Details

analyze2.1s

Algorithm: search

sample99.0ms

Algorithm

intervals

Results

20.0ms	192×	body	80	valid
12.0ms	69×	body	80	invalid
12.0ms	24×	body	640	valid
10.0ms	15×	body	1280	valid
9.0ms	19×	body	640	invalid
5.0ms	16×	body	320	valid
4.0ms	6×	body	1280	invalid
2.0ms	9×	body	160	valid
2.0ms	5×	body	320	invalid
1.0ms	3×	body	160	invalid

simplify56.0ms

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

prune6.0ms

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: 39.3b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
2.7b	(cos (/ (+ phi1 phi2) 2.0))
2.7b	(cos (/ (+ phi1 phi2) 2.0))
36.1b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

130×	`associate-*l/`
97×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
12×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube`
5×	`associate-l`
4×	`add-log-exp`
3×	`associate-r` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

7.0ms	(* (- 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))))

series178.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
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))))

simplify59.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1312	3623
1	5002	3528

prune283.0ms

Filtered

77 candidates to 127 candidates (-64.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	121	6	127
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	121	7	128

Merged error: 25.2b

Counts

128 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- lambda1 lambda2))
2.7b	(cos (/ (+ phi1 phi2) 2.0))
2.7b	(cos (/ (+ phi1 phi2) 2.0))
36.1b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite255.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 684

Calls

4 calls:

3.0ms	(cbrt (- lambda1 lambda2))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
80.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series194.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(cbrt (- lambda1 lambda2))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
152.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify400.0ms

Algorithm

egg-herbie

Counts

696 → 696

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5002	44972

prune4.4s

Filtered

688 candidates to 696 candidates (-1.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	695	1	696
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	695	8	703

Merged error: 25.1b

Counts

703 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

2.7b	(cos (/ (+ phi1 phi2) 2.0))
2.7b	(cos (/ (+ phi1 phi2) 2.0))
37.2b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
37.2b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

256×	`associate-*l/`
192×	`flip3--` `flip--`
132×	`cbrt-div`
128×	`frac-times` `frac-add`
64×	`associate-*r/`
6×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`flip3-+` `pow1/3` `flip-+`

Counts

4 → 168

Calls

4 calls:

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

series401.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
195.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
196.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify85.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1313	6856
1	5001	6776

prune568.0ms

Filtered

100 candidates to 180 candidates (-80.0%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	180	8	188

Merged error: 25.1b

Counts

188 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

2.7b	(cos (/ (+ phi1 phi2) 2.0))
2.7b	(cos (/ (+ phi1 phi2) 2.0))
6.2b	(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
36.1b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 179

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(exp (log (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))))

series297.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
143.0ms	(exp (log (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))))

simplify89.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1513	6939
1	5002	6823

prune558.0ms

Filtered

98 candidates to 191 candidates (-94.9%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	185	6	191
Fresh	0	4	4
Picked	1	0	1
Done	0	3	3
Total	186	13	199

Merged error: 25.1b

Counts

199 → 13

regimes1.5s

Accuracy

73.9% (3.5b remaining)

Error of 28.9b against oracle of 25.4b and baseline of 38.8b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	34
1	27	34

end0.0ms

analyze2.1s

Algorithm: search

sample2.8s

Algorithm

intervals

Results

595.0ms	5839×	body	80	valid
410.0ms	876×	body	640	valid
328.0ms	471×	body	1280	valid
240.0ms	2329×	body	80	invalid
214.0ms	447×	body	640	invalid
191.0ms	286×	body	1280	invalid
191.0ms	528×	body	320	valid
72.0ms	205×	body	320	invalid
69.0ms	286×	body	160	valid
26.0ms	115×	body	160	invalid

Details

analyze2.1s

sample99.0ms

simplify56.0ms

prune6.0ms

localize18.0ms

rewrite51.0ms

series178.0ms

simplify59.0ms

prune283.0ms

localize23.0ms

rewrite255.0ms

series194.0ms

simplify400.0ms

prune4.4s

localize24.0ms

rewrite70.0ms

series401.0ms

simplify85.0ms

prune568.0ms

localize24.0ms

rewrite82.0ms

series297.0ms

simplify89.0ms

prune558.0ms

regimes1.5s

bsearch2.0ms

simplify2.0ms

end0.0ms

analyze2.1s

sample2.8s

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