Details

analyze2.8s

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

sample177.0ms

Algorithm

intervals

Results

67.0ms	50×	body	1280	valid
36.0ms	146×	body	80	valid
34.0ms	34×	body	640	valid
16.0ms	22×	body	320	valid
2.0ms	4×	body	160	valid

simplify107.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	5502	37

prune18.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 18.4b

Counts

2 → 1

localize30.0ms

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)
8.2b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
9.0b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite69.0ms

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)))
9.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
16.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
36.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

series168.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
57.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
45.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
50.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify106.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4977	2466
1	4977	2466

prune332.0ms

Filtered

68 candidates to 97 candidates (-42.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	92	5	97
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	92	6	98

Merged error: 13.0b

Counts

98 → 6

localize52.0ms

Local error

Found 4 expressions with local error:

2.2b	(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
2.3b	(* (* (* -2.0 J) (cos (/ K 2.0))) (fabs (cbrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* J 2.0))) 2.0)))))
15.2b	(cbrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* J 2.0))) 2.0)))
15.2b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite46.0ms

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-r` `flip-+` `distribute-lft-out`
2×	`rem-sqrt-square` `sqrt-pow1` `sqrt-div`
1×	`pow1/2` `associate-l` `*-commutative`

Counts

4 → 70

Calls

4 calls:

12.0ms	(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (fabs (cbrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* J 2.0))) 2.0)))))
10.0ms	(cbrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* J 2.0))) 2.0)))
14.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series380.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
59.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (fabs (cbrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* J 2.0))) 2.0)))))
111.0ms	(cbrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* J 2.0))) 2.0)))
100.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify161.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	4936	2784
1	4936	2784

prune470.0ms

Filtered

63 candidates to 82 candidates (-30.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	82	6	88

Merged error: 13.0b

Counts

88 → 6

localize43.0ms

Local error

Found 4 expressions with local error:

8.2b	(sqrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* J 2.0))) 2.0)))
9.0b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* J 2.0))) 2.0))))
9.0b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* J 2.0))) 2.0))))
9.0b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* J 2.0))) 2.0))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

8.0ms	(sqrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* J 2.0))) 2.0)))
18.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* J 2.0))) 2.0))))
34.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* J 2.0))) 2.0))))
32.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* J 2.0))) 2.0))))

series250.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* J 2.0))) 2.0)))
70.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* J 2.0))) 2.0))))
83.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* J 2.0))) 2.0))))
53.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* J 2.0))) 2.0))))

simplify93.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5365	3621

prune773.0ms

Filtered

62 candidates to 109 candidates (-75.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	109	6	115

Merged error: 13.0b

Counts

115 → 6

localize57.0ms

Local error

Found 4 expressions with local error:

8.5b	(cbrt (- (* 1.0 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (* 2.0 2))))
12.5b	(/ (cbrt (- (* 1.0 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (* 2.0 2)))) (cbrt (- 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
15.2b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
15.2b	(cbrt (- 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

153×	`cbrt-prod`
128×	`add-sqr-sqrt`
90×	`times-frac`
73×	`*-un-lft-identity`
69×	`difference-of-squares`
49×	`add-cube-cbrt`
23×	`unpow-prod-down` `sqr-pow`
11×	`distribute-lft-out--`
10×	`cbrt-div` `associate-/r*`
9×	`associate-/l*`
6×	`add-exp-log`
4×	`pow1` `flip3--` `add-cbrt-cube` `flip--` `add-log-exp`
3×	`pow1/3`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv` `distribute-lft-out`

Counts

4 → 172

Calls

4 calls:

18.0ms	(cbrt (- (* 1.0 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (* 2.0 2))))
47.0ms	(/ (cbrt (- (* 1.0 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (* 2.0 2)))) (cbrt (- 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
16.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
17.0ms	(cbrt (- 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(cbrt (- (* 1.0 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (* 2.0 2))))
109.0ms	(/ (cbrt (- (* 1.0 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (* 2.0 2)))) (cbrt (- 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
84.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
120.0ms	(cbrt (- 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify189.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5345	13398

prune2.5s

Filtered

163 candidates to 184 candidates (-12.9%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	184	6	190

Merged error: 13.0b

Counts

190 → 6

regimes620.0ms

Accuracy

88.5% (0.6b remaining)

Error of 13.1b against oracle of 12.5b and baseline of 17.9b

bsearch2.0ms

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	154
1	46	154

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.7s	1481×	body	1280	valid
1.0s	1243×	body	640	valid
706.0ms	4273×	body	80	valid
402.0ms	693×	body	320	valid
117.0ms	310×	body	160	valid
0.0ms	2×	body	80	invalid

Details

analyze2.8s

sample177.0ms

simplify107.0ms

prune18.0ms

localize30.0ms

rewrite69.0ms

series168.0ms

simplify106.0ms

prune332.0ms

localize52.0ms

rewrite46.0ms

series380.0ms

simplify161.0ms

prune470.0ms

localize43.0ms

rewrite96.0ms

series250.0ms

simplify93.0ms

prune773.0ms

localize57.0ms

rewrite116.0ms

series383.0ms

simplify189.0ms

prune2.5s

regimes620.0ms

bsearch2.0ms

simplify5.0ms

end0.0ms

sample4.2s

Profiling