Details

sample185.0ms

Algorithm

intervals

Results

111.0ms	122×	body	1280	valid
34.0ms	61×	body	640	valid
9.0ms	23×	body	320	valid
4.0ms	43×	body	80	valid
2.0ms	7×	body	160	valid

simplify50.0ms

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

prune5.0ms

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: 3.6b

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 kx) 2.0)
0.3b	(pow (sin ky) 2.0)
3.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite36.0ms

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:

16.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
2.0ms	(pow (sin kx) 2.0)
2.0ms	(pow (sin ky) 2.0)
12.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series427.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
101.0ms	(pow (sin kx) 2.0)
103.0ms	(pow (sin ky) 2.0)
76.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify41.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (32.0ms)

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

prune548.0ms

Filtered

113 candidates to 78 candidates (69.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	102	11	113
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	102	12	114

Merged error: 2.7b

Counts

114 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
0.3b	(* (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))))
3.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite41.0ms

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:

2.0ms	(pow (sin ky) 2.0)
16.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
10.0ms	(/ (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)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(pow (sin ky) 2.0)
141.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
121.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
76.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify58.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	412	1572
1	1810	1426
2	5001	1423

prune580.0ms

Filtered

145 candidates to 86 candidates (59.3%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	140	5	145
Fresh	2	8	10
Picked	0	1	1
Done	0	1	1
Total	142	15	157

Merged error: 2.7b

Counts

157 → 15

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
0.3b	(* (sin ky) (/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th))))
0.3b	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th)))
3.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

346×	`times-frac`
262×	`*-un-lft-identity`
193×	`add-sqr-sqrt`
171×	`add-cube-cbrt`
112×	`sqrt-prod`
89×	`associate-r`
47×	`unpow-prod-down`
44×	`distribute-lft-out`
35×	`add-exp-log`
28×	`associate-/r*`
18×	`add-cbrt-cube`
14×	`div-exp`
9×	`pow1` `div-inv`
7×	`prod-exp` `unswap-sqr`
6×	`cbrt-undiv`
4×	`rec-exp` `1-exp` `add-log-exp`
3×	`pow-unpow` `associate-l` `cbrt-unprod` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`pow-to-exp` `rem-sqrt-square` `pow-flip` `pow-pow` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `un-div-inv` `-commutative` `flip-+` `inv-pow` `sqr-pow`

Counts

4 → 290

Calls

4 calls:

2.0ms	(pow (sin ky) 2.0)
32.0ms	(* (sin ky) (/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th))))
13.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th)))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(pow (sin ky) 2.0)
144.0ms	(* (sin ky) (/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th))))
146.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th)))
77.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify119.0ms

Algorithm

egg-herbie

Counts

302 → 302

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	894	4106
1	4712	3634
2	5001	3373

prune864.0ms

Filtered

302 candidates to 131 candidates (43.4%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	300	2	302
Fresh	1	11	12
Picked	0	1	1
Done	1	1	2
Total	302	15	317

Merged error: 2.7b

Counts

317 → 15

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
0.3b	(* (sin ky) (/ (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin th))))
0.4b	(/ (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin th)))
3.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

2014×	`times-frac`
1180×	`*-un-lft-identity`
900×	`add-sqr-sqrt`
841×	`add-cube-cbrt`
416×	`sqrt-prod`
395×	`associate-r`
167×	`unpow-prod-down`
164×	`distribute-lft-out`
103×	`add-exp-log`
90×	`div-inv`
64×	`div-exp`
56×	`sqrt-div` `associate-/r/`
34×	`add-cbrt-cube`
30×	`associate-/l*`
28×	`flip3-+` `flip-+`
17×	`prod-exp`
16×	`cbrt-undiv` `rec-exp` `1-exp` `unswap-sqr`
13×	`associate-/r*`
8×	`pow1`
5×	`cbrt-unprod`
4×	`add-log-exp`
3×	`pow-unpow` `associate-l`
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` `associate-/l/` `sqr-pow`

Counts

4 → 945

Calls

4 calls:

2.0ms	(pow (sin ky) 2.0)
92.0ms	(* (sin ky) (/ (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin th))))
23.0ms	(/ (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin th)))
10.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series596.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(pow (sin ky) 2.0)
142.0ms	(* (sin ky) (/ (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin th))))
277.0ms	(/ (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin th)))
79.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify194.0ms

Algorithm

egg-herbie

Counts

957 → 957

Iterations

Useful iterations: 1 (55.0ms)

Iter	Nodes	Cost
0	2962	16552
1	5001	14805

prune2.4s

Filtered

957 candidates to 363 candidates (37.9%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	957	0	957
Fresh	0	12	12
Picked	0	1	1
Done	0	2	2
Total	957	15	972

Merged error: 2.7b

Counts

972 → 15

regimes1.1s

Accuracy

0% (1.3b remaining)

Error of 3.9b against oracle of 2.6b and baseline of 3.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	10
1	15	10

end0.0ms

sample5.6s

Algorithm

intervals

Results

3.6s	3704×	body	1280	valid
1.2s	2035×	body	640	valid
310.0ms	766×	body	320	valid
130.0ms	1220×	body	80	valid
67.0ms	275×	body	160	valid

Details

sample185.0ms

simplify50.0ms

prune5.0ms

localize15.0ms

rewrite36.0ms

series427.0ms

simplify41.0ms

prune548.0ms

localize18.0ms

rewrite41.0ms

series440.0ms

simplify58.0ms

prune580.0ms

localize16.0ms

rewrite71.0ms

series471.0ms

simplify119.0ms

prune864.0ms

localize18.0ms

rewrite220.0ms

series596.0ms

simplify194.0ms

prune2.4s

regimes1.1s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.6s

Profiling