Details

sample66.0ms

Algorithm

intervals

Results

17.0ms	267×	body	80	valid
12.0ms	44×	body	640	valid
7.0ms	18×	body	1280	valid
5.0ms	22×	body	320	valid
2.0ms	13×	body	160	valid

simplify56.0ms

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: 3.0b

localize19.0ms

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)))
3.5b	(cos (/ (+ phi1 phi2) 2.0))

rewrite43.0ms

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))
7.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
23.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
11.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

606.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
490.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
95.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
35.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify42.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (31.0ms)

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

prune266.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.9b

localize15.0ms

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)))
3.5b	(cos (/ (+ phi1 phi2) 2.0))

rewrite45.0ms

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))
7.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
23.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
13.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

394.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
485.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
93.0ms	(* (- 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 (30.0ms)

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

prune271.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (/ (+ phi1 phi2) 2.0)))
3.5b	(cos (/ (+ phi1 phi2) 2.0))
3.5b	(cos (/ (+ phi1 phi2) 2.0))
3.5b	(cos (/ (+ phi1 phi2) 2.0))

rewrite36.0ms

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)))
10.0ms	(cos (/ (+ phi1 phi2) 2.0))
10.0ms	(cos (/ (+ phi1 phi2) 2.0))
13.0ms	(cos (/ (+ phi1 phi2) 2.0))

series196.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(cbrt (cos (/ (+ phi1 phi2) 2.0)))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))
30.0ms	(cos (/ (+ phi1 phi2) 2.0))
28.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify174.0ms

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

prune248.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 2.9b

localize21.0ms

Local error

Found 4 expressions with local error:

3.5b	(cos (/ (+ phi1 phi2) 2.0))
3.5b	(cos (/ (+ phi1 phi2) 2.0))
3.5b	(cos (/ (+ phi1 phi2) 2.0))
3.5b	(cos (/ (+ phi1 phi2) 2.0))

rewrite45.0ms

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:

12.0ms	(cos (/ (+ phi1 phi2) 2.0))
10.0ms	(cos (/ (+ phi1 phi2) 2.0))
10.0ms	(cos (/ (+ phi1 phi2) 2.0))
11.0ms	(cos (/ (+ phi1 phi2) 2.0))

series110.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(cos (/ (+ phi1 phi2) 2.0))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify100.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 4 (27.0ms)

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

prune251.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 2.9b

regimes319.0ms

Accuracy

0% (0.1b 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	22	8
1	24	8
2	24	8

end0.0ms

sample2.0s

Algorithm

intervals

Results

546.0ms	8402×	body	80	valid
368.0ms	1272×	body	640	valid
325.0ms	763×	body	1280	valid
155.0ms	730×	body	320	valid
57.0ms	395×	body	160	valid