Details

sample113.0ms

Algorithm

intervals

Results

74.0ms	228×	body	10240	exit
10.0ms	206×	body	80	valid
3.0ms	24×	body	320	valid
3.0ms	11×	body	640	valid
1.0ms	15×	body	160	valid

simplify608.0ms

Counts

1 → 1

Iterations

Useful iterations: done (607.0ms)

Iter	Nodes	Cost
0	8	16
1	20	15
2	48	15
3	109	15
4	398	15
done	5000	14

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.5b

localize24.0ms

Local error

Found 3 expressions with local error:

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

rewrite287.0ms

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))
111.0ms	(/ (- (/ wj 1) (/ x (exp wj))) (+ 1 wj))
163.0ms	(- wj (/ (- (/ wj 1) (/ x (exp wj))) (+ 1 wj)))

series177.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ x (exp wj))
65.0ms	(/ (- (/ wj 1) (/ x (exp wj))) (+ 1 wj))
76.0ms	(- wj (/ (- (/ wj 1) (/ x (exp wj))) (+ 1 wj)))

simplify1.7s

Counts

129 → 129

Iterations

Useful iterations: 2 (994.0ms)

Iter	Nodes	Cost
0	221	2443
1	539	2027
2	2159	1968
done	5001	1968

prune438.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite51.0ms

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:

32.0ms	(* 2 (* wj x))
17.0ms	(+ x (pow wj 2))

series93.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(* 2 (* wj x))
59.0ms	(+ x (pow wj 2))

simplify822.0ms

Counts

36 → 36

Iterations

Useful iterations: done (821.0ms)

Iter	Nodes	Cost
0	57	283
1	152	263
2	654	233
done	5000	229

prune140.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (exp wj))
0.0b	(/ (- wj (/ x (exp wj))) (- 1 (pow wj 2)))
0.0b	(* (/ (- wj (/ x (exp wj))) (- 1 (pow wj 2))) (- 1 wj))
4.6b	(- wj (* (/ (- wj (/ x (exp wj))) (- 1 (pow wj 2))) (- 1 wj)))

rewrite418.0ms

Algorithm

rewrite-expression-head

Rules

289×	`add-sqr-sqrt`
183×	`*-un-lft-identity`
179×	`times-frac`
156×	`difference-of-squares`
78×	`associate-l`
52×	`add-cube-cbrt`
39×	`distribute-lft-out--`
26×	`unpow-prod-down` `unpow2` `sqr-pow`
15×	`associate-/r*`
13×	`add-cbrt-cube`
12×	`add-exp-log`
9×	`associate-/l*`
6×	`pow1` `flip3--` `associate-r` `flip--` `add-log-exp`
5×	`sub-neg`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-/r/` `associate--r+`
3×	`cbrt-undiv` `div-exp` `div-inv`
2×	`frac-times` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`diff-log` `div-sub` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 258

Calls

4 calls:

14.0ms	(/ x (exp wj))
119.0ms	(/ (- wj (/ x (exp wj))) (- 1 (pow wj 2)))
239.0ms	(* (/ (- wj (/ x (exp wj))) (- 1 (pow wj 2))) (- 1 wj))
7.0ms	(- wj (* (/ (- wj (/ x (exp wj))) (- 1 (pow wj 2))) (- 1 wj)))

series361.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ x (exp wj))
93.0ms	(/ (- wj (/ x (exp wj))) (- 1 (pow wj 2)))
70.0ms	(* (/ (- wj (/ x (exp wj))) (- 1 (pow wj 2))) (- 1 wj))
154.0ms	(- wj (* (/ (- wj (/ x (exp wj))) (- 1 (pow wj 2))) (- 1 wj)))

simplify3.4s

Counts

270 → 270

Iterations

Useful iterations: 2 (1.4s)

Iter	Nodes	Cost
0	397	5436
1	1068	5138
2	4962	4714
done	5000	4714

prune989.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- wj (/ x (exp wj))) (- 1 (pow wj 2)))
0.0b	(- (- wj (/ (- wj (/ x (exp wj))) (- 1 (pow wj 2)))) (* (- wj) (/ (- wj (/ x (exp wj))) (- 1 (pow wj 2)))))
0.0b	(* (- wj) (/ (- wj (/ x (exp wj))) (- 1 (pow wj 2))))
4.2b	(- wj (/ (- wj (/ x (exp wj))) (- 1 (pow wj 2))))

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

285×	`add-sqr-sqrt`
176×	`*-un-lft-identity`
171×	`times-frac`
156×	`difference-of-squares`
78×	`associate-r`
46×	`add-cube-cbrt`
39×	`distribute-lft-out--`
26×	`unpow-prod-down` `unpow2` `sqr-pow`
12×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
10×	`associate-l`
6×	`pow1` `flip3--` `flip--` `associate-/l*`
4×	`diff-log` `associate-/r/`
3×	`distribute-lft-neg-in` `sub-neg` `distribute-rgt-neg-in` `div-sub` `associate-*r/` `associate--l+`
2×	`cbrt-undiv` `div-exp` `prod-exp` `frac-sub` `cbrt-unprod` `div-inv` `associate-/l/` `associate--r-` `unswap-sqr`
1×	`distribute-lft-neg-out` `associate--l-` `neg-mul-1` `frac-2neg` `pow-prod-down` `clear-num` `*-commutative`

Counts

4 → 247

Calls

4 calls:

116.0ms	(/ (- wj (/ x (exp wj))) (- 1 (pow wj 2)))
1.3s	(- (- wj (/ (- wj (/ x (exp wj))) (- 1 (pow wj 2)))) (* (- wj) (/ (- wj (/ x (exp wj))) (- 1 (pow wj 2)))))
185.0ms	(* (- wj) (/ (- wj (/ x (exp wj))) (- 1 (pow wj 2))))
158.0ms	(- wj (/ (- wj (/ x (exp wj))) (- 1 (pow wj 2))))

series412.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (- wj (/ x (exp wj))) (- 1 (pow wj 2)))
153.0ms	(- (- wj (/ (- wj (/ x (exp wj))) (- 1 (pow wj 2)))) (* (- wj) (/ (- wj (/ x (exp wj))) (- 1 (pow wj 2)))))
87.0ms	(* (- wj) (/ (- wj (/ x (exp wj))) (- 1 (pow wj 2))))
81.0ms	(- wj (/ (- wj (/ x (exp wj))) (- 1 (pow wj 2))))

simplify718.0ms

Counts

259 → 259

Iterations

Useful iterations: done (710.0ms)

Iter	Nodes	Cost
0	379	5858
1	1169	5296
done	5001	4871

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

regimes78.0ms

Accuracy

67.3% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 1.7b

bsearch43.0ms

Steps

Iters	Range		Point
6	3.960614984267581e-08	3.8036156446576786e-07	3.256044322215378e-07

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	47
1	32	47
2	36	47
3	39	47
done	39	47

end0.0ms

sample6.7s

Algorithm

intervals

Results

5.2s	7815×	body	10240	exit
455.0ms	6308×	body	80	valid
204.0ms	445×	body	640	valid
150.0ms	817×	body	320	valid
61.0ms	507×	body	160	valid