Details

sample207.0ms

Algorithm

intervals

Results

57.0ms	96×	body	640	valid
57.0ms	69×	body	1280	valid
28.0ms	261×	body	80	valid
13.0ms	38×	body	320	valid
4.0ms	16×	body	160	valid

simplify8.4s

Counts

1 → 1

Iterations

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

prune44.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.1b

localize56.0ms

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 2.0)))
7.4b	(- (* (exp l) J) (/ J (exp l)))

rewrite198.0ms

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:

23.0ms	(* (exp l) J)
9.0ms	(/ J (exp l))
131.0ms	(* (- (* (exp l) J) (/ J (exp l))) (cos (/ K 2.0)))
27.0ms	(- (* (exp l) J) (/ J (exp l)))

series496.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (exp l) J)
62.0ms	(/ J (exp l))
230.0ms	(* (- (* (exp l) J) (/ J (exp l))) (cos (/ K 2.0)))
152.0ms	(- (* (exp l) J) (/ J (exp l)))

simplify7.6s

Counts

93 → 93

Iterations

Iter	Nodes
done	5004
3	4649
2	1109
1	319
0	141

prune1.4s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ U (* (* (+ l l) J) (cos (/ K 2.0))))
0.1b	(* (* (+ l l) J) (cos (/ K 2.0)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 33

Calls

2 calls:

19.0ms	(+ U (* (* (+ l l) J) (cos (/ K 2.0))))
56.0ms	(* (* (+ l l) J) (cos (/ K 2.0)))

series291.0ms

Counts

2 → 6

Calls

2 calls:

173.0ms	(+ U (* (* (+ l l) J) (cos (/ K 2.0))))
118.0ms	(* (* (+ l l) J) (cos (/ K 2.0)))

simplify8.7s

Counts

39 → 39

Iterations

Iter	Nodes
done	5000
3	4005
2	726
1	219
0	82

prune633.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ U (* (+ l l) (* J (cos (/ K 2.0)))))
0.1b	(* (+ l l) (* J (cos (/ K 2.0))))
0.2b	(* J (cos (/ K 2.0)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

15×	`associate-l`
12×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`add-log-exp`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`distribute-rgt-out` `insert-posit16` `distribute-lft-out`
2×	`flip3-+` `associate-l/` `-commutative` `flip-+`
1×	`+-commutative` `sum-log` `distribute-lft1-in` `count-2` `distribute-rgt1-in` `unswap-sqr`

Counts

3 → 61

Calls

3 calls:

13.0ms	(+ U (* (+ l l) (* J (cos (/ K 2.0)))))
49.0ms	(* (+ l l) (* J (cos (/ K 2.0))))
10.0ms	(* J (cos (/ K 2.0)))

series385.0ms

Counts

3 → 9

Calls

3 calls:

166.0ms	(+ U (* (+ l l) (* J (cos (/ K 2.0)))))
129.0ms	(* (+ l l) (* J (cos (/ K 2.0))))
90.0ms	(* J (cos (/ K 2.0)))

simplify9.3s

Counts

70 → 70

Iterations

Iter	Nodes
done	5001
3	4696
2	898
1	271
0	107

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize94.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

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:

25.0ms	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
2.0ms	(cbrt (cos (/ K 2.0)))
2.0ms	(cbrt (cos (/ K 2.0)))
2.0ms	(cbrt (cos (/ K 2.0)))

series1.5s

Counts

4 → 12

Calls

4 calls:

521.0ms	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
271.0ms	(cbrt (cos (/ K 2.0)))
350.0ms	(cbrt (cos (/ K 2.0)))
365.0ms	(cbrt (cos (/ K 2.0)))

simplify4.6s

Counts

89 → 89

Iterations

Iter	Nodes
done	5001
4	2058
3	769
2	332
1	154
0	72

prune1.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes1.7s

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	14
1	14
0	11

end0.0ms

sample8.3s

Algorithm

intervals

Results

2.5s	2748×	body	1280	valid
2.0s	8449×	body	80	valid
1.8s	2591×	body	640	valid
626.0ms	1494×	body	320	valid
292.0ms	788×	body	160	valid