Details

sample54.0ms

Algorithm

intervals

Results

13.0ms	553×	pre	80	true
10.0ms	163×	body	160	valid
9.0ms	297×	body	80	nan
4.0ms	39×	body	320	valid
2.0ms	54×	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: 45.2b

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))
41.3b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

rewrite69.0ms

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:

3.0ms	(- (* b b) (* (* 3.0 a) c))
7.0ms	(* (* 3.0 a) c)
40.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
18.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

series249.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* 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))
80.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

simplify824.0ms

Counts

87 → 87

Iterations

Useful iterations: done (822.0ms)

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

prune217.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.9b

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

prune33.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.9b

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite25.0ms

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)
11.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))
8.0ms	(* -1.5 (/ (* a c) b))

series66.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(/ (* a c) b)
20.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))
27.0ms	(* -1.5 (/ (* a c) b))

simplify722.0ms

Counts

87 → 87

Iterations

Useful iterations: 2 (181.0ms)

Iter	Nodes	Cost
0	123	1086
1	377	1045
2	1876	761
done	5001	761

prune166.0ms

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 4.9b

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 83

Calls

3 calls:

7.0ms	(* a (/ c b))
10.0ms	(* -1.5 (* a (/ c b)))
12.0ms	(/ (* -1.5 (* a (/ c b))) (* 3.0 a))

series67.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(* a (/ c b))
27.0ms	(* -1.5 (* a (/ c b)))
21.0ms	(/ (* -1.5 (* a (/ c b))) (* 3.0 a))

simplify809.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (210.0ms)

Iter	Nodes	Cost
0	139	1118
1	419	1071
2	2053	787
done	5001	787

prune124.0ms

Pruning

30 alts after pruning (29 fresh and 1 done)

Merged error: 4.9b

regimes388.0ms

Accuracy

13.9% (6.1b remaining)

Error of 11.1b against oracle of 5.0b and baseline of 12.1b

bsearch45.0ms

Steps

Iters	Range		Point
6	0.00017659738910379716	0.0013183985859660308	0.00017936624356974993

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

307.0ms	4846×	body	160	valid
290.0ms	16153×	pre	80	true
239.0ms	8153×	body	80	nan
126.0ms	1342×	body	320	valid
58.0ms	1812×	body	80	valid