Details

sample36.0ms

Algorithm

intervals

Results

7.0ms	33×	body	2560	valid
6.0ms	185×	body	80	valid
4.0ms	25×	body	1280	valid
3.0ms	97×	body	80	nan
2.0ms	17×	body	640	valid
2.0ms	7×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	4×	body	160	valid

simplify8.0ms

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

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: 34.8b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b	(- (* b_2 b_2) (* a c))
1.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite19.0ms

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

series243.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
32.0ms	(- (* b_2 b_2) (* a c))
68.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
62.0ms	(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

prune98.0ms

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: 5.8b

Counts

32 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
3.3b	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.2b	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite25.0ms

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:

4.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(/ (/ (* 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)))

series442.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* b_2 b_2) (* a c))
155.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
184.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify87.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	259	249
1	793	234
2	3321	222
3	5001	221

prune93.0ms

Filtered

37 candidates to 31 candidates (83.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	34	3	37
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	38	7	45

Merged error: 5.7b

Counts

45 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (* 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b	(- (* b_2 b_2) (* a c))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite20.0ms

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)))
5.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series340.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(/ c (* 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
69.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
32.0ms	(- (* b_2 b_2) (* a c))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify100.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	203	183
1	706	173
2	3130	170
3	5001	170

prune78.0ms

Filtered

30 candidates to 24 candidates (80.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	29	1	30
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	30	7	37

Merged error: 5.7b

Counts

37 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* c (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b	(- (* b_2 b_2) (* a c))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 20

Calls

4 calls:

7.0ms	(* c (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
5.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series344.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(* c (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
68.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
35.0ms	(- (* b_2 b_2) (* a c))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify72.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	194	158
1	661	150
2	2740	147
3	5001	147

prune62.0ms

Filtered

32 candidates to 23 candidates (71.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	32	0	32
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	32	7	39

Merged error: 5.7b

Counts

39 → 7

regimes146.0ms

Accuracy

95.9% (1.0b remaining)

Error of 6.4b against oracle of 5.5b and baseline of 29.4b

bsearch136.0ms

Steps

Iters	Range	Point
8	4.088553977120381e+100	8.044751807128501e+103	1.0673291895585486e+103
11	1.8145151230270015e-269	9.272403512084269e-250	1.6944972861664959e-264
6	-1.2994787762702041e+157	-3.0529494422842112e+156	-3.0812943354752785e+156

Iters

Range

Point

4.088553977120381e+100

8.044751807128501e+103

1.0673291895585486e+103

1.8145151230270015e-269

9.272403512084269e-250

1.6944972861664959e-264

-1.2994787762702041e+157

-3.0529494422842112e+156

-3.0812943354752785e+156

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	19
1	39	19
2	39	19

end0.0ms

sample1.0s

Algorithm

intervals

Results

205.0ms	1052×	body	2560	valid
197.0ms	5925×	body	80	valid
154.0ms	900×	body	1280	valid
90.0ms	2937×	body	80	nan
57.0ms	438×	body	640	valid
28.0ms	115×	body	5120	valid
24.0ms	197×	body	320	valid
8.0ms	130×	body	160	valid