Details

sample24.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 4.248047%

Guaranteed chance to sample good point: 16.407445%

Results

19.0ms	187×	body	80	valid
17.0ms	35×	body	640	valid
12.0ms	18×	body	640	invalid
11.0ms	16×	body	1280	invalid
10.0ms	14×	body	1280	valid
6.0ms	58×	body	80	invalid
4.0ms	13×	body	320	valid
2.0ms	7×	body	160	valid
2.0ms	5×	body	320	invalid
1.0ms	4×	body	160	invalid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	17
1	71	17
2	241	17
3	747	17
4	2196	17
5	5001	17

prune5.0ms

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: 36.7b

Counts

2 → 1

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))))
3.7b	(cos (/ (+ phi1 phi2) 2.0))
3.7b	(cos (/ (+ phi1 phi2) 2.0))
33.6b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite51.0ms

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))))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
17.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series173.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* (- 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))
132.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify59.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1373	3924
1	5001	3756

prune247.0ms

Filtered

77 candidates to 147 candidates (-90.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	141	6	147
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	141	7	148

Merged error: 24.2b

Counts

148 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
3.7b	(cos (/ (+ phi1 phi2) 2.0))
3.7b	(cos (/ (+ phi1 phi2) 2.0))
33.6b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

5.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
17.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series147.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
133.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify55.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1296	3713
1	5001	3633

prune252.0ms

Filtered

70 candidates to 120 candidates (-71.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	121	6	127

Merged error: 24.2b

Counts

127 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
3.7b	(cos (/ (+ phi1 phi2) 2.0))
3.7b	(cos (/ (+ phi1 phi2) 2.0))
33.6b	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

6.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
18.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series143.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
129.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify59.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1292	3883
1	5001	3801

prune290.0ms

Filtered

71 candidates to 120 candidates (-69.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	119	7	126

Merged error: 24.2b

Counts

126 → 7

localize26.0ms

Local error

Found 4 expressions with local error:

3.7b	(cos (/ (+ phi1 phi2) 2.0))
3.7b	(cos (/ (+ phi1 phi2) 2.0))
33.6b	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
33.6b	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

256×	`associate-*l/`
192×	`flip3--` `flip--`
132×	`sqrt-div`
128×	`frac-times` `frac-add`
64×	`associate-*r/`
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))
20.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
18.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series272.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(cos (/ (+ phi1 phi2) 2.0))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
128.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
134.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify86.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1268	7458
1	5001	7334

prune677.0ms

Filtered

100 candidates to 184 candidates (-84.0%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	183	1	184
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	183	8	191

Merged error: 24.2b

Counts

191 → 8

regimes1.0s

Accuracy

74% (3.5b remaining)

Error of 28.9b against oracle of 25.4b and baseline of 38.8b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	34
1	27	34

end0.0ms

sample28.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 4.248047%

Guaranteed chance to sample good point: 16.407445%

Results

627.0ms	5899×	body	80	valid
417.0ms	854×	body	640	valid
358.0ms	505×	body	1280	valid
226.0ms	448×	body	640	invalid
204.0ms	2004×	body	80	invalid
192.0ms	273×	body	1280	invalid
165.0ms	476×	body	320	valid
78.0ms	236×	body	320	invalid
69.0ms	266×	body	160	valid
26.0ms	116×	body	160	invalid

Details

sample24.4s

simplify51.0ms

prune5.0ms

localize17.0ms

rewrite51.0ms

series173.0ms

simplify59.0ms

prune247.0ms

localize24.0ms

rewrite40.0ms

series147.0ms

simplify55.0ms

prune252.0ms

localize21.0ms

rewrite44.0ms

series143.0ms

simplify59.0ms

prune290.0ms

localize26.0ms

rewrite65.0ms

series272.0ms

simplify86.0ms

prune677.0ms

regimes1.0s

bsearch1.0ms

simplify1.0ms

end0.0ms

sample28.3s

Profiling