Details

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

sample86.0ms

Algorithm

intervals

Results

19.0ms	193×	body	80	valid
16.0ms	24×	body	640	valid
11.0ms	17×	body	1280	valid
5.0ms	55×	body	80	invalid
4.0ms	13×	body	320	valid
4.0ms	8×	body	640	invalid
3.0ms	5×	body	1280	invalid
2.0ms	9×	body	160	valid
2.0ms	6×	body	320	invalid
1.0ms	4×	body	160	invalid

simplify100.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	5091	32

prune15.0ms

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: 39.4b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
2.5b	(cos (/ (+ phi1 phi2) 2.0))
2.5b	(cos (/ (+ phi1 phi2) 2.0))
36.6b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite90.0ms

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:

8.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
9.0ms	(cos (/ (+ phi1 phi2) 2.0))
9.0ms	(cos (/ (+ phi1 phi2) 2.0))
23.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series160.0ms

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))
143.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify102.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4972	11939
1	4972	11939

prune496.0ms

Filtered

138 candidates to 204 candidates (-47.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	193	11	204
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	195	11	206

Merged error: 20.1b

Counts

206 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (pow (cos (/ (+ phi1 phi2) 2.0)) 2))
0.3b	(pow (cos (/ (+ phi1 phi2) 2.0)) 2)
2.5b	(cos (/ (+ phi1 phi2) 2.0))
36.6b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cos (/ (+ phi1 phi2) 2.0)) 2))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

97×	`flip3--` `flip--`
82×	`associate-*l/`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
19×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-exp-log` `add-cube-cbrt`
8×	`associate-r`
7×	`unpow-prod-down`
6×	`pow1` `add-cbrt-cube`
5×	`associate-l`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-unpow` `prod-exp` `sqrt-prod` `unpow2` `sqr-pow`
2×	`pow-to-exp` `pow-exp`
1×	`rem-sqrt-square` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 135

Calls

4 calls:

8.0ms	(* (- lambda1 lambda2) (pow (cos (/ (+ phi1 phi2) 2.0)) 2))
2.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 2)
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
17.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cos (/ (+ phi1 phi2) 2.0)) 2))) (* (- phi1 phi2) (- phi1 phi2))))

series179.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (- lambda1 lambda2) (pow (cos (/ (+ phi1 phi2) 2.0)) 2))
8.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 2)
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
135.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cos (/ (+ phi1 phi2) 2.0)) 2))) (* (- phi1 phi2) (- phi1 phi2))))

simplify44.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5008	6272

prune301.0ms

Filtered

98 candidates to 147 candidates (-50.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	147	11	158

Merged error: 20.1b

Counts

158 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 6))
0.8b	(pow (cos (/ (+ phi1 phi2) 2.0)) 6)
2.5b	(cos (/ (+ phi1 phi2) 2.0))
36.6b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 6)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

2.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 6))
2.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 6)
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
18.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 6)))) (* (- phi1 phi2) (- phi1 phi2))))

series166.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 6))
15.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 6)
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
138.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 6)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify44.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5024	6178

prune267.0ms

Filtered

75 candidates to 130 candidates (-73.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	130	11	141

Merged error: 20.1b

Counts

141 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

2.5b	(cos (/ (+ phi1 phi2) 2.0))
2.5b	(cos (/ (+ phi1 phi2) 2.0))
2.5b	(cos (/ (+ phi1 phi2) 2.0))
36.6b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cbrt (* (pow (cos (/ (+ phi1 phi2) 2.0)) 2) (pow (cos (/ (+ phi1 phi2) 2.0)) 2))) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 2))))) (* (- 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/`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 100

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
22.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cbrt (* (pow (cos (/ (+ phi1 phi2) 2.0)) 2) (pow (cos (/ (+ phi1 phi2) 2.0)) 2))) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 2))))) (* (- phi1 phi2) (- phi1 phi2))))

series154.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
139.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cbrt (* (pow (cos (/ (+ phi1 phi2) 2.0)) 2) (pow (cos (/ (+ phi1 phi2) 2.0)) 2))) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 2))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify62.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4969	6731
1	4969	6731

prune270.0ms

Filtered

67 candidates to 112 candidates (-67.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	111	12	123

Merged error: 20.1b

Counts

123 → 12

regimes1.0s

Accuracy

30.5% (11.3b remaining)

Error of 33.9b against oracle of 22.6b and baseline of 38.9b

bsearch48.0ms

Steps

Iters	Range		Point
6	2.7803433206253862e+17	3.743927020544241e+18	3.6773742881661286e+18

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	36
1	56	36

end0.0ms

sample2.7s

Algorithm

intervals

Results

606.0ms	5901×	body	80	valid
389.0ms	847×	body	640	valid
332.0ms	491×	body	1280	valid
234.0ms	2395×	body	80	invalid
208.0ms	442×	body	640	invalid
190.0ms	286×	body	1280	invalid
165.0ms	495×	body	320	valid
78.0ms	245×	body	320	invalid
65.0ms	266×	body	160	valid
24.0ms	109×	body	160	invalid

Details

analyze2.2s

sample86.0ms

simplify100.0ms

prune15.0ms

localize17.0ms

rewrite90.0ms

series160.0ms

simplify102.0ms

prune496.0ms

localize17.0ms

rewrite45.0ms

series179.0ms

simplify44.0ms

prune301.0ms

localize21.0ms

rewrite36.0ms

series166.0ms

simplify44.0ms

prune267.0ms

localize23.0ms

rewrite47.0ms

series154.0ms

simplify62.0ms

prune270.0ms

regimes1.0s

bsearch48.0ms

simplify1.0ms

end0.0ms

sample2.7s

Profiling