Details

analyze2.0s

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

sample123.0ms

Algorithm

intervals

Results

58.0ms	66×	body	1280	valid
25.0ms	41×	body	640	valid
14.0ms	113×	body	80	valid
11.0ms	26×	body	320	valid
3.0ms	10×	body	160	valid

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5501	24

prune19.0ms

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: 15.7b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.2b	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
6.3b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (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)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
22×	`add-cbrt-cube`
16×	`*-un-lft-identity`
15×	`pow1`
13×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `prod-exp`
9×	`cbrt-unprod`
8×	`sqrt-prod`
7×	`unpow-prod-down` `associate-r`
6×	`times-frac` `div-exp` `pow-prod-down`
4×	`sqrt-div` `pow-exp` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `associate-/l*`
2×	`flip3-+` `associate-*r/` `flip-+` `div-inv` `distribute-lft-out`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-l` `clear-num` `associate-/r` `-commutative` `sqr-pow`

Counts

4 → 90

Calls

4 calls:

6.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
7.0ms	(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))))
7.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series125.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
30.0ms	(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))))
36.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify30.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5274	1735

prune268.0ms

Filtered

72 candidates to 102 candidates (-41.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	94	8	102
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	94	10	104

Merged error: 11.3b

Counts

104 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ U (* J (* 2.0 (cos (/ K 2.0)))))
0.2b	(pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)
6.3b	(* J (* (cos (/ K 2.0)) (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)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

6.0ms	(/ U (* J (* 2.0 (cos (/ K 2.0)))))
7.0ms	(pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)
12.0ms	(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))))
7.0ms	(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))

series127.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ U (* J (* 2.0 (cos (/ K 2.0)))))
31.0ms	(pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)
46.0ms	(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))))
33.0ms	(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))

simplify39.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5083	1532

prune252.0ms

Filtered

66 candidates to 95 candidates (-43.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	91	4	95
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	93	12	105

Merged error: 11.2b

Counts

105 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ U J) (* 2.0 (cos (/ K 2.0))))
0.2b	(pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) 2.0)
6.3b	(* J (* (cos (/ K 2.0)) (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)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

53×	`times-frac`
34×	`add-exp-log`
31×	`*-un-lft-identity`
30×	`add-sqr-sqrt`
29×	`add-cube-cbrt`
21×	`add-cbrt-cube`
17×	`unpow-prod-down`
13×	`associate-/l*`
12×	`div-exp`
11×	`pow1`
7×	`prod-exp`
6×	`cbrt-undiv`
5×	`pow-exp` `cbrt-unprod` `div-inv`
4×	`sqrt-div` `associate-*r/` `sqrt-prod` `add-log-exp`
3×	`pow-unpow` `associate-l` `pow-prod-down`
2×	`flip3-+` `flip-+`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r` `clear-num` `associate-/r` `-commutative` `associate-/l/` `distribute-lft-out` `sqr-pow`

Counts

4 → 117

Calls

4 calls:

7.0ms	(/ (/ U J) (* 2.0 (cos (/ K 2.0))))
10.0ms	(pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) 2.0)
16.0ms	(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) 2.0)))))
11.0ms	(sqrt (+ 1.0 (pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) 2.0)))

series124.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (/ U J) (* 2.0 (cos (/ K 2.0))))
33.0ms	(pow (/ (/ U J) (* 2.0 (cos (/ K 2.0)))) 2.0)
41.0ms	(* J (* (cos (/ K 2.0)) (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)))

simplify46.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5154	2065

prune312.0ms

Filtered

95 candidates to 129 candidates (-35.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	129	12	141

Merged error: 11.2b

Counts

141 → 12

localize31.0ms

Local error

Found 4 expressions with local error:

1.7b	(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
1.9b	(* J (* -2.0 (* (cos (/ K 2.0)) (fabs (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)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

8.0ms	(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
6.0ms	(* J (* -2.0 (* (cos (/ K 2.0)) (fabs (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)))

series212.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
35.0ms	(* J (* -2.0 (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))))))
57.0ms	(cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
61.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify58.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5108	1766

prune298.0ms

Filtered

64 candidates to 82 candidates (-28.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	9	9
Picked	0	1	1
Done	1	1	2
Total	82	12	94

Merged error: 11.2b

Counts

94 → 12

regimes575.0ms

Accuracy

0% (5.6b remaining)

Error of 17.9b against oracle of 12.3b and baseline of 17.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	24
1	22	24

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.4s	1544×	body	1280	valid
767.0ms	1257×	body	640	valid
530.0ms	4281×	body	80	valid
269.0ms	626×	body	320	valid
83.0ms	292×	body	160	valid
1.0ms	6×	body	80	invalid

Details

analyze2.0s

sample123.0ms

simplify57.0ms

prune19.0ms

localize17.0ms

rewrite36.0ms

series125.0ms

simplify30.0ms

prune268.0ms

localize19.0ms

rewrite34.0ms

series127.0ms

simplify39.0ms

prune252.0ms

localize17.0ms

rewrite47.0ms

series124.0ms

simplify46.0ms

prune312.0ms

localize31.0ms

rewrite30.0ms

series212.0ms

simplify58.0ms

prune298.0ms

regimes575.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.2s

Profiling