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

sample98.0ms

Algorithm

intervals

Results

18.0ms	183×	body	80	valid
12.0ms	18×	body	1280	valid
12.0ms	27×	body	640	valid
12.0ms	76×	body	80	invalid
6.0ms	19×	body	320	valid
6.0ms	9×	body	1280	invalid
5.0ms	12×	body	640	invalid
2.0ms	9×	body	160	valid
2.0ms	5×	body	320	invalid
1.0ms	5×	body	160	invalid

simplify98.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	5091	32

prune16.0ms

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: 35.9b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
3.4b	(cos (/ (+ phi1 phi2) 2.0))
3.4b	(cos (/ (+ phi1 phi2) 2.0))
33.0b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

142×	`associate-*l/`
102×	`flip3--` `flip--`
68×	`frac-times`
66×	`sqrt-div`
64×	`frac-add`
44×	`pow1`
34×	`associate-*r/`
17×	`pow-prod-down`
16×	`add-exp-log` `add-cbrt-cube`
8×	`prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`pow-sqr` `pow-prod-up` `add-log-exp`
3×	`sqrt-prod`
2×	`pow-plus`
1×	`pow2` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `swap-sqr` `associate-r` `associate-l` `*-commutative` `flip-+`

Counts

4 → 135

Calls

4 calls:

12.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
21.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series183.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
142.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify48.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5172	6821

prune278.0ms

Filtered

78 candidates to 147 candidates (-88.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	138	9	147
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	139	10	149

Merged error: 23.7b

Counts

149 → 10

localize27.0ms

Local error

Found 4 expressions with local error:

3.4b	(cos (/ (+ phi1 phi2) 2.0))
3.4b	(cos (/ (+ phi1 phi2) 2.0))
3.4b	(cos (/ (+ phi1 phi2) 2.0))
33.0b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

128×	`associate-*l/`
96×	`flip3--` `flip--`
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))
26.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series159.0ms

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))
144.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify48.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5572	6483

prune331.0ms

Filtered

80 candidates to 112 candidates (-40.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	113	9	122

Merged error: 23.7b

Counts

122 → 9

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 3)
3.4b	(cos (/ (+ phi1 phi2) 2.0))
3.4b	(cos (/ (+ phi1 phi2) 2.0))
33.0b	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 123

Calls

4 calls:

3.0ms	(pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 3)
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
19.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

series169.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 3)
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
140.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify49.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5026	6119

prune266.0ms

Filtered

76 candidates to 135 candidates (-77.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	135	9	144

Merged error: 23.7b

Counts

144 → 9

localize28.0ms

Local error

Found 4 expressions with local error:

3.4b	(cos (/ (+ phi1 phi2) 2.0))
3.4b	(cos (/ (+ phi1 phi2) 2.0))
33.0b	(sqrt (+ (* (- lambda1 lambda2) (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6) (- lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))
33.0b	(sqrt (+ (* (- lambda1 lambda2) (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6) (- lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

192×	`flip3--` `flip--`
160×	`associate-*r/`
132×	`sqrt-div`
128×	`frac-times` `frac-add`
64×	`associate-*l/`
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:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
17.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6) (- lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))
18.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6) (- lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

series291.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
140.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6) (- lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))
141.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6) (- lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

simplify86.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4989	11450
1	4989	11450

prune475.0ms

Filtered

100 candidates to 184 candidates (-84.0%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	184	9	193

Merged error: 23.7b

Counts

193 → 9

regimes1.1s

Accuracy

73% (3.8b remaining)

Error of 28.9b against oracle of 25.0b and baseline of 39.2b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	69
1	53	69

end0.0ms

sample3.1s

Algorithm

intervals

Results

825.0ms	5837×	body	80	valid
438.0ms	919×	body	640	valid
338.0ms	479×	body	1280	valid
244.0ms	2379×	body	80	invalid
222.0ms	326×	body	1280	invalid
213.0ms	448×	body	640	invalid
177.0ms	518×	body	320	valid
72.0ms	224×	body	320	invalid
58.0ms	247×	body	160	valid
24.0ms	107×	body	160	invalid

Details

analyze2.2s

sample98.0ms

simplify98.0ms

prune16.0ms

localize17.0ms

rewrite53.0ms

series183.0ms

simplify48.0ms

prune278.0ms

localize27.0ms

rewrite50.0ms

series159.0ms

simplify48.0ms

prune331.0ms

localize25.0ms

rewrite41.0ms

series169.0ms

simplify49.0ms

prune266.0ms

localize28.0ms

rewrite62.0ms

series291.0ms

simplify86.0ms

prune475.0ms

regimes1.1s

bsearch1.0ms

simplify2.0ms

end0.0ms

sample3.1s

Profiling