Details

sample215.0ms

Algorithm

intervals

Results

138.0ms	127×	body	1280	valid
42.0ms	66×	body	640	valid
12.0ms	23×	body	320	valid
5.0ms	36×	body	80	valid
1.0ms	4×	body	160	valid

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4766	16
1	4766	16

prune21.0ms

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: 3.9b

Counts

2 → 2

localize16.0ms

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)
3.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite30.0ms

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

series102.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
17.0ms	(pow (sin kx) 2.0)
22.0ms	(pow (sin ky) 2.0)
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify77.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5251	1477

prune276.0ms

Filtered

77 candidates to 113 candidates (-46.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	102	11	113
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	103	12	115

Merged error: 2.6b

Counts

115 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.2b	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.3b	(pow (sin ky) 2.0)
3.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite42.0ms

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:

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))))
2.0ms	(pow (sin ky) 2.0)
9.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series121.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
42.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
17.0ms	(pow (sin ky) 2.0)
18.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify57.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5102	2217

prune284.0ms

Filtered

86 candidates to 145 candidates (-68.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	145	12	157

Merged error: 2.6b

Counts

157 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 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)))))
3.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite47.0ms

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 ky) 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)))
9.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (sin ky) 2.0)
21.0ms	(* (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
18.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify59.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5073	2018

prune305.0ms

Filtered

74 candidates to 154 candidates (-108.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	154	12	166

Merged error: 2.6b

Counts

166 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
0.3b	(pow (sin ky) 2.0)
4.1b	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.1b	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
10×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down`
6×	`pow1` `add-exp-log` `pow-unpow`
4×	`cbrt-div` `add-cbrt-cube` `distribute-lft-out` `add-log-exp`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow1/3` `pow-exp` `flip-+` `sqr-pow`

Counts

4 → 64

Calls

4 calls:

5.0ms	(pow (sin ky) 2.0)
3.0ms	(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)))

series92.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(pow (sin ky) 2.0)
18.0ms	(pow (sin ky) 2.0)
27.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
28.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify50.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5078	816

prune193.0ms

Filtered

52 candidates to 76 candidates (-46.2%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	76	12	88

Merged error: 2.6b

Counts

88 → 12

regimes919.0ms

Accuracy

0% (1.5b remaining)

Error of 4.0b against oracle of 2.4b and baseline of 4.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	16
1	15	16

end0.0ms

sample6.6s

Algorithm

intervals

Results

4.2s	3652×	body	1280	valid
1.5s	2081×	body	640	valid
330.0ms	680×	body	320	valid
163.0ms	1289×	body	80	valid
98.0ms	298×	body	160	valid

Details

sample215.0ms

simplify61.0ms

prune21.0ms

localize16.0ms

rewrite30.0ms

series102.0ms

simplify77.0ms

prune276.0ms

localize16.0ms

rewrite42.0ms

series121.0ms

simplify57.0ms

prune284.0ms

localize19.0ms

rewrite47.0ms

series76.0ms

simplify59.0ms

prune305.0ms

localize20.0ms

rewrite23.0ms

series92.0ms

simplify50.0ms

prune193.0ms

regimes919.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample6.6s

Profiling