Details

sample69.0ms

Algorithm

intervals

Results

18.0ms	263×	body	80	valid
13.0ms	43×	body	640	valid
11.0ms	25×	body	1280	valid
8.0ms	22×	body	320	valid
1.0ms	9×	body	160	valid

simplify61.0ms

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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.2b

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)))
2.9b	(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))

series937.0ms

Counts

4 → 12

Calls

4 calls:

368.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
450.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
88.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
30.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify38.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (31.0ms)

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

prune268.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
0.1b	(* (pow (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) 1) R)
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
2.9b	(cos (/ (+ phi1 phi2) 2.0))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

0.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
5.0ms	(* (pow (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) 1) R)
11.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series940.0ms

Counts

4 → 12

Calls

4 calls:

370.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
452.0ms	(* (pow (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) 1) R)
88.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
30.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify41.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	367	771
1	1264	678
2	5001	661

prune313.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (cos (/ (+ phi1 phi2) 2.0)))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
2.9b	(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))

series195.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(cbrt (cos (/ (+ phi1 phi2) 2.0)))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
31.0ms	(cos (/ (+ phi1 phi2) 2.0))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify176.0ms

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

prune275.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 2.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
0.4b	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
2.9b	(cos (/ (+ phi1 phi2) 2.0))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`associate-l`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`sqrt-prod`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

5.0ms	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
10.0ms	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R))
8.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

652.0ms	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
446.0ms	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify42.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	318	932
1	1240	780
2	5002	773

prune276.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 2.1b

regimes356.0ms

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	21	8
1	21	8

end0.0ms

sample1.9s

Algorithm

intervals

Results

563.0ms	8392×	body	80	valid
386.0ms	1283×	body	640	valid
358.0ms	816×	body	1280	valid
152.0ms	690×	body	320	valid
54.0ms	358×	body	160	valid