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

sample102.0ms

Algorithm

intervals

Results

17.0ms	176×	body	80	valid
16.0ms	17×	body	1280	valid
13.0ms	30×	body	640	valid
8.0ms	19×	body	640	invalid
7.0ms	11×	body	1280	invalid
6.0ms	18×	body	320	valid
6.0ms	59×	body	80	invalid
3.0ms	15×	body	160	valid
3.0ms	10×	body	320	invalid
1.0ms	5×	body	160	invalid

simplify102.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	5091	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: 40.1b

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)))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
36.3b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite59.0ms

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))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series156.0ms

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))
139.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify105.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4972	11939
1	4972	11939

prune519.0ms

Filtered

138 candidates to 204 candidates (-47.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	193	11	204
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	193	12	205

Merged error: 26.7b

Counts

205 → 12

localize25.0ms

Local error

Found 4 expressions with local error:

3.2b	(cos (/ (+ phi1 phi2) 2.0))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
36.3b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 4) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (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/`
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))
23.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 4) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series149.0ms

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))
135.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 4) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify43.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	4977	5877
1	4977	5877

prune273.0ms

Filtered

66 candidates to 112 candidates (-69.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	112	12	124

Merged error: 26.7b

Counts

124 → 12

localize26.0ms

Local error

Found 4 expressions with local error:

3.2b	(cos (/ (+ phi1 phi2) 2.0))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
36.3b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (* (cbrt (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)) (cbrt (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (cbrt (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite55.0ms

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))
31.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (* (cbrt (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)) (cbrt (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (cbrt (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))))) (* (- phi1 phi2) (- phi1 phi2))))

series150.0ms

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))
136.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (* (cbrt (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)) (cbrt (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (cbrt (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify62.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4981	6143
1	4981	6143

prune333.0ms

Filtered

67 candidates to 112 candidates (-67.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	8	9
Picked	1	0	1
Done	0	2	2
Total	113	11	124

Merged error: 26.7b

Counts

124 → 11

localize32.0ms

Local error

Found 4 expressions with local error:

3.2b	(cos (/ (+ phi1 phi2) 2.0))
36.3b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)) 3))) (* (- phi1 phi2) (- phi1 phi2))))
36.3b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)) 3))) (* (- phi1 phi2) (- phi1 phi2))))
36.3b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)) 3))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

288×	`flip3--` `flip--`
240×	`associate-*l/`
198×	`sqrt-div`
192×	`frac-times` `frac-add`
96×	`associate-*r/`
10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 244

Calls

4 calls:

7.0ms	(cos (/ (+ phi1 phi2) 2.0))
21.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)) 3))) (* (- phi1 phi2) (- phi1 phi2))))
22.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)) 3))) (* (- phi1 phi2) (- phi1 phi2))))
21.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)) 3))) (* (- phi1 phi2) (- phi1 phi2))))

series410.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
134.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)) 3))) (* (- phi1 phi2) (- phi1 phi2))))
133.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)) 3))) (* (- phi1 phi2) (- phi1 phi2))))
138.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)) 3))) (* (- phi1 phi2) (- phi1 phi2))))

simplify102.0ms

Algorithm

egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4967	17021
1	4967	17021

prune1.1s

Filtered

132 candidates to 256 candidates (-93.9%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	256	0	256
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	256	11	267

Merged error: 26.7b

Counts

267 → 11

regimes755.0ms

Accuracy

13.2% (14.4b remaining)

Error of 37.1b against oracle of 22.6b and baseline of 39.3b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	117	120
1	117	120

end0.0ms

sample2.7s

Algorithm

intervals

Results

584.0ms	5848×	body	80	valid
406.0ms	873×	body	640	valid
334.0ms	490×	body	1280	valid
228.0ms	2334×	body	80	invalid
200.0ms	440×	body	640	invalid
198.0ms	293×	body	1280	invalid
173.0ms	520×	body	320	valid
77.0ms	248×	body	320	invalid
61.0ms	269×	body	160	valid
30.0ms	125×	body	160	invalid

Details

analyze2.0s

sample102.0ms

simplify102.0ms

prune11.0ms

localize17.0ms

rewrite59.0ms

series156.0ms

simplify105.0ms

prune519.0ms

localize25.0ms

rewrite46.0ms

series149.0ms

simplify43.0ms

prune273.0ms

localize26.0ms

rewrite55.0ms

series150.0ms

simplify62.0ms

prune333.0ms

localize32.0ms

rewrite98.0ms

series410.0ms

simplify102.0ms

prune1.1s

regimes755.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample2.7s

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