Details

analyze2.3s (22.3%)

Algorithm

1×

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

sample100.0ms (1%)

Algorithm

1×

intervals

Results

21.0ms	175×	body	80	valid
15.0ms	33×	body	640	valid
11.0ms	17×	body	1280	valid
10.0ms	15×	body	1280	invalid
7.0ms	78×	body	80	invalid
7.0ms	21×	body	320	valid
4.0ms	9×	body	640	invalid
2.0ms	10×	body	160	valid
2.0ms	5×	body	320	invalid
1.0ms	3×	body	160	invalid

simplify99.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	5091	32

prune10.0ms (0.1%)

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: 39.1b

Counts

2 → 1

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
3.4b	(cos (/ (+ phi1 phi2) 2.0))
3.4b	(cos (/ (+ phi1 phi2) 2.0))
36.1b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite50.0ms (0.5%)

Algorithm

1×	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:

22.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
7.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series174.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

143.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
21.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify43.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5062	6382

prune398.0ms (3.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	119	8	127
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	8	128

Merged error: 26.5b

Counts

128 → 8

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

3.4b	(cos (/ (+ phi1 phi2) 2.0))
3.4b	(cos (/ (+ phi1 phi2) 2.0))
29.0b	(/ (* (cos (/ (+ phi1 phi2) 2.0)) (- (* lambda1 lambda1) (* lambda2 lambda2))) (+ lambda1 lambda2))
36.1b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (/ (* (cos (/ (+ phi1 phi2) 2.0)) (- (* lambda1 lambda1) (* lambda2 lambda2))) (+ lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite45.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`associate-*l/`
47×	`flip3--` `flip--`
42×	`sqrt-div`
40×	`frac-add`
36×	`frac-times`
20×	`associate-*r/`
11×	`*-un-lft-identity`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
5×	`pow1`
4×	`times-frac` `associate-/r*` `add-log-exp`
3×	`sqrt-prod`
2×	`cbrt-undiv` `flip3-+` `div-exp` `associate-/r/` `flip-+` `associate-/l/` `distribute-lft-out`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 96

Calls

4 calls:

19.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (/ (* (cos (/ (+ phi1 phi2) 2.0)) (- (* lambda1 lambda1) (* lambda2 lambda2))) (+ lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))
10.0ms	(/ (* (cos (/ (+ phi1 phi2) 2.0)) (- (* lambda1 lambda1) (* lambda2 lambda2))) (+ lambda1 lambda2))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series275.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

201.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (/ (* (cos (/ (+ phi1 phi2) 2.0)) (- (* lambda1 lambda1) (* lambda2 lambda2))) (+ lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))
64.0ms	(/ (* (cos (/ (+ phi1 phi2) 2.0)) (- (* lambda1 lambda1) (* lambda2 lambda2))) (+ lambda1 lambda2))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify52.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4984	4756
1	4984	4756

prune302.0ms (3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	108	8	116

Merged error: 26.5b

Counts

116 → 8

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

6.5b	(/ (- (* lambda1 lambda1) (* lambda2 lambda2)) (cbrt (+ lambda1 lambda2)))
7.9b	(* (/ (- (* lambda1 lambda1) (* lambda2 lambda2)) (cbrt (+ lambda1 lambda2))) (/ (cos (/ (+ phi1 phi2) 2.0)) (cbrt (+ lambda1 lambda2))))
14.4b	(/ (* (/ (- (* lambda1 lambda1) (* lambda2 lambda2)) (cbrt (+ lambda1 lambda2))) (/ (cos (/ (+ phi1 phi2) 2.0)) (cbrt (+ lambda1 lambda2)))) (cbrt (+ lambda1 lambda2)))
36.1b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (/ (* (/ (- (* lambda1 lambda1) (* lambda2 lambda2)) (cbrt (+ lambda1 lambda2))) (/ (cos (/ (+ phi1 phi2) 2.0)) (cbrt (+ lambda1 lambda2)))) (cbrt (+ lambda1 lambda2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite110.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`times-frac`
88×	`add-sqr-sqrt`
85×	`*-un-lft-identity`
62×	`cbrt-prod`
60×	`associate-*l/`
57×	`add-cube-cbrt`
47×	`flip3--` `flip--`
42×	`sqrt-div`
40×	`frac-add`
38×	`frac-times`
36×	`add-exp-log`
34×	`associate-l`
27×	`associate-r`
22×	`add-cbrt-cube`
20×	`associate-*r/`
15×	`difference-of-squares`
14×	`cbrt-undiv` `div-exp` `associate-/r*` `distribute-lft-out`
9×	`unswap-sqr`
8×	`cbrt-div` `prod-exp` `associate-/r/` `cbrt-unprod`
7×	`pow1`
5×	`flip3-+` `flip-+` `associate-/l/` `associate-/l*`
4×	`div-inv` `add-log-exp`
3×	`sqrt-prod`
2×	`frac-2neg` `clear-num`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-sub` `pow-prod-down` `*-commutative`

Counts

4 → 241

Calls

4 calls:

34.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (/ (* (/ (- (* lambda1 lambda1) (* lambda2 lambda2)) (cbrt (+ lambda1 lambda2))) (/ (cos (/ (+ phi1 phi2) 2.0)) (cbrt (+ lambda1 lambda2)))) (cbrt (+ lambda1 lambda2)))) (* (- phi1 phi2) (- phi1 phi2))))
29.0ms	(* (/ (- (* lambda1 lambda1) (* lambda2 lambda2)) (cbrt (+ lambda1 lambda2))) (/ (cos (/ (+ phi1 phi2) 2.0)) (cbrt (+ lambda1 lambda2))))
20.0ms	(/ (* (/ (- (* lambda1 lambda1) (* lambda2 lambda2)) (cbrt (+ lambda1 lambda2))) (/ (cos (/ (+ phi1 phi2) 2.0)) (cbrt (+ lambda1 lambda2)))) (cbrt (+ lambda1 lambda2)))
9.0ms	(/ (- (* lambda1 lambda1) (* lambda2 lambda2)) (cbrt (+ lambda1 lambda2)))

series359.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

219.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (/ (* (/ (- (* lambda1 lambda1) (* lambda2 lambda2)) (cbrt (+ lambda1 lambda2))) (/ (cos (/ (+ phi1 phi2) 2.0)) (cbrt (+ lambda1 lambda2)))) (cbrt (+ lambda1 lambda2)))) (* (- phi1 phi2) (- phi1 phi2))))
77.0ms	(* (/ (- (* lambda1 lambda1) (* lambda2 lambda2)) (cbrt (+ lambda1 lambda2))) (/ (cos (/ (+ phi1 phi2) 2.0)) (cbrt (+ lambda1 lambda2))))
39.0ms	(/ (* (/ (- (* lambda1 lambda1) (* lambda2 lambda2)) (cbrt (+ lambda1 lambda2))) (/ (cos (/ (+ phi1 phi2) 2.0)) (cbrt (+ lambda1 lambda2)))) (cbrt (+ lambda1 lambda2)))
24.0ms	(/ (- (* lambda1 lambda1) (* lambda2 lambda2)) (cbrt (+ lambda1 lambda2)))

simplify64.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5414	9864

prune764.0ms (7.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	251	2	253
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	251	10	261

Merged error: 26.0b

Counts

261 → 10

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.4b	(cos (/ (+ phi1 phi2) 2.0))
3.4b	(cos (/ (+ phi1 phi2) 2.0))
36.1b	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
36.1b	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite72.0ms (0.7%)

Algorithm

1×	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:

22.0ms	(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))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series300.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

147.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
141.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
6.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify90.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4964	12042
1	4964	12042

prune923.0ms (9%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	184	10	194

Merged error: 26.0b

Counts

194 → 10

regimes786.0ms (7.7%)

Accuracy

Total 9.4b remaining (27.6%)

Threshold costs 0b (0%)

bsearch45.0ms (0.4%)

Steps

Iters	Range		Point
6	9.222308414957667e+34	4.363912301045353e+35	4.192323342123785e+35

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	72	49
1	72	49

end0.0ms (0%)

sample2.8s (27.3%)

Algorithm

1×

intervals

Results

593.0ms	5813×	body	80	valid
418.0ms	880×	body	640	valid
362.0ms	518×	body	1280	valid
227.0ms	2351×	body	80	invalid
212.0ms	311×	body	1280	invalid
190.0ms	417×	body	640	invalid
169.0ms	519×	body	320	valid
70.0ms	224×	body	320	invalid
67.0ms	270×	body	160	valid
28.0ms	112×	body	160	invalid

Details

analyze2.3s (22.3%)

sample100.0ms (1%)

simplify99.0ms (1%)

prune10.0ms (0.1%)

localize16.0ms (0.2%)

rewrite50.0ms (0.5%)

series174.0ms (1.7%)

simplify43.0ms (0.4%)

prune398.0ms (3.9%)

localize26.0ms (0.3%)

rewrite45.0ms (0.4%)

series275.0ms (2.7%)

simplify52.0ms (0.5%)

prune302.0ms (3%)

localize27.0ms (0.3%)

rewrite110.0ms (1.1%)

series359.0ms (3.5%)

simplify64.0ms (0.6%)

prune764.0ms (7.5%)

localize22.0ms (0.2%)

rewrite72.0ms (0.7%)

series300.0ms (2.9%)

simplify90.0ms (0.9%)

prune923.0ms (9%)

regimes786.0ms (7.7%)

bsearch45.0ms (0.4%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.8s (27.3%)

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