Details

sample222.0ms

Algorithm

intervals

Results

142.0ms	135×	body	1280	valid
41.0ms	65×	body	640	valid
5.0ms	11×	body	320	valid
4.0ms	34×	body	80	valid
3.0ms	11×	body	160	valid

simplify54.0ms

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 (100.0%)

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: 3.4b

Counts

2 → 1

localize21.0ms

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))
0.3b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
3.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite32.0ms

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)
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series110.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
22.0ms	(pow (sin kx) 2.0)
20.0ms	(pow (sin ky) 2.0)
20.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify46.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	425	1022
1	1522	960
2	5001	946

prune285.0ms

Filtered

113 candidates to 78 candidates (31.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	100	13	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	13	114

Merged error: 1.8b

Counts

114 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

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))
0.3b	(pow (sin ky) 2.0)
3.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
37×	`add-sqr-sqrt`
33×	`associate-l`
29×	`add-exp-log`
28×	`times-frac`
24×	`add-cube-cbrt`
22×	`sqrt-prod`
18×	`add-cbrt-cube`
13×	`pow1` `prod-exp`
11×	`unpow-prod-down`
8×	`distribute-lft-out`
7×	`cbrt-unprod`
5×	`unswap-sqr`
4×	`sqrt-div` `div-exp` `associate-r` `pow-prod-down` `add-log-exp`
3×	`pow-unpow`
2×	`cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `associate-l/` `associate-/r/` `-commutative` `flip-+`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `associate-*r/` `pow-exp` `div-inv` `sqr-pow`

Counts

4 → 111

Calls

4 calls:

16.0ms	(* (sin ky) (* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th)))
17.0ms	(* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
3.0ms	(pow (sin ky) 2.0)
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series131.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin ky) (* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th)))
43.0ms	(* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
21.0ms	(pow (sin ky) 2.0)
20.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify55.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	443	1278
1	1840	1119
2	5001	1095

prune264.0ms

Filtered

123 candidates to 80 candidates (35.0%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	122	14	136

Merged error: 1.8b

Counts

136 → 14

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
1.0b	(exp (log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
1.4b	(log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
16×	`log-prod`
15×	`sqrt-prod`
13×	`add-sqr-sqrt`
12×	`add-cube-cbrt`
10×	`pow1`
9×	`unpow-prod-down`
8×	`exp-sum`
6×	`add-exp-log` `exp-prod` `sqrt-div` `log-pow` `distribute-lft-out`
4×	`log-div` `add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
2×	`exp-diff`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `rem-log-exp` `pow-exp` `rem-exp-log` `sqr-pow`

Counts

4 → 79

Calls

4 calls:

3.0ms	(pow (sin ky) 2.0)
10.0ms	(exp (log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
8.0ms	(log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
9.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series85.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(pow (sin ky) 2.0)
19.0ms	(exp (log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
25.0ms	(log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
20.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify87.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 3 (78.0ms)

Iter	Nodes	Cost
0	268	791
1	771	745
2	2592	714
3	5001	708

prune225.0ms

Filtered

91 candidates to 56 candidates (38.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	88	3	91
Fresh	2	10	12
Picked	1	0	1
Done	0	1	1
Total	91	14	105

Merged error: 1.8b

Counts

105 → 14

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
1.1b	(pow E (log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
1.4b	(log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
16×	`log-prod`
15×	`sqrt-prod`
14×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`unpow-prod-down`
11×	`pow1`
9×	`pow-unpow`
8×	`unpow-prod-up`
7×	`add-exp-log`
6×	`sqrt-div` `log-pow` `distribute-lft-out`
4×	`log-div` `add-cbrt-cube` `add-log-exp`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `pow-exp` `flip-+`
2×	`pow-to-exp` `pow-pow` `pow-sub` `sqr-pow`
1×	`rem-sqrt-square` `e-exp-1` `rem-log-exp`

Counts

4 → 86

Calls

4 calls:

3.0ms	(pow (sin ky) 2.0)
10.0ms	(pow E (log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
8.0ms	(log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series100.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (sin ky) 2.0)
33.0ms	(pow E (log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
28.0ms	(log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
20.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify134.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (124.0ms)

Iter	Nodes	Cost
0	342	948
1	1110	870
2	4194	850
3	5002	830

prune171.0ms

Filtered

98 candidates to 58 candidates (40.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	2	10	12
Picked	1	0	1
Done	0	1	1
Total	98	14	112

Merged error: 1.8b

Counts

112 → 14

regimes1.2s

Accuracy

0% (1.3b remaining)

Error of 3.4b against oracle of 2.2b and baseline of 3.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	11
1	20	11

end0.0ms

sample6.5s

Algorithm

intervals

Results

4.3s	3974×	body	1280	valid
1.3s	2029×	body	640	valid
302.0ms	683×	body	320	valid
138.0ms	998×	body	80	valid
94.0ms	316×	body	160	valid

Details

sample222.0ms

simplify54.0ms

prune5.0ms

localize21.0ms

rewrite32.0ms

series110.0ms

simplify46.0ms

prune285.0ms

localize20.0ms

rewrite47.0ms

series131.0ms

simplify55.0ms

prune264.0ms

localize21.0ms

rewrite32.0ms

series85.0ms

simplify87.0ms

prune225.0ms

localize25.0ms

rewrite30.0ms

series100.0ms

simplify134.0ms

prune171.0ms

regimes1.2s

bsearch0.0ms

simplify2.0ms

end0.0ms

sample6.5s

Profiling