Details

sample212.0ms

Algorithm

intervals

Results

75.0ms	83×	body	1280	valid
43.0ms	89×	body	640	valid
29.0ms	265×	body	80	valid
16.0ms	51×	body	320	valid
5.0ms	25×	body	160	valid

simplify3.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	3179
6	1004
5	361
4	183
3	80
2	41
1	23
0	14

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.4b

localize29.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
5.9b	(- (exp l) (exp (- l)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 34

Calls

2 calls:

58.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
19.0ms	(- (exp l) (exp (- l)))

series209.0ms

Counts

2 → 6

Calls

2 calls:

157.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
52.0ms	(- (exp l) (exp (- l)))

simplify2.9s

Counts

40 → 40

Iterations

Iter	Nodes
done	5000
3	3489
2	770
1	240
0	95

prune329.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize72.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* J (+ (* 1/60 (pow l 5)) (* l (+ 2 (* 1/3 (* l l)))))) (cos (/ K 2.0))) U)
0.1b	(* 1/60 (pow l 5))
0.1b	(* (* J (+ (* 1/60 (pow l 5)) (* l (+ 2 (* 1/3 (* l l)))))) (cos (/ K 2.0)))
0.2b	(* 1/3 (* l l))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
16×	`add-cbrt-cube`
15×	`add-sqr-sqrt`
14×	`pow1`
11×	`associate-r`
9×	`*-un-lft-identity` `prod-exp` `add-cube-cbrt`
7×	`associate-l` `cbrt-unprod`
6×	`pow-prod-down` `add-log-exp`
4×	`unpow-prod-down` `unswap-sqr`
3×	`*-commutative`
2×	`flip3-+` `associate-l/` `associate-r/` `flip-+` `sqr-pow`
1×	`pow-to-exp` `+-commutative` `sum-log` `pow-exp`

Counts

4 → 75

Calls

4 calls:

67.0ms	(+ (* (* J (+ (* 1/60 (pow l 5)) (* l (+ 2 (* 1/3 (* l l)))))) (cos (/ K 2.0))) U)
20.0ms	(* 1/60 (pow l 5))
74.0ms	(* (* J (+ (* 1/60 (pow l 5)) (* l (+ 2 (* 1/3 (* l l)))))) (cos (/ K 2.0)))
27.0ms	(* 1/3 (* l l))

series921.0ms

Counts

4 → 12

Calls

4 calls:

489.0ms	(+ (* (* J (+ (* 1/60 (pow l 5)) (* l (+ 2 (* 1/3 (* l l)))))) (cos (/ K 2.0))) U)
98.0ms	(* 1/60 (pow l 5))
305.0ms	(* (* J (+ (* 1/60 (pow l 5)) (* l (+ 2 (* 1/3 (* l l)))))) (cos (/ K 2.0)))
29.0ms	(* 1/3 (* l l))

simplify1.9s

Counts

87 → 87

Iterations

Iter	Nodes
done	5019
2	1732
1	469
0	167

prune735.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize78.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/60 (pow l 5))
0.1b	(* (+ (* 1/60 (pow l 5)) (* l (+ 2 (* 1/3 (* l l))))) (cos (/ K 2.0)))
0.1b	(* J (* (+ (* 1/60 (pow l 5)) (* l (+ 2 (* 1/3 (* l l))))) (cos (/ K 2.0))))
0.2b	(* 1/3 (* l l))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log`
19×	`add-sqr-sqrt`
18×	`add-cbrt-cube`
16×	`pow1`
12×	`associate-r` `associate-l`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`prod-exp`
8×	`cbrt-unprod`
7×	`pow-prod-down`
5×	`unswap-sqr`
4×	`unpow-prod-down` `associate-l/` `-commutative` `add-log-exp`
2×	`flip3-+` `associate-*r/` `flip-+` `sqr-pow`
1×	`pow-to-exp` `pow-exp`

Counts

4 → 84

Calls

4 calls:

19.0ms	(* 1/60 (pow l 5))
46.0ms	(* (+ (* 1/60 (pow l 5)) (* l (+ 2 (* 1/3 (* l l))))) (cos (/ K 2.0)))
44.0ms	(* J (* (+ (* 1/60 (pow l 5)) (* l (+ 2 (* 1/3 (* l l))))) (cos (/ K 2.0))))
27.0ms	(* 1/3 (* l l))

series529.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(* 1/60 (pow l 5))
118.0ms	(* (+ (* 1/60 (pow l 5)) (* l (+ 2 (* 1/3 (* l l))))) (cos (/ K 2.0)))
269.0ms	(* J (* (+ (* 1/60 (pow l 5)) (* l (+ 2 (* 1/3 (* l l))))) (cos (/ K 2.0))))
53.0ms	(* 1/3 (* l l))

simplify2.6s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
2	1519
1	452
0	172

prune749.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

11.0ms	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
1.0ms	(cbrt (cos (/ K 2.0)))
1.0ms	(cbrt (cos (/ K 2.0)))
1.0ms	(cbrt (cos (/ K 2.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

424.0ms	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
208.0ms	(cbrt (cos (/ K 2.0)))
227.0ms	(cbrt (cos (/ K 2.0)))
205.0ms	(cbrt (cos (/ K 2.0)))

simplify2.4s

Counts

85 → 85

Iterations

Iter	Nodes
done	5001
4	2167
3	775
2	319
1	152
0	70

prune675.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes627.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	29
1	29
0	21

end0.0ms

sample8.1s

Algorithm

intervals

Results

2.7s	2614×	body	1280	valid
1.6s	8383×	body	80	valid
1.5s	2545×	body	640	valid
638.0ms	805×	body	160	valid
632.0ms	1442×	body	320	valid