Details

sample179.0ms

Algorithm

intervals

Results

46.0ms	26×	body	1280	valid
42.0ms	254×	body	80	valid
31.0ms	43×	body	640	valid
12.0ms	24×	body	320	valid
3.0ms	8×	body	160	valid

simplify5.0s

Counts

1 → 1

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	17	32
1	34	16
2	76	16
3	257	16
4	826	16
5	2355	16
done	5000	16

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.2b

localize17.0ms

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)))
2.8b	(cos (/ (+ phi1 phi2) 2.0))

rewrite64.0ms

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))
8.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
26.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
28.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

538.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
738.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
165.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
43.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify2.8s

Counts

75 → 75

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	139	1279
1	327	1271
2	960	1077
3	3194	1060
done	5000	1059

prune451.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.1b

localize24.0ms

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)))
2.8b	(cos (/ (+ phi1 phi2) 2.0))

rewrite92.0ms

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))
13.0ms	(* (pow (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) 1) R)
45.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
32.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

589.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
769.0ms	(* (pow (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) 1) R)
137.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
44.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify2.9s

Counts

83 → 83

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	157	1525
1	360	1408
2	1079	1236
3	3943	1219
done	5001	1218

prune478.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (/ (+ phi1 phi2) 2.0)))
2.8b	(cos (/ (+ phi1 phi2) 2.0))
2.8b	(cos (/ (+ phi1 phi2) 2.0))
2.8b	(cos (/ (+ phi1 phi2) 2.0))

rewrite57.0ms

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:

2.0ms	(cbrt (cos (/ (+ phi1 phi2) 2.0)))
12.0ms	(cos (/ (+ phi1 phi2) 2.0))
19.0ms	(cos (/ (+ phi1 phi2) 2.0))
23.0ms	(cos (/ (+ phi1 phi2) 2.0))

series284.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(cbrt (cos (/ (+ phi1 phi2) 2.0)))
48.0ms	(cos (/ (+ phi1 phi2) 2.0))
43.0ms	(cos (/ (+ phi1 phi2) 2.0))
50.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify2.7s

Counts

52 → 52

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	48	501
1	89	494
2	154	444
3	288	437
4	603	433
5	993	433
6	2089	433
done	5001	409

prune387.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.1b

localize68.0ms

Local error

Found 4 expressions with local error:

2.8b	(cos (/ (+ phi1 phi2) 2.0))
2.8b	(cos (/ (+ phi1 phi2) 2.0))
2.8b	(cos (/ (+ phi1 phi2) 2.0))
2.8b	(cos (/ (+ phi1 phi2) 2.0))

rewrite77.0ms

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:

11.0ms	(cos (/ (+ phi1 phi2) 2.0))
18.0ms	(cos (/ (+ phi1 phi2) 2.0))
24.0ms	(cos (/ (+ phi1 phi2) 2.0))
23.0ms	(cos (/ (+ phi1 phi2) 2.0))

series173.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(cos (/ (+ phi1 phi2) 2.0))
32.0ms	(cos (/ (+ phi1 phi2) 2.0))
50.0ms	(cos (/ (+ phi1 phi2) 2.0))
45.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify5.4s

Counts

48 → 48

Iterations

Useful iterations: 4 (132.0ms)

Iter	Nodes	Cost
0	29	436
1	54	432
2	90	384
3	158	380
4	288	376
5	395	376
6	522	376
7	755	376
8	1365	376
9	4193	376
done	5000	376

prune465.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 4.1b

regimes610.0ms

Accuracy

0% (0.1b remaining)

Error of 3.9b against oracle of 3.8b and baseline of 3.9b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	16	18
1	21	16
done	21	16

end0.0ms

sample5.5s

Algorithm

intervals

Results

1.8s	1350×	body	640	valid
1.6s	8334×	body	80	valid
812.0ms	859×	body	1280	valid
397.0ms	704×	body	320	valid
97.0ms	379×	body	160	valid