Details

sample60.0ms

Algorithm

intervals

Results

15.0ms	249×	body	80	valid
14.0ms	51×	body	640	valid
10.0ms	25×	body	1280	valid
2.0ms	12×	body	320	valid
2.0ms	12×	body	160	valid

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	32	17
1	71	17
2	241	17
3	747	17
4	2196	17
5	5001	17

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: 41.3b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
3.3b	(cos (/ (+ phi1 phi2) 2.0))
3.3b	(cos (/ (+ phi1 phi2) 2.0))
37.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

276×	`*-un-lft-identity`
142×	`associate-*l/`
113×	`associate-l`
102×	`flip3--` `flip--`
92×	`swap-sqr`
75×	`distribute-lft-out--`
68×	`frac-times`
66×	`sqrt-div`
64×	`frac-add`
51×	`sqrt-prod`
48×	`distribute-lft-out`
46×	`add-sqr-sqrt`
44×	`pow1`
34×	`associate-*r/`
26×	`associate-r`
17×	`add-cube-cbrt` `pow-prod-down`
16×	`add-exp-log` `add-cbrt-cube`
12×	`unswap-sqr`
8×	`prod-exp` `cbrt-unprod`
5×	`*-commutative`
4×	`pow-sqr` `pow-prod-up` `add-log-exp` `difference-of-squares`
2×	`pow-plus`
1×	`pow2` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 232

Calls

4 calls:

26.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
6.0ms	(cos (/ (+ phi1 phi2) 2.0))
6.0ms	(cos (/ (+ phi1 phi2) 2.0))
96.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series587.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
29.0ms	(cos (/ (+ phi1 phi2) 2.0))
34.0ms	(cos (/ (+ phi1 phi2) 2.0))
427.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify84.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1551	5319
1	5001	5234

prune479.0ms

Filtered

244 candidates to 103 candidates (57.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	235	9	244
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	236	9	245

Merged error: 29.4b

Counts

245 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- lambda1 lambda2))
3.3b	(cos (/ (+ phi1 phi2) 2.0))
3.3b	(cos (/ (+ phi1 phi2) 2.0))
37.9b	(sqrt (+ (* (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2))) (* (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite421.0ms

Algorithm

rewrite-expression-head

Rules

1408×	`frac-times`
1376×	`associate-*l/`
1345×	`flip3--` `flip--`
1298×	`cbrt-div`
642×	`sqrt-div`
640×	`frac-add`
512×	`associate-*r/`
49×	`*-un-lft-identity`
19×	`associate-l`
16×	`sqrt-prod`
13×	`distribute-lft-out`
9×	`add-sqr-sqrt`
8×	`swap-sqr` `distribute-lft-out--`
6×	`add-cube-cbrt`
5×	`pow1` `cbrt-prod`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `flip-+` `difference-of-squares`

Counts

4 → 697

Calls

4 calls:

6.0ms	(cbrt (- lambda1 lambda2))
6.0ms	(cos (/ (+ phi1 phi2) 2.0))
6.0ms	(cos (/ (+ phi1 phi2) 2.0))
239.0ms	(sqrt (+ (* (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2))) (* (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series644.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(cbrt (- lambda1 lambda2))
32.0ms	(cos (/ (+ phi1 phi2) 2.0))
28.0ms	(cos (/ (+ phi1 phi2) 2.0))
431.0ms	(sqrt (+ (* (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2))) (* (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify414.0ms

Algorithm

egg-herbie

Counts

709 → 709

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5001	45266

prune6.5s

Filtered

709 candidates to 687 candidates (3.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	707	2	709
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	708	10	718

Merged error: 29.3b

Counts

718 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

3.3b	(cos (/ (+ phi1 phi2) 2.0))
3.3b	(cos (/ (+ phi1 phi2) 2.0))
37.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
37.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite239.0ms

Algorithm

rewrite-expression-head

Rules

476×	`*-un-lft-identity`
256×	`associate-*l/`
192×	`flip3--` `flip--`
144×	`swap-sqr`
142×	`associate-l`
134×	`distribute-lft-out--`
132×	`sqrt-div`
128×	`frac-times` `frac-add`
102×	`sqrt-prod`
96×	`distribute-lft-out`
64×	`associate-*r/`
8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 268

Calls

4 calls:

6.0ms	(cos (/ (+ phi1 phi2) 2.0))
7.0ms	(cos (/ (+ phi1 phi2) 2.0))
93.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
95.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series920.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(cos (/ (+ phi1 phi2) 2.0))
32.0ms	(cos (/ (+ phi1 phi2) 2.0))
428.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
432.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify108.0ms

Algorithm

egg-herbie

Counts

280 → 280

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1259	8312
1	5001	8196

prune702.0ms

Filtered

280 candidates to 98 candidates (65.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	280	0	280
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	280	10	290

Merged error: 29.3b

Counts

290 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

3.3b	(cos (/ (+ phi1 phi2) 2.0))
3.3b	(cos (/ (+ phi1 phi2) 2.0))
3.3b	(cos (/ (+ phi1 phi2) 2.0))
37.9b	(sqrt (+ (* (* (* (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (* (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite7.0s

Algorithm

rewrite-expression-head

Rules

29888×	`associate-*l/`
23328×	`cbrt-div`
20416×	`frac-times`
16032×	`flip3--` `flip--`
5984×	`associate-*r/`
5826×	`sqrt-div`
5824×	`frac-add`
133×	`*-un-lft-identity`
66×	`associate-l`
40×	`swap-sqr`
35×	`sqrt-prod`
32×	`distribute-lft-out`
24×	`distribute-lft-out--`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 5892

Calls

4 calls:

6.0ms	(cos (/ (+ phi1 phi2) 2.0))
6.0ms	(cos (/ (+ phi1 phi2) 2.0))
6.0ms	(cos (/ (+ phi1 phi2) 2.0))
4.6s	(sqrt (+ (* (* (* (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (* (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series510.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(cos (/ (+ phi1 phi2) 2.0))
28.0ms	(cos (/ (+ phi1 phi2) 2.0))
28.0ms	(cos (/ (+ phi1 phi2) 2.0))
422.0ms	(sqrt (+ (* (* (* (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (* (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify6.0s

Algorithm

egg-herbie

Counts

5904 → 5904

Iterations

Useful iterations: 0 (263.0ms)

Iter	Nodes	Cost
0	21778	637999

prune1.2m

Filtered

5904 candidates to 5866 candidates (0.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	5903	1	5904
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	5904	10	5914

Merged error: 29.3b

Counts

5914 → 10

regimes641.0ms

Accuracy

71.9% (4.0b remaining)

Error of 28.8b against oracle of 24.8b and baseline of 39.0b

bsearch3.0ms

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	41
1	37	41

end0.0ms

sample1.8s

Algorithm

intervals

Results

516.0ms	8310×	body	80	valid
356.0ms	1293×	body	640	valid
319.0ms	790×	body	1280	valid
143.0ms	693×	body	320	valid
55.0ms	387×	body	160	valid