Details

sample68.0ms

Algorithm

intervals

Results

22.0ms	293×	body	80	valid
11.0ms	35×	body	640	valid
11.0ms	18×	body	1280	valid
3.0ms	15×	body	320	valid
2.0ms	11×	body	160	valid

simplify53.0ms

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

prune3.0ms

Filtered

1 candidates to 0 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: 36.9b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
3.9b	(cos (/ (+ phi1 phi2) 2.0))
3.9b	(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))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

130×	`associate-*l/`
97×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
12×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube`
5×	`associate-l`
4×	`add-log-exp`
3×	`associate-r` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

10.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
18.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series533.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
29.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
393.0ms	(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

127 → 127

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1312	3623
1	5002	3528

prune408.0ms

Filtered

127 candidates to 77 candidates (60.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	120	7	127
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	120	8	128

Merged error: 23.6b

Counts

128 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

3.9b	(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))))
33.6b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
33.6b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

384×	`associate-*l/`
288×	`flip3--` `flip--`
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:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
20.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
18.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
17.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.2s

Counts

4 → 12

Calls

4 calls:

26.0ms	(cos (/ (+ phi1 phi2) 2.0))
399.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
392.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
402.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify117.0ms

Algorithm

egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1266	10063
1	5001	9903

prune1.0s

Filtered

256 candidates to 132 candidates (51.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	256	0	256
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	256	8	264

Merged error: 23.6b

Counts

264 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
3.9b	(cos (/ (+ phi1 phi2) 2.0))
4.2b	(+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2)))
28.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

193×	`flip3--` `flip--`
162×	`associate-*l/`
128×	`frac-times` `frac-add`
66×	`sqrt-div`
64×	`associate-*r/`
12×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`associate-l`
4×	`distribute-rgt-in` `sub-neg` `associate-+l+` `associate-+r+` `distribute-lft-in`
3×	`associate-r` `sqrt-prod`
2×	`flip3-+` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 191

Calls

4 calls:

7.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
19.0ms	(+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2)))
15.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2))))

series1.0s

Counts

4 → 12

Calls

4 calls:

89.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
503.0ms	(+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2)))
394.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2))))

simplify84.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1371	6076
1	5002	5956

prune621.0ms

Filtered

203 candidates to 109 candidates (53.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	196	7	203
Fresh	1	4	5
Picked	1	0	1
Done	1	1	2
Total	199	12	211

Merged error: 23.4b

Counts

211 → 12

localize25.0ms

Local error

Found 4 expressions with local error:

3.9b	(cos (/ (+ phi1 phi2) 2.0))
3.9b	(cos (/ (+ phi1 phi2) 2.0))
4.2b	(+ (* (* (* (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2)))
28.9b	(sqrt (+ (* (* (* (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2))))

rewrite452.0ms

Algorithm

rewrite-expression-head

Rules

4000×	`associate-*l/`
2816×	`frac-times`
2688×	`flip3--` `flip--`
2592×	`cbrt-div`
1280×	`frac-add`
736×	`associate-*r/`
642×	`sqrt-div`
6×	`add-sqr-sqrt` `add-log-exp`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `distribute-rgt-in` `sub-neg` `associate-+l+` `associate-+r+` `distribute-lft-in` `add-cbrt-cube`
3×	`sqrt-prod`
2×	`flip3-+` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 1328

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
39.0ms	(+ (* (* (* (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2)))
66.0ms	(sqrt (+ (* (* (* (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2))))

series969.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(cos (/ (+ phi1 phi2) 2.0))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))
508.0ms	(+ (* (* (* (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2)))
407.0ms	(sqrt (+ (* (* (* (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (- lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2))))

simplify800.0ms

Algorithm

egg-herbie

Counts

1340 → 1340

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5001	93697

prune12.7s

Filtered

1340 candidates to 1327 candidates (99.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	1339	1	1340
Fresh	0	10	10
Picked	1	0	1
Done	0	1	1
Total	1340	12	1352

Merged error: 23.4b

Counts

1352 → 12

regimes753.0ms

Accuracy

72.8% (3.8b remaining)

Error of 28.6b against oracle of 24.9b and baseline of 38.8b

bsearch4.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	34
1	27	34

end0.0ms

sample2.1s

Algorithm

intervals

Results

650.0ms	8387×	body	80	valid
443.0ms	1292×	body	640	valid
362.0ms	785×	body	1280	valid
166.0ms	688×	body	320	valid
65.0ms	380×	body	160	valid