Details

sample55.0ms

Algorithm

intervals

Results

13.0ms	529×	pre	80	true
11.0ms	139×	body	160	valid
10.0ms	273×	body	80	nan
5.0ms	117×	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: 27.7b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b	(- (* b b) (* (* 4.0 a) c))
27.7b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite23.0ms

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

series298.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
103.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
47.0ms	(- (* b b) (* (* 4.0 a) c))
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify122.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (118.0ms)

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

prune79.0ms

Filtered

31 candidates to 27 candidates (87.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	28	3	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	29	3	32

Merged error: 0.3b

Counts

32 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

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

11.0ms	(/ (/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
6.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series451.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ (/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
76.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms	(- (* b b) (* (* 4.0 a) c))
183.0ms	(/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify41.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (34.0ms)

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

prune161.0ms

Filtered

51 candidates to 42 candidates (82.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	44	7	51
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	47	7	54

Merged error: 0.0b

Counts

54 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
20×	`associate-/r/`
15×	`*-commutative` `div-inv`
14×	`associate-/l/`
12×	`associate-/l*`
7×	`frac-2neg` `clear-num`
6×	`flip3--` `flip--`
4×	`associate-/r*`
2×	`sub-neg`
1×	`associate--l-` `neg-sub0`

Counts

4 → 57

Calls

4 calls:

6.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms	(/ (/ (* 4.0 c) (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a)) (* 2.0 a))
5.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(/ (* 4.0 c) (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a))

series476.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
172.0ms	(/ (/ (* 4.0 c) (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a)) (* 2.0 a))
47.0ms	(- (* b b) (* (* 4.0 a) c))
184.0ms	(/ (* 4.0 c) (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a))

simplify57.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	436	689
1	1672	603
2	5001	590

prune199.0ms

Filtered

69 candidates to 57 candidates (82.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	64	5	69
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	69	7	76

Merged error: 0.0b

Counts

76 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-commutative`
10×	`times-frac`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
5×	`associate-/l*`
3×	`neg-mul-1`
2×	`flip3--` `flip3-+` `sqrt-div` `associate-l/` `associate-/r` `associate-/r/` `flip--` `flip-+`
1×	`+-commutative` `neg-sub0` `sub-neg` `frac-2neg` `pow1/2` `div-sub` `distribute-frac-neg` `clear-num` `div-inv`

Counts

4 → 34

Calls

4 calls:

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

series367.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
175.0ms	(/ (- (* 4.0 c)) (* (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))) 2.0))
79.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(- (* b b) (* (* 4.0 a) c))

simplify84.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (78.0ms)

Iter	Nodes	Cost
0	256	377
1	846	366
2	2969	357
3	5002	356

prune126.0ms

Filtered

46 candidates to 42 candidates (91.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	44	2	46
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	47	6	53

Merged error: 0b

Counts

53 → 6

regimes95.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	28
1	41	28
2	41	28

end0.0ms

sample1.5s

Algorithm

intervals

Results

349.0ms	4450×	body	160	valid
321.0ms	8870×	body	80	nan
319.0ms	16870×	pre	80	true
141.0ms	3550×	body	80	valid