Details

analyze2.4s (23.6%)

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

19.0ms	185×	body	80	valid
15.0ms	32×	body	640	valid
10.0ms	16×	body	320	valid
10.0ms	13×	body	1280	valid
8.0ms	16×	body	640	invalid
6.0ms	56×	body	80	invalid
5.0ms	7×	body	1280	invalid
3.0ms	10×	body	160	valid
2.0ms	6×	body	320	invalid
1.0ms	4×	body	160	invalid

simplify130.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (128.0ms)

Iter	Nodes	Cost
0	5091	32

prune10.0ms (0.1%)

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: 37.6b

Counts

2 → 1

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
2.9b	(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))))

rewrite47.0ms (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:

18.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
9.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series182.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

148.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
24.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify44.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5062	6382

prune391.0ms (3.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	121	6	127
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	122	6	128

Merged error: 23.4b

Counts

128 → 6

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
2.9b	(cos (/ (+ phi1 phi2) 2.0))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
34.8b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite42.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

128×	`associate-*l/`
96×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1`
5×	`add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `cube-prod` `sqrt-prod`
1×	`cube-mult` `pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `unpow3` `pow-exp` `flip-+` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 116

Calls

4 calls:

20.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
2.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)

series170.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

147.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))
12.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
6.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify48.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5110	5951

prune401.0ms (3.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	128	6	134

Merged error: 23.4b

Counts

134 → 6

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
2.9b	(cos (/ (+ phi1 phi2) 2.0))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
34.8b	(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite45.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

128×	`associate-*l/`
96×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1`
5×	`add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `cube-prod` `sqrt-prod`
1×	`cube-mult` `pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `unpow3` `pow-exp` `flip-+` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 116

Calls

4 calls:

22.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
2.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)

series171.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

149.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))
12.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify46.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5239	5951

prune440.0ms (4.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	128	6	134

Merged error: 23.4b

Counts

134 → 6

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.9b	(cos (/ (+ phi1 phi2) 2.0))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
35.8b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
35.8b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite66.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

256×	`associate-*l/`
192×	`flip3--` `flip--`
132×	`cbrt-div`
128×	`frac-times` `frac-add`
64×	`associate-*r/`
6×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`flip3-+` `pow1/3` `flip-+`

Counts

4 → 168

Calls

4 calls:

19.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
18.0ms	(cbrt (+ (* (* (- 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))

series404.0ms (4%)

Counts

4 → 12

Calls

4 calls:

199.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
195.0ms	(cbrt (+ (* (* (- 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))

simplify68.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5004	12224

prune1.1s (11.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	179	1	180
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	180	6	186

Merged error: 23.4b

Counts

186 → 6

regimes747.0ms (7.3%)

Accuracy

Total 4.1b remaining (13.8%)

Threshold costs 0b (0%)

bsearch2.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	72
1	62	72

end0.0ms (0%)

sample3.0s (29.6%)

Algorithm

1×

intervals

Results

651.0ms	5891×	body	80	valid
451.0ms	898×	body	640	valid
373.0ms	503×	body	1280	valid
249.0ms	2277×	body	80	invalid
221.0ms	445×	body	640	invalid
218.0ms	303×	body	1280	invalid
158.0ms	436×	body	320	valid
73.0ms	215×	body	320	invalid
68.0ms	272×	body	160	valid
27.0ms	116×	body	160	invalid

Details

analyze2.4s (23.6%)

sample100.0ms (1%)

simplify130.0ms (1.3%)

prune10.0ms (0.1%)

localize17.0ms (0.2%)

rewrite47.0ms (0.5%)

series182.0ms (1.8%)

simplify44.0ms (0.4%)

prune391.0ms (3.8%)

localize21.0ms (0.2%)

rewrite42.0ms (0.4%)

series170.0ms (1.7%)

simplify48.0ms (0.5%)

prune401.0ms (3.9%)

localize24.0ms (0.2%)

rewrite45.0ms (0.4%)

series171.0ms (1.7%)

simplify46.0ms (0.5%)

prune440.0ms (4.3%)

localize25.0ms (0.2%)

rewrite66.0ms (0.6%)

series404.0ms (4%)

simplify68.0ms (0.7%)

prune1.1s (11.1%)

regimes747.0ms (7.3%)

bsearch2.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.0s (29.6%)

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