Details

sample67.0ms

Algorithm

intervals

Results

25.0ms	56×	body	1280	valid
10.0ms	33×	body	640	valid
10.0ms	131×	body	80	valid
6.0ms	22×	body	320	valid
2.0ms	14×	body	160	valid

simplify46.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	34	13
1	74	13
2	138	13
3	203	13
4	368	13
5	1361	13
6	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: 15.7b

Counts

2 → 1

localize20.0ms

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)
6.4b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.3b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log`
20×	`pow1`
18×	`add-cbrt-cube`
15×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `prod-exp`
11×	`add-cube-cbrt`
10×	`associate-r`
9×	`pow-prod-down` `cbrt-unprod`
8×	`sqrt-prod`
7×	`unpow-prod-down`
4×	`sqrt-div` `pow-exp` `add-log-exp`
3×	`pow-unpow` `times-frac` `div-exp`
2×	`flip3-+` `associate-r/` `associate-l` `-commutative` `flip-+` `distribute-lft-out`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `div-inv` `sqr-pow`

Counts

4 → 85

Calls

4 calls:

5.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
7.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
13.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series516.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
131.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
189.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
146.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify59.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	453	1006
1	1965	898
2	5001	898

prune298.0ms

Filtered

97 candidates to 62 candidates (63.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	89	8	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	8	98

Merged error: 11.2b

Counts

98 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

6.4b	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
6.4b	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.3b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.3b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite34.0ms

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:

8.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
11.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
7.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series711.0ms

Counts

4 → 12

Calls

4 calls:

211.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
214.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
143.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
142.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify58.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	189	1016
1	461	986
2	1696	986
3	5001	962

prune401.0ms

Filtered

88 candidates to 62 candidates (70.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	87	9	96

Merged error: 11.2b

Counts

96 → 9

localize29.0ms

Local error

Found 4 expressions with local error:

8.3b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
13.2b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
13.2b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
13.2b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
12×	`cbrt-prod`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt`
6×	`cbrt-div`
5×	`pow1`
4×	`add-exp-log` `flip3-+` `sqrt-prod` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`
3×	`pow1/3`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

7.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
7.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
7.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
7.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series783.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
211.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
214.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
213.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify53.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	179	931
1	406	873
2	1387	861
3	5002	850

prune453.0ms

Filtered

70 candidates to 59 candidates (84.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	70	9	79

Merged error: 11.2b

Counts

79 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))
6.4b	(* (* (* (* -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))))
8.3b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1`
29×	`add-exp-log`
20×	`add-cbrt-cube`
19×	`pow-prod-down` `prod-exp` `cbrt-unprod`
13×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt`
8×	`sqrt-prod`
7×	`associate-r`
6×	`cbrt-prod`
4×	`sqrt-div` `add-log-exp`
2×	`flip3-+` `pow1/3` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative`

Counts

4 → 74

Calls

4 calls:

1.0ms	(cbrt (cos (/ K 2.0)))
1.0ms	(cbrt (cos (/ K 2.0)))
20.0ms	(* (* (* (* -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))))
6.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series606.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(cbrt (cos (/ K 2.0)))
142.0ms	(cbrt (cos (/ K 2.0)))
185.0ms	(* (* (* (* -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))))
135.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify60.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	401	1337
1	1828	1008
2	5002	913

prune315.0ms

Filtered

86 candidates to 55 candidates (64.0%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	81	5	86
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	83	12	95

Merged error: 11.2b

Counts

95 → 12

regimes486.0ms

Accuracy

85.6% (0.8b remaining)

Error of 13.5b against oracle of 12.7b and baseline of 18.2b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	61
1	50	61

end0.0ms

sample1.9s

Algorithm

intervals

Results

690.0ms	1495×	body	1280	valid
410.0ms	1266×	body	640	valid
333.0ms	4264×	body	80	valid
161.0ms	656×	body	320	valid
54.0ms	322×	body	160	valid