Details

sample54.0ms

Algorithm

intervals

Results

12.0ms	117×	body	320	valid
10.0ms	509×	pre	80	true
8.0ms	253×	body	80	nan
5.0ms	80×	body	160	valid
2.0ms	13×	body	640	valid
2.0ms	46×	body	80	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	9
1	43	9
2	83	9
3	110	9
4	118	9
5	118	9

prune3.0ms

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: 49.9b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 3.0 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.2b	(* (* 3.0 a) c)
24.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-commutative`
8×	`prod-diff`
6×	`associate-l`
2×	`neg-sub0` `associate-+l-` `flip3-+` `fma-neg` `associate-/r*` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-mul-1` `sub-neg` `flip3--` `fma-def` `frac-2neg` `div-sub` `clear-num` `flip--` `div-inv`

Counts

4 → 30

Calls

4 calls:

6.0ms	(- (* b b) (* (* 3.0 a) c))
8.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
7.0ms	(* (* 3.0 a) c)
6.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series258.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b b) (* (* 3.0 a) c))
110.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
20.0ms	(* (* 3.0 a) c)
84.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify135.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 3 (126.0ms)

Iter	Nodes	Cost
0	296	286
1	1077	259
2	4554	250
3	5001	248

prune76.0ms

Filtered

42 candidates to 27 candidates (64.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	40	2	42
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	40	3	43

Merged error: 0.2b

Counts

43 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.3b	(/ (fma (* 3.0 c) a 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.3b	(fma (* 3.0 c) a 0)
0.4b	(/ (/ (fma (* 3.0 c) a 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-/r/`
6×	`times-frac` `*-commutative`
5×	`div-inv`
4×	`flip3--` `flip--`
3×	`frac-2neg` `clear-num` `associate-/l/` `associate-/l*`
2×	`associate-l` `associate-/r*`
1×	`fma-udef`

Counts

4 → 26

Calls

4 calls:

4.0ms	(* (* 3.0 a) c)
7.0ms	(/ (fma (* 3.0 c) a 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
1.0ms	(fma (* 3.0 c) a 0)
9.0ms	(/ (/ (fma (* 3.0 c) a 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

series437.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (* 3.0 a) c)
198.0ms	(/ (fma (* 3.0 c) a 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
34.0ms	(fma (* 3.0 c) a 0)
185.0ms	(/ (/ (fma (* 3.0 c) a 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

simplify84.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (79.0ms)

Iter	Nodes	Cost
0	228	376
1	682	340
2	3406	294
3	5001	292

prune110.0ms

Filtered

38 candidates to 29 candidates (76.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	33	5	38
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	34	7	41

Merged error: 0.0b

Counts

41 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.2b	(* (* 3.0 a) c)
0.3b	(/ (- (* (* 3.0 a) c)) (+ b (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.4b	(/ (/ (- (* (* 3.0 a) c)) (+ b (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

21×	`associate-/l*`
16×	`*-commutative`
12×	`associate-l` `associate-/l/`
8×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-/r/`
6×	`times-frac`
5×	`div-inv`
4×	`flip3-+` `flip-+`
3×	`frac-2neg` `div-sub` `distribute-frac-neg` `clear-num`
2×	`neg-sub0` `neg-mul-1` `associate-/r*`

Counts

4 → 50

Calls

4 calls:

3.0ms	(* (* 3.0 a) c)
7.0ms	(* (* 3.0 a) c)
9.0ms	(/ (- (* (* 3.0 a) c)) (+ b (sqrt (- (* b b) (* (* 3.0 a) c)))))
12.0ms	(/ (/ (- (* (* 3.0 a) c)) (+ b (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

series396.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
20.0ms	(* (* 3.0 a) c)
197.0ms	(/ (- (* (* 3.0 a) c)) (+ b (sqrt (- (* b b) (* (* 3.0 a) c)))))
159.0ms	(/ (/ (- (* (* 3.0 a) c)) (+ b (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

simplify37.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	313	563
1	1190	512
2	5001	482

prune164.0ms

Filtered

62 candidates to 52 candidates (83.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	59	3	62
Fresh	4	1	5
Picked	0	1	1
Done	1	0	1
Total	64	5	69

Merged error: 0b

Counts

69 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ b (sqrt (- (* b b) (* (* 3.0 a) c))))
0.1b	(- (* b b) (* (* 3.0 a) c))
0.1b	(/ (* 1 c) (+ b (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.2b	(* (* 3.0 a) c)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-commutative`
8×	`prod-diff`
6×	`associate-l`
2×	`flip3-+` `fma-neg` `associate-/r/` `flip-+` `associate-/l*`
1×	`+-commutative` `sub-neg` `flip3--` `frac-2neg` `clear-num` `flip--` `div-inv`

Counts

4 → 27

Calls

4 calls:

5.0ms	(+ b (sqrt (- (* b b) (* (* 3.0 a) c))))
10.0ms	(- (* b b) (* (* 3.0 a) c))
8.0ms	(/ (* 1 c) (+ b (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(* (* 3.0 a) c)

series331.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(+ b (sqrt (- (* b b) (* (* 3.0 a) c))))
45.0ms	(- (* b b) (* (* 3.0 a) c))
181.0ms	(/ (* 1 c) (+ b (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.0ms	(* (* 3.0 a) c)

simplify132.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 3 (128.0ms)

Iter	Nodes	Cost
0	225	254
1	890	228
2	4646	219
3	5001	218

prune75.0ms

Filtered

39 candidates to 23 candidates (59.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	38	1	39
Fresh	1	2	3
Picked	0	1	1
Done	1	0	1
Total	40	4	44

Merged error: 0b

Counts

44 → 4

regimes88.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	21	9
1	27	8
2	32	8
3	32	8

end0.0ms

sample1.5s

Algorithm

intervals

Results

359.0ms	3618×	body	320	valid
302.0ms	15996×	pre	80	true
247.0ms	7996×	body	80	nan
192.0ms	2919×	body	160	valid
68.0ms	501×	body	640	valid
32.0ms	962×	body	80	valid