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

sample95.0ms

Algorithm

intervals

Results

24.0ms	200×	body	80	valid
11.0ms	17×	body	1280	invalid
10.0ms	15×	body	1280	valid
8.0ms	17×	body	640	valid
6.0ms	20×	body	320	valid
6.0ms	65×	body	80	invalid
5.0ms	11×	body	640	invalid
2.0ms	6×	body	320	invalid
1.0ms	5×	body	160	invalid
1.0ms	4×	body	160	valid

simplify102.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	5091	32

prune10.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 37.8b

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))))
2.6b	(cos (/ (+ phi1 phi2) 2.0))
2.6b	(cos (/ (+ phi1 phi2) 2.0))
34.8b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite58.0ms

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))
23.0ms	(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:

31.0ms	(* (* (- 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))
138.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify50.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5172	6821

prune252.0ms

Filtered

78 candidates to 147 candidates (-88.5%)

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: 23.5b

Counts

148 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

2.6b	(cos (/ (+ phi1 phi2) 2.0))
2.6b	(cos (/ (+ phi1 phi2) 2.0))
34.8b	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
34.8b	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

192×	`flip3--` `flip--`
160×	`associate-r/` `associate-l/`
132×	`sqrt-div`
128×	`frac-times` `frac-add`
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))
19.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
22.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series284.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
135.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
138.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify91.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4964	12042
1	4964	12042

prune477.0ms

Filtered

98 candidates to 184 candidates (-87.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	184	8	192

Merged error: 23.5b

Counts

192 → 8

localize29.0ms

Local error

Found 4 expressions with local error:

2.6b	(cos (/ (+ phi1 phi2) 2.0))
34.8b	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
34.8b	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
34.8b	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

288×	`flip3--` `flip--`
240×	`associate-r/` `associate-l/`
198×	`sqrt-div`
192×	`frac-times` `frac-add`
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))
19.0ms	(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))))
20.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series415.0ms

Counts

4 → 12

Calls

4 calls:

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))))
134.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
140.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify124.0ms

Algorithm

egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4964	17897
1	4964	17897

prune932.0ms

Filtered

129 candidates to 256 candidates (-98.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	256	0	256
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	256	8	264

Merged error: 23.5b

Counts

264 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- phi1 phi2) (- phi1 phi2))
2.6b	(+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* (* lambda1 lambda2) -2)))
2.7b	(+ (* lambda2 lambda2) (* (* lambda1 lambda2) -2))
34.8b	(sqrt (+ (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* (* lambda1 lambda2) -2))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`flip3--` `sqrt-div` `flip--`
16×	`frac-add`
12×	`pow1` `frac-times`
11×	`flip3-+` `flip-+` `add-log-exp`
9×	`add-cube-cbrt`
7×	`swap-sqr`
6×	`add-exp-log` `associate-r/` `associate-l/` `add-cbrt-cube` `distribute-lft-out--`
5×	`associate-r` `associate-l`
4×	`sum-log` `difference-of-squares`
3×	`sqrt-prod`
2×	`+-commutative` `sub-neg`
1×	`pow2` `distribute-rgt-in` `rem-sqrt-square` `associate-+r+` `distribute-lft-in` `sqrt-pow1` `pow-plus` `pow1/2` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

9.0ms	(* (- phi1 phi2) (- phi1 phi2))
9.0ms	(+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* (* lambda1 lambda2) -2)))
4.0ms	(+ (* lambda2 lambda2) (* (* lambda1 lambda2) -2))
11.0ms	(sqrt (+ (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* (* lambda1 lambda2) -2))) (* (- phi1 phi2) (- phi1 phi2))))

series63.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (- phi1 phi2) (- phi1 phi2))
6.0ms	(+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* (* lambda1 lambda2) -2)))
6.0ms	(+ (* lambda2 lambda2) (* (* lambda1 lambda2) -2))
47.0ms	(sqrt (+ (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* (* lambda1 lambda2) -2))) (* (- phi1 phi2) (- phi1 phi2))))

simplify40.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5272	2526

prune142.0ms

Filtered

72 candidates to 110 candidates (-52.8%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	108	10	118

Merged error: 22.9b

Counts

118 → 10

regimes1.1s

Accuracy

70% (4.5b remaining)

Error of 28.7b against oracle of 24.2b and baseline of 39.1b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	108
1	59	108

end0.0ms

sample2.7s

Algorithm

intervals

Results

586.0ms	5952×	body	80	valid
394.0ms	843×	body	640	valid
329.0ms	482×	body	1280	valid
231.0ms	2389×	body	80	invalid
211.0ms	463×	body	640	invalid
196.0ms	289×	body	1280	invalid
159.0ms	464×	body	320	valid
75.0ms	239×	body	320	invalid
60.0ms	259×	body	160	valid
25.0ms	119×	body	160	invalid

Details

analyze2.3s

sample95.0ms

simplify102.0ms

prune10.0ms

localize17.0ms

rewrite58.0ms

series178.0ms

simplify50.0ms

prune252.0ms

localize22.0ms

rewrite72.0ms

series284.0ms

simplify91.0ms

prune477.0ms

localize29.0ms

rewrite97.0ms

series415.0ms

simplify124.0ms

prune932.0ms

localize14.0ms

rewrite38.0ms

series63.0ms

simplify40.0ms

prune142.0ms

regimes1.1s

bsearch2.0ms

simplify2.0ms

end0.0ms

sample2.7s

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