Details

sample27.0ms

Algorithm

intervals

Results

14.0ms

256×

body

valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	7
1	27	7
2	33	7
3	34	7
4	34	7

prune2.0ms

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: 39.8b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.9b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 12

Calls

2 calls:

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

series219.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
166.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	133	138
1	508	132
2	1691	126
3	5001	123

prune62.0ms

Filtered

18 candidates to 16 candidates (88.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	13	5	18
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	13	6	19

Merged error: 18.6b

Counts

19 → 6

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 0.3333333333333333 (fma z z (fma x x (* y y))))
37.0b	(sqrt (* 0.3333333333333333 (fma z z (fma x x (* y y)))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

2×	`sqrt-prod` `*-commutative` `fma-udef`
1×	`distribute-rgt-in` `distribute-lft-in` `pow1/2`

Counts

2 → 6

Calls

2 calls:

2.0ms	(* 0.3333333333333333 (fma z z (fma x x (* y y))))
2.0ms	(sqrt (* 0.3333333333333333 (fma z z (fma x x (* y y)))))

series231.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(* 0.3333333333333333 (fma z z (fma x x (* y y))))
172.0ms	(sqrt (* 0.3333333333333333 (fma z z (fma x x (* y y)))))

simplify66.0ms

Algorithm

egg-herbie

Counts

12 → 12

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	58	45
1	143	42
2	325	39
3	679	39
4	1816	39
5	5002	39

prune26.0ms

Filtered

12 candidates to 7 candidates (58.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	10	2	12
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	10	8	18

Merged error: 6.8b

Counts

18 → 8

localize10.0ms

Local error

Found 2 expressions with local error:

0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
36.9b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 9

Calls

2 calls:

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

series316.0ms

Counts

2 → 6

Calls

2 calls:

215.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
101.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify90.0ms

Algorithm

egg-herbie

Counts

15 → 15

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	92	105
1	263	103
2	916	102
3	3821	102
4	5001	102

prune53.0ms

Filtered

15 candidates to 12 candidates (80.0%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	12	3	15
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	12	11	23

Merged error: 6.7b

Counts

23 → 11

localize5.0ms

Local error

Found 1 expressions with local error:

0.2b	(* x (sqrt 0.3333333333333333))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

1×	`*-commutative`

Counts

1 → 1

Calls

1 calls:

3.0ms

(* x (sqrt 0.3333333333333333))

series49.0ms

Counts

1 → 3

Calls

1 calls:

49.0ms

(* x (sqrt 0.3333333333333333))

simplify4.0ms

Algorithm

egg-herbie

Counts

4 → 4

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	5	6
1	5	6

prune2.0ms

Filtered

4 candidates to 1 candidates (25.0%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	4	0	4
Fresh	0	7	7
Picked	0	1	1
Done	0	3	3
Total	4	11	15

Merged error: 6.7b

Counts

15 → 11

regimes556.0ms

Accuracy

37.3% (19.7b remaining)

Error of 26.1b against oracle of 6.4b and baseline of 37.8b

bsearch121.0ms

Steps

Iters	Range		Point
4	3.4998900038905293e+129	6.14958975458552e+129	5.1872092242977175e+129
8	-4.419830676218405e-53	-1.489312294692343e-55	-4.352681642110856e-53
8	-2.528216661513648e-07	-9.746209037285112e-11	-9.875653154507083e-11
11	-1.9658258378654302e+115	-9.407094719653012e+95	-1.517842864509148e+115

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	19
1	47	19
2	47	19

end0.0ms

sample430.0ms

Algorithm

intervals

Results

269.0ms

8000×

body

valid