Details

sample18.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	22	7
2	24	7
3	24	7

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 38.9b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.2b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

5×	`sqrt-div`
4×	`flip3-+` `flip-+` `associate-/l/`
3×	`+-commutative`
2×	`associate-+l+` `frac-2neg` `clear-num` `div-inv`
1×	`pow1/2` `sqrt-prod`

Counts

4 → 20

Calls

4 calls:

7.0ms	(+ (+ (* x x) (* y y)) (* z z))
4.0ms	(+ (* x x) (* y y))
8.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
6.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series286.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (+ (* x x) (* y y)) (* z z))
27.0ms	(+ (* x x) (* y y))
52.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
170.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify66.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	185	234
1	712	227
2	2006	223
3	5001	219

prune95.0ms

Filtered

32 candidates to 26 candidates (81.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	27	5	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	28	5	33

Merged error: 18.4b

Counts

33 → 5

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow x 2) (+ (pow y 2) (pow z 2)))
0.1b	(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
36.2b	(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

6×	`+-commutative` `associate-+r+`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/`
3×	`flip3-+` `flip-+`
2×	`sqrt-div` `sqrt-prod` `*-commutative`
1×	`pow1/2`

Counts

3 → 21

Calls

3 calls:

5.0ms	(+ (pow x 2) (+ (pow y 2) (pow z 2)))
6.0ms	(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
6.0ms	(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

series247.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(+ (pow x 2) (+ (pow y 2) (pow z 2)))
51.0ms	(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
160.0ms	(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

simplify52.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	123	209
1	435	206
2	1432	206
3	5002	206

prune71.0ms

Filtered

30 candidates to 17 candidates (56.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	30	0	30
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	30	5	35

Merged error: 18.4b

Counts

35 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
36.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

4×	`flip3-+` `sqrt-div` `flip-+`
3×	`+-commutative`
2×	`associate-+l+` `associate-/l/`
1×	`sqrt-undiv` `frac-2neg` `pow1/2` `clear-num` `div-inv`

Counts

4 → 17

Calls

4 calls:

7.0ms	(+ (+ (* x x) (* y y)) (* z z))
4.0ms	(+ (* x x) (* y y))
7.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (+ (* x x) (* y y)) (* z z))
27.0ms	(+ (* x x) (* y y))
217.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
96.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify59.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	158	197
1	596	193
2	1632	189
3	5002	189

prune88.0ms

Filtered

29 candidates to 23 candidates (79.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	26	3	29
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	26	8	34

Merged error: 18.2b

Counts

34 → 8

localize3.0ms

Local error

Found 1 expressions with local error:

0.3b	(/ z (sqrt 3.0))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

1×	`frac-2neg` `clear-num` `div-inv`

Counts

1 → 3

Calls

1 calls:

2.0ms

(/ z (sqrt 3.0))

series58.0ms

Counts

1 → 3

Calls

1 calls:

58.0ms

(/ z (sqrt 3.0))

simplify4.0ms

Algorithm

egg-herbie

Counts

6 → 6

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	13
1	11	13

prune6.0ms

Filtered

6 candidates to 3 candidates (50.0%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	4	2	6
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	4	10	14

Merged error: 18.2b

Counts

14 → 10

regimes396.0ms

Accuracy

64.7% (7.2b remaining)

Error of 25.3b against oracle of 18.1b and baseline of 38.4b

bsearch77.0ms

Steps

Iters	Range		Point
8	1.74384754595472e+119	1.5789597603016236e+122	8.139421225416975e+121
9	-6.311616513999659e+143	-9.938214279124584e+135	-9.575588976650983e+141

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	12
1	33	12
2	33	12

end0.0ms

sample459.0ms

Algorithm

intervals

Results

274.0ms

8000×

body

valid