Details

sample6.5s

Algorithm

intervals

sampling

Space saved by range analysis: 4.481588%

Space saved by search: 0.243902%

Guaranteed chance to sample good point: 0%

Results

19.0ms	192×	body	80	valid
10.0ms	23×	body	640	valid
9.0ms	13×	body	1280	valid
8.0ms	78×	body	80	invalid
6.0ms	18×	body	320	valid
6.0ms	13×	body	640	invalid
3.0ms	5×	body	1280	invalid
3.0ms	9×	body	320	invalid
2.0ms	10×	body	160	valid
1.0ms	4×	body	160	invalid

simplify52.0ms

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: 37.0b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
1.7b	(cos (/ (+ phi1 phi2) 2.0))
1.7b	(cos (/ (+ phi1 phi2) 2.0))
33.9b	(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))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
4.0ms	(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))))

series190.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (* (- 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))
146.0ms	(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	3925
1	5001	3756

prune264.0ms

Filtered

77 candidates to 147 candidates (-90.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	139	8	147
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	139	9	148

Merged error: 22.9b

Counts

148 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
1.7b	(cos (/ (+ phi1 phi2) 2.0))
1.7b	(cos (/ (+ phi1 phi2) 2.0))
33.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite43.0ms

Algorithm

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:

2.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
18.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

series165.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
141.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify58.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1349	3745
1	5002	3672

prune262.0ms

Filtered

69 candidates to 128 candidates (-85.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	128	9	137

Merged error: 22.9b

Counts

137 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
1.7b	(cos (/ (+ phi1 phi2) 2.0))
1.7b	(cos (/ (+ phi1 phi2) 2.0))
33.9b	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

198×	`flip3--` `flip--`
196×	`frac-times`
138×	`sqrt-div`
136×	`frac-add`
130×	`associate-*l/`
74×	`associate-*r/`
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` `rem-sqrt-square` `sqr-cos` `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)))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
23.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series161.0ms

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

simplify103.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	2471	7439
1	5001	7337

prune336.0ms

Filtered

102 candidates to 204 candidates (-100.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	203	1	204
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	205	8	213

Merged error: 22.9b

Counts

213 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0))))))
0.6b	(+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))))
1.6b	(cos (* 2 (/ (+ phi1 phi2) 2.0)))
33.9b	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

356×	`frac-times`
318×	`flip3--` `flip--`
210×	`sqrt-div`
208×	`frac-add`
178×	`associate-*l/`
124×	`associate-*r/`
83×	`flip3-+` `flip-+`
10×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
3×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
1×	`+-commutative` `distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `associate-l` `sum-log` `*-commutative` `cos-2` `unswap-sqr`

Counts

4 → 289

Calls

4 calls:

13.0ms	(* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0))))))
3.0ms	(+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))))
2.0ms	(cos (* 2 (/ (+ phi1 phi2) 2.0)))
29.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series505.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0))))))
8.0ms	(+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))))
5.0ms	(cos (* 2 (/ (+ phi1 phi2) 2.0)))
461.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify190.0ms

Algorithm

egg-herbie

Counts

301 → 301

Iterations

Useful iterations: 1 (58.0ms)

Iter	Nodes	Cost
0	3823	15164
1	5003	15050

prune774.0ms

Filtered

154 candidates to 301 candidates (-95.5%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	298	3	301
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	299	10	309

Merged error: 22.9b

Counts

309 → 10

regimes1.2s

Accuracy

72.6% (3.9b remaining)

Error of 28.9b against oracle of 25.0b and baseline of 39.1b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	53
1	33	53

end0.0ms

sample9.5s

Algorithm

intervals

sampling

Space saved by range analysis: 4.481588%

Space saved by search: 0.243902%

Guaranteed chance to sample good point: 0%

Results

614.0ms	5884×	body	80	valid
398.0ms	833×	body	640	valid
342.0ms	486×	body	1280	valid
236.0ms	479×	body	640	invalid
220.0ms	314×	body	1280	invalid
201.0ms	1978×	body	80	invalid
169.0ms	502×	body	320	valid
72.0ms	224×	body	320	invalid
70.0ms	295×	body	160	valid
22.0ms	100×	body	160	invalid

Details

sample6.5s

simplify52.0ms

prune5.0ms

localize16.0ms

rewrite51.0ms

series190.0ms

simplify59.0ms

prune264.0ms

localize20.0ms

rewrite43.0ms

series165.0ms

simplify58.0ms

prune262.0ms

localize17.0ms

rewrite62.0ms

series161.0ms

simplify103.0ms

prune336.0ms

localize19.0ms

rewrite83.0ms

series505.0ms

simplify190.0ms

prune774.0ms

regimes1.2s

bsearch1.0ms

simplify2.0ms

end0.0ms

sample9.5s

Profiling