Details

sample293.0ms

Algorithm

intervals

Results

8.0ms	40×	body	2560	valid
7.0ms	198×	body	80	valid
5.0ms	23×	body	1280	valid
3.0ms	103×	body	80	nan
2.0ms	16×	body	640	valid
0.0ms	2×	body	5120	valid
0.0ms	5×	body	160	valid
0.0ms	1×	body	320	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	7
1	22	7
2	25	7
3	27	7
4	29	7
5	29	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: 34.2b

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))
1.5b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 17

Calls

4 calls:

7.0ms	(/ (+ (- 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)))

series288.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
34.0ms	(- (* b_2 b_2) (* a c))
75.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
85.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify80.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	234	195
1	769	185
2	2680	176
3	5001	175

prune93.0ms

Filtered

29 candidates to 25 candidates (86.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	22	7	29
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	22	8	30

Merged error: 6.1b

Counts

30 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.2b	(- (* b_2 b_2) (* a c))
1.5b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

6×	`frac-times`
5×	`flip3-+` `flip-+`
4×	`clear-num`
3×	`frac-2neg` `associate-*r/`
2×	`flip3--` `sqrt-div` `associate-*l/` `un-div-inv` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `pow1/2` `associate-r` `*-commutative` `div-inv`

Counts

4 → 26

Calls

4 calls:

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

series264.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
33.0ms	(- (* b_2 b_2) (* a c))
74.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify138.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	255	302
1	1030	285
2	4852	255
3	5003	255

prune99.0ms

Filtered

38 candidates to 29 candidates (76.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	36	2	38
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	39	7	46

Merged error: 6.1b

Counts

46 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.5b	(* (/ (+ (* a c) 0) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
10.2b	(/ (+ (* a c) 0) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

15×	`frac-times`
12×	`clear-num`
11×	`frac-2neg`
10×	`associate-/l/`
5×	`flip3-+` `associate-*l/` `flip-+`
4×	`flip3--` `associate-/r/` `flip--`
3×	`associate-r/` `associate-l*` `div-inv`
2×	`sqrt-div` `un-div-inv`
1×	`associate--l-` `neg-sub0` `sub-neg` `pow1/2` `associate-r` `*-commutative`

Counts

4 → 45

Calls

4 calls:

5.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
10.0ms	(* (/ (+ (* a c) 0) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
8.0ms	(/ (+ (* a c) 0) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series452.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
142.0ms	(* (/ (+ (* a c) 0) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
174.0ms	(/ (+ (* a c) 0) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify87.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	399	456
1	2107	418
2	5002	397

prune147.0ms

Filtered

57 candidates to 47 candidates (82.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	56	1	57
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	57	7	64

Merged error: 6.0b

Counts

64 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.2b	(- (* b_2 b_2) (* a c))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 17

Calls

4 calls:

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

series336.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
33.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify61.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 3 (57.0ms)

Iter	Nodes	Cost
0	195	197
1	634	192
2	2046	180
3	5001	179

prune64.0ms

Filtered

29 candidates to 24 candidates (82.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	29	0	29
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	29	7	36

Merged error: 6.0b

Counts

36 → 7

regimes204.0ms

Accuracy

96.3% (0.9b remaining)

Error of 6.4b against oracle of 5.5b and baseline of 29.2b

bsearch120.0ms

Steps

Iters	Range	Point
6	2.066422626357648e+110	1.9801395410105552e+111	3.969902647964137e+110
8	-2.3862131106328103e-184	-9.444153407873295e-189	-1.8132672640965176e-188
8	-2.083222696695489e+156	-8.927571262924557e+151	-1.3324370156406744e+154

Iters

Range

Point

2.066422626357648e+110

1.9801395410105552e+111

3.969902647964137e+110

-2.3862131106328103e-184

-9.444153407873295e-189

-1.8132672640965176e-188

-2.083222696695489e+156

-8.927571262924557e+151

-1.3324370156406744e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	21
1	35	21

end0.0ms

sample1.0s

Algorithm

intervals

Results

214.0ms	1094×	body	2560	valid
205.0ms	5873×	body	80	valid
141.0ms	877×	body	1280	valid
87.0ms	2851×	body	80	nan
59.0ms	453×	body	640	valid
30.0ms	117×	body	5120	valid
21.0ms	221×	body	320	valid
7.0ms	113×	body	160	valid