Details

sample156.0ms

Algorithm

intervals

Results

92.0ms	232×	body	10240	exit
28.0ms	207×	body	80	valid
5.0ms	16×	body	640	valid
4.0ms	19×	body	320	valid
2.0ms	15×	body	160	valid

simplify11.0s

Counts

1 → 1

Iterations

Useful iterations: done (11.0s)

Iter	Nodes	Cost
0	8	16
1	32	15
2	163	15
done	5001	14

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.6b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (exp wj))
0.0b	(/ (- (/ wj 1) (/ x (exp wj))) (+ wj 1))
4.8b	(- wj (/ (- (/ wj 1) (/ x (exp wj))) (+ wj 1)))

rewrite260.0ms

Algorithm

rewrite-expression-head

Rules

118×	`add-sqr-sqrt`
99×	`times-frac`
94×	`*-un-lft-identity`
32×	`difference-of-squares`
28×	`add-cube-cbrt`
14×	`associate-/l*`
12×	`distribute-lft-out`
11×	`distribute-lft-out--`
7×	`associate-/r*` `add-cbrt-cube`
6×	`add-exp-log`
5×	`add-log-exp`
3×	`pow1` `associate-/l/`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `clear-num` `associate-/r/` `flip--` `div-inv`
1×	`sub-neg` `flip3-+` `diff-log` `frac-sub` `flip-+` `associate--r-`

Counts

3 → 120

Calls

3 calls:

7.0ms	(/ x (exp wj))
126.0ms	(/ (- (/ wj 1) (/ x (exp wj))) (+ wj 1))
121.0ms	(- wj (/ (- (/ wj 1) (/ x (exp wj))) (+ wj 1)))

series149.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ x (exp wj))
49.0ms	(/ (- (/ wj 1) (/ x (exp wj))) (+ wj 1))
65.0ms	(- wj (/ (- (/ wj 1) (/ x (exp wj))) (+ wj 1)))

simplify8.1s

Counts

129 → 129

Iterations

Useful iterations: done (8.1s)

Iter	Nodes	Cost
0	221	2443
1	4244	2027
done	5000	1967

prune388.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

18.0ms	(+ x (pow wj 2))
32.0ms	(* 2 (* wj x))

series82.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(+ x (pow wj 2))
22.0ms	(* 2 (* wj x))

simplify7.8s

Counts

36 → 36

Iterations

Useful iterations: done (7.8s)

Iter	Nodes	Cost
0	57	283
1	290	259
2	3231	229
done	5001	227

prune119.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
0.5b	(cbrt (+ x (pow wj 2)))
0.5b	(cbrt (+ x (pow wj 2)))
0.5b	(cbrt (+ x (pow wj 2)))

rewrite154.0ms

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:

104.0ms	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
16.0ms	(cbrt (+ x (pow wj 2)))
15.0ms	(cbrt (+ x (pow wj 2)))
16.0ms	(cbrt (+ x (pow wj 2)))

series2.0s

Counts

4 → 12

Calls

4 calls:

434.0ms	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
532.0ms	(cbrt (+ x (pow wj 2)))
536.0ms	(cbrt (+ x (pow wj 2)))
524.0ms	(cbrt (+ x (pow wj 2)))

simplify5.3s

Counts

107 → 107

Iterations

Useful iterations: done (5.3s)

Iter	Nodes	Cost
0	119	1691
1	670	1534
done	5000	1382

prune393.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* wj (exp wj))
0.0b	(* wj (exp wj))
0.3b	(/ (- (* wj (exp wj)) x) (+ (exp wj) (* wj (exp wj))))
4.8b	(- wj (/ (- (* wj (exp wj)) x) (+ (exp wj) (* wj (exp wj)))))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
18×	`add-cube-cbrt`
16×	`times-frac`
10×	`add-cbrt-cube`
8×	`pow1` `add-exp-log`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`associate-/r*`
4×	`distribute-rgt-out` `distribute-rgt1-in`
3×	`associate-/l*`
2×	`flip3--` `div-sub` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `flip--` `cbrt-unprod` `associate-/l/` `difference-of-squares` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `flip-+` `div-inv` `distribute-lft-out--` `associate--r-`

Counts

4 → 92

Calls

4 calls:

24.0ms	(* wj (exp wj))
12.0ms	(* wj (exp wj))
40.0ms	(/ (- (* wj (exp wj)) x) (+ (exp wj) (* wj (exp wj))))
81.0ms	(- wj (/ (- (* wj (exp wj)) x) (+ (exp wj) (* wj (exp wj)))))

series212.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* wj (exp wj))
35.0ms	(* wj (exp wj))
62.0ms	(/ (- (* wj (exp wj)) x) (+ (exp wj) (* wj (exp wj))))
70.0ms	(- wj (/ (- (* wj (exp wj)) x) (+ (exp wj) (* wj (exp wj)))))

simplify3.8s

Counts

104 → 104

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	149	1664
1	1758	1500
done	5000	1439

prune387.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.1b

regimes173.0ms

Accuracy

32.3% (1.2b remaining)

Error of 1.5b against oracle of 0.3b and baseline of 2.1b

bsearch68.0ms

Steps

Iters	Range		Point
9	-1.9918553488737634e-08	-1.2276846442872278e-14	-5.00771993997508e-09

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	31
1	22	31
done	22	31

end0.0ms

sample6.5s

Algorithm

intervals

Results

5.0s	7577×	body	10240	exit
403.0ms	6323×	body	80	valid
224.0ms	747×	body	320	valid
134.0ms	482×	body	640	valid
60.0ms	513×	body	160	valid