Details

sample203.0ms

Algorithm

intervals

Results

136.0ms	135×	body	1280	valid
39.0ms	65×	body	640	valid
9.0ms	23×	body	320	valid
4.0ms	30×	body	80	valid
1.0ms	3×	body	160	valid

simplify53.0ms

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: 2.2b

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

rewrite26.0ms

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:

11.0ms	(/ (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)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
104.0ms	(pow (sin kx) 2.0)
102.0ms	(pow (sin ky) 2.0)
76.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify40.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	329	1021
1	1106	946
2	5001	943

prune339.0ms

Filtered

112 candidates to 70 candidates (62.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	102	10	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	10	113

Merged error: 1.5b

Counts

113 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

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:

14.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
3.0ms	(pow (sin kx) 2.0)
3.0ms	(pow (sin ky) 2.0)
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series404.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
108.0ms	(pow (sin kx) 2.0)
100.0ms	(pow (sin ky) 2.0)
76.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify75.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	642	2586
1	2882	2323
2	5003	2175

prune363.0ms

Filtered

199 candidates to 80 candidates (40.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	196	3	199
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	198	11	209

Merged error: 1.5b

Counts

209 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

1005×	`times-frac`
608×	`*-un-lft-identity`
437×	`add-sqr-sqrt`
436×	`add-cube-cbrt`
215×	`sqrt-prod`
92×	`unpow-prod-down`
86×	`distribute-lft-out`
46×	`add-exp-log` `div-inv`
32×	`div-exp`
30×	`sqrt-div` `associate-/l*`
29×	`associate-/r/`
16×	`add-cbrt-cube`
15×	`flip3-+` `flip-+`
13×	`associate-/r*`
8×	`cbrt-undiv` `rec-exp` `1-exp`
7×	`pow1`
6×	`pow-unpow`
4×	`add-log-exp`
2×	`pow-to-exp` `pow-pow` `pow-exp` `sqr-pow`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 516

Calls

4 calls:

25.0ms	(/ (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin ky)))
3.0ms	(pow (sin kx) 2.0)
3.0ms	(pow (sin ky) 2.0)
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series412.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin ky)))
111.0ms	(pow (sin kx) 2.0)
103.0ms	(pow (sin ky) 2.0)
79.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify143.0ms

Algorithm

egg-herbie

Counts

528 → 528

Iterations

Useful iterations: 1 (42.0ms)

Iter	Nodes	Cost
0	2007	10420
1	5001	9350

prune842.0ms

Filtered

528 candidates to 177 candidates (33.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	527	1	528
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	528	11	539

Merged error: 1.5b

Counts

539 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin kx) 2)
0.3b	(pow (sin ky) 2)
0.3b	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
2.1b	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
45×	`sqrt-prod`
41×	`add-sqr-sqrt`
34×	`times-frac`
28×	`add-cube-cbrt`
24×	`associate-l`
18×	`unpow-prod-down`
12×	`distribute-lft-out`
10×	`pow1`
8×	`add-exp-log`
6×	`pow-unpow` `add-cbrt-cube`
4×	`associate-/r/` `add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square` `sqrt-pow1` `associate-r`
2×	`pow-to-exp` `pow-pow` `flip3-+` `sqrt-div` `pow-exp` `flip-+` `div-inv` `unpow2` `sqr-pow`
1×	`pow-flip` `pow1/2` `pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `inv-pow`

Counts

4 → 115

Calls

4 calls:

3.0ms	(pow (sin kx) 2)
3.0ms	(pow (sin ky) 2)
16.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
10.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

series265.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (sin kx) 2)
23.0ms	(pow (sin ky) 2)
119.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
104.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

simplify50.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	369	1075
1	1256	984
2	5001	947

prune308.0ms

Filtered

127 candidates to 74 candidates (58.3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	1	7	8
Picked	0	1	1
Done	0	2	2
Total	127	11	138

Merged error: 1.5b

Counts

138 → 11

regimes455.0ms

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	19	11
1	19	11

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.7s	3645×	body	1280	valid
1.4s	2075×	body	640	valid
315.0ms	741×	body	320	valid
155.0ms	1236×	body	80	valid
82.0ms	303×	body	160	valid

Details

sample203.0ms

simplify53.0ms

prune3.0ms

localize15.0ms

rewrite26.0ms

series405.0ms

simplify40.0ms

prune339.0ms

localize17.0ms

rewrite35.0ms

series404.0ms

simplify75.0ms

prune363.0ms

localize18.0ms

rewrite80.0ms

series412.0ms

simplify143.0ms

prune842.0ms

localize21.0ms

rewrite35.0ms

series265.0ms

simplify50.0ms

prune308.0ms

regimes455.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.9s

Profiling