Details

sample74.0ms

Algorithm

intervals

Results

21.0ms	273×	body	80	valid
13.0ms	27×	body	1280	valid
12.0ms	33×	body	640	valid
6.0ms	23×	body	320	valid
3.0ms	20×	body	160	valid

simplify56.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	8
1	78	8
2	261	8
3	834	8
4	2600	8
5	5001	8

prune10.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 2.5b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
3.4b	(cos (/ (+ phi1 phi2) 2.0))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
6×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`hypot-udef` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 63

Calls

4 calls:

1.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
3.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
7.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series931.0ms

Counts

4 → 12

Calls

4 calls:

367.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
447.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
89.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify37.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	328	677
1	1130	579
2	5001	569

prune259.0ms

Filtered

75 candidates to 62 candidates (82.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	63	12	75
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	65	12	77

Merged error: 2.4b

Counts

77 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (cos (/ (+ phi1 phi2) 2.0)))
3.4b	(cos (/ (+ phi1 phi2) 2.0))
3.4b	(cos (/ (+ phi1 phi2) 2.0))
3.4b	(cos (/ (+ phi1 phi2) 2.0))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

1.0ms	(cbrt (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series194.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(cbrt (cos (/ (+ phi1 phi2) 2.0)))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
30.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify174.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 4 (49.0ms)

Iter	Nodes	Cost
0	88	284
1	165	254
2	433	252
3	1255	252
4	4860	243
5	5001	243

prune415.0ms

Filtered

52 candidates to 46 candidates (88.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	51	13	64

Merged error: 2.4b

Counts

64 → 13

localize22.0ms

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))
3.4b	(cos (/ (+ phi1 phi2) 2.0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 36

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series109.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
29.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify98.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 4 (26.0ms)

Iter	Nodes	Cost
0	54	240
1	97	212
2	247	212
3	653	212
4	2375	204
5	5001	204

prune249.0ms

Filtered

48 candidates to 44 candidates (91.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	48	0	48
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	48	13	61

Merged error: 2.4b

Counts

61 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-div` `associate-*l/`
1×	`cbrt-prod` `flip3--` `pow1/3` `flip--`

Counts

4 → 40

Calls

4 calls:

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

series305.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
29.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify135.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 4 (130.0ms)

Iter	Nodes	Cost
0	205	337
1	463	303
2	1378	300
3	4710	291
4	5001	285

prune205.0ms

Filtered

52 candidates to 47 candidates (90.4%)

Pruning

16 alts after pruning (13 fresh and 3 done)

	Pruned	Kept	Total
New	49	3	52
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	49	16	65

Merged error: 2.4b

Counts

65 → 16

regimes423.0ms

Accuracy

0% (0.3b remaining)

Error of 4.0b against oracle of 3.7b and baseline of 4.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	19
1	21	19

end0.0ms

sample2.1s

Algorithm

intervals

Results

651.0ms	8332×	body	80	valid
448.0ms	1327×	body	640	valid
375.0ms	778×	body	1280	valid
184.0ms	727×	body	320	valid
66.0ms	377×	body	160	valid