Details

analyze4.0s

Algorithm

sampling

Space saved by range analysis: 0.146413%

Space saved by search: 0.146413%

Guaranteed chance to sample good point: 70.898438%

sample223.0ms

Algorithm

intervals

Results

145.0ms	126×	body	1280	valid
48.0ms	59×	body	640	valid
9.0ms	19×	body	320	valid
6.0ms	44×	body	80	valid
2.0ms	8×	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

prune4.0ms

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: 3.4b

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))))
0.2b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
3.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
25×	`sqrt-prod`
24×	`times-frac`
16×	`unpow-prod-down`
10×	`distribute-lft-out`
8×	`add-exp-log` `associate-/r*`
7×	`pow1`
6×	`pow-unpow` `add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`associate-/l*`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `associate-/r/` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

10.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
2.0ms	(pow (sin kx) 2.0)
2.0ms	(pow (sin ky) 2.0)
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series93.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
18.0ms	(pow (sin kx) 2.0)
23.0ms	(pow (sin ky) 2.0)
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	363	1053
1	1249	978
2	5002	961

prune249.0ms

Filtered

70 candidates to 112 candidates (-60.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	102	10	112
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	102	11	113

Merged error: 2.3b

Counts

113 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
0.2b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
3.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac`
150×	`*-un-lft-identity`
99×	`add-sqr-sqrt`
98×	`add-cube-cbrt`
65×	`sqrt-prod`
32×	`unpow-prod-down`
28×	`associate-/r*`
26×	`distribute-lft-out`
17×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
7×	`div-exp`
6×	`pow-unpow`
5×	`div-inv`
4×	`add-log-exp`
3×	`cbrt-undiv` `associate-/l*`
2×	`pow-to-exp` `rec-exp` `pow-pow` `sqrt-div` `1-exp` `pow-exp` `sqr-pow`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `clear-num` `associate-/r/` `flip-+` `inv-pow`

Counts

4 → 187

Calls

4 calls:

16.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
2.0ms	(pow (sin kx) 2.0)
2.0ms	(pow (sin ky) 2.0)
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series89.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
18.0ms	(pow (sin kx) 2.0)
18.0ms	(pow (sin ky) 2.0)
18.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify77.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	675	2618
1	3016	2355
2	5002	2204

prune244.0ms

Filtered

81 candidates to 199 candidates (-145.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	198	1	199
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	199	11	210

Merged error: 2.3b

Counts

210 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
0.3b	(* (/ 1 (fabs (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin ky) (sqrt (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
3.5b	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.5b	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-sqr-sqrt`
60×	`*-un-lft-identity`
59×	`times-frac`
39×	`associate-r`
36×	`add-cube-cbrt`
30×	`sqrt-prod`
28×	`cbrt-prod`
27×	`add-exp-log`
16×	`add-cbrt-cube`
13×	`unpow-prod-down` `associate-l`
12×	`unswap-sqr`
10×	`distribute-lft-out`
8×	`div-exp` `prod-exp`
7×	`pow1`
6×	`cbrt-div`
4×	`cbrt-undiv` `cbrt-unprod` `add-log-exp`
3×	`pow-unpow` `flip3-+` `flip-+`
2×	`rec-exp` `pow1/3` `sqrt-div` `1-exp` `associate-/r/` `div-inv`
1×	`frac-times` `pow-to-exp` `pow-pow` `associate-r/` `pow-prod-down` `associate-l/` `pow-exp` `*-commutative` `sqr-pow`

Counts

4 → 135

Calls

4 calls:

3.0ms	(pow (sin ky) 2.0)
26.0ms	(* (/ 1 (fabs (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin ky) (sqrt (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
7.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series147.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin ky) 2.0)
72.0ms	(* (/ 1 (fabs (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin ky) (sqrt (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
27.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
30.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify85.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	746	2651
1	3385	2421
2	5002	2374

prune448.0ms

Filtered

92 candidates to 147 candidates (-59.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	145	2	147
Fresh	1	7	8
Picked	1	0	1
Done	0	2	2
Total	147	11	158

Merged error: 2.3b

Counts

158 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
30×	`cbrt-prod` `sqrt-prod`
25×	`add-sqr-sqrt`
24×	`times-frac`
22×	`add-cube-cbrt`
12×	`unpow-prod-down` `distribute-lft-out`
8×	`sqrt-div`
7×	`pow1`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`associate-/r/`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 90

Calls

4 calls:

12.0ms	(cbrt (/ (sin ky) (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)))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series107.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
18.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
18.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
18.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify121.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 3 (108.0ms)

Iter	Nodes	Cost
0	308	1314
1	909	1257
2	4097	1241
3	5003	1236

prune340.0ms

Filtered

68 candidates to 102 candidates (-50.0%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	102	11	113

Merged error: 2.3b

Counts

113 → 11

regimes892.0ms

Accuracy

0% (1.2b remaining)

Error of 3.9b against oracle of 2.7b 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

analyze4.0s

Algorithm

sampling

Space saved by range analysis: 0.146413%

Space saved by search: 0.146413%

Guaranteed chance to sample good point: 70.898438%

sample6.4s

Algorithm

intervals

Results

4.2s	3789×	body	1280	valid
1.4s	1999×	body	640	valid
304.0ms	673×	body	320	valid
171.0ms	1251×	body	80	valid
91.0ms	288×	body	160	valid

Details

analyze4.0s

sample223.0ms

simplify52.0ms

prune4.0ms

localize15.0ms

rewrite25.0ms

series93.0ms

simplify43.0ms

prune249.0ms

localize16.0ms

rewrite37.0ms

series89.0ms

simplify77.0ms

prune244.0ms

localize23.0ms

rewrite47.0ms

series147.0ms

simplify85.0ms

prune448.0ms

localize21.0ms

rewrite36.0ms

series107.0ms

simplify121.0ms

prune340.0ms

regimes892.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze4.0s

sample6.4s

Profiling