Details

analyze1.9s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
15.6%	84.3%	0.1%	8
15.6%	84.3%	0.1%	9
15.6%	84.3%	0.1%	10
30.4%	69.4%	0.1%	11
30.4%	69.4%	0.1%	12
30.4%	69.4%	0.1%	13
39.6%	60.3%	0.1%	14

sample102.0ms

Algorithm

intervals

Results

30.0ms	36×	body	1280	valid
26.0ms	46×	body	640	valid
21.0ms	137×	body	80	valid
11.0ms	28×	body	320	valid
2.0ms	9×	body	160	valid

simplify55.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5501	24

prune13.0ms

Filtered

1 candidates to 1 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: 18.6b

Counts

2 → 2

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)
8.5b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.9b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite39.0ms

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)
10.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
14.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

series114.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
30.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
35.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
41.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify82.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4983	1601
1	4983	1601

prune248.0ms

Filtered

67 candidates to 97 candidates (-44.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	90	7	97
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	91	8	99

Merged error: 14.4b

Counts

99 → 8

localize28.0ms

Local error

Found 4 expressions with local error:

8.5b	(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))
8.5b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
9.0b	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.0b	(sqrt (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (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:

8.0ms	(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))
7.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0))))

series213.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))
35.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
58.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
87.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0))))

simplify64.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4904	1580
1	4904	1580

prune310.0ms

Filtered

62 candidates to 88 candidates (-41.9%)

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: 14.4b

Counts

96 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

8.5b	(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))
9.0b	(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))))
9.0b	(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))))
9.0b	(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

9.0ms	(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))
13.0ms	(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))))
13.0ms	(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))))
13.0ms	(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))))

series154.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))
42.0ms	(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))))
39.0ms	(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))))
39.0ms	(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))))

simplify49.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4988	1743
1	4988	1743

prune427.0ms

Filtered

59 candidates to 88 candidates (-49.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	87	9	96

Merged error: 14.4b

Counts

96 → 9

localize30.0ms

Local error

Found 4 expressions with local error:

8.5b	(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))
8.5b	(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))
9.0b	(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))))
9.0b	(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

8.0ms	(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))
8.0ms	(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))
14.0ms	(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))))
13.0ms	(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))))

series148.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))
34.0ms	(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))
42.0ms	(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))))
40.0ms	(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))))

simplify51.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4988	1610
1	4988	1610

prune416.0ms

Filtered

58 candidates to 84 candidates (-44.8%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	84	9	93

Merged error: 14.4b

Counts

93 → 9

regimes540.0ms

Accuracy

92.4% (0.4b remaining)

Error of 12.5b against oracle of 12.1b and baseline of 17.7b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	99
1	45	99

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.5s	1518×	body	1280	valid
764.0ms	1274×	body	640	valid
504.0ms	4277×	body	80	valid
267.0ms	630×	body	320	valid
80.0ms	301×	body	160	valid
1.0ms	1×	body	1280	invalid
0.0ms	1×	body	320	invalid
0.0ms	2×	body	80	invalid

Details

analyze1.9s

sample102.0ms

simplify55.0ms

prune13.0ms

localize15.0ms

rewrite39.0ms

series114.0ms

simplify82.0ms

prune248.0ms

localize28.0ms

rewrite33.0ms

series213.0ms

simplify64.0ms

prune310.0ms

localize22.0ms

rewrite50.0ms

series154.0ms

simplify49.0ms

prune427.0ms

localize30.0ms

rewrite45.0ms

series148.0ms

simplify51.0ms

prune416.0ms

regimes540.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample3.4s

Profiling