Details

sample109.0ms

Algorithm

intervals

Results

31.0ms	160×	body	160	valid
20.0ms	302×	body	80	nan
17.0ms	558×	pre	80	true
9.0ms	44×	body	320	valid
3.0ms	52×	body	80	valid

simplify86.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	104
5	104
4	96
3	76
2	41
1	21
0	12

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* 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))
38.3b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
14×	`add-cbrt-cube` `add-exp-log`
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×	`clear-num` `associate-/r` `frac-2neg` `div-sub` `associate-l` `-commutative` `div-inv`

Counts

4 → 75

Calls

4 calls:

9.0ms	(- (* b b) (* (* 3.0 a) c))
13.0ms	(* (* 3.0 a) c)
89.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
39.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

series356.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (* b b) (* (* 3.0 a) c))
21.0ms	(* (* 3.0 a) c)
153.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
108.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

simplify1.7s

Counts

87 → 87

Iterations

Iter	Nodes
done	5000
2	2483
1	428
0	155

prune536.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.4b

localize12.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune95.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 5.4b

localize29.0ms

Local error

Found 3 expressions with local error:

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

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 78

Calls

3 calls:

22.0ms	(* -1.5 (/ (* a c) b))
7.0ms	(/ (* a c) b)
18.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

series113.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(* -1.5 (/ (* a c) b))
33.0ms	(/ (* a c) b)
45.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

simplify1.6s

Counts

87 → 87

Iterations

Iter	Nodes
done	5000
2	2793
1	391
0	123

prune606.0ms

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 5.3b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

158×	`add-exp-log`
92×	`add-cbrt-cube`
70×	`div-exp`
53×	`prod-exp`
37×	`cbrt-undiv`
29×	`times-frac` `cbrt-unprod`
22×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
10×	`associate-/r*`
9×	`rec-exp` `1-exp`
8×	`div-inv`
7×	`pow1` `associate-r`
6×	`associate-*r/` `associate-/r/`
5×	`associate-/l*`
4×	`add-log-exp`
3×	`clear-num` `frac-2neg` `associate-l`
1×	`pow-prod-down` `*-commutative` `pow-flip` `inv-pow` `unswap-sqr`

Counts

4 → 154

Calls

4 calls:

15.0ms	(* -1.5 (/ (* a c) b))
43.0ms	(/ 1 (/ (* 3.0 a) (* -1.5 (/ (* a c) b))))
7.0ms	(/ (* a c) b)
16.0ms	(/ (* 3.0 a) (* -1.5 (/ (* a c) b)))

series127.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* -1.5 (/ (* a c) b))
36.0ms	(/ 1 (/ (* 3.0 a) (* -1.5 (/ (* a c) b))))
31.0ms	(/ (* a c) b)
23.0ms	(/ (* 3.0 a) (* -1.5 (/ (* a c) b)))

simplify2.1s

Counts

166 → 166

Iterations

Iter	Nodes
done	5000
2	4392
1	655
0	213

prune622.0ms

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 5.3b

regimes965.0ms

Accuracy

8.6% (6.4b remaining)

Error of 11.4b against oracle of 5.0b and baseline of 11.9b

bsearch41.0ms

Steps

Iters	Range		Point
4	6.789181744096528e-08	1.2662217397802895e-07	6.961131476357277e-08

simplify8.0ms

Iterations

Iter	Nodes
done	31
1	31
0	23

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.0s	16122×	pre	80	true
812.0ms	4806×	body	160	valid
606.0ms	8122×	body	80	nan
492.0ms	1832×	body	80	valid
285.0ms	1362×	body	320	valid