Details

sample118.0ms

Algorithm

intervals

Results

86.0ms	233×	body	10240	exit
8.0ms	210×	body	80	valid
2.0ms	13×	body	640	valid
2.0ms	19×	body	320	valid
1.0ms	16×	body	160	valid

simplify43.0ms

Counts: 1 → 1

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ wj (+ wj 1))
0.0b	(/ x (+ wj 1))
0.0b	(/ (/ x (+ wj 1)) (exp wj))
4.2b	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

rewrite796.0ms

Algorithm

rewrite-expression-head

Rules

127×	`times-frac`
118×	`*-un-lft-identity`
78×	`add-sqr-sqrt`
73×	`add-cube-cbrt`
24×	`associate-/l*`
21×	`distribute-lft-out`
13×	`add-cbrt-cube`
12×	`associate-/r/`
11×	`add-exp-log` `associate-/r*`
9×	`add-log-exp`
7×	`flip3-+` `flip-+` `div-inv`
5×	`cbrt-undiv` `div-exp`
4×	`pow1`
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 → 176

Calls

4 calls:

11.0ms	(/ wj (+ wj 1))
11.0ms	(/ x (+ wj 1))
26.0ms	(/ (/ x (+ wj 1)) (exp wj))
741.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

series166.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ wj (+ wj 1))
29.0ms	(/ x (+ wj 1))
46.0ms	(/ (/ x (+ wj 1)) (exp wj))
68.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

simplify88.0ms

Counts: 188 → 188

prune473.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.4b

localize10.0ms

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))

rewrite102.0ms

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:

9.0ms	(+ x (pow wj 2))
76.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))
16.0ms	(* 2 (* wj x))

series89.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(+ x (pow wj 2))
33.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))
22.0ms	(* 2 (* wj x))

simplify139.0ms

Counts: 53 → 53

prune119.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.4b

localize16.0ms

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)))

rewrite91.0ms

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:

62.0ms	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
11.0ms	(cbrt (+ x (pow wj 2)))
7.0ms	(cbrt (+ x (pow wj 2)))
7.0ms	(cbrt (+ x (pow wj 2)))

series1.3s

Counts

4 → 12

Calls

4 calls:

303.0ms	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
355.0ms	(cbrt (+ x (pow wj 2)))
349.0ms	(cbrt (+ x (pow wj 2)))
332.0ms	(cbrt (+ x (pow wj 2)))

simplify181.0ms

Counts: 107 → 107

prune319.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.4b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

30×	`cbrt-prod`
18×	`*-un-lft-identity`
12×	`cbrt-div`
10×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`

Counts

4 → 62

Calls

4 calls:

7.0ms	(cbrt (+ x (pow wj 2)))
7.0ms	(cbrt (+ x (pow wj 2)))
8.0ms	(cbrt (cbrt (+ x (pow wj 2))))
13.0ms	(cbrt (cbrt (+ x (pow wj 2))))

series1.4s

Counts

4 → 12

Calls

4 calls:

352.0ms	(cbrt (+ x (pow wj 2)))
345.0ms	(cbrt (+ x (pow wj 2)))
351.0ms	(cbrt (cbrt (+ x (pow wj 2))))
354.0ms	(cbrt (cbrt (+ x (pow wj 2))))

simplify90.0ms

Counts: 74 → 74

prune323.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.4b

regimes136.0ms

Accuracy

60.8% (0.8b remaining)

Error of 1.1b against oracle of 0.3b and baseline of 2.3b

bsearch33.0ms

Steps

Iters	Range		Point
8	6.152066266068123e-12	1.6430535565209345e-07	9.50840758158314e-09

simplify1.0ms

end0.0ms

sample4.5s

Algorithm

intervals

Results

3.5s	7633×	body	10240	exit
344.0ms	6258×	body	80	valid
100.0ms	804×	body	320	valid
85.0ms	464×	body	640	valid
42.0ms	543×	body	160	valid