Details

analyze2.1s

Algorithm: search

sample97.0ms

Algorithm

intervals

Results

20.0ms	34×	body	640	valid
19.0ms	194×	body	80	valid
8.0ms	11×	body	1280	valid
7.0ms	16×	body	640	invalid
7.0ms	73×	body	80	invalid
6.0ms	9×	body	1280	invalid
4.0ms	13×	body	320	valid
3.0ms	8×	body	320	invalid
1.0ms	5×	body	160	invalid
1.0ms	4×	body	160	valid

simplify50.0ms

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: 38.4b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
35.4b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite48.0ms

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))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
16.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series174.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (* (- 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))
135.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify60.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1373	3924
1	5001	3756

prune264.0ms

Filtered

77 candidates to 147 candidates (-90.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	138	9	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	139	9	148

Merged error: 23.6b

Counts

148 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
35.4b	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite57.0ms

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))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
22.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series148.0ms

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))
131.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify101.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	2471	7439
1	5001	7337

prune353.0ms

Filtered

102 candidates to 204 candidates (-100.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	202	2	204
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	203	10	213

Merged error: 23.6b

Counts

213 → 10

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0))))))
0.5b	(+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))))
2.8b	(cos (* 2 (/ (+ phi1 phi2) 2.0)))
35.4b	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite82.0ms

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)))
25.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series511.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0))))))
16.0ms	(+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))))
5.0ms	(cos (* 2 (/ (+ phi1 phi2) 2.0)))
443.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify185.0ms

Algorithm

egg-herbie

Counts

301 → 301

Iterations

Useful iterations: 1 (58.0ms)

Iter	Nodes	Cost
0	3823	15164
1	5003	15050

prune854.0ms

Filtered

155 candidates to 301 candidates (-94.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	296	5	301
Fresh	3	5	8
Picked	0	1	1
Done	0	1	1
Total	299	12	311

Merged error: 23.6b

Counts

311 → 12

localize22.0ms

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))
35.4b	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

96×	`flip3--` `associate-*l/` `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)
7.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
18.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

series156.0ms

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))
134.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (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	1336	3748
1	5002	3672

prune223.0ms

Filtered

69 candidates to 128 candidates (-85.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	0	9	9
Picked	1	0	1
Done	0	2	2
Total	128	12	140

Merged error: 23.6b

Counts

140 → 12

regimes1.1s

Accuracy

73.3% (3.6b remaining)

Error of 29.2b against oracle of 25.6b and baseline of 39.1b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	33
1	41	33

end0.0ms

analyze2.1s

Algorithm: search

sample2.8s

Algorithm

intervals

Results

603.0ms	5945×	body	80	valid
408.0ms	860×	body	640	valid
317.0ms	460×	body	1280	valid
252.0ms	2384×	body	80	invalid
216.0ms	485×	body	640	invalid
211.0ms	308×	body	1280	invalid
160.0ms	485×	body	320	valid
86.0ms	231×	body	320	invalid
60.0ms	250×	body	160	valid
27.0ms	106×	body	160	invalid

Details

analyze2.1s

sample97.0ms

simplify50.0ms

prune5.0ms

localize22.0ms

rewrite48.0ms

series174.0ms

simplify60.0ms

prune264.0ms

localize18.0ms

rewrite57.0ms

series148.0ms

simplify101.0ms

prune353.0ms

localize25.0ms

rewrite82.0ms

series511.0ms

simplify185.0ms

prune854.0ms

localize22.0ms

rewrite42.0ms

series156.0ms

simplify58.0ms

prune223.0ms

regimes1.1s

bsearch2.0ms

simplify2.0ms

end0.0ms

analyze2.1s

sample2.8s

Profiling