Details

sample61.0ms

Algorithm

intervals

Results

13.0ms	272×	body	80	nan
12.0ms	168×	body	160	valid
10.0ms	528×	pre	80	true
4.0ms	40×	body	320	valid
2.0ms	48×	body	80	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	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: 45.8b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
40.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 19

Calls

4 calls:

5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
5.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series306.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
49.0ms	(- (* b b) (* (* 4.0 a) c))
105.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify121.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (117.0ms)

Iter	Nodes	Cost
0	269	246
1	985	235
2	3930	225
3	5002	224

prune80.0ms

Filtered

31 candidates to 27 candidates (87.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	29	2	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	2	32

Merged error: 0.2b

Counts

32 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

11×	`associate-/l*`
8×	`associate-/r/` `*-commutative`
7×	`associate-/l/`
6×	`flip3--` `times-frac` `flip--`
5×	`div-inv`
4×	`associate-r`
3×	`frac-2neg` `clear-num`
2×	`sub-neg` `associate-/r*`
1×	`associate--l-` `neg-sub0`

Counts

4 → 39

Calls

4 calls:

5.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(/ (/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.0ms	(/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series466.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms	(- (* b b) (* (* 4.0 a) c))
149.0ms	(/ (/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
190.0ms	(/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify41.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	355	552
1	1419	505
2	5002	479

prune169.0ms

Filtered

51 candidates to 42 candidates (82.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	42	9	51
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	43	10	53

Merged error: 0b

Counts

53 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-commutative`
10×	`times-frac` `associate-*r/`
8×	`associate-l`
6×	`clear-num` `associate-/r/` `div-inv` `associate-/l/`
5×	`associate-/r*`
4×	`flip3--` `frac-2neg` `associate-r` `flip--`
2×	`div-sub` `un-div-inv` `associate-/l*`
1×	`associate--l-` `neg-sub0` `sub-neg`

Counts

4 → 47

Calls

4 calls:

7.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a)
11.0ms	(/ (* 4.0 c) (* (* 2.0 a) (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a)))
5.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(* (* 2.0 a) (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a))

series416.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a)
180.0ms	(/ (* 4.0 c) (* (* 2.0 a) (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a)))
49.0ms	(- (* b b) (* (* 4.0 a) c))
92.0ms	(* (* 2.0 a) (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a))

simplify44.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	373	471
1	1571	450
2	5001	440

prune180.0ms

Filtered

59 candidates to 50 candidates (84.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	55	4	59
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	63	6	69

Merged error: 0b

Counts

69 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

36×	`associate-/r/`
30×	`times-frac`
20×	`*-commutative`
19×	`associate-/r*`
14×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
8×	`frac-2neg` `clear-num` `div-inv`
7×	`neg-mul-1`
5×	`associate-/l*`
2×	`flip3--` `flip3-+` `sqrt-div` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-sub0` `sub-neg` `pow1/2` `div-sub` `distribute-frac-neg`

Counts

4 → 62

Calls

4 calls:

9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(/ (- (* 4.0 c)) (/ (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ a (* 2.0 a))))

series382.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
82.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms	(- (* b b) (* (* 4.0 a) c))
182.0ms	(/ (- (* 4.0 c)) (/ (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ a (* 2.0 a))))

simplify45.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	419	717
1	1577	665
2	5001	650

prune193.0ms

Filtered

74 candidates to 60 candidates (81.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	71	3	74
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	75	5	80

Merged error: 0b

Counts

80 → 5

regimes86.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	30
1	43	30
2	43	30

end0.0ms

sample1.5s

Algorithm

intervals

Results

358.0ms	4824×	body	160	valid
300.0ms	16295×	pre	80	true
288.0ms	8295×	body	80	nan
148.0ms	1370×	body	320	valid
67.0ms	1806×	body	80	valid