Details

sample51.0ms

Algorithm

intervals

Results

10.0ms	150×	body	160	valid
10.0ms	531×	pre	80	true
9.0ms	275×	body	80	nan
4.0ms	106×	body	80	valid

simplify55.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	45	16
3	87	16
4	106	16
5	114	16
done	114	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.3b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
29.4b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
135×	`add-sqr-sqrt`
108×	`*-un-lft-identity`
82×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
22×	`associate-/l*`
19×	`prod-diff`
13×	`distribute-lft-out--`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `div-sub`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 183

Calls

4 calls:

4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(- (* b b) (* (* 4.0 a) c))
38.0ms	(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
25.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series306.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
47.0ms	(- (* b b) (* (* 4.0 a) c))
106.0ms	(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
81.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify1.2s

Counts

195 → 195

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	321	4967
1	780	4592
2	3017	4265
done	5001	4264

prune513.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 9.1b

localize4.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify1.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune67.0ms

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 9.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
0.3b	(/ (* a c) b)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
27×	`add-exp-log` `add-cbrt-cube`
20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
13×	`cbrt-undiv` `div-exp`
8×	`associate-/l*`
6×	`associate-/r*` `div-inv`
5×	`prod-exp` `cbrt-unprod`
2×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
1×	`associate-/l/`

Counts

2 → 77

Calls

2 calls:

10.0ms	(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
3.0ms	(/ (* a c) b)

series41.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
20.0ms	(/ (* a c) b)

simplify788.0ms

Counts

83 → 83

Iterations

Useful iterations: 2 (163.0ms)

Iter	Nodes	Cost
0	171	1200
1	459	1154
2	2303	992
done	5001	992

prune237.0ms

Pruning

36 alts after pruning (35 fresh and 1 done)

Merged error: 9.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ 1 (/ b (* a c)))
0.3b	(/ b (* a c))
0.3b	(/ (/ (* -2.0 (/ 1 (/ b (* a c)))) 2.0) a)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-exp-log`
69×	`times-frac`
49×	`div-exp`
44×	`add-cbrt-cube`
37×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
23×	`cbrt-undiv`
17×	`prod-exp`
13×	`associate-/l*`
11×	`associate-/r*` `div-inv`
7×	`cbrt-unprod`
6×	`rec-exp` `1-exp`
4×	`pow1`
3×	`expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
1×	`pow-flip` `associate-/r/` `associate-/l/` `inv-pow`

Counts

3 → 143

Calls

3 calls:

7.0ms	(/ 1 (/ b (* a c)))
3.0ms	(/ b (* a c))
17.0ms	(/ (/ (* -2.0 (/ 1 (/ b (* a c)))) 2.0) a)

series61.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(/ 1 (/ b (* a c)))
24.0ms	(/ b (* a c))
16.0ms	(/ (/ (* -2.0 (/ 1 (/ b (* a c)))) 2.0) a)

simplify1.6s

Counts

152 → 152

Iterations

Useful iterations: 2 (286.0ms)

Iter	Nodes	Cost
0	266	2208
1	707	2029
2	3221	1559
done	5000	1559

prune220.0ms

Pruning

41 alts after pruning (41 fresh and 0 done)

Merged error: 9.0b

regimes507.0ms

Accuracy

39.3% (8.4b remaining)

Error of 17.3b against oracle of 8.9b and baseline of 22.8b

bsearch4.0ms

Steps

Iters	Range		Point
0	17.302597776335716	18.126688132261577	17.714642954298647

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	27	46
1	33	44
done	33	44

end0.0ms

sample1.4s

Algorithm

intervals

Results

313.0ms	4493×	body	160	valid
302.0ms	16612×	pre	80	true
301.0ms	8612×	body	80	nan
128.0ms	3507×	body	80	valid