Details

sample59.0ms

Algorithm

intervals

Results

18.0ms	291×	body	80	valid
11.0ms	39×	body	640	valid
7.0ms	18×	body	1280	valid
4.0ms	21×	body	320	valid
1.0ms	8×	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

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 3.5b

Counts

2 → 1

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
4.0b	(cos (/ (+ phi1 phi2) 2.0))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

3.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
9.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
6.0ms	(cos (/ (+ phi1 phi2) 2.0))

series578.0ms

Counts

3 → 9

Calls

3 calls:

459.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
91.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
28.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify100.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (90.0ms)

Iter	Nodes	Cost
0	288	525
1	998	448
2	4736	442
3	5001	440

prune165.0ms

Filtered

62 candidates to 49 candidates (79.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	53	9	62
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	53	10	63

Merged error: 3.3b

Counts

63 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (+ phi1 phi2) 2.0)))
0.2b	(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
0.5b	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
4.0b	(cos (/ (+ phi1 phi2) 2.0))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
12×	`add-cube-cbrt`
9×	`log-prod` `exp-prod`
8×	`pow1` `log-pow`
7×	`add-exp-log` `associate-r`
6×	`add-cbrt-cube`
5×	`associate-l` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`rem-log-exp` `associate-*l/`
1×	`flip3--` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `rem-exp-log` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 74

Calls

4 calls:

6.0ms	(exp (cos (/ (+ phi1 phi2) 2.0)))
13.0ms	(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
6.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
6.0ms	(cos (/ (+ phi1 phi2) 2.0))

series199.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(exp (cos (/ (+ phi1 phi2) 2.0)))
90.0ms	(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
27.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
30.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify65.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	222	596
1	700	507
2	3155	501
3	5002	501

prune252.0ms

Filtered

86 candidates to 66 candidates (76.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	86	10	96

Merged error: 3.3b

Counts

96 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (cos (/ (+ phi1 phi2) 2.0)))
4.0b	(cos (/ (+ phi1 phi2) 2.0))
4.0b	(cos (/ (+ phi1 phi2) 2.0))
4.0b	(cos (/ (+ phi1 phi2) 2.0))

rewrite23.0ms

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:

4.0ms	(cbrt (cos (/ (+ phi1 phi2) 2.0)))
6.0ms	(cos (/ (+ phi1 phi2) 2.0))
6.0ms	(cos (/ (+ phi1 phi2) 2.0))
6.0ms	(cos (/ (+ phi1 phi2) 2.0))

series200.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(cbrt (cos (/ (+ phi1 phi2) 2.0)))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))
31.0ms	(cos (/ (+ phi1 phi2) 2.0))
29.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify173.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 4 (48.0ms)

Iter	Nodes	Cost
0	88	284
1	165	254
2	433	252
3	1249	252
4	4821	243
5	5001	243

prune209.0ms

Filtered

52 candidates to 46 candidates (88.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	51	11	62

Merged error: 3.3b

Counts

62 → 11

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
4.0b	(cos (/ (+ phi1 phi2) 2.0))
4.0b	(cos (/ (+ phi1 phi2) 2.0))
4.0b	(cos (/ (+ phi1 phi2) 2.0))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `log-pow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `exp-prod`
2×	`rem-log-exp`

Counts

4 → 45

Calls

4 calls:

6.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
6.0ms	(cos (/ (+ phi1 phi2) 2.0))
6.0ms	(cos (/ (+ phi1 phi2) 2.0))
6.0ms	(cos (/ (+ phi1 phi2) 2.0))

series115.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))
32.0ms	(cos (/ (+ phi1 phi2) 2.0))
28.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify118.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 4 (33.0ms)

Iter	Nodes	Cost
0	82	290
1	137	256
2	317	256
3	829	256
4	3208	248
5	5002	248

prune232.0ms

Filtered

57 candidates to 49 candidates (86.0%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	57	11	68

Merged error: 3.3b

Counts

68 → 11

regimes323.0ms

Accuracy

0% (0.2b remaining)

Error of 3.7b against oracle of 3.6b and baseline of 3.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	8
1	17	8

end0.0ms

sample1.8s

Algorithm

intervals

Results

539.0ms	8282×	body	80	valid
360.0ms	1271×	body	640	valid
327.0ms	805×	body	1280	valid
151.0ms	730×	body	320	valid
54.0ms	390×	body	160	valid