Details

sample82.0ms

Algorithm

intervals

Results

21.0ms	120×	body	320	valid
11.0ms	517×	pre	80	true
11.0ms	261×	body	80	nan
8.0ms	96×	body	160	valid
3.0ms	14×	body	640	valid
1.0ms	26×	body	80	valid

simplify110.0ms

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	88	16
5	96	16
done	96	16

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 52.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0)
0.1b	(/ (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0) a)
0.3b	(* (* 3.0 a) c)
25.3b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

rewrite760.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
147×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
79×	`add-cube-cbrt`
34×	`difference-of-squares`
28×	`associate-/l*`
17×	`sqrt-prod` `distribute-lft-out--`
16×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`associate-/r*` `div-inv` `add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`div-sub` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `diff-log` `associate-l` `*-commutative`

Counts

4 → 182

Calls

4 calls:

146.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0)
135.0ms	(/ (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0) a)
26.0ms	(* (* 3.0 a) c)
432.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

series488.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0)
175.0ms	(/ (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0) a)
33.0ms	(* (* 3.0 a) c)
135.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

simplify1.9s

Counts

194 → 194

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	287	4775
1	689	4627
2	1984	4417
done	5000	4407

prune835.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.5b

localize8.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune43.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 2.5b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log` `add-cbrt-cube`
42×	`times-frac`
29×	`add-sqr-sqrt`
27×	`add-cube-cbrt` `*-un-lft-identity`
21×	`cbrt-undiv` `div-exp`
13×	`prod-exp` `cbrt-unprod`
9×	`associate-/r` `associate-/l`
8×	`div-inv`
7×	`associate-r`
6×	`pow1`
4×	`add-log-exp`
3×	`frac-2neg` `associate-l` `clear-num`
2×	`associate-*r/` `associate-/l/`
1×	`pow-prod-down` `*-commutative` `unswap-sqr`

Counts

4 → 126

Calls

4 calls:

22.0ms	(/ (* -1.5 (/ (* a c) b)) 3.0)
40.0ms	(/ (/ (* -1.5 (/ (* a c) b)) 3.0) a)
10.0ms	(/ (* a c) b)
33.0ms	(* -1.5 (/ (* a c) b))

series164.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (* -1.5 (/ (* a c) b)) 3.0)
31.0ms	(/ (/ (* -1.5 (/ (* a c) b)) 3.0) a)
31.0ms	(/ (* a c) b)
50.0ms	(* -1.5 (/ (* a c) b))

simplify1.0s

Counts

138 → 138

Iterations

Useful iterations: 2 (332.0ms)

Iter	Nodes	Cost
0	192	1856
1	482	1786
2	1836	1478
done	5000	1478

prune408.0ms

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 2.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* a c) b)
0.4b	(/ (/ (* a c) b) (sqrt 3.0))
0.4b	(* (/ -1.5 (sqrt 3.0)) (/ (/ (/ (* a c) b) (sqrt 3.0)) a))
1.0b	(/ -1.5 (sqrt 3.0))

rewrite302.0ms

Algorithm

rewrite-expression-head

Rules

443×	`times-frac`
239×	`add-sqr-sqrt`
192×	`add-cube-cbrt` `*-un-lft-identity`
142×	`associate-r`
115×	`sqrt-prod`
65×	`add-exp-log` `add-cbrt-cube`
33×	`div-inv`
31×	`cbrt-undiv` `div-exp`
22×	`associate-l`
15×	`associate-/r*`
14×	`prod-exp` `cbrt-unprod`
12×	`unswap-sqr`
11×	`associate-/l*`
6×	`pow1`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `associate-/l/`

Counts

4 → 340

Calls

4 calls:

20.0ms	(/ (* a c) b)
29.0ms	(/ (/ (* a c) b) (sqrt 3.0))
198.0ms	(* (/ -1.5 (sqrt 3.0)) (/ (/ (/ (* a c) b) (sqrt 3.0)) a))
10.0ms	(/ -1.5 (sqrt 3.0))

series446.0ms

Counts

4 → 10

Calls

4 calls:

35.0ms	(/ (* a c) b)
144.0ms	(/ (/ (* a c) b) (sqrt 3.0))
267.0ms	(* (/ -1.5 (sqrt 3.0)) (/ (/ (/ (* a c) b) (sqrt 3.0)) a))
0.0ms	(/ -1.5 (sqrt 3.0))

simplify1.1s

Counts

350 → 350

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	507	6012
1	1599	5470
done	5001	5120

prune1.1s

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 2.4b

regimes469.0ms

Accuracy

4.1% (3.5b remaining)

Error of 6.2b against oracle of 2.7b and baseline of 6.3b

bsearch99.0ms

Steps

Iters	Range		Point
8	3.0026527018200954e-17	2.4173674189391156e-14	3.0547987684067384e-17

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	39
1	24	39
done	24	39

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.3s	3623×	body	320	valid
706.0ms	8232×	body	80	nan
593.0ms	16232×	pre	80	true
518.0ms	2910×	body	160	valid
236.0ms	529×	body	640	valid
158.0ms	938×	body	80	valid