Details

sample64.0ms

Algorithm

intervals

Results

39.0ms	213×	body	10240	exit
6.0ms	205×	body	80	valid
2.0ms	16×	body	640	valid
2.0ms	22×	body	320	valid
1.0ms	15×	body	160	valid

simplify48.0ms

Counts

1 → 1

Iterations

Useful iterations: 3 (7.0ms)

Iter	Nodes	Cost
0	21	9
1	52	9
2	113	9
3	240	8
4	1625	8
5	5001	8
done	5001	8

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.4b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite663.0ms

Algorithm

rewrite-expression-head

Rules

231×	`*-un-lft-identity`
175×	`times-frac`
129×	`add-sqr-sqrt`
124×	`add-cube-cbrt`
72×	`prod-diff`
52×	`distribute-lft-out`
24×	`associate-/l*`
20×	`associate-/r/`
13×	`add-cbrt-cube`
11×	`add-exp-log` `flip3-+` `associate-/r*` `flip-+` `div-inv`
9×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `fma-neg` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
2×	`diff-log` `frac-sub` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--` `associate-/l/`

Counts

4 → 260

Calls

4 calls:

11.0ms	(/ wj (+ wj 1))
23.0ms	(/ (/ x (+ wj 1)) (exp wj))
11.0ms	(/ x (+ wj 1))
601.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

series154.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ wj (+ wj 1))
48.0ms	(/ (/ x (+ wj 1)) (exp wj))
24.0ms	(/ x (+ wj 1))
60.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

simplify123.0ms

Counts

272 → 272

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	1015	4090
1	4555	3249
2	5001	3243
done	5001	3243

prune522.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity`
6×	`add-log-exp`
4×	`fma-neg` `prod-diff`
3×	`add-sqr-sqrt` `add-cube-cbrt`
2×	`diff-log` `distribute-lft-out`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `associate--l+` `sum-log` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

1 → 24

Calls

1 calls:

90.0ms

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

series32.0ms

Counts

1 → 3

Calls

1 calls:

32.0ms

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

simplify120.0ms

Counts

27 → 27

Iterations

Useful iterations: 3 (117.0ms)

Iter	Nodes	Cost
0	129	214
1	565	175
2	4080	160
3	5001	152
done	5001	152

prune65.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ x (+ (pow wj 3) 1)) (/ (+ (* wj wj) (- 1 (* wj 1))) (exp wj)))
0.0b	(/ wj (+ wj 1))
0.0b	(/ (+ (* wj wj) (- 1 (* wj 1))) (exp wj))
4.8b	(- (+ (* (/ x (+ (pow wj 3) 1)) (/ (+ (* wj wj) (- 1 (* wj 1))) (exp wj))) wj) (/ wj (+ wj 1)))

rewrite578.0ms

Algorithm

rewrite-expression-head

Rules

113×	`*-un-lft-identity`
96×	`add-sqr-sqrt`
83×	`times-frac`
79×	`add-cube-cbrt`
54×	`prod-diff`
20×	`add-cbrt-cube`
18×	`associate-l`
17×	`add-exp-log`
16×	`distribute-lft-out`
13×	`associate-r`
10×	`associate-/r/`
9×	`add-log-exp`
7×	`flip3-+` `associate-/r*` `flip-+` `div-inv`
6×	`pow1` `cbrt-undiv` `div-exp` `associate-/l*`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
3×	`fma-neg`
2×	`frac-2neg` `diff-log` `clear-num` `frac-sub` `associate-/l/` `difference-of-squares`
1×	`frac-times` `associate-+r-` `sub-neg` `flip3--` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `associate--l+` `sum-log` `*-commutative` `flip--` `distribute-lft-out--`

Counts

4 → 202

Calls

4 calls:

106.0ms	(* (/ x (+ (pow wj 3) 1)) (/ (+ (* wj wj) (- 1 (* wj 1))) (exp wj)))
11.0ms	(/ wj (+ wj 1))
48.0ms	(/ (+ (* wj wj) (- 1 (* wj 1))) (exp wj))
405.0ms	(- (+ (* (/ x (+ (pow wj 3) 1)) (/ (+ (* wj wj) (- 1 (* wj 1))) (exp wj))) wj) (/ wj (+ wj 1)))

series327.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (/ x (+ (pow wj 3) 1)) (/ (+ (* wj wj) (- 1 (* wj 1))) (exp wj)))
21.0ms	(/ wj (+ wj 1))
24.0ms	(/ (+ (* wj wj) (- 1 (* wj 1))) (exp wj))
187.0ms	(- (+ (* (/ x (+ (pow wj 3) 1)) (/ (+ (* wj wj) (- 1 (* wj 1))) (exp wj))) wj) (/ wj (+ wj 1)))

simplify59.0ms

Counts

214 → 214

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1103	4446
1	5001	3611
done	5001	3611

prune605.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ x (+ (pow wj 3) 1)) (/ (+ (* wj wj) (- 1 (* wj 1))) (exp wj)))
0.0b	(/ (+ (* wj wj) (- 1 (* wj 1))) (exp wj))
0.2b	(/ 1 (/ (+ wj 1) wj))
5.3b	(- (+ (* (/ x (+ (pow wj 3) 1)) (/ (+ (* wj wj) (- 1 (* wj 1))) (exp wj))) wj) (/ 1 (/ (+ wj 1) wj)))

rewrite819.0ms

Algorithm

rewrite-expression-head

Rules

388×	`times-frac`
342×	`*-un-lft-identity`
279×	`add-sqr-sqrt`
253×	`add-cube-cbrt`
159×	`prod-diff`
42×	`distribute-lft-out`
26×	`add-exp-log`
23×	`add-cbrt-cube`
21×	`div-inv`
19×	`associate-/r*`
18×	`associate-l`
13×	`associate-r`
12×	`div-exp`
9×	`add-log-exp`
8×	`cbrt-undiv`
7×	`pow1`
6×	`associate-/r/` `associate-/l*`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
3×	`flip3-+` `fma-neg` `flip-+`
2×	`rec-exp` `frac-2neg` `diff-log` `1-exp` `clear-num` `frac-sub` `associate-/l/` `distribute-lft-out--`
1×	`frac-times` `associate-+r-` `sub-neg` `flip3--` `pow-flip` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `associate--l+` `sum-log` `*-commutative` `flip--` `inv-pow`

Counts

4 → 366

Calls

4 calls:

106.0ms	(* (/ x (+ (pow wj 3) 1)) (/ (+ (* wj wj) (- 1 (* wj 1))) (exp wj)))
49.0ms	(/ (+ (* wj wj) (- 1 (* wj 1))) (exp wj))
17.0ms	(/ 1 (/ (+ wj 1) wj))
624.0ms	(- (+ (* (/ x (+ (pow wj 3) 1)) (/ (+ (* wj wj) (- 1 (* wj 1))) (exp wj))) wj) (/ 1 (/ (+ wj 1) wj)))

series323.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (/ x (+ (pow wj 3) 1)) (/ (+ (* wj wj) (- 1 (* wj 1))) (exp wj)))
23.0ms	(/ (+ (* wj wj) (- 1 (* wj 1))) (exp wj))
21.0ms	(/ 1 (/ (+ wj 1) wj))
185.0ms	(- (+ (* (/ x (+ (pow wj 3) 1)) (/ (+ (* wj wj) (- 1 (* wj 1))) (exp wj))) wj) (/ 1 (/ (+ wj 1) wj)))

simplify118.0ms

Counts

378 → 378

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1831	11908
1	5001	8808
done	5001	8808

prune681.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

regimes91.0ms

Accuracy

55.1% (0.8b remaining)

Error of 1.1b against oracle of 0.3b and baseline of 2.1b

bsearch27.0ms

Steps

Iters	Range		Point
6	1.6364485262755118e-17	1.0549554552646143e-16	1.0431539000350864e-16

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	20
1	48	20
2	48	20
done	48	20

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.5s	7768×	body	10240	exit
201.0ms	6281×	body	80	valid
81.0ms	817×	body	320	valid
69.0ms	432×	body	640	valid
38.0ms	552×	body	160	valid