Details

sample187.0ms

Algorithm

intervals

Results

114.0ms	118×	body	1280	valid
41.0ms	71×	body	640	valid
9.0ms	22×	body	320	valid
4.0ms	30×	body	80	valid
4.0ms	15×	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	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: 1.6b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.2b	(pow (sin kx) 2.0)
0.2b	(pow (sin ky) 2.0)
1.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite28.0ms

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

series412.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
101.0ms	(pow (sin kx) 2.0)
103.0ms	(pow (sin ky) 2.0)
77.0ms	(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

prune333.0ms

Filtered

112 candidates to 70 candidates (62.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	103	9	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	9	113

Merged error: 0.7b

Counts

113 → 9

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)))
0.2b	(pow (sin kx) 2.0)
0.2b	(pow (sin ky) 2.0)
1.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite42.0ms

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:

18.0ms	(/ 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)
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series399.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
102.0ms	(pow (sin kx) 2.0)
101.0ms	(pow (sin ky) 2.0)
78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify79.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (52.0ms)

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

prune357.0ms

Filtered

199 candidates to 82 candidates (41.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	197	2	199
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	200	8	208

Merged error: 0.7b

Counts

208 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin ky) 2)
0.2b	(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
0.3b	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
1.5b	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

rewrite49.0ms

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 ky) 2)
10.0ms	(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
20.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
11.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

series318.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (sin ky) 2)
77.0ms	(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
117.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
105.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

simplify57.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	380	1401
1	1455	1278
2	5001	1220

prune357.0ms

Filtered

150 candidates to 82 candidates (54.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	150	8	158

Merged error: 0.7b

Counts

158 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin ky) 2.0)
0.3b	(* (fabs (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
1.9b	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
1.9b	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`add-cube-cbrt`
11×	`associate-r`
10×	`sqrt-prod`
9×	`unpow-prod-down`
7×	`pow1` `add-exp-log`
6×	`cbrt-div` `add-cbrt-cube` `distribute-lft-out`
4×	`add-log-exp`
3×	`pow-unpow` `flip3-+` `associate-l` `flip-+` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/`
1×	`pow-to-exp` `pow-pow` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `sqr-pow`

Counts

4 → 77

Calls

4 calls:

3.0ms	(pow (sin ky) 2.0)
17.0ms	(* (fabs (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (cbrt (+ (pow (sin kx) 2.0) (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)))

series410.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(pow (sin ky) 2.0)
112.0ms	(* (fabs (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
96.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
97.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify150.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	338	1091
1	1137	1019
2	4670	1007
3	5001	1007

prune307.0ms

Filtered

89 candidates to 63 candidates (70.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	89	8	97

Merged error: 0.7b

Counts

97 → 8

regimes422.0ms

Accuracy

0% (1.5b remaining)

Error of 4.2b against oracle of 2.7b and baseline of 4.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	11
1	20	11

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.6s	3690×	body	1280	valid
1.2s	2043×	body	640	valid
301.0ms	725×	body	320	valid
283.0ms	1253×	body	80	valid
79.0ms	289×	body	160	valid