Details

sample73.0ms

Algorithm

intervals

Results

48.0ms	276×	body	10240	exit
6.0ms	198×	body	80	valid
3.0ms	19×	body	640	valid
2.0ms	20×	body	320	valid
1.0ms	21×	body	160	valid

simplify5.5s

Counts

1 → 1

Iterations

Useful iterations: 5 (130.0ms)

Iter	Nodes	Cost
0	8	16
1	20	15
2	48	15
3	105	15
4	190	14
5	636	12
6	2552	12
done	5000	12

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (exp wj))
0.0b	(/ (- (/ x (exp wj)) wj) (+ wj 1))
4.5b	(+ (/ (- (/ x (exp wj)) wj) (+ wj 1)) wj)

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 91

Calls

3 calls:

3.0ms	(/ x (exp wj))
31.0ms	(/ (- (/ x (exp wj)) wj) (+ wj 1))
78.0ms	(+ (/ (- (/ x (exp wj)) wj) (+ wj 1)) wj)

series123.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(/ x (exp wj))
42.0ms	(/ (- (/ x (exp wj)) wj) (+ wj 1))
56.0ms	(+ (/ (- (/ x (exp wj)) wj) (+ wj 1)) wj)

simplify1.6s

Counts

100 → 100

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	169	1488
1	404	1420
2	926	1357
3	2473	1347
done	5000	1346

prune211.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 44

Calls

3 calls:

4.0ms	(+ x (pow wj 2))
38.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))
6.0ms	(* 2 (* wj x))

series78.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ x (pow wj 2))
28.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))
21.0ms	(* 2 (* wj x))

simplify2.0s

Counts

53 → 53

Iterations

Useful iterations: 3 (494.0ms)

Iter	Nodes	Cost
0	77	568
1	206	513
2	708	481
3	2601	441
done	5000	441

prune105.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
0.6b	(cbrt (+ x (pow wj 2)))
0.6b	(cbrt (+ x (pow wj 2)))
0.6b	(cbrt (+ x (pow wj 2)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
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 → 95

Calls

4 calls:

36.0ms	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
4.0ms	(cbrt (+ x (pow wj 2)))
4.0ms	(cbrt (+ x (pow wj 2)))
4.0ms	(cbrt (+ x (pow wj 2)))

series1.2s

Counts

4 → 12

Calls

4 calls:

274.0ms	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
313.0ms	(cbrt (+ x (pow wj 2)))
312.0ms	(cbrt (+ x (pow wj 2)))
312.0ms	(cbrt (+ x (pow wj 2)))

simplify1.1s

Counts

107 → 107

Iterations

Useful iterations: 3 (360.0ms)

Iter	Nodes	Cost
0	119	1691
1	254	1528
2	667	1430
3	1911	1257
done	5000	1257

prune290.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.5b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ wj (+ wj 1))
0.0b	(/ x (exp wj))
0.0b	(/ (/ x (exp wj)) (+ wj 1))
6.5b	(- (/ wj (+ wj 1)) wj)

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

119×	`times-frac`
108×	`*-un-lft-identity`
75×	`add-sqr-sqrt`
70×	`add-cube-cbrt`
19×	`associate-/l*`
18×	`distribute-lft-out`
13×	`add-cbrt-cube`
11×	`add-exp-log` `associate-/r*`
8×	`div-inv`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `associate-/r/`
3×	`frac-2neg` `clear-num`
2×	`flip3-+` `flip-+` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `associate-/l/` `distribute-lft-out--`

Counts

4 → 161

Calls

4 calls:

5.0ms	(/ wj (+ wj 1))
3.0ms	(/ x (exp wj))
10.0ms	(/ (/ x (exp wj)) (+ wj 1))
28.0ms	(- (/ wj (+ wj 1)) wj)

series117.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ wj (+ wj 1))
29.0ms	(/ x (exp wj))
38.0ms	(/ (/ x (exp wj)) (+ wj 1))
29.0ms	(- (/ wj (+ wj 1)) wj)

simplify2.5s

Counts

173 → 173

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	254	2328
1	575	2191
2	1465	2101
3	4253	2090
done	5001	2090

prune381.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes70.0ms

Accuracy

63% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 1.2b

bsearch45.0ms

Steps

Iters	Range		Point
10	5.139006765554396e-07	57105.47172318877	0.0756709219093341

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	43
1	29	43
done	29	43

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.4s	7788×	body	10240	exit
187.0ms	6281×	body	80	valid
77.0ms	498×	body	640	valid
73.0ms	771×	body	320	valid
32.0ms	530×	body	160	valid