Details

sample256.0ms

Algorithm

intervals

Results

73.0ms	69×	body	1280	valid
68.0ms	261×	body	80	valid
60.0ms	96×	body	640	valid
16.0ms	38×	body	320	valid
4.0ms	16×	body	160	valid

simplify3.6s

Counts

1 → 1

Iterations

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

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp l) J)
0.0b	(/ J (exp l))
0.0b	(* (- (* (exp l) J) (/ J (exp l))) (cos (/ K 2)))
7.4b	(- (* (exp l) J) (/ J (exp l)))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
10×	`add-cbrt-cube`
9×	`times-frac`
8×	`pow1` `add-exp-log`
6×	`associate-r` `associate-l` `add-log-exp`
4×	`insert-posit16`
3×	`associate-/r` `associate-/l`
2×	`flip3--` `pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `flip--` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `div-inv`

Counts

4 → 81

Calls

4 calls:

13.0ms	(* (exp l) J)
11.0ms	(/ J (exp l))
91.0ms	(* (- (* (exp l) J) (/ J (exp l))) (cos (/ K 2)))
40.0ms	(- (* (exp l) J) (/ J (exp l)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (exp l) J)
45.0ms	(/ J (exp l))
135.0ms	(* (- (* (exp l) J) (/ J (exp l))) (cos (/ K 2)))
93.0ms	(- (* (exp l) J) (/ J (exp l)))

simplify3.0s

Counts

93 → 93

Iterations

Iter	Nodes
done	5002
3	4806
2	1089
1	313
0	137

prune630.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ U (* (* 2 (* J l)) (cos (/ K 2))))
0.0b	(* 2 (* J l))
0.1b	(* (* 2 (* J l)) (cos (/ K 2)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
4×	`associate-r` `associate-l`
3×	`insert-posit16`
2×	`*-commutative`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+`

Counts

3 → 53

Calls

3 calls:

15.0ms	(+ U (* (* 2 (* J l)) (cos (/ K 2))))
25.0ms	(* 2 (* J l))
72.0ms	(* (* 2 (* J l)) (cos (/ K 2)))

series222.0ms

Counts

3 → 9

Calls

3 calls:

102.0ms	(+ U (* (* 2 (* J l)) (cos (/ K 2))))
25.0ms	(* 2 (* J l))
95.0ms	(* (* 2 (* J l)) (cos (/ K 2)))

simplify3.8s

Counts

62 → 62

Iterations

Iter	Nodes
done	5002
3	4463
2	856
1	245
0	93

prune350.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

14.0ms	(* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))
1.0ms	(cbrt (cos (/ K 2)))
1.0ms	(cbrt (cos (/ K 2)))
1.0ms	(cbrt (cos (/ K 2)))

series727.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))
141.0ms	(cbrt (cos (/ K 2)))
179.0ms	(cbrt (cos (/ K 2)))
182.0ms	(cbrt (cos (/ K 2)))

simplify2.0s

Counts

89 → 89

Iterations

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

prune573.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

16×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `add-log-exp`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (cos (/ K 2)))
1.0ms	(cbrt (cos (/ K 2)))
1.0ms	(cbrt (cbrt (cos (/ K 2))))
6.0ms	(cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))))

series577.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(cbrt (cos (/ K 2)))
147.0ms	(cbrt (cos (/ K 2)))
133.0ms	(cbrt (cbrt (cos (/ K 2))))
176.0ms	(cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))))

simplify2.4s

Counts

61 → 61

Iterations

Iter	Nodes
done	5000
5	2835
4	1057
3	446
2	192
1	115
0	67

prune405.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes543.0ms

Accuracy

0% (0.5b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	15
1	15
0	11

end0.0ms

sample7.9s

Algorithm

intervals

Results

2.5s	2748×	body	1280	valid
2.4s	8449×	body	80	valid
1.8s	2591×	body	640	valid
557.0ms	1494×	body	320	valid
227.0ms	788×	body	160	valid