Details

sample283.0ms

Algorithm

intervals

Results

8.0ms	44×	body	2560	valid
7.0ms	172×	body	80	valid
6.0ms	37×	body	1280	valid
3.0ms	103×	body	80	nan
3.0ms	21×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	4×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	32	7
2	41	7
3	44	7
4	44	7

prune4.0ms

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: 37.5b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(- (* b_2 b_2) (* a c))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

4×	`flip3--` `flip--`
2×	`associate--l-` `neg-sub0` `sub-neg` `sqrt-div` `div-sub` `associate-/l/`
1×	`frac-2neg` `pow1/2` `clear-num` `div-inv`

Counts

4 → 19

Calls

4 calls:

6.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series283.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms	(- (* b_2 b_2) (* a c))
74.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
86.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify65.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	223	208
1	712	203
2	2280	193
3	5001	190

prune99.0ms

Filtered

31 candidates to 26 candidates (83.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	23	8	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	8	32

Merged error: 6.1b

Counts

32 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
5.2b	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.5b	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

7×	`associate-/l*`
5×	`associate-/l/`
4×	`flip3--` `associate-/r/` `flip--`
3×	`frac-2neg` `clear-num` `div-inv`
2×	`sqrt-div` `*-commutative`
1×	`sub-neg` `pow1/2`

Counts

4 → 25

Calls

4 calls:

5.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
7.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series495.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
159.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
196.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify95.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 3 (91.0ms)

Iter	Nodes	Cost
0	276	257
1	838	242
2	3489	228
3	5001	227

prune104.0ms

Filtered

37 candidates to 34 candidates (91.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	32	5	37
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	37	8	45

Merged error: 6.0b

Counts

45 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (* 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.2b	(- (* b_2 b_2) (* a c))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

4×	`flip3--` `flip--`
2×	`sub-neg` `sqrt-div` `associate-r/` `associate-/r` `associate-/r/`
1×	`frac-2neg` `pow1/2` `clear-num` `*-commutative` `div-inv`

Counts

4 → 18

Calls

4 calls:

7.0ms	(/ c (* 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
4.0ms	(- (* b_2 b_2) (* a c))
5.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(/ c (* 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
36.0ms	(- (* b_2 b_2) (* a c))
75.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify98.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	203	183
1	706	173
2	3130	170
3	5002	170

prune77.0ms

Filtered

30 candidates to 24 candidates (80.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	29	1	30
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	30	8	38

Merged error: 6.0b

Counts

38 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.9b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
5.2b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
23.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

10×	`associate-/r/`
8×	`associate-/l/`
6×	`associate-/l*`
5×	`frac-2neg` `clear-num` `div-inv`
4×	`flip3--` `flip--`
2×	`sqrt-div` `associate-/r*`
1×	`sub-neg` `pow1/2`

Counts

4 → 29

Calls

4 calls:

5.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
8.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series445.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
171.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
138.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify178.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	284	260
1	949	246
2	4602	238
3	5002	238

prune91.0ms

Filtered

41 candidates to 34 candidates (82.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	40	1	41
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	41	8	49

Merged error: 6.0b

Counts

49 → 8

regimes185.0ms

Accuracy

96.4% (0.9b remaining)

Error of 6.4b against oracle of 5.5b and baseline of 29.5b

bsearch107.0ms

Steps

Iters	Range	Point
6	2.066422626357648e+110	1.9801395410105552e+111	1.703504653326294e+111
5	5.655525127217964e-251	1.9763919052369517e-250	6.3411928596588654e-251
8	-2.083222696695489e+156	-8.927571262924557e+151	-8.764892488422707e+153

Iters

Range

Point

2.066422626357648e+110

1.9801395410105552e+111

1.703504653326294e+111

5.655525127217964e-251

1.9763919052369517e-250

6.3411928596588654e-251

-2.083222696695489e+156

-8.927571262924557e+151

-8.764892488422707e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	22
1	43	22
2	43	22

end0.0ms

sample1.0s

Algorithm

intervals

Results

220.0ms	1098×	body	2560	valid
200.0ms	5864×	body	80	valid
143.0ms	877×	body	1280	valid
94.0ms	2851×	body	80	nan
62.0ms	480×	body	640	valid
25.0ms	106×	body	5120	valid
19.0ms	198×	body	320	valid
8.0ms	122×	body	160	valid