Details

sample50.0ms

Algorithm

intervals

Results

10.0ms	568×	pre	80	true
10.0ms	312×	body	80	nan
9.0ms	137×	body	160	valid
4.0ms	119×	body	80	valid

simplify52.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

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: 27.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 3.0 a) c)
0.3b	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
0.3b	(- (* b b) (* (* 3.0 a) c))
27.3b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

rewrite66.0ms

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:

7.0ms	(* (* 3.0 a) c)
37.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
3.0ms	(- (* b b) (* (* 3.0 a) c))
18.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

series258.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (* 3.0 a) c)
109.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
48.0ms	(- (* b b) (* (* 3.0 a) c))
82.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

simplify944.0ms

Counts

87 → 87

Iterations

Useful iterations: done (941.0ms)

Iter	Nodes	Cost
0	155	1464
1	402	1392
2	1579	1226
done	5001	1225

prune227.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 9.8b

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

prune48.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 9.8b

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite23.0ms

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))
9.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

series72.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(/ (* a c) b)
28.0ms	(* -1.5 (/ (* a c) b))
25.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

simplify787.0ms

Counts

87 → 87

Iterations

Useful iterations: 2 (195.0ms)

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

prune185.0ms

Pruning

32 alts after pruning (31 fresh and 1 done)

Merged error: 9.7b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

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×	`add-cube-cbrt` `*-un-lft-identity`
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×	`frac-2neg` `associate-l` `clear-num`
1×	`pow-flip` `pow-prod-down` `*-commutative` `inv-pow` `unswap-sqr`

Counts

4 → 154

Calls

4 calls:

19.0ms	(/ 1 (/ (* 3.0 a) (* -1.5 (/ (* a c) b))))
3.0ms	(/ (* a c) b)
8.0ms	(* -1.5 (/ (* a c) b))
8.0ms	(/ (* 3.0 a) (* -1.5 (/ (* a c) b)))

series94.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ 1 (/ (* 3.0 a) (* -1.5 (/ (* a c) b))))
19.0ms	(/ (* a c) b)
29.0ms	(* -1.5 (/ (* a c) b))
21.0ms	(/ (* 3.0 a) (* -1.5 (/ (* a c) b)))

simplify1000.0ms

Counts

166 → 166

Iterations

Useful iterations: 2 (300.0ms)

Iter	Nodes	Cost
0	213	2646
1	593	2395
2	2433	1803
done	5000	1803

prune176.0ms

Pruning

36 alts after pruning (35 fresh and 1 done)

Merged error: 9.7b

regimes605.0ms

Accuracy

47.5% (7.2b remaining)

Error of 16.2b against oracle of 9.1b and baseline of 22.7b

bsearch2.0ms

Steps

Iters	Range		Point
0	3187.1734153117472	3187.188536646724	3187.1809759792354

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample1.3s

Algorithm

intervals

Results

310.0ms	16640×	pre	80	true
283.0ms	4488×	body	160	valid
272.0ms	8640×	body	80	nan
118.0ms	3511×	body	80	valid
0.0ms	1×	body	320	valid