Details

sample94.0ms

Algorithm

intervals

Results

47.0ms	129×	body	10240	exit
13.0ms	198×	body	80	valid
10.0ms	122×	body	80	overflowed
5.0ms	26×	body	320	valid
4.0ms	15×	body	640	valid
2.0ms	19×	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

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.2b

localize9.0ms

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

rewrite372.0ms

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))
12.0ms	(/ (/ x (+ wj 1)) (exp wj))
5.0ms	(/ x (+ wj 1))
341.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

series144.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ wj (+ wj 1))
42.0ms	(/ (/ x (+ wj 1)) (exp wj))
23.0ms	(/ x (+ wj 1))
58.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

simplify76.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (60.0ms)

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

prune433.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize7.0ms

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))

rewrite54.0ms

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:

5.0ms	(+ x (pow wj 2))
42.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))
6.0ms	(* 2 (* wj x))

series80.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ x (pow wj 2))
32.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))
19.0ms	(* 2 (* wj x))

simplify126.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	202	247
1	793	231
2	4232	228
3	5001	228

prune103.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.5b

localize11.0ms

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)))

rewrite55.0ms

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:

39.0ms	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
4.0ms	(cbrt (+ x (pow wj 2)))
4.0ms	(cbrt (+ x (pow wj 2)))
4.0ms	(cbrt (+ x (pow wj 2)))

series1.2s

Counts

4 → 12

Calls

4 calls:

277.0ms	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
316.0ms	(cbrt (+ x (pow wj 2)))
317.0ms	(cbrt (+ x (pow wj 2)))
318.0ms	(cbrt (+ x (pow wj 2)))

simplify166.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 3 (157.0ms)

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

prune289.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt (+ x (pow wj 2))))
0.6b	(cbrt (cbrt (+ x (pow wj 2))))
0.6b	(cbrt (cbrt (+ x (pow wj 2))))
0.9b	(pow (cbrt (cbrt (+ x (pow wj 2)))) 4)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

44×	`cbrt-prod`
22×	`*-un-lft-identity`
14×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`cbrt-div`
10×	`unpow-prod-down`
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 → 76

Calls

4 calls:

5.0ms	(cbrt (cbrt (+ x (pow wj 2))))
5.0ms	(cbrt (cbrt (+ x (pow wj 2))))
5.0ms	(cbrt (cbrt (+ x (pow wj 2))))
10.0ms	(pow (cbrt (cbrt (+ x (pow wj 2)))) 4)

series1.4s

Counts

4 → 12

Calls

4 calls:

328.0ms	(cbrt (cbrt (+ x (pow wj 2))))
329.0ms	(cbrt (cbrt (+ x (pow wj 2))))
325.0ms	(cbrt (cbrt (+ x (pow wj 2))))
421.0ms	(pow (cbrt (cbrt (+ x (pow wj 2)))) 4)

simplify123.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (115.0ms)

Iter	Nodes	Cost
0	270	715
1	918	672
2	3646	641
3	5002	629

prune283.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.5b

regimes104.0ms

Accuracy

63.7% (0.8b remaining)

Error of 1.1b against oracle of 0.3b and baseline of 2.4b

bsearch43.0ms

Steps

Iters	Range		Point
8	2.921432904961236e-10	1.5703764843175337e-06	9.06252678575456e-09

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	16
1	31	16

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.4s	3816×	body	10240	exit
424.0ms	6236×	body	80	valid
232.0ms	3757×	body	80	overflowed
144.0ms	822×	body	320	valid
124.0ms	480×	body	640	valid
71.0ms	548×	body	160	valid