Details

sample63.0ms

Algorithm

intervals

Results

41.0ms	225×	body	10240	exit
6.0ms	216×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	7×	body	640	valid
1.0ms	16×	body	160	valid

simplify3.3s

Counts

1 → 1

Iterations

Useful iterations: 5 (82.0ms)

Iter	Nodes	Cost
0	8	16
1	20	15
2	48	15
3	105	15
4	195	14
5	533	12
6	3015	12
done	5000	12

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.8b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- (/ x (exp wj)) wj) (+ wj 1))
0.0b	(/ x (exp wj))
4.6b	(+ (/ (- (/ x (exp wj)) wj) (+ wj 1)) wj)

rewrite118.0ms

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:

32.0ms	(/ (- (/ x (exp wj)) wj) (+ wj 1))
3.0ms	(/ x (exp wj))
79.0ms	(+ (/ (- (/ x (exp wj)) wj) (+ wj 1)) wj)

series121.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(/ (- (/ x (exp wj)) wj) (+ wj 1))
24.0ms	(/ x (exp wj))
54.0ms	(+ (/ (- (/ x (exp wj)) wj) (+ wj 1)) wj)

simplify792.0ms

Counts

100 → 100

Iterations

Useful iterations: done (789.0ms)

Iter	Nodes	Cost
0	169	1488
1	404	1420
2	1157	1357
done	5000	1345

prune203.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

4×	`associate-+l+`
3×	`add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
1×	`pow1` `add-exp-log` `+-commutative` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `flip3-+` `sum-log` `add-cbrt-cube` `flip-+`

Counts

1 → 15

Calls

1 calls:

5.0ms

(+ (* wj (- wj (* 2 x))) x)

series23.0ms

Counts

1 → 3

Calls

1 calls:

23.0ms

(+ (* wj (- wj (* 2 x))) x)

simplify574.0ms

Counts

18 → 18

Iterations

Useful iterations: 3 (112.0ms)

Iter	Nodes	Cost
0	38	246
1	116	239
2	283	215
3	1080	209
done	5000	209

prune35.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (/ (- (/ x (exp wj)) wj) (+ wj 1)) wj)) (cbrt (+ (/ (- (/ x (exp wj)) wj) (+ wj 1)) wj)))
4.6b	(+ (/ (- (/ x (exp wj)) wj) (+ wj 1)) wj)
4.6b	(+ (/ (- (/ x (exp wj)) wj) (+ wj 1)) wj)
4.6b	(+ (/ (- (/ x (exp wj)) wj) (+ wj 1)) wj)

rewrite621.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
24×	`cbrt-prod`
20×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `cbrt-div`
11×	`pow1`
10×	`add-log-exp`
9×	`flip3-+` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `pow1/3`
4×	`frac-times` `add-cbrt-cube` `unswap-sqr`
3×	`+-commutative` `associate-+l-` `div-sub` `sum-log`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 92

Calls

4 calls:

381.0ms	(* (cbrt (+ (/ (- (/ x (exp wj)) wj) (+ wj 1)) wj)) (cbrt (+ (/ (- (/ x (exp wj)) wj) (+ wj 1)) wj)))
78.0ms	(+ (/ (- (/ x (exp wj)) wj) (+ wj 1)) wj)
79.0ms	(+ (/ (- (/ x (exp wj)) wj) (+ wj 1)) wj)
80.0ms	(+ (/ (- (/ x (exp wj)) wj) (+ wj 1)) wj)

series406.0ms

Counts

4 → 12

Calls

4 calls:

236.0ms	(* (cbrt (+ (/ (- (/ x (exp wj)) wj) (+ wj 1)) wj)) (cbrt (+ (/ (- (/ x (exp wj)) wj) (+ wj 1)) wj)))
57.0ms	(+ (/ (- (/ x (exp wj)) wj) (+ wj 1)) wj)
54.0ms	(+ (/ (- (/ x (exp wj)) wj) (+ wj 1)) wj)
58.0ms	(+ (/ (- (/ x (exp wj)) wj) (+ wj 1)) wj)

simplify2.5s

Counts

104 → 104

Iterations

Useful iterations: 3 (850.0ms)

Iter	Nodes	Cost
0	146	3038
1	338	2852
2	1043	2668
3	4615	2274
done	5000	2274

prune276.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (exp wj))
0.0b	(- (/ (- (/ x (exp wj)) wj) (+ wj 1)) wj)
3.0b	(- (* (/ (- (/ x (exp wj)) wj) (+ wj 1)) (/ (- (/ x (exp wj)) wj) (+ wj 1))) (* wj wj))
21.6b	(/ (- (* (/ (- (/ x (exp wj)) wj) (+ wj 1)) (/ (- (/ x (exp wj)) wj) (+ wj 1))) (* wj wj)) (- (/ (- (/ x (exp wj)) wj) (+ wj 1)) wj))

rewrite307.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
39×	`times-frac`
36×	`*-un-lft-identity`
24×	`add-cube-cbrt`
20×	`difference-of-squares`
9×	`associate-/r*`
8×	`add-cbrt-cube` `add-log-exp`
7×	`add-exp-log` `associate-/l*`
6×	`distribute-lft-out--`
4×	`pow1` `flip3--` `flip--`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `associate-/r/` `div-inv` `associate-/l/`
1×	`associate--l-`

Counts

4 → 107

Calls

4 calls:

3.0ms	(/ x (exp wj))
106.0ms	(- (/ (- (/ x (exp wj)) wj) (+ wj 1)) wj)
26.0ms	(- (* (/ (- (/ x (exp wj)) wj) (+ wj 1)) (/ (- (/ x (exp wj)) wj) (+ wj 1))) (* wj wj))
169.0ms	(/ (- (* (/ (- (/ x (exp wj)) wj) (+ wj 1)) (/ (- (/ x (exp wj)) wj) (+ wj 1))) (* wj wj)) (- (/ (- (/ x (exp wj)) wj) (+ wj 1)) wj))

series683.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ x (exp wj))
57.0ms	(- (/ (- (/ x (exp wj)) wj) (+ wj 1)) wj)
179.0ms	(- (* (/ (- (/ x (exp wj)) wj) (+ wj 1)) (/ (- (/ x (exp wj)) wj) (+ wj 1))) (* wj wj))
421.0ms	(/ (- (* (/ (- (/ x (exp wj)) wj) (+ wj 1)) (/ (- (/ x (exp wj)) wj) (+ wj 1))) (* wj wj)) (- (/ (- (/ x (exp wj)) wj) (+ wj 1)) wj))

simplify599.0ms

Counts

119 → 119

Iterations

Useful iterations: 2 (197.0ms)

Iter	Nodes	Cost
0	197	4181
1	477	3952
2	1740	3348
done	5001	3348

prune314.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

regimes57.0ms

Accuracy

0% (1.9b remaining)

Error of 2.2b against oracle of 0.3b and baseline of 2.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	10	9
done	10	9

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.6s	7745×	body	10240	exit
192.0ms	6321×	body	80	valid
72.0ms	754×	body	320	valid
69.0ms	457×	body	640	valid
33.0ms	540×	body	160	valid