Details

sample346.0ms

Algorithm

intervals

Results

142.0ms	87×	body	1280	valid
81.0ms	96×	body	640	valid
45.0ms	244×	body	80	valid
33.0ms	55×	body	320	valid
13.0ms	33×	body	160	valid

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
9	2326
8	1689
7	945
6	535
5	284
4	183
3	80
2	41
1	23
0	14

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.1b

localize40.0ms

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)))
6.2b	(- (exp l) (exp (- l)))

rewrite171.0ms

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:

68.0ms	(* J (- (exp l) (exp (- l))))
84.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
18.0ms	(- (exp l) (exp (- l)))

series268.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(* J (- (exp l) (exp (- l))))
111.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
58.0ms	(- (exp l) (exp (- l)))

simplify1.3s

Counts

72 → 72

Iterations

Iter	Nodes
3	3015
2	731
1	276
0	114

prune915.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

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

rewrite172.0ms

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:

49.0ms	(* l (+ (* 1/3 (* l l)) 2))
16.0ms	(* (pow l 5) 1/60)
79.0ms	(* (* J (+ (* (pow l 5) 1/60) (* l (+ (* 1/3 (* l l)) 2)))) (cos (/ K 2)))
26.0ms	(* 1/3 (* l l))

series443.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(* l (+ (* 1/3 (* l l)) 2))
69.0ms	(* (pow l 5) 1/60)
213.0ms	(* (* J (+ (* (pow l 5) 1/60) (* l (+ (* 1/3 (* l l)) 2)))) (cos (/ K 2)))
39.0ms	(* 1/3 (* l l))

simplify6.0s

Counts

102 → 102

Iterations

Iter	Nodes
3	11459
2	1950
1	515
0	180

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize82.0ms

Local error

Found 4 expressions with local error:

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

rewrite410.0ms

Algorithm

rewrite-expression-head

Rules

34×	`pow1`
25×	`add-cbrt-cube` `add-exp-log`
13×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
10×	`associate-l`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`associate-r`
5×	`pow-prod-up`
4×	`associate-l/` `-commutative` `insert-posit16` `add-log-exp`
2×	`flip3-+` `associate-*r/` `flip-+` `unswap-sqr`
1×	`pow2` `pow-plus` `cube-unmult` `pow-sqr`

Counts

4 → 89

Calls

4 calls:

13.0ms	(* l (* l l))
171.0ms	(* J (* (+ (+ (* 2 l) (* 1/60 (* (* l (* l l)) (* l l)))) (* (* (* l l) l) 1/3)) (cos (/ K 2))))
158.0ms	(* (+ (+ (* 2 l) (* 1/60 (* (* l (* l l)) (* l l)))) (* (* (* l l) l) 1/3)) (cos (/ K 2)))
66.0ms	(* (* (* l l) l) 1/3)

series451.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* l (* l l))
197.0ms	(* J (* (+ (+ (* 2 l) (* 1/60 (* (* l (* l l)) (* l l)))) (* (* (* l l) l) 1/3)) (cos (/ K 2))))
135.0ms	(* (+ (+ (* 2 l) (* 1/60 (* (* l (* l l)) (* l l)))) (* (* (* l l) l) 1/3)) (cos (/ K 2)))
75.0ms	(* (* (* l l) l) 1/3)

simplify4.0s

Counts

101 → 101

Iterations

Iter	Nodes
3	8290
2	1438
1	418
0	160

prune1.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 1/3 (* l l))
0.2b	(* 1/3 (* l l))
0.4b	(* l (sqrt (+ (* 1/3 (* l l)) 2)))
0.5b	(* (* l (sqrt (+ (* 1/3 (* l l)) 2))) (sqrt (+ (* 1/3 (* l l)) 2)))

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1` `add-cbrt-cube` `add-exp-log`
17×	`add-sqr-sqrt`
14×	`sqrt-div` `associate-r`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`associate-l` `pow-prod-down` `prod-exp` `associate-*r/` `cbrt-unprod`
7×	`flip3-+` `sqrt-prod` `flip-+`
4×	`frac-times` `*-commutative` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`associate-*l/`

Counts

4 → 95

Calls

4 calls:

13.0ms	(* 1/3 (* l l))
18.0ms	(* 1/3 (* l l))
50.0ms	(* l (sqrt (+ (* 1/3 (* l l)) 2)))
124.0ms	(* (* l (sqrt (+ (* 1/3 (* l l)) 2))) (sqrt (+ (* 1/3 (* l l)) 2)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* 1/3 (* l l))
49.0ms	(* 1/3 (* l l))
212.0ms	(* l (sqrt (+ (* 1/3 (* l l)) 2)))
152.0ms	(* (* l (sqrt (+ (* 1/3 (* l l)) 2))) (sqrt (+ (* 1/3 (* l l)) 2)))

simplify1.7s

Counts

107 → 107

Iterations

Iter	Nodes
3	3940
2	1121
1	378
0	142

prune2.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes867.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	30
1	30
0	21

end0.0ms

sample10.4s

Algorithm

intervals

Results

3.3s	2641×	body	1280	valid
2.6s	2557×	body	640	valid
2.3s	8491×	body	80	valid
1.3s	1448×	body	320	valid
309.0ms	794×	body	160	valid