Details

sample20.0ms

Algorithm

intervals

Results

10.0ms

440×

body

valid

simplify318.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	13	7
1	23	6
2	35	4
3	45	4
4	54	4
5	87	4
6	156	4
7	206	4
8	219	4
9	312	4
10	640	4
11	3180	4
12	5001	4

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.1b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 3 (* y y)) (* x x))
0.2b	(* 3 (* y y))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
18×	`associate-r`
16×	`*-un-lft-identity`
10×	`associate-l`
8×	`add-cube-cbrt`
7×	`pow1` `add-exp-log` `add-cbrt-cube` `unswap-sqr`
4×	`swap-sqr` `distribute-lft-out` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

2 → 52

Calls

2 calls:

27.0ms	(+ (* 3 (* y y)) (* x x))
9.0ms	(* 3 (* y y))

series66.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(+ (* 3 (* y y)) (* x x))
30.0ms	(* 3 (* y y))

simplify42.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	221	231
1	1011	211
2	5001	202

prune69.0ms

Filtered

58 candidates to 33 candidates (43.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	55	3	58
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	55	4	59

Merged error: 0b

Counts

59 → 4

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (* (fabs y) 3) (sqrt (* y y))) (* x x))
0.2b	(* (* (fabs y) 3) (sqrt (* y y)))
18.7b	(sqrt (* y y))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
40×	`sqrt-prod`
30×	`associate-l`
29×	`*-un-lft-identity`
27×	`associate-r`
24×	`unswap-sqr`
17×	`add-cube-cbrt`
16×	`pow1`
9×	`swap-sqr`
8×	`add-exp-log` `add-cbrt-cube`
7×	`*-commutative`
6×	`sqrt-pow1` `distribute-lft-out`
5×	`rem-sqrt-square` `add-log-exp`
4×	`pow-prod-down`
3×	`prod-exp` `cbrt-unprod`
1×	`+-commutative` `pow2` `flip3-+` `pow-plus` `pow1/2` `sum-log` `pow-sqr` `pow-prod-up` `flip-+`

Counts

3 → 107

Calls

3 calls:

47.0ms	(+ (* (* (fabs y) 3) (sqrt (* y y))) (* x x))
15.0ms	(* (* (fabs y) 3) (sqrt (* y y)))
5.0ms	(sqrt (* y y))

series118.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(+ (* (* (fabs y) 3) (sqrt (* y y))) (* x x))
47.0ms	(* (* (fabs y) 3) (sqrt (* y y)))
9.0ms	(sqrt (* y y))

simplify56.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	334	638
1	1272	575
2	5002	541

prune359.0ms

Filtered

116 candidates to 69 candidates (40.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	114	2	116
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	116	4	120

Merged error: 0b

Counts

120 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* (fabs y) (* (cbrt 3) (cbrt 3))) (* (fabs y) (cbrt 3))) (* x x))
0.1b	(* (fabs y) (* (cbrt 3) (cbrt 3)))
0.2b	(* (* (fabs y) (* (cbrt 3) (cbrt 3))) (* (fabs y) (cbrt 3)))
0.3b	(* (fabs y) (cbrt 3))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

219×	`add-sqr-sqrt`
127×	`unswap-sqr`
94×	`associate-r`
80×	`cbrt-prod`
77×	`associate-l`
74×	`add-cbrt-cube`
68×	`cbrt-unprod`
44×	`*-un-lft-identity`
32×	`pow1` `add-exp-log` `add-cube-cbrt`
22×	`swap-sqr`
19×	`pow-prod-down` `prod-exp`
12×	`*-commutative`
6×	`distribute-lft-out` `add-log-exp`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 224

Calls

4 calls:

89.0ms	(+ (* (* (fabs y) (* (cbrt 3) (cbrt 3))) (* (fabs y) (cbrt 3))) (* x x))
16.0ms	(* (fabs y) (* (cbrt 3) (cbrt 3)))
33.0ms	(* (* (fabs y) (* (cbrt 3) (cbrt 3))) (* (fabs y) (cbrt 3)))
5.0ms	(* (fabs y) (cbrt 3))

series325.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(+ (* (* (fabs y) (* (cbrt 3) (cbrt 3))) (* (fabs y) (cbrt 3))) (* x x))
65.0ms	(* (fabs y) (* (cbrt 3) (cbrt 3)))
99.0ms	(* (* (fabs y) (* (cbrt 3) (cbrt 3))) (* (fabs y) (cbrt 3)))
47.0ms	(* (fabs y) (cbrt 3))

simplify149.0ms

Algorithm

egg-herbie

Counts

236 → 236

Iterations

Useful iterations: 2 (129.0ms)

Iter	Nodes	Cost
0	747	2508
1	4122	2138
2	5002	1866

prune361.0ms

Filtered

236 candidates to 135 candidates (42.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	235	1	236
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	236	4	240

Merged error: 0b

Counts

240 → 4

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b

(+ (* (* (pow (fabs y) 2) (* (pow (cbrt 3) 2) (sqrt (cbrt 3)))) (sqrt (cbrt 3))) (* x x))

0.2b

(* (* (pow (fabs y) 2) (* (pow (cbrt 3) 2) (sqrt (cbrt 3)))) (sqrt (cbrt 3)))

0.2b

(* (pow (fabs y) 2) (* (pow (cbrt 3) 2) (sqrt (cbrt 3))))

rewrite366.0ms

Algorithm

rewrite-expression-head

Rules

931×	`add-sqr-sqrt`
845×	`unswap-sqr`
368×	`sqrt-prod`
256×	`cbrt-prod`
230×	`unpow-prod-down`
164×	`associate-l`
150×	`unpow2` `sqr-pow`
107×	`associate-r`
69×	`add-exp-log`
55×	`prod-exp`
37×	`*-un-lft-identity`
25×	`add-cube-cbrt`
17×	`pow1` `add-cbrt-cube`
14×	`pow-to-exp` `pow-exp`
9×	`pow-prod-down` `cbrt-unprod`
6×	`distribute-lft-out`
5×	`*-commutative` `add-log-exp`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

3 → 501

Calls

3 calls:

235.0ms

(+ (* (* (pow (fabs y) 2) (* (pow (cbrt 3) 2) (sqrt (cbrt 3)))) (sqrt (cbrt 3))) (* x x))

57.0ms

(* (* (pow (fabs y) 2) (* (pow (cbrt 3) 2) (sqrt (cbrt 3)))) (sqrt (cbrt 3)))

28.0ms

(* (pow (fabs y) 2) (* (pow (cbrt 3) 2) (sqrt (cbrt 3))))

series408.0ms

Counts

3 → 9

Calls

3 calls:

123.0ms

(+ (* (* (pow (fabs y) 2) (* (pow (cbrt 3) 2) (sqrt (cbrt 3)))) (sqrt (cbrt 3))) (* x x))

102.0ms

(* (* (pow (fabs y) 2) (* (pow (cbrt 3) 2) (sqrt (cbrt 3)))) (sqrt (cbrt 3)))

184.0ms

(* (pow (fabs y) 2) (* (pow (cbrt 3) 2) (sqrt (cbrt 3))))

simplify190.0ms

Algorithm

egg-herbie

Counts

510 → 510

Iterations

Useful iterations: 2 (120.0ms)

Iter	Nodes	Cost
0	1180	8670
1	4028	7873
2	5001	7196

prune686.0ms

Filtered

510 candidates to 197 candidates (61.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	510	0	510
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	510	4	514

Merged error: 0b

Counts

514 → 4

regimes70.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	4
1	9	4

end0.0ms

sample549.0ms

Algorithm

intervals

Results

329.0ms

14197×

body

valid