Details

sample17.0ms

Algorithm

intervals

Results

8.0ms

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: 38.9b

Counts

2 → 1

localize12.0ms

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+` `fma-def` `frac-2neg` `clear-num` `div-inv`
1×	`pow1/2` `sqrt-prod` `*-commutative`

Counts

4 → 22

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))

series269.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (+ (* x x) (* y y)) (* z z))
28.0ms	(+ (* x x) (* y y))
47.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
159.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify60.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	197	218
1	789	203
2	2348	189
3	5001	182

prune98.0ms

Filtered

34 candidates to 26 candidates (76.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	29	5	34
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	5	35

Merged error: 18.4b

Counts

35 → 5

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (fma y y (* z z)))
0.1b	(* 0.3333333333333333 (fma x x (fma y y (* z z))))
36.2b	(sqrt (* 0.3333333333333333 (fma x x (fma y y (* z z)))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 7

Calls

3 calls:

1.0ms	(fma x x (fma y y (* z z)))
2.0ms	(* 0.3333333333333333 (fma x x (fma y y (* z z))))
2.0ms	(sqrt (* 0.3333333333333333 (fma x x (fma y y (* z z)))))

series298.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(fma x x (fma y y (* z z)))
60.0ms	(* 0.3333333333333333 (fma x x (fma y y (* z z))))
195.0ms	(sqrt (* 0.3333333333333333 (fma x x (fma y y (* z z)))))

simplify72.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	63	55
1	151	49
2	339	49
3	697	49
4	1833	49
5	5001	49

prune30.0ms

Filtered

16 candidates to 6 candidates (37.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	16	0	16
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	16	5	21

Merged error: 18.4b

Counts

21 → 5

localize11.0ms

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)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 19

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))
6.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (+ (* x x) (* y y)) (* z z))
26.0ms	(+ (* x x) (* y y))
214.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
98.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify52.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	168	185
1	661	174
2	1917	166
3	5002	162

prune84.0ms

Filtered

31 candidates to 23 candidates (74.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	28	3	31
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	28	8	36

Merged error: 18.2b

Counts

36 → 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))

series54.0ms

Counts

1 → 3

Calls

1 calls:

54.0ms

(/ z (sqrt 3.0))

simplify4.0ms

Algorithm

egg-herbie

Counts

6 → 6

Iterations

Useful iterations: 0 (1.0ms)

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

regimes387.0ms

Accuracy

64.7% (7.2b remaining)

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

bsearch64.0ms

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	26	10
1	28	10
2	28	10

end0.0ms

sample437.0ms

Algorithm

intervals

Results

269.0ms

8000×

body

valid