Details

sample156.0ms

Algorithm

intervals

Results

93.0ms	119×	body	1280	valid
37.0ms	68×	body	640	valid
6.0ms	17×	body	320	valid
4.0ms	41×	body	80	valid
2.0ms	11×	body	160	valid

simplify50.0ms

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

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))))
0.2b	(pow (sin kx) 2.0)
0.2b	(pow (sin ky) 2.0)
3.3b	(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))))
3.0ms	(pow (sin kx) 2.0)
3.0ms	(pow (sin ky) 2.0)
13.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series409.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
102.0ms	(pow (sin kx) 2.0)
104.0ms	(pow (sin ky) 2.0)
76.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	329	1021
1	1106	946
2	5002	943

prune354.0ms

Filtered

112 candidates to 70 candidates (62.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 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)
3.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite36.0ms

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)))

series419.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
109.0ms	(pow (sin kx) 2.0)
101.0ms	(pow (sin ky) 2.0)
90.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify71.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (50.0ms)

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

prune406.0ms

Filtered

199 candidates to 81 candidates (40.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin ky)))
0.2b	(pow (sin kx) 2.0)
0.2b	(pow (sin ky) 2.0)
3.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite84.0ms

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:

26.0ms	(/ (/ 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)
11.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series401.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin ky)))
103.0ms	(pow (sin kx) 2.0)
109.0ms	(pow (sin ky) 2.0)
72.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify118.0ms

Algorithm

egg-herbie

Counts

528 → 528

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	2007	10422
1	5001	9352

prune946.0ms

Filtered

528 candidates to 177 candidates (33.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 (sin ky)) (/ (cbrt 1) (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)
3.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

1869×	`times-frac`
1140×	`*-un-lft-identity`
801×	`add-sqr-sqrt`
800×	`add-cube-cbrt`
425×	`sqrt-prod`
336×	`cbrt-prod`
176×	`unpow-prod-down`
170×	`distribute-lft-out`
70×	`div-inv`
54×	`associate-/r*`
30×	`sqrt-div`
29×	`associate-/r/`
28×	`add-exp-log`
16×	`div-exp`
15×	`flip3-+` `flip-+`
14×	`add-cbrt-cube`
13×	`associate-/l*`
8×	`cbrt-undiv`
7×	`pow1`
6×	`pow-unpow`
4×	`add-log-exp`
2×	`pow-to-exp` `rec-exp` `pow-pow` `1-exp` `pow-exp` `sqr-pow`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 844

Calls

4 calls:

38.0ms	(/ (/ 1 (sin ky)) (/ (cbrt 1) (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)
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series390.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (/ 1 (sin ky)) (/ (cbrt 1) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
106.0ms	(pow (sin kx) 2.0)
100.0ms	(pow (sin ky) 2.0)
80.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify198.0ms

Algorithm

egg-herbie

Counts

856 → 856

Iterations

Useful iterations: 1 (48.0ms)

Iter	Nodes	Cost
0	2982	19753
1	5001	18608

prune2.0s

Filtered

856 candidates to 292 candidates (34.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 1.7b

regimes422.0ms

Accuracy

0% (2.3b remaining)

Error of 4.3b against oracle of 2.0b and baseline of 4.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	11
1	19	11

end0.0ms

sample4.7s

Algorithm

intervals

Results

3.1s	3710×	body	1280	valid
1.0s	2044×	body	640	valid
239.0ms	710×	body	320	valid
129.0ms	1263×	body	80	valid
63.0ms	273×	body	160	valid