Details

sample177.0ms

Algorithm

intervals

Results

74.0ms	299×	body	80	valid
24.0ms	25×	body	1280	valid
23.0ms	33×	body	640	valid
9.0ms	17×	body	320	valid
3.0ms	9×	body	160	valid

simplify4.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	4415
4	917
3	240
2	69
1	32
0	17

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.9b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
2.8b	(cos (/ (+ phi1 phi2) 2.0))
2.8b	(cos (/ (+ phi1 phi2) 2.0))
34.1b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

142×	`associate-*l/`
102×	`flip3--` `flip--`
68×	`frac-times`
66×	`sqrt-div`
64×	`frac-add`
44×	`pow1`
34×	`associate-*r/`
17×	`pow-prod-down`
16×	`add-cbrt-cube` `add-exp-log`
8×	`prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`pow-sqr` `pow-prod-up` `add-log-exp`
3×	`sqrt-prod`
2×	`pow-plus`
1×	`pow2` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `swap-sqr` `associate-r` `associate-l` `*-commutative` `flip-+`

Counts

4 → 135

Calls

4 calls:

78.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
8.0ms	(cos (/ (+ phi1 phi2) 2.0))
12.0ms	(cos (/ (+ phi1 phi2) 2.0))
107.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series881.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
40.0ms	(cos (/ (+ phi1 phi2) 2.0))
43.0ms	(cos (/ (+ phi1 phi2) 2.0))
668.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.8s

Counts

147 → 147

Iterations

Iter	Nodes
done	5000
1	1387
0	458

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 22.6b

localize72.0ms

Local error

Found 4 expressions with local error:

0.4b	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
2.8b	(cos (/ (+ phi1 phi2) 2.0))
2.8b	(cos (/ (+ phi1 phi2) 2.0))
34.1b	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

128×	`associate-*l/`
96×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
8×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `log-pow` `add-log-exp`
3×	`log-prod` `exp-prod` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `rem-log-exp` `flip-+`

Counts

4 → 108

Calls

4 calls:

28.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
13.0ms	(cos (/ (+ phi1 phi2) 2.0))
8.0ms	(cos (/ (+ phi1 phi2) 2.0))
139.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series803.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
34.0ms	(cos (/ (+ phi1 phi2) 2.0))
43.0ms	(cos (/ (+ phi1 phi2) 2.0))
684.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.9s

Counts

120 → 120

Iterations

Iter	Nodes
done	5000
1	1340
0	444

prune998.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 22.6b

localize126.0ms

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))
34.1b	(sqrt (+ (* (* (- lambda1 lambda2) (+ (log (* (cbrt (exp (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (exp (cos (/ (+ phi1 phi2) 2.0)))))) (log (cbrt (exp (cos (/ (+ phi1 phi2) 2.0))))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite467.0ms

Algorithm

rewrite-expression-head

Rules

328×	`frac-times`
308×	`associate-*l/`
300×	`flip3--` `flip--`
210×	`sqrt-div`
208×	`frac-add`
116×	`associate-*r/`
73×	`flip3-+` `flip-+`
6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 244

Calls

4 calls:

9.0ms	(cos (/ (+ phi1 phi2) 2.0))
9.0ms	(cos (/ (+ phi1 phi2) 2.0))
9.0ms	(cos (/ (+ phi1 phi2) 2.0))
408.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (+ (log (* (cbrt (exp (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (exp (cos (/ (+ phi1 phi2) 2.0)))))) (log (cbrt (exp (cos (/ (+ phi1 phi2) 2.0))))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series7.4s

Counts

4 → 12

Calls

4 calls:

34.0ms	(cos (/ (+ phi1 phi2) 2.0))
47.0ms	(cos (/ (+ phi1 phi2) 2.0))
32.0ms	(cos (/ (+ phi1 phi2) 2.0))
7.3s	(sqrt (+ (* (* (- lambda1 lambda2) (+ (log (* (cbrt (exp (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (exp (cos (/ (+ phi1 phi2) 2.0)))))) (log (cbrt (exp (cos (/ (+ phi1 phi2) 2.0))))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify7.4s

Counts

256 → 256

Iterations

Iter	Nodes
done	5001
1	3949
0	1257

prune3.3s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 20.0b

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b	(* R (- phi2 phi1))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
5×	`-un-lft-identity` `associate-r*`
3×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-cube-cbrt`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*r/`
1×	`flip3--` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `distribute-lft-out--` `add-log-exp` `difference-of-squares` `unswap-sqr`

Counts

1 → 26

Calls

1 calls:

18.0ms

(* R (- phi2 phi1))

series53.0ms

Counts

1 → 3

Calls

1 calls:

52.0ms

(* R (- phi2 phi1))

simplify1.6s

Counts

29 → 29

Iterations

Iter	Nodes
done	5000
3	1612
2	375
1	124
0	52

prune126.0ms

Pruning

19 alts after pruning (15 fresh and 4 done)

Merged error: 20.0b

regimes3.3s

Accuracy

61.9% (6.3b remaining)

Error of 28.6b against oracle of 22.3b and baseline of 38.9b

bsearch6.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	33
1	33
0	25

end0.0ms

sample5.2s

Algorithm

intervals

Results

1.6s	751×	body	1280	valid
1.4s	8464×	body	80	valid
1.0s	1272×	body	640	valid
389.0ms	762×	body	320	valid
136.0ms	350×	body	160	valid