0ms	4391×	body	80	valid
153.0ms	628×	body	320	valid
52.0ms	308×	body	160	valid