Details

sample153.0ms

Algorithm

intervals

Results

108.0ms	228×	body	10240	exit
11.0ms	192×	body	80	valid
5.0ms	19×	body	640	valid
4.0ms	27×	body	320	valid
3.0ms	24×	body	160	valid

simplify735.0ms

Counts: 1 → 1

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ wj (+ wj 1))
0.0b	(/ x (+ wj 1))
0.3b	(/ (/ x (+ wj 1)) (exp wj))
5.6b	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

rewrite773.0ms

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:

16.0ms	(/ wj (+ wj 1))
11.0ms	(/ x (+ wj 1))
38.0ms	(/ (/ x (+ wj 1)) (exp wj))
696.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

series217.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ wj (+ wj 1))
43.0ms	(/ x (+ wj 1))
78.0ms	(/ (/ x (+ wj 1)) (exp wj))
71.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

simplify1.2s

Counts: 188 → 188

prune668.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.5b

localize12.0ms

Local error

Found 2 expressions with local error:

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

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:

17.0ms	(+ x (pow wj 2))
33.0ms	(* 2 (* wj x))

series87.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(+ x (pow wj 2))
43.0ms	(* 2 (* wj x))

simplify1.1s

Counts: 36 → 36

prune120.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.5b

localize25.0ms

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)))

rewrite113.0ms

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:

85.0ms	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
10.0ms	(cbrt (+ x (pow wj 2)))
7.0ms	(cbrt (+ x (pow wj 2)))
7.0ms	(cbrt (+ x (pow wj 2)))

series1.9s

Counts

4 → 12

Calls

4 calls:

405.0ms	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
452.0ms	(cbrt (+ x (pow wj 2)))
529.0ms	(cbrt (+ x (pow wj 2)))
512.0ms	(cbrt (+ x (pow wj 2)))

simplify618.0ms

Counts: 107 → 107

prune484.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.5b

localize37.0ms

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))))
0.9b	(pow (cbrt (cbrt (+ x (pow wj 2)))) 4)

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

30×	`cbrt-prod`
20×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`unpow-prod-down`
8×	`cbrt-div`
5×	`pow1` `add-exp-log`
4×	`pow1/3` `add-cbrt-cube` `distribute-lft-out` `add-log-exp`
3×	`pow-unpow` `flip3-+` `flip-+`
2×	`pow-pow`
1×	`pow-to-exp` `pow-exp` `sqr-pow`

Counts

4 → 70

Calls

4 calls:

15.0ms	(cbrt (+ x (pow wj 2)))
14.0ms	(cbrt (+ x (pow wj 2)))
16.0ms	(cbrt (cbrt (+ x (pow wj 2))))
23.0ms	(pow (cbrt (cbrt (+ x (pow wj 2)))) 4)

series2.1s

Counts

4 → 12

Calls

4 calls:

507.0ms	(cbrt (+ x (pow wj 2)))
507.0ms	(cbrt (+ x (pow wj 2)))
494.0ms	(cbrt (cbrt (+ x (pow wj 2))))
626.0ms	(pow (cbrt (cbrt (+ x (pow wj 2)))) 4)

simplify1.9s

Counts: 82 → 82

prune559.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.5b

regimes216.0ms

Accuracy

60.3% (0.7b remaining)

Error of 1.0b against oracle of 0.3b and baseline of 2.1b

bsearch52.0ms

Steps

Iters	Range		Point
7	1.1362596833603348e-09	1.5244367550608482e-07	7.48741129916649e-09

simplify685.0ms

end0.0ms

sample6.4s

Algorithm

intervals

Results

4.4s	7477×	body	10240	exit
883.0ms	6222×	body	80	valid
212.0ms	492×	body	640	valid
211.0ms	820×	body	320	valid
62.0ms	547×	body	160	valid