Details

analyze2.0s

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

18.0ms	42×	body	640	valid
17.0ms	183×	body	80	valid
7.0ms	11×	body	1280	valid
7.0ms	11×	body	1280	invalid
7.0ms	69×	body	80	invalid
6.0ms	4×	body	320	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

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	32
1	37	32

prune11.0ms

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))))

rewrite57.0ms

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))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
25.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series155.0ms

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

simplify110.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5516	11780

prune480.0ms

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

localize21.0ms

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))))

rewrite42.0ms

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:

5.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
7.0ms	(cos (/ (+ phi1 phi2) 2.0))
17.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (log (exp (cos (/ (+ phi1 phi2) 2.0))))))) (* (- phi1 phi2) (- phi1 phi2))))

series150.0ms

Counts

4 → 12

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

simplify58.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4968	6302
1	4968	6302

prune254.0ms

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))))

rewrite42.0ms

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:

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

series151.0ms

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))
137.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (log (exp (cos (/ (+ phi1 phi2) 2.0)))) (log (exp (cos (/ (+ phi1 phi2) 2.0))))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify58.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4968	6302
1	4968	6302

prune268.0ms

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

localize27.0ms

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)))

rewrite48.0ms

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:

4.0ms	(cos (/ (+ phi1 phi2) 2.0))
14.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cos (/ (+ phi1 phi2) 2.0)) 2))) (pow (- phi1 phi2) 2)))
14.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cos (/ (+ phi1 phi2) 2.0)) 2))) (pow (- phi1 phi2) 2)))
14.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cos (/ (+ phi1 phi2) 2.0)) 2))) (pow (- phi1 phi2) 2)))

series406.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
133.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cos (/ (+ phi1 phi2) 2.0)) 2))) (pow (- phi1 phi2) 2)))
133.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cos (/ (+ phi1 phi2) 2.0)) 2))) (pow (- phi1 phi2) 2)))
135.0ms	(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

prune302.0ms

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

regimes838.0ms

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

analyze2.0s

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

sample2.7s

Algorithm

intervals

Results

577.0ms	5876×	body	80	valid
411.0ms	899×	body	640	valid
338.0ms	499×	body	1280	valid
228.0ms	2318×	body	80	invalid
208.0ms	462×	body	640	invalid
203.0ms	301×	body	1280	invalid
163.0ms	478×	body	320	valid
65.0ms	211×	body	320	invalid
63.0ms	248×	body	160	valid
20.0ms	94×	body	160	invalid

Details

analyze2.0s

sample95.0ms

simplify3.0ms

prune11.0ms

localize17.0ms

rewrite57.0ms

series155.0ms

simplify110.0ms

prune480.0ms

localize21.0ms

rewrite42.0ms

series150.0ms

simplify58.0ms

prune254.0ms

localize23.0ms

rewrite42.0ms

series151.0ms

simplify58.0ms

prune268.0ms

localize27.0ms

rewrite48.0ms

series406.0ms

simplify37.0ms

prune302.0ms

regimes838.0ms

bsearch2.6s

simplify1.0ms

end0.0ms

analyze2.0s

sample2.7s

Profiling