Details

sample61.0ms

Algorithm

intervals

Results

29.0ms	276×	body	80	valid
7.0ms	78×	body	80	nan

simplify98.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	20	38
1	35	38
2	65	37
3	115	37
4	138	37
5	151	37
6	152	37
done	152	37

prune13.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 18.2b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
1.7b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-log-exp`
7×	`sqrt-prod`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `difference-of-squares`
1×	`distribute-lft-out--`

Counts

4 → 57

Calls

4 calls:

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

series73.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (* b b) (* (* 4.0 a) c))
17.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
30.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify787.0ms

Counts

69 → 69

Iterations

Useful iterations: 3 (222.0ms)

Iter	Nodes	Cost
0	91	1130
1	205	1004
2	681	944
3	2362	936
done	5000	936

prune202.0ms

Filtered

54 candidates to 69 candidates (-27.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	61	8	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	8	70

Merged error: 8.2b

Counts

70 → 8

localize29.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`sqrt-prod`
9×	`*-un-lft-identity`
7×	`pow1` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`difference-of-squares`
1×	`sub-neg` `diff-log` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

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

series68.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify713.0ms

Counts

72 → 72

Iterations

Useful iterations: 3 (182.0ms)

Iter	Nodes	Cost
0	81	1195
1	186	1036
2	593	994
3	1938	984
done	5001	984

prune255.0ms

Filtered

58 candidates to 72 candidates (-24.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	71	9	80

Merged error: 8.2b

Counts

80 → 9

localize37.0ms

Local error

Found 4 expressions with local error:

21.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `flip--` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify656.0ms

Counts

72 → 72

Iterations

Useful iterations: 3 (133.0ms)

Iter	Nodes	Cost
0	53	1140
1	127	1012
2	427	940
3	1537	932
done	5001	932

prune363.0ms

Filtered

60 candidates to 72 candidates (-20.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	72	9	81

Merged error: 8.2b

Counts

81 → 9

localize27.0ms

Local error

Found 4 expressions with local error:

11.0b	(- (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) b)
21.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod` `add-log-exp`
5×	`pow1`
4×	`add-exp-log` `cbrt-div` `flip3--` `add-cbrt-cube` `flip--`
3×	`sqrt-prod`
2×	`pow1/3` `sqrt-div`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 53

Calls

4 calls:

10.0ms	(- (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) b)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series113.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) b)
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
28.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
32.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify950.0ms

Counts

65 → 65

Iterations

Useful iterations: 3 (317.0ms)

Iter	Nodes	Cost
0	151	1492
1	348	1412
2	1044	1194
3	3356	1147
done	5000	1147

prune216.0ms

Filtered

56 candidates to 65 candidates (-16.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	64	10	74

Merged error: 8.2b

Counts

74 → 10

regimes328.0ms

Accuracy

91.7% (1.0b remaining)

Error of 9.0b against oracle of 8.0b and baseline of 20.3b

bsearch70.0ms

Steps

Iters	Range		Point
6	1.1487243557305423e+102	6.148420459531844e+102	1.1692565862096847e+102
9	-1.589409284886386e+110	-1.5966504054646543e+104	-1.5601353151121372e+110

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	132
1	47	132
done	47	132

end0.0ms

sample1.7s

Algorithm

intervals

Results

877.0ms	8720×	body	80	valid
282.0ms	2972×	body	80	nan

Details

sample61.0ms

simplify98.0ms

prune13.0ms

localize24.0ms

rewrite25.0ms

series73.0ms

simplify787.0ms

prune202.0ms

localize29.0ms

rewrite23.0ms

series68.0ms

simplify713.0ms

prune255.0ms

localize37.0ms

rewrite20.0ms

series66.0ms

simplify656.0ms

prune363.0ms

localize27.0ms

rewrite24.0ms

series113.0ms

simplify950.0ms

prune216.0ms

regimes328.0ms

bsearch70.0ms

simplify4.0ms

end0.0ms

sample1.7s

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