Details

sample99.0ms

Algorithm

intervals

Results

52.0ms	274×	body	80	valid
12.0ms	104×	body	80	nan

simplify159.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	151
7	151
6	150
5	143
4	131
3	103
2	61
1	35
0	20

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.6b

localize152.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `add-log-exp`
7×	`sqrt-prod`
6×	`pow1` `add-cube-cbrt`
4×	`add-cbrt-cube` `sqrt-div` `add-exp-log`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `sum-log` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `+-commutative` `sub-neg` `flip3-+` `associate-+l-` `flip-+`

Counts

4 → 63

Calls

4 calls:

38.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series445.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
128.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
104.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
106.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts

75 → 75

Iterations

Iter	Nodes
done	5001
3	3019
2	764
1	246
0	100

prune626.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.8b

localize239.0ms

Local error

Found 4 expressions with local error:

21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series423.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
94.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
102.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
97.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts

72 → 72

Iterations

Iter	Nodes
done	5002
3	1620
2	414
1	129
0	52

prune720.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.8b

localize230.0ms

Local error

Found 4 expressions with local error:

21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series424.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
98.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
116.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
102.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts

72 → 72

Iterations

Iter	Nodes
done	5002
3	1620
2	414
1	129
0	52

prune919.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.8b

localize334.0ms

Local error

Found 4 expressions with local error:

21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series392.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
80.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
105.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
126.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts

72 → 72

Iterations

Iter	Nodes
done	5002
3	1620
2	414
1	129
0	52

prune852.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.8b

regimes358.0ms

Accuracy

87.4% (1.6b remaining)

Error of 9.3b against oracle of 7.7b and baseline of 20.1b

bsearch330.0ms

Steps

Iters	Range		Point
8	5.631099529881209e+40	2.2779562270647888e+45	2.2352971002606818e+45
10	-8.897020078895062e+156	-1.101416214509623e+146	-1.329101530168951e+154

simplify29.0ms

Iterations

Iter	Nodes
done	57
1	57
0	46

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.1s	8684×	body	80	valid
787.0ms	2885×	body	80	nan