Details

sample75.0ms

Algorithm

intervals

Results

20.0ms	268×	body	80	valid
13.0ms	26×	body	1280	valid
12.0ms	36×	body	640	valid
5.0ms	19×	body	320	valid
2.0ms	13×	body	160	valid

simplify822.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	17	32
1	34	16
2	76	16
3	196	16
4	497	16
5	1405	16
done	5000	16

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
3.6b	(cos (/ (+ phi1 phi2) 2.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

4.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
11.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
6.0ms	(cos (/ (+ phi1 phi2) 2.0))

series584.0ms

Counts

3 → 9

Calls

3 calls:

465.0ms	(* (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))

simplify1.5s

Counts

62 → 62

Iterations

Useful iterations: 3 (375.0ms)

Iter	Nodes	Cost
0	125	990
1	279	983
2	913	835
3	3895	824
done	5001	824

prune227.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.4b

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b	(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)))
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
3.6b	(cos (/ (+ phi1 phi2) 2.0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

3.0ms	(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)))
11.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series694.0ms

Counts

3 → 9

Calls

3 calls:

559.0ms	(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)))
107.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
28.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify1.7s

Counts

62 → 62

Iterations

Useful iterations: 3 (392.0ms)

Iter	Nodes	Cost
0	125	990
1	279	983
2	953	835
3	4496	824
done	5000	824

prune238.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (+ phi1 phi2) 2.0)))
0.2b	(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
0.5b	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
3.6b	(cos (/ (+ phi1 phi2) 2.0))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

5.0ms	(exp (cos (/ (+ phi1 phi2) 2.0)))
18.0ms	(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
10.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series190.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(exp (cos (/ (+ phi1 phi2) 2.0)))
87.0ms	(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
26.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
30.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify1.4s

Counts

85 → 85

Iterations

Useful iterations: 3 (258.0ms)

Iter	Nodes	Cost
0	120	1104
1	228	993
2	659	873
3	2433	868
done	5000	868

prune320.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (cos (/ (+ phi1 phi2) 2.0)))
3.6b	(cos (/ (+ phi1 phi2) 2.0))
3.6b	(cos (/ (+ phi1 phi2) 2.0))
3.6b	(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))

series191.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(cbrt (cos (/ (+ phi1 phi2) 2.0)))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
31.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify2.2s

Counts

52 → 52

Iterations

Useful iterations: 4 (182.0ms)

Iter	Nodes	Cost
0	48	501
1	89	494
2	165	444
3	378	437
4	1092	433
5	3311	433
done	5000	433

prune227.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.4b

regimes333.0ms

Accuracy

0% (0.2b remaining)

Error of 3.7b against oracle of 3.5b and baseline of 3.7b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	16
1	17	16
done	17	16

end0.0ms

sample2.1s

Algorithm

intervals

Results

595.0ms	1326×	body	640	valid
565.0ms	8366×	body	80	valid
334.0ms	787×	body	1280	valid
166.0ms	722×	body	320	valid
52.0ms	371×	body	160	valid