Details

sample64.0ms

Algorithm

intervals

Results

18.0ms	289×	body	80	valid
12.0ms	29×	body	1280	valid
10.0ms	36×	body	640	valid
4.0ms	18×	body	320	valid
1.0ms	9×	body	160	valid

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize18.0ms

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)))
2.2b	(cos (/ (+ phi1 phi2) 2.0))

rewrite16.0ms

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)
6.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

375.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
646.0ms	(* (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))

simplify37.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (30.0ms)

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

prune263.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (/ (+ phi1 phi2) 2.0)))
2.2b	(cos (/ (+ phi1 phi2) 2.0))
2.2b	(cos (/ (+ phi1 phi2) 2.0))
2.2b	(cos (/ (+ phi1 phi2) 2.0))

rewrite17.0ms

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))

series187.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(cbrt (cos (/ (+ phi1 phi2) 2.0)))
25.0ms	(cos (/ (+ phi1 phi2) 2.0))
25.0ms	(cos (/ (+ phi1 phi2) 2.0))
28.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify172.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 4 (50.0ms)

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

prune243.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.4b

localize24.0ms

Local error

Found 4 expressions with local error:

2.2b	(cos (/ (+ phi1 phi2) 2.0))
2.2b	(cos (/ (+ phi1 phi2) 2.0))
2.2b	(cos (/ (+ phi1 phi2) 2.0))
2.2b	(cos (/ (+ phi1 phi2) 2.0))

rewrite21.0ms

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))

series106.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cos (/ (+ phi1 phi2) 2.0))
28.0ms	(cos (/ (+ phi1 phi2) 2.0))
25.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify101.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 4 (28.0ms)

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

prune263.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.4b

localize23.0ms

Local error

Found 4 expressions with local error:

2.2b	(cos (/ (+ phi1 phi2) 2.0))
2.2b	(cos (/ (+ phi1 phi2) 2.0))
2.2b	(cos (/ (+ phi1 phi2) 2.0))
2.2b	(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))

series106.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(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))

simplify104.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 4 (28.0ms)

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

prune263.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.4b

regimes259.0ms

Accuracy

0% (0.2b remaining)

Error of 3.6b against oracle of 3.5b and baseline of 3.6b

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

519.0ms	8364×	body	80	valid
366.0ms	1283×	body	640	valid
314.0ms	783×	body	1280	valid
135.0ms	696×	body	320	valid
51.0ms	361×	body	160	valid