Details

sample80.0ms

Algorithm

intervals

Results

28.0ms	44×	body	1280	valid
16.0ms	35×	body	640	valid
14.0ms	152×	body	80	valid
5.0ms	15×	body	320	valid
2.0ms	10×	body	160	valid

simplify49.0ms

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: 20.4b

Counts

2 → 1

localize22.0ms

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)
8.6b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
10.6b	(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)))

series526.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
133.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
194.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
147.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify58.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 1 (12.0ms)

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

prune268.0ms

Filtered

97 candidates to 62 candidates (63.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	90	7	97
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	90	8	98

Merged error: 14.6b

Counts

98 → 8

localize16.0ms

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)
8.6b	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
10.6b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

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)
17.0ms	(* (* -2.0 J) (* (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)))

series514.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
140.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
188.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
140.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify67.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	488	987
1	2021	866
2	5002	866

prune236.0ms

Filtered

94 candidates to 58 candidates (61.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	94	8	102

Merged error: 14.6b

Counts

102 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

8.6b	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.6b	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
10.6b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
10.6b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite33.0ms

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:

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

series719.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
213.0ms	(sqrt (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)))
152.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify61.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (45.0ms)

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

prune303.0ms

Filtered

88 candidates to 62 candidates (70.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	88	8	96

Merged error: 14.6b

Counts

96 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

8.6b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
10.6b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
10.6b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
10.6b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

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)))
6.0ms	(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)))

series626.0ms

Counts

4 → 12

Calls

4 calls:

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)))
145.0ms	(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)))

simplify43.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	254	1060
1	1124	971
2	5001	961

prune278.0ms

Filtered

87 candidates to 58 candidates (66.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	87	8	95

Merged error: 14.6b

Counts

95 → 8

regimes319.0ms

Accuracy

91.1% (0.5b remaining)

Error of 13.2b against oracle of 12.8b and baseline of 18.1b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	50
1	47	50

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.0s	1493×	body	1280	valid
638.0ms	1280×	body	640	valid
427.0ms	4274×	body	80	valid
229.0ms	644×	body	320	valid
76.0ms	310×	body	160	valid