Details

sample191.0ms

Algorithm

intervals

Results

120.0ms	120×	body	1280	valid
44.0ms	73×	body	640	valid
7.0ms	17×	body	320	valid
5.0ms	41×	body	80	valid
1.0ms	5×	body	160	valid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	10
1	35	10
2	63	10
3	137	10
4	417	10
5	1798	10
6	5002	10

prune3.0ms

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: 6.0b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
0.2b	(pow (sin ky) 2.0)
0.2b	(pow (sin kx) 2.0)
5.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
30×	`associate-l`
26×	`times-frac`
25×	`add-cube-cbrt`
21×	`sqrt-prod`
14×	`unpow-prod-down`
11×	`add-exp-log`
9×	`pow1` `add-cbrt-cube`
8×	`distribute-lft-out`
6×	`pow-unpow`
4×	`sqrt-div` `add-log-exp`
3×	`associate-r` `unswap-sqr`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 101

Calls

4 calls:

15.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
2.0ms	(pow (sin ky) 2.0)
3.0ms	(pow (sin kx) 2.0)
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
110.0ms	(pow (sin ky) 2.0)
104.0ms	(pow (sin kx) 2.0)
78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	391	990
1	1382	928
2	5001	927

prune376.0ms

Filtered

113 candidates to 78 candidates (69.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	102	11	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	11	114

Merged error: 4.5b

Counts

114 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin kx) 2.0)
0.2b	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.3b	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
5.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

72×	`*-un-lft-identity`
50×	`times-frac`
49×	`add-sqr-sqrt`
41×	`sqrt-prod`
40×	`add-cube-cbrt`
30×	`associate-r`
19×	`unpow-prod-down`
16×	`distribute-lft-out`
12×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`pow1` `associate-/r*`
6×	`sqrt-div`
4×	`associate-/r/` `add-log-exp`
3×	`pow-unpow` `flip3-+` `associate-l` `flip-+` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `sqr-pow`

Counts

4 → 133

Calls

4 calls:

3.0ms	(pow (sin kx) 2.0)
17.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
11.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series452.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(pow (sin kx) 2.0)
144.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
127.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify55.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	412	1572
1	1672	1426
2	5002	1423

prune369.0ms

Filtered

145 candidates to 86 candidates (59.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	146	10	156

Merged error: 4.5b

Counts

156 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin ky) (* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)))
0.3b	(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
0.3b	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
5.5b	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

77×	`*-un-lft-identity`
49×	`times-frac`
48×	`add-sqr-sqrt`
45×	`sqrt-prod`
35×	`add-cube-cbrt`
27×	`associate-l`
20×	`unpow-prod-down` `distribute-lft-out`
15×	`add-exp-log`
14×	`pow1`
13×	`add-cbrt-cube`
6×	`associate-/r/`
5×	`associate-/r*`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `sqrt-div` `flip-+` `div-inv` `associate-/l*`
2×	`pow-flip` `div-exp` `associate-l/` `-commutative` `inv-pow`
1×	`cbrt-undiv` `rec-exp` `frac-2neg` `pow1/2` `1-exp` `associate-*r/` `clear-num`

Counts

4 → 139

Calls

4 calls:

19.0ms	(* (sin ky) (* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)))
9.0ms	(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
15.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
10.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

series480.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(* (sin ky) (* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)))
79.0ms	(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
144.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
104.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

simplify52.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	378	1609
1	1452	1453
2	5001	1395

prune358.0ms

Filtered

151 candidates to 85 candidates (56.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	149	2	151
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	152	9	161

Merged error: 4.5b

Counts

161 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin kx) 2.0)
0.5b	(* (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
5.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
5.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

100×	`sqrt-prod`
52×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
34×	`sqrt-pow1`
30×	`pow1`
28×	`sqrt-div`
20×	`add-cube-cbrt`
19×	`swap-sqr`
18×	`pow1/2`
15×	`unpow-prod-down`
14×	`distribute-lft-out`
11×	`associate-r` `associate-l`
9×	`pow-prod-up` `unswap-sqr`
8×	`flip3-+` `flip-+`
7×	`add-exp-log`
6×	`add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `add-log-exp`
3×	`pow-unpow`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`pow2` `pow-to-exp` `pow-pow` `pow-plus` `sqrt-unprod` `pow-exp` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `sqr-pow`

Counts

4 → 142

Calls

4 calls:

3.0ms	(pow (sin kx) 2.0)
22.0ms	(* (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(pow (sin kx) 2.0)
78.0ms	(* (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
80.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify54.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	309	1456
1	1174	1355
2	5001	1324

prune330.0ms

Filtered

154 candidates to 74 candidates (48.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	154	9	163

Merged error: 4.5b

Counts

163 → 9

regimes405.0ms

Accuracy

0% (1.4b remaining)

Error of 4.0b against oracle of 2.6b and baseline of 4.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	10
1	15	10

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.7s	3670×	body	1280	valid
1.4s	2049×	body	640	valid
291.0ms	713×	body	320	valid
157.0ms	1265×	body	80	valid
90.0ms	303×	body	160	valid

Details

sample191.0ms

simplify52.0ms

prune3.0ms

localize15.0ms

rewrite31.0ms

series438.0ms

simplify43.0ms

prune376.0ms

localize19.0ms

rewrite43.0ms

series452.0ms

simplify55.0ms

prune369.0ms

localize17.0ms

rewrite60.0ms

series480.0ms

simplify52.0ms

prune358.0ms

localize24.0ms

rewrite46.0ms

series338.0ms

simplify54.0ms

prune330.0ms

regimes405.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.9s

Profiling