Details

sample136.0ms

Algorithm

intervals

Results

42.0ms	34×	body	1280	valid
36.0ms	278×	body	80	valid
18.0ms	32×	body	640	valid
8.0ms	20×	body	320	valid
3.0ms	12×	body	160	valid

simplify4.1s

Counts

1 → 1

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	17	466
1	34	361
2	72	361
3	231	361
4	761	361
5	1878	361
done	5003	361

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.2b

localize25.0ms

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)))
3.8b	(cos (/ (+ phi1 phi2) 2.0))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-cube-cbrt`
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))
10.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
39.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
14.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

596.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
678.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
144.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
44.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify3.6s

Counts

75 → 75

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	142	26234
1	362	24716
2	1097	24346
3	4308	24121
done	5000	23966

prune772.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2)) (- phi1 phi2))
0.1b	(* (hypot (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2)) (- phi1 phi2)) R)
0.2b	(* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2))
3.8b	(cos (/ (+ phi1 phi2) 2.0))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in`
8×	`pow1` `add-cbrt-cube` `associate-r` `add-exp-log`
6×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`hypot-udef` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 85

Calls

4 calls:

0.0ms	(hypot (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2)) (- phi1 phi2))
11.0ms	(* (hypot (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2)) (- phi1 phi2)) R)
41.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2))
9.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.7s

Counts

4 → 12

Calls

4 calls:

889.0ms	(hypot (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2)) (- phi1 phi2))
627.0ms	(* (hypot (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2)) (- phi1 phi2)) R)
166.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2))
46.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify3.8s

Counts

97 → 97

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	183	43164
1	414	39111
2	1072	35457
3	3851	35182
done	5153	34067

prune711.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (* (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))) (cos (/ (+ phi1 phi2) 2.0))))
3.8b	(cos (/ (+ phi1 phi2) 2.0))
3.8b	(cos (/ (+ phi1 phi2) 2.0))
3.8b	(cos (/ (+ phi1 phi2) 2.0))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `pow3` `associate-*l/` `cos-mult` `rem-cbrt-cube`

Counts

4 → 40

Calls

4 calls:

12.0ms	(cbrt (* (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))) (cos (/ (+ phi1 phi2) 2.0))))
10.0ms	(cos (/ (+ phi1 phi2) 2.0))
16.0ms	(cos (/ (+ phi1 phi2) 2.0))
13.0ms	(cos (/ (+ phi1 phi2) 2.0))

series167.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(cbrt (* (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))) (cos (/ (+ phi1 phi2) 2.0))))
45.0ms	(cos (/ (+ phi1 phi2) 2.0))
49.0ms	(cos (/ (+ phi1 phi2) 2.0))
41.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify5.5s

Counts

52 → 52

Iterations

Useful iterations: 4 (331.0ms)

Iter	Nodes	Cost
0	47	13106
1	79	12223
2	130	12223
3	261	10697
4	590	10597
5	1321	10597
6	3912	10597
done	5005	10597

prune607.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2))
0.5b	(* (sqrt (hypot (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2)) (- phi1 phi2))) (sqrt (hypot (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2)) (- phi1 phi2))))
3.8b	(cos (/ (+ phi1 phi2) 2.0))
3.8b	(cos (/ (+ phi1 phi2) 2.0))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
21×	`pow1`
18×	`prod-diff` `sqrt-prod`
11×	`distribute-rgt-in` `distribute-lft-in` `associate-r`
9×	`associate-l`
8×	`sqrt-pow1` `add-cbrt-cube` `pow1/2` `swap-sqr` `add-exp-log`
5×	`pow-prod-up` `unswap-sqr`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`pow-sqr`
2×	`sub-neg` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod`
1×	`pow2` `rem-square-sqrt` `pow-plus` `flip3--` `sqrt-unprod` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 115

Calls

4 calls:

38.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2))
19.0ms	(* (sqrt (hypot (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2)) (- phi1 phi2))) (sqrt (hypot (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2)) (- phi1 phi2))))
16.0ms	(cos (/ (+ phi1 phi2) 2.0))
16.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

190.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2))
848.0ms	(* (sqrt (hypot (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2)) (- phi1 phi2))) (sqrt (hypot (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2)) (- phi1 phi2))))
32.0ms	(cos (/ (+ phi1 phi2) 2.0))
47.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify3.4s

Counts

127 → 127

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	186	53804
1	422	47043
2	892	43479
3	2474	43339
done	5010	42299

prune791.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 3.0b

regimes1.1s

Accuracy

0% (0.2b remaining)

Error of 3.6b against oracle of 3.4b and baseline of 3.6b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	361
1	17	361
done	17	361

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.2s	8401×	body	80	valid
1.2s	789×	body	1280	valid
846.0ms	1264×	body	640	valid
422.0ms	773×	body	320	valid
98.0ms	344×	body	160	valid