Details

sample146.0ms

Algorithm

intervals

Results

51.0ms	52×	body	640	valid
30.0ms	257×	body	80	valid
20.0ms	26×	body	1280	valid
10.0ms	29×	body	320	valid
2.0ms	10×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	32
1	32	32
2	69	32
3	240	32
4	960	32
done	5000	32

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
1.7b	(cos (/ (+ phi1 phi2) 2.0))
1.7b	(cos (/ (+ phi1 phi2) 2.0))
36.5b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

130×	`associate-*l/`
97×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
12×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube`
5×	`associate-l`
4×	`add-log-exp`
3×	`associate-r` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

39.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
21.0ms	(cos (/ (+ phi1 phi2) 2.0))
13.0ms	(cos (/ (+ phi1 phi2) 2.0))
124.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series773.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
28.0ms	(cos (/ (+ phi1 phi2) 2.0))
30.0ms	(cos (/ (+ phi1 phi2) 2.0))
593.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify613.0ms

Counts

127 → 127

Iterations

Useful iterations: done (597.0ms)

Iter	Nodes	Cost
0	441	7086
1	1301	6625
done	5000	6422

prune740.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 25.5b

localize50.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
1.7b	(cos (/ (+ phi1 phi2) 2.0))
1.7b	(cos (/ (+ phi1 phi2) 2.0))
36.5b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite278.0ms

Algorithm

rewrite-expression-head

Rules

128×	`associate-*l/`
96×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1`
5×	`add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `cube-prod` `sqrt-prod`
1×	`cube-mult` `pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `unpow3` `pow-exp` `flip-+` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 116

Calls

4 calls:

7.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
23.0ms	(cos (/ (+ phi1 phi2) 2.0))
23.0ms	(cos (/ (+ phi1 phi2) 2.0))
199.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

series815.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
33.0ms	(cos (/ (+ phi1 phi2) 2.0))
31.0ms	(cos (/ (+ phi1 phi2) 2.0))
682.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify843.0ms

Counts

128 → 128

Iterations

Useful iterations: done (830.0ms)

Iter	Nodes	Cost
0	449	7330
1	1421	6543
done	5002	6371

prune808.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 25.5b

localize57.0ms

Local error

Found 4 expressions with local error:

1.7b	(cos (/ (+ phi1 phi2) 2.0))
1.7b	(cos (/ (+ phi1 phi2) 2.0))
1.7b	(cos (/ (+ phi1 phi2) 2.0))
36.5b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (* (- lambda1 lambda2) (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite719.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

20.0ms	(cos (/ (+ phi1 phi2) 2.0))
14.0ms	(cos (/ (+ phi1 phi2) 2.0))
12.0ms	(cos (/ (+ phi1 phi2) 2.0))
648.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (* (- lambda1 lambda2) (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series737.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(cos (/ (+ phi1 phi2) 2.0))
38.0ms	(cos (/ (+ phi1 phi2) 2.0))
31.0ms	(cos (/ (+ phi1 phi2) 2.0))
638.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (* (- lambda1 lambda2) (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.1s

Counts

112 → 112

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	423	8318
1	1270	7826
done	5001	7681

prune885.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 25.5b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(* R (- phi2 phi1))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 26

Calls

1 calls:

37.0ms

(* R (- phi2 phi1))

series66.0ms

Counts

1 → 3

Calls

1 calls:

66.0ms

(* R (- phi2 phi1))

simplify1.2s

Counts

29 → 29

Iterations

Useful iterations: 3 (432.0ms)

Iter	Nodes	Cost
0	52	217
1	125	206
2	384	188
3	1725	186
done	5002	186

prune65.0ms

Pruning

14 alts after pruning (10 fresh and 4 done)

Merged error: 25.5b

regimes916.0ms

Accuracy

72.2% (3.8b remaining)

Error of 28.9b against oracle of 25.1b and baseline of 38.9b

bsearch2.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	69
1	27	69
done	27	69

end0.0ms

sample5.6s

Algorithm

intervals

Results

1.5s	800×	body	1280	valid
1.5s	8249×	body	80	valid
1.3s	1306×	body	640	valid
358.0ms	726×	body	320	valid
94.0ms	334×	body	160	valid