Details

sample157.0ms

Algorithm

intervals

Results

97.0ms	115×	body	1280	valid
33.0ms	68×	body	640	valid
6.0ms	20×	body	320	valid
5.0ms	49×	body	80	valid
1.0ms	4×	body	160	valid

simplify51.0ms

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	1785	10
6	5002	10

prune4.0ms

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: 3.2b

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

rewrite32.0ms

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)
13.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series451.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
113.0ms	(pow (sin kx) 2.0)
111.0ms	(pow (sin ky) 2.0)
84.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify38.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	328	1021
1	1094	946
2	5001	943

prune296.0ms

Filtered

112 candidates to 70 candidates (37.5%)

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: 2.4b

Counts

113 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
0.3b	(pow (sin kx) 2)
0.3b	(pow (sin ky) 2)
3.0b	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

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-+` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 102

Calls

4 calls:

11.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
2.0ms	(pow (sin kx) 2)
2.0ms	(pow (sin ky) 2)
7.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
19.0ms	(pow (sin kx) 2)
20.0ms	(pow (sin ky) 2)
83.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

simplify42.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	326	1009
1	1099	907
2	5002	900

prune279.0ms

Filtered

114 candidates to 64 candidates (43.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	107	7	114
Fresh	7	4	11
Picked	0	1	1
Done	0	0	0
Total	114	12	126

Merged error: 2.4b

Counts

126 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin ky)))
0.3b	(pow (sin kx) 2)
0.3b	(pow (sin ky) 2)
3.0b	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac`
158×	`*-un-lft-identity`
102×	`add-sqr-sqrt`
101×	`add-cube-cbrt`
70×	`sqrt-prod`
34×	`unpow-prod-down`
31×	`associate-/r*`
28×	`distribute-lft-out`
17×	`add-exp-log`
16×	`associate-/r/`
12×	`associate-/l*`
9×	`add-cbrt-cube`
8×	`pow1`
7×	`div-exp`
6×	`pow-unpow`
5×	`div-inv`
4×	`sqrt-div` `add-log-exp`
3×	`cbrt-undiv` `clear-num`
2×	`pow-to-exp` `rec-exp` `pow-pow` `frac-2neg` `flip3-+` `1-exp` `pow-exp` `flip-+` `associate-/l/` `remove-double-div` `unpow2` `sqr-pow`
1×	`rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `inv-pow`

Counts

4 → 206

Calls

4 calls:

17.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin ky)))
2.0ms	(pow (sin kx) 2)
2.0ms	(pow (sin ky) 2)
8.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin ky)))
20.0ms	(pow (sin kx) 2)
20.0ms	(pow (sin ky) 2)
85.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

simplify84.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	649	2669
1	2815	2331
2	5002	2183

prune349.0ms

Filtered

218 candidates to 83 candidates (61.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	216	2	218
Fresh	3	7	10
Picked	1	0	1
Done	0	1	1
Total	220	10	230

Merged error: 2.4b

Counts

230 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2)
0.3b	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
3.0b	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
3.0b	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

62×	`sqrt-prod`
56×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
33×	`times-frac`
32×	`add-cube-cbrt`
15×	`unpow-prod-down`
12×	`distribute-lft-out`
11×	`associate-/r*`
8×	`sqrt-div`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-unpow` `flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `div-exp` `pow-exp` `clear-num` `div-inv` `unpow2` `sqr-pow`

Counts

4 → 113

Calls

4 calls:

6.0ms	(pow (sin ky) 2)
13.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
7.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
7.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(pow (sin ky) 2)
163.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
85.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
80.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

simplify51.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	333	1426
1	1152	1292
2	5001	1282

prune324.0ms

Filtered

125 candidates to 72 candidates (42.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	125	10	135

Merged error: 2.4b

Counts

135 → 10

regimes323.0ms

Accuracy

0% (1.3b remaining)

Error of 3.8b against oracle of 2.6b and baseline of 3.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	10
1	15	10

end0.0ms

sample5.0s

Algorithm

intervals

Results

3.3s	3676×	body	1280	valid
1.0s	2074×	body	640	valid
261.0ms	741×	body	320	valid
124.0ms	1237×	body	80	valid
59.0ms	272×	body	160	valid