Details

sample170.0ms

Algorithm

intervals

Results

43.0ms	274×	body	80	valid
30.0ms	29×	body	1280	valid
28.0ms	40×	body	640	valid
20.0ms	23×	body	320	valid
6.0ms	18×	body	160	valid

simplify4.6s

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.8b

localize41.0ms

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)))
3.2b	(cos (/ (+ phi1 phi2) 2.0))

rewrite85.0ms

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))
14.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
46.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
22.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

577.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
791.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
125.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
46.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify2.6s

Counts

75 → 75

Iterations

Useful iterations: done (2.6s)

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

prune403.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
0.2b	(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
0.3b	(log1p (cos (/ (+ phi1 phi2) 2.0)))
3.2b	(cos (/ (+ phi1 phi2) 2.0))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
5×	`expm1-log1p-u` `associate-l`
4×	`log1p-expm1-u` `add-log-exp`
3×	`associate-r`
2×	`associate-*l/`
1×	`log1p-udef` `expm1-log1p` `flip3--` `log1p-expm1` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `expm1-udef` `difference-of-squares` `unswap-sqr`

Counts

4 → 55

Calls

4 calls:

24.0ms	(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
0.0ms	(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
0.0ms	(log1p (cos (/ (+ phi1 phi2) 2.0)))
11.0ms	(cos (/ (+ phi1 phi2) 2.0))

series314.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
61.0ms	(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
59.0ms	(log1p (cos (/ (+ phi1 phi2) 2.0)))
35.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify3.8s

Counts

67 → 67

Iterations

Useful iterations: 4 (2.5s)

Iter	Nodes	Cost
0	98	808
1	191	718
2	473	622
3	1375	619
4	4671	616
done	5000	616

prune391.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.5b

localize47.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
3.2b	(cos (/ (+ phi1 phi2) 2.0))

rewrite47.0ms

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 (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
11.0ms	(cos (/ (+ phi1 phi2) 2.0))
12.0ms	(cos (/ (+ phi1 phi2) 2.0))
22.0ms	(cos (/ (+ phi1 phi2) 2.0))

series326.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(cbrt (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
31.0ms	(cos (/ (+ phi1 phi2) 2.0))
37.0ms	(cos (/ (+ phi1 phi2) 2.0))
42.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify2.7s

Counts

52 → 52

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	52	537
1	93	494
2	159	444
3	296	437
4	611	433
5	1007	433
6	2023	433
done	5000	409

prune426.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.5b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
0.5b	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))))
3.2b	(cos (/ (+ phi1 phi2) 2.0))
3.2b	(cos (/ (+ phi1 phi2) 2.0))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

36.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
13.0ms	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))))
11.0ms	(cos (/ (+ phi1 phi2) 2.0))
11.0ms	(cos (/ (+ phi1 phi2) 2.0))

series861.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
647.0ms	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))))
46.0ms	(cos (/ (+ phi1 phi2) 2.0))
30.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify2.0s

Counts

105 → 105

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	131	2511
1	270	1753
2	731	1513
3	2213	1424
done	5002	1381

prune495.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.5b

regimes599.0ms

Accuracy

0% (0.2b remaining)

Error of 3.8b against oracle of 3.6b and baseline of 3.8b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	18
1	19	18
done	19	18

end0.0ms

sample5.8s

Algorithm

intervals

Results

1.8s	790×	body	1280	valid
1.5s	8362×	body	80	valid
1.0s	1335×	body	640	valid
353.0ms	743×	body	320	valid
143.0ms	333×	body	160	valid