Details

analyze2.3s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
4.7%	95.1%	0.2%	12
5.9%	93.2%	0.8%	13
8.5%	90.2%	1.3%	14

sample98.0ms

Algorithm

intervals

Results

19.0ms	188×	body	80	valid
12.0ms	26×	body	640	valid
11.0ms	10×	body	1280	invalid
11.0ms	16×	body	1280	valid
8.0ms	78×	body	80	invalid
7.0ms	20×	body	320	valid
6.0ms	12×	body	640	invalid
2.0ms	6×	body	320	invalid
1.0ms	6×	body	160	valid
1.0ms	4×	body	160	invalid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	37	32
1	37	32

prune19.0ms

Filtered

1 candidates to 1 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: 39.3b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
36.8b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite42.0ms

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:

6.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
17.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series166.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
137.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify44.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5053	6382

prune233.0ms

Filtered

77 candidates to 127 candidates (-64.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	122	5	127
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	122	7	129

Merged error: 26.0b

Counts

129 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
36.8b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

198×	`flip3--` `flip--`
196×	`frac-times`
138×	`sqrt-div`
136×	`frac-add`
98×	`associate-r/` `associate-l/`
73×	`cos-mult`
12×	`pow1` `add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l` `sqrt-prod`
1×	`pow2` `sqr-cos-a` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow-plus` `pow1/2` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 192

Calls

4 calls:

4.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
6.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
21.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series153.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
136.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify105.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5516	11780

prune442.0ms

Filtered

137 candidates to 204 candidates (-48.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	198	6	204
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	201	10	211

Merged error: 22.9b

Counts

211 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- lambda1 lambda2))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
36.8b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2))) (* (cos (/ (+ phi1 phi2) 2.0)) (cbrt (- lambda1 lambda2))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

1408×	`frac-times`
1345×	`flip3--` `flip--`
1298×	`cbrt-div`
992×	`associate-*r/`
944×	`associate-*l/`
642×	`sqrt-div`
640×	`frac-add`
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))
10.0ms	(cos (/ (+ phi1 phi2) 2.0))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
64.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2))) (* (cos (/ (+ phi1 phi2) 2.0)) (cbrt (- lambda1 lambda2))))) (* (- phi1 phi2) (- phi1 phi2))))

series173.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt (- lambda1 lambda2))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
139.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2))) (* (cos (/ (+ phi1 phi2) 2.0)) (cbrt (- lambda1 lambda2))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify333.0ms

Algorithm

egg-herbie

Counts

696 → 696

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5733	78545

prune3.8s

Filtered

689 candidates to 696 candidates (-1.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	694	2	696
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	695	11	706

Merged error: 22.9b

Counts

706 → 11

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b	(* R (- phi2 phi1))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
5×	`-un-lft-identity` `associate-r*`
3×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
2×	`sub-neg` `associate-*r/`
1×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `add-log-exp` `difference-of-squares` `unswap-sqr`

Counts

1 → 24

Calls

1 calls:

6.0ms

(* R (- phi2 phi1))

series7.0ms

Counts

1 → 3

Calls

1 calls:

7.0ms

(* R (- phi2 phi1))

simplify28.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5155	172

prune24.0ms

Filtered

17 candidates to 27 candidates (-58.8%)

Pruning

18 alts after pruning (15 fresh and 3 done)

	Pruned	Kept	Total
New	20	7	27
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	20	18	38

Merged error: 22.8b

Counts

38 → 18

regimes1.5s

Accuracy

57% (7.0b remaining)

Error of 29.8b against oracle of 22.8b and baseline of 39.0b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	108
1	33	108

end0.0ms

analyze2.2s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
4.7%	95.1%	0.2%	12
5.9%	93.2%	0.8%	13
8.5%	90.2%	1.3%	14

sample2.8s

Algorithm

intervals

Results

604.0ms	5858×	body	80	valid
425.0ms	882×	body	640	valid
369.0ms	508×	body	1280	valid
242.0ms	2295×	body	80	invalid
228.0ms	319×	body	1280	invalid
207.0ms	426×	body	640	invalid
175.0ms	520×	body	320	valid
73.0ms	221×	body	320	invalid
55.0ms	232×	body	160	valid
24.0ms	106×	body	160	invalid

Details

analyze2.3s

sample98.0ms

simplify3.0ms

prune19.0ms

localize16.0ms

rewrite42.0ms

series166.0ms

simplify44.0ms

prune233.0ms

localize17.0ms

rewrite56.0ms

series153.0ms

simplify105.0ms

prune442.0ms

localize21.0ms

rewrite227.0ms

series173.0ms

simplify333.0ms

prune3.8s

localize4.0ms

rewrite6.0ms

series7.0ms

simplify28.0ms

prune24.0ms

regimes1.5s

bsearch2.0ms

simplify1.0ms

end0.0ms

analyze2.2s

sample2.8s

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