Details

sample46.0ms

Algorithm

intervals

Results

10.0ms	152×	body	160	valid
9.0ms	523×	pre	80	true
8.0ms	267×	body	80	nan
3.0ms	104×	body	80	valid

simplify43.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	12	17
1	21	17
2	41	16
3	75	16
4	87	16
5	95	16
done	95	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* b b) (* (* 3.0 a) c))
0.3b	(* (* 3.0 a) c)
0.4b	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
29.2b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
14×	`add-exp-log` `add-cbrt-cube`
13×	`*-un-lft-identity`
9×	`pow1`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`times-frac` `associate-/l*` `difference-of-squares`
4×	`prod-exp` `cbrt-unprod`
3×	`flip3--` `associate-r` `pow-prod-down` `sqrt-prod` `flip--` `distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `associate-/l/`
1×	`frac-2neg` `div-sub` `associate-l` `clear-num` `associate-/r` `-commutative` `div-inv`

Counts

4 → 75

Calls

4 calls:

2.0ms	(- (* b b) (* (* 3.0 a) c))
6.0ms	(* (* 3.0 a) c)
39.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
18.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

series246.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* (* 3.0 a) c))
19.0ms	(* (* 3.0 a) c)
104.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
77.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

simplify605.0ms

Counts

87 → 87

Iterations

Useful iterations: done (602.0ms)

Iter	Nodes	Cost
0	155	1464
1	402	1392
2	1586	1226
done	5000	1225

prune202.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.3b

localize3.0ms

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

prune36.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 9.3b

localize7.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ (* a c) b)
0.3b	(* -1.5 (/ (* a c) b))
0.4b	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log` `add-cbrt-cube`
17×	`prod-exp` `cbrt-unprod`
16×	`cbrt-undiv` `div-exp`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`times-frac` `associate-r`
5×	`pow1`
4×	`associate-/r*`
3×	`associate-l` `div-inv` `add-log-exp`
2×	`frac-2neg` `associate-r/` `clear-num` `associate-/l`
1×	`pow-prod-down` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

3 → 78

Calls

3 calls:

3.0ms	(/ (* a c) b)
8.0ms	(* -1.5 (/ (* a c) b))
8.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

series67.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(/ (* a c) b)
26.0ms	(* -1.5 (/ (* a c) b))
23.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

simplify776.0ms

Counts

87 → 87

Iterations

Useful iterations: 2 (167.0ms)

Iter	Nodes	Cost
0	123	1086
1	377	1045
2	2011	761
done	5000	761

prune167.0ms

Pruning

31 alts after pruning (30 fresh and 1 done)

Merged error: 9.2b

localize8.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ b (* a c)))
0.3b	(/ b (* a c))
0.3b	(* -1.5 (/ 1 (/ b (* a c))))
0.4b	(/ (* -1.5 (/ 1 (/ b (* a c)))) (* 3.0 a))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

161×	`add-exp-log`
77×	`add-cbrt-cube`
72×	`div-exp`
69×	`times-frac`
54×	`prod-exp`
44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
37×	`add-cube-cbrt`
32×	`cbrt-undiv`
26×	`associate-r`
22×	`cbrt-unprod`
12×	`rec-exp` `1-exp`
11×	`div-inv`
9×	`associate-/r*`
7×	`pow1` `associate-/l*`
4×	`add-log-exp`
3×	`frac-2neg` `associate-l` `clear-num` `unswap-sqr`
2×	`associate-*r/` `associate-/r/` `un-div-inv` `associate-/l/`
1×	`pow-flip` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 181

Calls

4 calls:

6.0ms	(/ 1 (/ b (* a c)))
3.0ms	(/ b (* a c))
20.0ms	(* -1.5 (/ 1 (/ b (* a c))))
15.0ms	(/ (* -1.5 (/ 1 (/ b (* a c)))) (* 3.0 a))

series84.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ 1 (/ b (* a c)))
19.0ms	(/ b (* a c))
27.0ms	(* -1.5 (/ 1 (/ b (* a c))))
15.0ms	(/ (* -1.5 (/ 1 (/ b (* a c)))) (* 3.0 a))

simplify850.0ms

Counts

193 → 193

Iterations

Useful iterations: 2 (302.0ms)

Iter	Nodes	Cost
0	238	2623
1	710	2141
2	2727	1639
done	5000	1639

prune227.0ms

Pruning

33 alts after pruning (32 fresh and 1 done)

Merged error: 9.2b

regimes512.0ms

Accuracy

40.7% (8.0b remaining)

Error of 17.1b against oracle of 9.0b and baseline of 22.6b

bsearch2.0ms

Steps

Iters	Range		Point
0	17.302597776335716	18.126688132261577	17.714642954298647

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	39
1	30	39
done	30	39

end0.0ms

sample1.3s

Algorithm

intervals

Results

304.0ms	16491×	pre	80	true
294.0ms	4519×	body	160	valid
266.0ms	8491×	body	80	nan
115.0ms	3481×	body	80	valid