Details

sample140.0ms

Algorithm

intervals

Results

102.0ms	262×	body	10240	exit
9.0ms	193×	body	80	valid
4.0ms	21×	body	640	valid
4.0ms	28×	body	320	valid
2.0ms	18×	body	160	valid

simplify4.8s

Counts

1 → 1

Iterations

Useful iterations: 5 (552.0ms)

Iter	Nodes	Cost
0	8	16
1	20	15
2	48	15
3	105	15
4	190	14
5	621	12
6	2585	12
done	5001	12

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.2b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (exp wj))
0.0b	(/ (- wj (/ x (exp wj))) (+ wj 1))
5.0b	(- wj (/ (- wj (/ x (exp wj))) (+ wj 1)))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
39×	`times-frac`
23×	`add-cube-cbrt`
12×	`difference-of-squares`
9×	`associate-/l*`
7×	`associate-/r*` `add-cbrt-cube` `distribute-lft-out`
6×	`add-exp-log` `distribute-lft-out--`
5×	`add-log-exp`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `clear-num` `associate-/r/` `flip--` `div-inv` `associate-/l/`
1×	`sub-neg` `flip3-+` `diff-log` `flip-+` `associate--r-`

Counts

3 → 94

Calls

3 calls:

14.0ms	(/ x (exp wj))
91.0ms	(/ (- wj (/ x (exp wj))) (+ wj 1))
110.0ms	(- wj (/ (- wj (/ x (exp wj))) (+ wj 1)))

series193.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(/ x (exp wj))
73.0ms	(/ (- wj (/ x (exp wj))) (+ wj 1))
77.0ms	(- wj (/ (- wj (/ x (exp wj))) (+ wj 1)))

simplify1.9s

Counts

103 → 103

Iterations

Useful iterations: 3 (938.0ms)

Iter	Nodes	Cost
0	174	1576
1	409	1496
2	960	1436
3	2266	1431
done	5001	1431

prune348.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (* wj (- wj (* 2 x))))
0.5b	(* wj (- wj (* 2 x)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `add-exp-log` `distribute-rgt-in` `add-cube-cbrt` `sub-neg` `associate-+r+` `*-un-lft-identity` `distribute-lft-in` `add-cbrt-cube` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`associate-*r/`
1×	`+-commutative` `flip3--` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

2 → 39

Calls

2 calls:

8.0ms	(+ x (* wj (- wj (* 2 x))))
17.0ms	(* wj (- wj (* 2 x)))

series94.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(+ x (* wj (- wj (* 2 x))))
61.0ms	(* wj (- wj (* 2 x)))

simplify1.8s

Counts

45 → 45

Iterations

Useful iterations: 2 (118.0ms)

Iter	Nodes	Cost
0	70	507
1	186	473
2	543	431
3	2139	431
done	5000	431

prune126.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (- wj (* 2 x))) (cbrt (- wj (* 2 x))))
1.1b	(cbrt (- wj (* 2 x)))
1.1b	(cbrt (- wj (* 2 x)))
1.1b	(cbrt (- wj (* 2 x)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3--` `pow1/3` `flip--`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

46.0ms	(* (cbrt (- wj (* 2 x))) (cbrt (- wj (* 2 x))))
6.0ms	(cbrt (- wj (* 2 x)))
6.0ms	(cbrt (- wj (* 2 x)))
3.0ms	(cbrt (- wj (* 2 x)))

series850.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(* (cbrt (- wj (* 2 x))) (cbrt (- wj (* 2 x))))
222.0ms	(cbrt (- wj (* 2 x)))
234.0ms	(cbrt (- wj (* 2 x)))
222.0ms	(cbrt (- wj (* 2 x)))

simplify3.9s

Counts

99 → 99

Iterations

Useful iterations: done (3.9s)

Iter	Nodes	Cost
0	129	1635
1	274	1504
2	679	1418
3	1592	1281
4	3937	1225
done	5000	1180

prune418.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (exp wj))
0.0b	(/ (+ wj 1) (- wj (/ x (exp wj))))
0.2b	(/ 1 (/ (+ wj 1) (- wj (/ x (exp wj)))))
6.9b	(- wj (/ 1 (/ (+ wj 1) (- wj (/ x (exp wj))))))

rewrite252.0ms

Algorithm

rewrite-expression-head

Rules

246×	`times-frac`
218×	`add-sqr-sqrt`
208×	`*-un-lft-identity`
99×	`add-cube-cbrt`
47×	`difference-of-squares`
39×	`associate-/r*`
31×	`distribute-lft-out`
23×	`distribute-lft-out--`
18×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`associate-/r/`
10×	`associate-/l*`
9×	`div-exp`
8×	`div-inv`
6×	`flip3--` `flip--` `add-log-exp`
5×	`pow1` `cbrt-undiv`
3×	`frac-2neg` `clear-num`
2×	`rec-exp` `1-exp` `associate-/l/`
1×	`sub-neg` `pow-flip` `flip3-+` `diff-log` `flip-+` `inv-pow`

Counts

4 → 240

Calls

4 calls:

9.0ms	(/ x (exp wj))
56.0ms	(/ (+ wj 1) (- wj (/ x (exp wj))))
62.0ms	(/ 1 (/ (+ wj 1) (- wj (/ x (exp wj)))))
94.0ms	(- wj (/ 1 (/ (+ wj 1) (- wj (/ x (exp wj))))))

series370.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ x (exp wj))
172.0ms	(/ (+ wj 1) (- wj (/ x (exp wj))))
81.0ms	(/ 1 (/ (+ wj 1) (- wj (/ x (exp wj)))))
85.0ms	(- wj (/ 1 (/ (+ wj 1) (- wj (/ x (exp wj))))))

simplify3.4s

Counts

252 → 252

Iterations

Useful iterations: 3 (2.0s)

Iter	Nodes	Cost
0	325	5147
1	714	4561
2	1600	4223
3	4399	4129
done	5000	4129

prune566.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.3b

regimes70.0ms

Accuracy

64.7% (0.6b remaining)

Error of 1.0b against oracle of 0.3b and baseline of 2.1b

bsearch45.0ms

Steps

Iters	Range		Point
7	1.0710839719517313e-09	3.960545047166202e-08	8.976401343690175e-09

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	33
1	27	33
done	27	33

end0.0ms

sample6.1s

Algorithm

intervals

Results

4.6s	7666×	body	10240	exit
496.0ms	6262×	body	80	valid
181.0ms	797×	body	320	valid
166.0ms	461×	body	640	valid
94.0ms	565×	body	160	valid