Details

sample7.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 4.248047%

Guaranteed chance to sample good point: 13.717491%

Results

18.0ms	181×	body	80	valid
16.0ms	35×	body	640	valid
12.0ms	17×	body	1280	valid
7.0ms	16×	body	640	invalid
7.0ms	10×	body	1280	invalid
7.0ms	68×	body	80	invalid
6.0ms	16×	body	320	valid
3.0ms	9×	body	320	invalid
2.0ms	7×	body	160	valid
1.0ms	5×	body	160	invalid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune10.0ms

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: 39.7b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
4.2b	(cos (/ (+ phi1 phi2) 2.0))
4.2b	(cos (/ (+ phi1 phi2) 2.0))
36.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

142×	`associate-*l/`
102×	`flip3--` `flip--`
68×	`frac-times`
66×	`sqrt-div`
64×	`frac-add`
44×	`pow1`
34×	`associate-*r/`
17×	`pow-prod-down`
16×	`add-exp-log` `add-cbrt-cube`
8×	`prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`pow-sqr` `pow-prod-up` `add-log-exp`
3×	`sqrt-prod`
2×	`pow-plus`
1×	`pow2` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `swap-sqr` `associate-r` `associate-l` `*-commutative` `flip-+`

Counts

4 → 135

Calls

4 calls:

13.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
19.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series192.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
149.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify61.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1373	3924
1	5001	3756

prune265.0ms

Filtered

77 candidates to 147 candidates (-90.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	140	7	147
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	140	8	148

Merged error: 26.1b

Counts

148 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

4.2b	(cos (/ (+ phi1 phi2) 2.0))
4.2b	(cos (/ (+ phi1 phi2) 2.0))
4.2b	(cos (/ (+ phi1 phi2) 2.0))
36.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

128×	`associate-*l/`
96×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 100

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series162.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
147.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify65.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1278	4428
1	5001	4345

prune397.0ms

Filtered

80 candidates to 112 candidates (-40.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	112	8	120

Merged error: 26.1b

Counts

120 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

4.2b	(cos (/ (+ phi1 phi2) 2.0))
4.2b	(cos (/ (+ phi1 phi2) 2.0))
36.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
36.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 172

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
18.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
18.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series303.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
144.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
148.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify81.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1266	6778
1	5001	6662

prune494.0ms

Filtered

100 candidates to 184 candidates (-84.0%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	184	8	192

Merged error: 26.1b

Counts

192 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

4.2b	(cos (/ (+ phi1 phi2) 2.0))
36.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
36.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
36.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

384×	`associate-*l/`
288×	`flip3--` `flip--`
198×	`sqrt-div`
192×	`frac-times` `frac-add`
96×	`associate-*r/`
10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 244

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
21.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
19.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
18.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series440.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
143.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
144.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
149.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify112.0ms

Algorithm

egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1266	10063
1	5001	9903

prune873.0ms

Filtered

132 candidates to 256 candidates (-93.9%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	256	0	256
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	256	8	264

Merged error: 26.1b

Counts

264 → 8

regimes1.2s

Accuracy

73.6% (3.8b remaining)

Error of 28.8b against oracle of 25.0b and baseline of 39.3b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	53
1	33	53

end0.0ms

sample10.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 4.248047%

Guaranteed chance to sample good point: 13.717491%

Results

635.0ms	5900×	body	80	valid
414.0ms	861×	body	640	valid
334.0ms	472×	body	1280	valid
215.0ms	473×	body	640	invalid
198.0ms	2010×	body	80	invalid
189.0ms	283×	body	1280	invalid
172.0ms	505×	body	320	valid
75.0ms	220×	body	320	invalid
63.0ms	262×	body	160	valid
25.0ms	112×	body	160	invalid

Details

sample7.3s

simplify52.0ms

prune10.0ms

localize17.0ms

rewrite53.0ms

series192.0ms

simplify61.0ms

prune265.0ms

localize23.0ms

rewrite51.0ms

series162.0ms

simplify65.0ms

prune397.0ms

localize23.0ms

rewrite66.0ms

series303.0ms

simplify81.0ms

prune494.0ms

localize25.0ms

rewrite92.0ms

series440.0ms

simplify112.0ms

prune873.0ms

regimes1.2s

bsearch2.0ms

simplify2.0ms

end0.0ms

sample10.3s

Profiling