Details

sample157.0ms

Algorithm

intervals

Results

97.0ms	120×	body	1280	valid
29.0ms	59×	body	640	valid
11.0ms	32×	body	320	valid
4.0ms	37×	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

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: 4.6b

Counts

2 → 1

localize24.0ms

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 ky) 2.0)
0.3b	(pow (sin kx) 2.0)
4.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite27.0ms

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

series420.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
105.0ms	(pow (sin ky) 2.0)
105.0ms	(pow (sin kx) 2.0)
79.0ms	(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	5002	943

prune385.0ms

Filtered

112 candidates to 70 candidates (62.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	100	12	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	12	113

Merged error: 3.4b

Counts

113 → 12

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 ky) 2.0)
0.3b	(pow (sin kx) 2.0)
4.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite41.0ms

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

series412.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
105.0ms	(pow (sin ky) 2.0)
113.0ms	(pow (sin kx) 2.0)
73.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify83.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	642	2588
1	2882	2325
2	5003	2177

prune445.0ms

Filtered

199 candidates to 82 candidates (41.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	196	3	199
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	201	10	211

Merged error: 3.4b

Counts

211 → 10

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 ky) 2.0)
0.3b	(pow (sin kx) 2.0)
4.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite86.0ms

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

series415.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(/ (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin ky)))
103.0ms	(pow (sin ky) 2.0)
107.0ms	(pow (sin kx) 2.0)
83.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify129.0ms

Algorithm

egg-herbie

Counts

528 → 528

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	2007	10422
1	5001	9352

prune999.0ms

Filtered

528 candidates to 178 candidates (33.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	528	0	528
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	528	10	538

Merged error: 3.4b

Counts

538 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin kx) 2)
0.3b	(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
0.3b	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
4.3b	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
49×	`add-sqr-sqrt` `times-frac`
45×	`sqrt-prod`
36×	`add-cube-cbrt`
24×	`associate-l`
23×	`unpow-prod-down`
20×	`distribute-lft-out`
11×	`add-exp-log`
10×	`pow1`
8×	`add-cbrt-cube`
6×	`associate-/r/`
5×	`associate-/r*`
4×	`add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square` `pow-unpow` `sqrt-pow1` `flip3-+` `associate-r` `flip-+` `div-inv` `associate-/l*`
2×	`pow-flip` `sqrt-div` `div-exp` `inv-pow`
1×	`cbrt-undiv` `pow-to-exp` `rec-exp` `pow-pow` `frac-2neg` `pow1/2` `1-exp` `pow-prod-down` `associate-l/` `pow-exp` `prod-exp` `clear-num` `-commutative` `cbrt-unprod` `unpow2` `sqr-pow`

Counts

4 → 138

Calls

4 calls:

3.0ms	(pow (sin kx) 2)
10.0ms	(/ 1 (+ (pow (sin kx) 2) (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))))

series313.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(pow (sin kx) 2)
70.0ms	(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
119.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
101.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

simplify48.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	384	1403
1	1356	1280
2	5001	1222

prune389.0ms

Filtered

150 candidates to 82 candidates (54.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	149	1	150
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	150	10	160

Merged error: 3.4b

Counts

160 → 10

regimes392.0ms

Accuracy

0% (1.4b remaining)

Error of 3.9b against oracle of 2.5b and baseline of 3.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	12
1	20	12

end0.0ms

sample5.0s

Algorithm

intervals

Results

3.1s	3743×	body	1280	valid
1.1s	1949×	body	640	valid
289.0ms	741×	body	320	valid
134.0ms	1282×	body	80	valid
62.0ms	285×	body	160	valid