Details

sample49.0ms

Algorithm

intervals

Results

10.0ms	157×	body	160	valid
9.0ms	506×	pre	80	true
8.0ms	250×	body	80	nan
5.0ms	52×	body	320	valid
2.0ms	47×	body	80	valid

simplify48.0ms

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: 46.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 3.0 a) c))
0.3b	(* (* 3.0 a) c)
0.3b	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
40.3b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

rewrite65.0ms

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)
34.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
20.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

series257.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b b) (* (* 3.0 a) c))
20.0ms	(* (* 3.0 a) c)
105.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
83.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

simplify1.0s

Counts

87 → 87

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	155	1464
1	402	1392
2	1577	1226
done	5000	1225

prune226.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.8b

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

prune29.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.8b

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite21.0ms

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:

7.0ms	(* -1.5 (/ (* a c) b))
3.0ms	(/ (* a c) b)
8.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

series69.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(* -1.5 (/ (* a c) b))
20.0ms	(/ (* a c) b)
20.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

simplify720.0ms

Counts

87 → 87

Iterations

Useful iterations: 2 (184.0ms)

Iter	Nodes	Cost
0	123	1086
1	377	1045
2	1876	761
done	5000	761

prune165.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 4.8b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-exp-log`
22×	`add-cbrt-cube`
20×	`div-exp`
19×	`prod-exp`
12×	`add-sqr-sqrt`
11×	`times-frac`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow-exp`
7×	`associate-r`
6×	`cbrt-undiv` `cbrt-unprod` `associate-/l*`
5×	`pow1`
4×	`associate-/r*`
3×	`associate-l` `div-inv` `add-log-exp`
2×	`pow-to-exp` `unpow-prod-down` `frac-2neg` `clear-num` `sqr-pow`
1×	`associate-r/` `pow-prod-down` `-commutative` `unswap-sqr`

Counts

3 → 83

Calls

3 calls:

10.0ms	(* -1.5 (/ (* a c) b))
3.0ms	(/ (* a c) b)
5.0ms	(/ (pow (* -1.5 (/ (* a c) b)) 1) (* 3.0 a))

series66.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(* -1.5 (/ (* a c) b))
18.0ms	(/ (* a c) b)
21.0ms	(/ (pow (* -1.5 (/ (* a c) b)) 1) (* 3.0 a))

simplify515.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (127.0ms)

Iter	Nodes	Cost
0	145	1148
1	353	991
2	1457	854
done	5000	854

prune144.0ms

Pruning

23 alts after pruning (21 fresh and 2 done)

Merged error: 4.8b

regimes336.0ms

Accuracy

13.4% (6.1b remaining)

Error of 11.1b against oracle of 5.0b and baseline of 12.0b

bsearch19.0ms

Steps

Iters	Range		Point
2	0.00025188901510240987	0.00029118470560064225	0.0002568009764146889

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample1.4s

Algorithm

intervals

Results

309.0ms	4807×	body	160	valid
302.0ms	16374×	pre	80	true
260.0ms	8374×	body	80	nan
136.0ms	1408×	body	320	valid
60.0ms	1785×	body	80	valid