Details

sample121.0ms

Algorithm

intervals

Results

51.0ms	292×	body	80	valid
21.0ms	34×	body	640	valid
20.0ms	24×	body	1280	valid
9.0ms	17×	body	320	valid
3.0ms	9×	body	160	valid

simplify921.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
5	1878
4	761
3	231
2	72
1	34
0	17

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.8b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
2.2b	(cos (/ (+ phi2 phi1) 2))

rewrite49.0ms

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` `insert-posit16` `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 → 67

Calls

4 calls:

0.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
6.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
26.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
15.0ms	(cos (/ (+ phi2 phi1) 2))

series1.3s

Counts

4 → 12

Calls

4 calls:

463.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
705.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
137.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
32.0ms	(cos (/ (+ phi2 phi1) 2))

simplify562.0ms

Counts

79 → 79

Iterations

Iter	Nodes
done	2000
2	1076
1	360
0	144

prune532.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 1.7b

localize62.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))))
2.2b	(cos (/ (+ phi2 phi1) 2))
2.2b	(cos (/ (+ phi2 phi1) 2))
2.2b	(cos (/ (+ phi2 phi1) 2))

rewrite32.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-div` `associate-*l/`
1×	`cbrt-prod` `flip3--` `pow1/3` `flip--`

Counts

4 → 44

Calls

4 calls:

7.0ms	(cbrt (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))))
8.0ms	(cos (/ (+ phi2 phi1) 2))
8.0ms	(cos (/ (+ phi2 phi1) 2))
9.0ms	(cos (/ (+ phi2 phi1) 2))

series434.0ms

Counts

4 → 12

Calls

4 calls:

344.0ms	(cbrt (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))))
36.0ms	(cos (/ (+ phi2 phi1) 2))
27.0ms	(cos (/ (+ phi2 phi1) 2))
27.0ms	(cos (/ (+ phi2 phi1) 2))

simplify778.0ms

Counts

56 → 56

Iterations

Iter	Nodes
done	2003
3	1059
2	432
1	207
0	99

prune982.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 1.7b

localize51.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))))
2.2b	(cos (/ (+ phi2 phi1) 2))
2.2b	(cos (/ (+ phi2 phi1) 2))
2.2b	(cos (/ (+ phi2 phi1) 2))

rewrite47.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-div` `associate-*l/`
1×	`cbrt-prod` `flip3--` `pow1/3` `flip--`

Counts

4 → 44

Calls

4 calls:

19.0ms	(cbrt (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))))
12.0ms	(cos (/ (+ phi2 phi1) 2))
8.0ms	(cos (/ (+ phi2 phi1) 2))
8.0ms	(cos (/ (+ phi2 phi1) 2))

series377.0ms

Counts

4 → 12

Calls

4 calls:

300.0ms	(cbrt (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))))
26.0ms	(cos (/ (+ phi2 phi1) 2))
28.0ms	(cos (/ (+ phi2 phi1) 2))
22.0ms	(cos (/ (+ phi2 phi1) 2))

simplify735.0ms

Counts

56 → 56

Iterations

Iter	Nodes
done	2003
3	1059
2	432
1	207
0	99

prune742.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 1.7b

localize83.0ms

Local error

Found 4 expressions with local error:

2.2b	(cos (/ (+ phi2 phi1) 2))
2.2b	(cos (/ (+ phi2 phi1) 2))
2.2b	(cos (/ (+ phi2 phi1) 2))
2.2b	(cos (/ (+ phi2 phi1) 2))

rewrite47.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 40

Calls

4 calls:

15.0ms	(cos (/ (+ phi2 phi1) 2))
15.0ms	(cos (/ (+ phi2 phi1) 2))
8.0ms	(cos (/ (+ phi2 phi1) 2))
8.0ms	(cos (/ (+ phi2 phi1) 2))

series122.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(cos (/ (+ phi2 phi1) 2))
22.0ms	(cos (/ (+ phi2 phi1) 2))
29.0ms	(cos (/ (+ phi2 phi1) 2))
41.0ms	(cos (/ (+ phi2 phi1) 2))

simplify1.1s

Counts

52 → 52

Iterations

Iter	Nodes
done	2000
5	1477
4	498
3	194
2	88
1	54
0	29

prune569.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 1.7b

regimes830.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample6.6s

Algorithm

intervals

Results

2.8s	8394×	body	80	valid
1.4s	1304×	body	640	valid
1.1s	787×	body	1280	valid
508.0ms	725×	body	320	valid
222.0ms	374×	body	160	valid