Details

sample284.0ms

Algorithm

intervals

Results

98.0ms	85×	body	1280	valid
70.0ms	297×	body	80	valid
53.0ms	67×	body	640	valid
25.0ms	46×	body	320	valid
9.0ms	25×	body	160	valid

simplify3.4s

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.1b

localize51.0ms

Local error

Found 3 expressions with local error:

0.0b	(* J (- (exp l) (exp (- l))))
0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
5.1b	(- (exp l) (exp (- l)))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log`
8×	`associate-r`
6×	`add-cube-cbrt`
5×	`add-log-exp`
4×	`associate-l` `pow-prod-down` `prod-exp` `associate-*r/` `cbrt-unprod`
3×	`sub-neg` `flip3--` `insert-posit16` `flip--`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-l/` `-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `unswap-sqr`

Counts

3 → 63

Calls

3 calls:

65.0ms	(* J (- (exp l) (exp (- l))))
99.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
21.0ms	(- (exp l) (exp (- l)))

series279.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(* J (- (exp l) (exp (- l))))
134.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
69.0ms	(- (exp l) (exp (- l)))

simplify3.4s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
3	3987
2	847
1	282
0	114

prune434.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize73.0ms

Local error

Found 4 expressions with local error:

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

rewrite252.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log`
19×	`add-sqr-sqrt`
18×	`add-cbrt-cube`
16×	`pow1`
14×	`associate-l`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`associate-r` `prod-exp`
8×	`cbrt-unprod`
7×	`pow-prod-down`
5×	`unswap-sqr`
4×	`unpow-prod-down` `associate-r/` `-commutative` `insert-posit16` `add-log-exp`
2×	`flip3-+` `associate-*l/` `flip-+` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow-exp`

Counts

4 → 90

Calls

4 calls:

60.0ms	(* l (+ (* 1/3 (* l l)) 2))
17.0ms	(* (pow l 5) 1/60)
156.0ms	(* (* J (+ (* l (+ (* 1/3 (* l l)) 2)) (* (pow l 5) 1/60))) (cos (/ K 2)))
18.0ms	(* 1/3 (* l l))

series428.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* l (+ (* 1/3 (* l l)) 2))
62.0ms	(* (pow l 5) 1/60)
220.0ms	(* (* J (+ (* l (+ (* 1/3 (* l l)) 2)) (* (pow l 5) 1/60))) (cos (/ K 2)))
38.0ms	(* 1/3 (* l l))

simplify2.2s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	2117
1	544
0	180

prune847.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize77.0ms

Local error

Found 4 expressions with local error:

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

rewrite727.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log`
19×	`add-sqr-sqrt`
18×	`add-cbrt-cube`
16×	`pow1` `associate-l`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`prod-exp`
8×	`associate-r` `cbrt-unprod`
7×	`pow-prod-down`
5×	`unswap-sqr`
4×	`unpow-prod-down` `associate-l/` `-commutative` `insert-posit16` `add-log-exp`
2×	`flip3-+` `associate-*r/` `flip-+` `sqr-pow`
1×	`pow-to-exp` `pow-exp`

Counts

4 → 88

Calls

4 calls:

12.0ms	(* (pow l 5) 1/60)
156.0ms	(* J (* (+ (* l (+ (* 1/3 (* l l)) 2)) (* (pow l 5) 1/60)) (cos (/ K 2))))
531.0ms	(* (+ (* l (+ (* 1/3 (* l l)) 2)) (* (pow l 5) 1/60)) (cos (/ K 2)))
27.0ms	(* 1/3 (* l l))

series426.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (pow l 5) 1/60)
201.0ms	(* J (* (+ (* l (+ (* 1/3 (* l l)) 2)) (* (pow l 5) 1/60)) (cos (/ K 2))))
111.0ms	(* (+ (* l (+ (* 1/3 (* l l)) 2)) (* (pow l 5) 1/60)) (cos (/ K 2)))
34.0ms	(* 1/3 (* l l))

simplify2.0s

Counts

100 → 100

Iterations

Iter	Nodes
done	5002
2	1640
1	455
0	173

prune699.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize95.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))
0.3b	(cbrt (cos (/ K 2)))
0.3b	(cbrt (cos (/ K 2)))
0.3b	(cbrt (cos (/ K 2)))

rewrite20.0ms

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` `insert-posit16` `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 → 77

Calls

4 calls:

10.0ms	(* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))
1.0ms	(cbrt (cos (/ K 2)))
1.0ms	(cbrt (cos (/ K 2)))
2.0ms	(cbrt (cos (/ K 2)))

series602.0ms

Counts

4 → 12

Calls

4 calls:

218.0ms	(* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))
126.0ms	(cbrt (cos (/ K 2)))
121.0ms	(cbrt (cos (/ K 2)))
137.0ms	(cbrt (cos (/ K 2)))

simplify2.2s

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
4	2096
3	795
2	342
1	154
0	71

prune671.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes466.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	28
1	28
0	20

end0.0ms

sample9.5s

Algorithm

intervals

Results

3.7s	2659×	body	1280	valid
2.0s	2569×	body	640	valid
1.6s	8451×	body	80	valid
1.3s	1447×	body	320	valid
266.0ms	775×	body	160	valid