Details

sample53.0ms

Algorithm

intervals

Results

11.0ms	157×	body	160	valid
10.0ms	524×	pre	80	true
9.0ms	268×	body	80	nan
4.0ms	39×	body	320	valid
2.0ms	60×	body	80	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	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: 43.0b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
38.2b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-commutative`
8×	`prod-diff`
4×	`associate-l`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `fma-neg` `sqrt-div` `associate-/r*` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-mul-1` `sub-neg` `fma-def` `frac-2neg` `pow1/2` `div-sub` `clear-num` `div-inv`

Counts

4 → 30

Calls

4 calls:

6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
6.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series307.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
44.0ms	(- (* b b) (* (* 4.0 a) c))
107.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
83.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify143.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 3 (137.0ms)

Iter	Nodes	Cost
0	322	329
1	1151	301
2	4760	289
3	5001	287

prune94.0ms

Filtered

42 candidates to 30 candidates (71.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	39	3	42
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	39	4	43

Merged error: 0.2b

Counts

43 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (/ (fma (* 4.0 c) a 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b	(/ (fma (* 4.0 c) a 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-commutative`
8×	`prod-diff` `associate-/r/`
6×	`flip3--` `times-frac` `flip--`
5×	`div-inv`
4×	`associate-l`
3×	`frac-2neg` `fma-neg` `clear-num` `associate-/l/` `associate-/l*`
2×	`sub-neg` `associate-/r*`
1×	`associate--l-` `neg-sub0` `neg-mul-1`

Counts

4 → 42

Calls

4 calls:

6.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
6.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(/ (/ (fma (* 4.0 c) a 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
7.0ms	(/ (fma (* 4.0 c) a 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series507.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(- (* b b) (* (* 4.0 a) c))
187.0ms	(/ (/ (fma (* 4.0 c) a 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
197.0ms	(/ (fma (* 4.0 c) a 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify41.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	360	567
1	1240	510
2	5001	474

prune163.0ms

Filtered

54 candidates to 37 candidates (68.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	46	8	54
Fresh	1	1	2
Picked	1	0	1
Done	1	0	1
Total	49	9	58

Merged error: 0b

Counts

58 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.2b	(* (/ (fma (* 4.0 c) a 0) a) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

27×	`frac-times`
21×	`clear-num`
19×	`frac-2neg`
14×	`associate-/l/`
13×	`associate-/l*`
10×	`associate-/r/` `*-commutative`
9×	`associate-*r/`
8×	`prod-diff` `div-inv`
7×	`flip3--` `flip--`
5×	`associate-l`
4×	`un-div-inv`
3×	`fma-neg` `associate-*l/`
2×	`sub-neg`
1×	`associate--l-` `neg-sub0` `neg-mul-1` `associate-r` `inv-pow`

Counts

4 → 72

Calls

4 calls:

6.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms	(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
6.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(* (/ (fma (* 4.0 c) a 0) a) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0))

series409.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
100.0ms	(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
43.0ms	(- (* b b) (* (* 4.0 a) c))
188.0ms	(* (/ (fma (* 4.0 c) a 0) a) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0))

simplify64.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	487	850
1	1970	763
2	5002	755

prune220.0ms

Filtered

84 candidates to 52 candidates (61.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	85	8	93

Merged error: 0b

Counts

93 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (fma (* 4.0 c) a 0) a)
0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(/ (/ (fma (* 4.0 c) a 0) a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.2b	(- (* b b) (* (* 4.0 a) c))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-commutative`
8×	`prod-diff`
4×	`associate-l`
3×	`flip3--` `frac-2neg` `fma-neg` `clear-num` `flip--` `div-inv` `associate-/l/`
2×	`sub-neg` `associate-/r/`
1×	`associate--l-` `neg-sub0` `neg-mul-1` `associate-/l*`

Counts

4 → 32

Calls

4 calls:

2.0ms	(/ (fma (* 4.0 c) a 0) a)
6.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms	(/ (/ (fma (* 4.0 c) a 0) a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
6.0ms	(- (* b b) (* (* 4.0 a) c))

series339.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (fma (* 4.0 c) a 0) a)
77.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
182.0ms	(/ (/ (fma (* 4.0 c) a 0) a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
43.0ms	(- (* b b) (* (* 4.0 a) c))

simplify35.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	284	331
1	1024	297
2	5001	281

prune94.0ms

Filtered

44 candidates to 26 candidates (59.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	45	7	52

Merged error: 0b

Counts

52 → 7

regimes116.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	11
1	23	11

end0.0ms

sample1.5s

Algorithm

intervals

Results

350.0ms	4856×	body	160	valid
301.0ms	16383×	pre	80	true
281.0ms	8383×	body	80	nan
140.0ms	1340×	body	320	valid
64.0ms	1804×	body	80	valid