Details

sample76.0ms

Algorithm

intervals

Results

39.0ms	117×	body	10240	exit
10.0ms	205×	body	80	valid
6.0ms	133×	body	80	overflowed
4.0ms	17×	body	640	valid
3.0ms	21×	body	320	valid
2.0ms	18×	body	160	valid

simplify45.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (6.0ms)

Iter	Nodes	Cost
0	20	9
1	48	9
2	107	9
3	224	8
4	1514	8
5	5001	8

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.7b

localize9.0ms

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))
4.5b	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

rewrite393.0ms

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:

5.0ms	(/ wj (+ wj 1))
5.0ms	(/ x (+ wj 1))
13.0ms	(/ (/ x (+ wj 1)) (exp wj))
361.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

series139.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ wj (+ wj 1))
22.0ms	(/ x (+ wj 1))
38.0ms	(/ (/ x (+ wj 1)) (exp wj))
56.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

simplify77.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	721	1524
1	3303	1471
2	5001	1469

prune409.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite12.0ms

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:

5.0ms	(+ x (pow wj 2))
6.0ms	(* 2 (* wj x))

series49.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(+ x (pow wj 2))
18.0ms	(* 2 (* wj x))

simplify66.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	149	122
1	550	108
2	2362	107
3	5001	107

prune71.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
0.5b	(cbrt (+ x (pow wj 2)))
0.5b	(cbrt (+ x (pow wj 2)))
0.5b	(cbrt (+ x (pow wj 2)))

rewrite57.0ms

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:

38.0ms	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
4.0ms	(cbrt (+ x (pow wj 2)))
7.0ms	(cbrt (+ x (pow wj 2)))
5.0ms	(cbrt (+ x (pow wj 2)))

series1.2s

Counts

4 → 12

Calls

4 calls:

270.0ms	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
317.0ms	(cbrt (+ x (pow wj 2)))
316.0ms	(cbrt (+ x (pow wj 2)))
308.0ms	(cbrt (+ x (pow wj 2)))

simplify163.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 3 (153.0ms)

Iter	Nodes	Cost
0	252	878
1	944	827
2	4715	760
3	5001	749

prune278.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ x (pow wj 2)))
0.5b	(cbrt (cbrt (+ x (pow wj 2))))
0.5b	(cbrt (cbrt (+ x (pow wj 2))))
1.1b	(pow (cbrt (cbrt (+ x (pow wj 2)))) 5)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

37×	`cbrt-prod`
21×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`unpow-prod-down` `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 → 73

Calls

4 calls:

4.0ms	(cbrt (+ x (pow wj 2)))
5.0ms	(cbrt (cbrt (+ x (pow wj 2))))
5.0ms	(cbrt (cbrt (+ x (pow wj 2))))
11.0ms	(pow (cbrt (cbrt (+ x (pow wj 2)))) 5)

series1.4s

Counts

4 → 12

Calls

4 calls:

321.0ms	(cbrt (+ x (pow wj 2)))
322.0ms	(cbrt (cbrt (+ x (pow wj 2))))
321.0ms	(cbrt (cbrt (+ x (pow wj 2))))
463.0ms	(pow (cbrt (cbrt (+ x (pow wj 2)))) 5)

simplify42.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	328	675
1	1159	641
2	5002	635

prune335.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.3b

regimes93.0ms

Accuracy

38.1% (1.2b remaining)

Error of 1.5b against oracle of 0.3b and baseline of 2.3b

bsearch6.0ms

Steps

Iters	Range		Point
1	3.0649639386435413e-28	3.2966406264355945e-28	3.238721454487581e-28

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	14
1	27	14

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	3766×	body	10240	exit
321.0ms	6268×	body	80	valid
176.0ms	3853×	body	80	overflowed
129.0ms	827×	body	320	valid
102.0ms	446×	body	640	valid
55.0ms	537×	body	160	valid