Details

sample144.0ms

Algorithm

intervals

Results

40.0ms	559×	pre	80	true
26.0ms	159×	body	160	valid
26.0ms	303×	body	80	nan
11.0ms	44×	body	320	valid
4.0ms	53×	body	80	valid

simplify87.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	111
5	111
4	102
3	78
2	44
1	24
0	14

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.9b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* c a) 4.0)))
0.2b	(/ (/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0) a)
0.2b	(- (* b b) (* (* c a) 4.0))
38.3b	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)

rewrite512.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
121×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
68×	`add-cube-cbrt`
26×	`difference-of-squares`
22×	`associate-/l*`
16×	`sqrt-prod`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
5×	`pow1` `div-inv`
3×	`cbrt-undiv` `associate-/r*` `flip3--` `div-exp` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `div-sub`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 149

Calls

4 calls:

16.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
78.0ms	(/ (/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0) a)
362.0ms	(- (* b b) (* (* c a) 4.0))
43.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)

series463.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
171.0ms	(/ (/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0) a)
65.0ms	(- (* b b) (* (* c a) 4.0))
109.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)

simplify1.9s

Counts

161 → 161

Iterations

Iter	Nodes
done	5001
2	3070
1	693
0	280

prune1.0s

Pruning

15 alts after pruning (15 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

prune90.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 5.4b

localize26.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
0.3b	(/ (* a c) b)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
27×	`add-cbrt-cube` `add-exp-log`
20×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
13×	`cbrt-undiv` `div-exp`
8×	`associate-/l*`
6×	`associate-/r*` `div-inv`
5×	`prod-exp` `cbrt-unprod`
2×	`pow1` `clear-num` `frac-2neg` `add-log-exp`
1×	`associate-/l/`

Counts

2 → 73

Calls

2 calls:

19.0ms	(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
7.0ms	(/ (* a c) b)

series63.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
22.0ms	(/ (* a c) b)

simplify1.7s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
2	3008
1	464
0	167

prune568.0ms

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 5.3b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (* -2.0 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) 2.0) a)
0.3b	(/ (* a c) b)
0.3b	(/ (* a c) b)
0.5b	(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

51×	`times-frac`
48×	`add-sqr-sqrt`
36×	`*-un-lft-identity` `add-cube-cbrt`
34×	`sqrt-prod`
30×	`add-cbrt-cube` `add-exp-log`
19×	`pow1`
12×	`swap-sqr`
11×	`cbrt-undiv` `div-exp` `div-inv`
10×	`associate-r` `associate-l`
9×	`associate-/r` `associate-/l`
8×	`sqrt-pow1` `pow1/2`
6×	`prod-exp` `cbrt-unprod`
5×	`pow-prod-up`
4×	`sqrt-div` `add-log-exp` `unswap-sqr`
3×	`clear-num` `frac-2neg` `pow-prod-down` `pow-sqr`
1×	`pow2` `frac-times` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `associate-l/` `associate-r/` `*-commutative` `associate-/l/`

Counts

4 → 156

Calls

4 calls:

90.0ms	(/ (/ (* -2.0 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) 2.0) a)
20.0ms	(/ (* a c) b)
14.0ms	(/ (* a c) b)
51.0ms	(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ (/ (* -2.0 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) 2.0) a)
35.0ms	(/ (* a c) b)
31.0ms	(/ (* a c) b)
93.0ms	(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))

simplify1.7s

Counts

168 → 168

Iterations

Iter	Nodes
done	5000
2	3671
1	577
0	231

prune763.0ms

Pruning

30 alts after pruning (28 fresh and 2 done)

Merged error: 5.3b

regimes917.0ms

Accuracy

8.2% (6.4b remaining)

Error of 11.4b against oracle of 5.0b and baseline of 12.0b

bsearch47.0ms

Steps

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

simplify5.0ms

Iterations

Iter	Nodes
done	32
1	32
0	26

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.1s	8177×	body	80	nan
945.0ms	4796×	body	160	valid
704.0ms	16177×	pre	80	true
428.0ms	1358×	body	320	valid
135.0ms	1846×	body	80	valid