Details

sample71.0ms

Algorithm

intervals

Results

18.0ms	275×	body	80	valid
14.0ms	37×	body	640	valid
12.0ms	29×	body	1280	valid
5.0ms	24×	body	320	valid
2.0ms	12×	body	160	valid

simplify59.0ms

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)

Merged error: 2.8b

localize14.0ms

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

rewrite20.0ms

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:

0.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
3.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
10.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series951.0ms

Counts

4 → 12

Calls

4 calls:

375.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
460.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
88.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
28.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify39.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (31.0ms)

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

prune274.0ms

Filtered

75 candidates to 62 candidates (82.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.6b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

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

series193.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(cbrt (cos (/ (+ phi1 phi2) 2.0)))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))
30.0ms	(cos (/ (+ phi1 phi2) 2.0))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify179.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 4 (51.0ms)

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

prune259.0ms

Filtered

52 candidates to 46 candidates (88.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.6b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

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:

7.0ms	(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:

30.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify96.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 4 (29.0ms)

Iter	Nodes	Cost
0	54	240
1	97	212
2	247	212
3	653	212
4	2670	204
5	5001	204

prune285.0ms

Filtered

48 candidates to 44 candidates (91.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 2.6b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

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

series476.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(cbrt (- lambda1 lambda2))
150.0ms	(cbrt (- lambda1 lambda2))
144.0ms	(cbrt (- lambda1 lambda2))
31.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify124.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 4 (118.0ms)

Iter	Nodes	Cost
0	199	399
1	419	377
2	1147	368
3	3713	347
4	5001	342

prune314.0ms

Filtered

72 candidates to 65 candidates (90.3%)

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 2.6b

regimes576.0ms

Accuracy

0% (0.3b remaining)

Error of 4.0b against oracle of 3.6b 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

sample1.9s

Algorithm

intervals

Results

566.0ms	8398×	body	80	valid
384.0ms	1289×	body	640	valid
345.0ms	796×	body	1280	valid
161.0ms	733×	body	320	valid
53.0ms	380×	body	160	valid