Details

analyze2.1s

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

sample99.0ms

Algorithm

intervals

Results

24.0ms	183×	body	80	valid
20.0ms	42×	body	640	valid
8.0ms	11×	body	1280	valid
7.0ms	11×	body	1280	invalid
7.0ms	69×	body	80	invalid
5.0ms	11×	body	640	invalid
4.0ms	13×	body	320	valid
2.0ms	7×	body	160	valid
1.0ms	6×	body	160	invalid
1.0ms	4×	body	320	invalid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	37	32
1	37	32

prune13.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 37.6b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
2.5b	(cos (/ (+ phi1 phi2) 2.0))
2.5b	(cos (/ (+ phi1 phi2) 2.0))
34.6b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite64.0ms

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)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
8.0ms	(cos (/ (+ phi1 phi2) 2.0))
24.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series163.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
145.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify107.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5516	11780

prune570.0ms

Filtered

138 candidates to 204 candidates (-47.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	194	10	204
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	194	11	205

Merged error: 23.0b

Counts

205 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
2.5b	(cos (/ (+ phi1 phi2) 2.0))
2.5b	(cos (/ (+ phi1 phi2) 2.0))
34.6b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (log (exp (cos (/ (+ phi1 phi2) 2.0))))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

6.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
18.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (log (exp (cos (/ (+ phi1 phi2) 2.0))))))) (* (- phi1 phi2) (- phi1 phi2))))

series155.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
140.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (log (exp (cos (/ (+ phi1 phi2) 2.0))))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify62.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4968	6302
1	4968	6302

prune303.0ms

Filtered

72 candidates to 120 candidates (-66.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	120	11	131

Merged error: 23.0b

Counts

131 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
2.5b	(cos (/ (+ phi1 phi2) 2.0))
2.5b	(cos (/ (+ phi1 phi2) 2.0))
34.6b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (log (exp (cos (/ (+ phi1 phi2) 2.0)))) (log (exp (cos (/ (+ phi1 phi2) 2.0))))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

6.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
20.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (log (exp (cos (/ (+ phi1 phi2) 2.0)))) (log (exp (cos (/ (+ phi1 phi2) 2.0))))))) (* (- phi1 phi2) (- phi1 phi2))))

series161.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
146.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (log (exp (cos (/ (+ phi1 phi2) 2.0)))) (log (exp (cos (/ (+ phi1 phi2) 2.0))))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify61.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4968	6302
1	4968	6302

prune324.0ms

Filtered

73 candidates to 120 candidates (-64.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	120	11	131

Merged error: 23.0b

Counts

131 → 11

localize26.0ms

Local error

Found 4 expressions with local error:

2.5b	(cos (/ (+ phi1 phi2) 2.0))
34.6b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cos (/ (+ phi1 phi2) 2.0)) 2))) (pow (- phi1 phi2) 2)))
34.6b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cos (/ (+ phi1 phi2) 2.0)) 2))) (pow (- phi1 phi2) 2)))
34.6b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cos (/ (+ phi1 phi2) 2.0)) 2))) (pow (- phi1 phi2) 2)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 52

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
16.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cos (/ (+ phi1 phi2) 2.0)) 2))) (pow (- phi1 phi2) 2)))
16.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cos (/ (+ phi1 phi2) 2.0)) 2))) (pow (- phi1 phi2) 2)))
18.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cos (/ (+ phi1 phi2) 2.0)) 2))) (pow (- phi1 phi2) 2)))

series430.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
142.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cos (/ (+ phi1 phi2) 2.0)) 2))) (pow (- phi1 phi2) 2)))
141.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cos (/ (+ phi1 phi2) 2.0)) 2))) (pow (- phi1 phi2) 2)))
142.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cos (/ (+ phi1 phi2) 2.0)) 2))) (pow (- phi1 phi2) 2)))

simplify37.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4973	1509
1	4973	1509

prune386.0ms

Filtered

54 candidates to 64 candidates (-18.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	64	11	75

Merged error: 23.0b

Counts

75 → 11

regimes877.0ms

Accuracy

34.7% (10.5b remaining)

Error of 33.9b against oracle of 23.4b and baseline of 39.5b

bsearch2.6s

Steps

Iters	Range		Point
8	-8.33489286311924e+105	-2.9355608733725575e+102	-4.8863841570454056e+104

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	41
1	29	41

end0.0ms

analyze2.1s

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	5876×	body	80	valid
426.0ms	899×	body	640	valid
363.0ms	499×	body	1280	valid
247.0ms	2318×	body	80	invalid
226.0ms	462×	body	640	invalid
202.0ms	301×	body	1280	invalid
164.0ms	478×	body	320	valid
73.0ms	211×	body	320	invalid
59.0ms	248×	body	160	valid
21.0ms	94×	body	160	invalid

Details

analyze2.1s

sample99.0ms

simplify3.0ms

prune13.0ms

localize17.0ms

rewrite64.0ms

series163.0ms

simplify107.0ms

prune570.0ms

localize22.0ms

rewrite47.0ms

series155.0ms

simplify62.0ms

prune303.0ms

localize23.0ms

rewrite46.0ms

series161.0ms

simplify61.0ms

prune324.0ms

localize26.0ms

rewrite55.0ms

series430.0ms

simplify37.0ms

prune386.0ms

regimes877.0ms

bsearch2.6s

simplify1.0ms

end0.0ms

analyze2.1s

sample2.8s

Profiling