Details

sample112.0ms

Algorithm

intervals

Results

34.0ms	159×	body	160	valid
18.0ms	266×	body	80	nan
16.0ms	522×	pre	80	true
9.0ms	37×	body	320	valid
4.0ms	60×	body	80	valid

simplify126.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	98
7	98
6	97
5	95
4	87
3	72
2	42
1	24
0	14

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.4b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* c a) 4.0)))
0.2b	(- (* b b) (* (* c a) 4.0))
0.2b	(/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) a)
39.6b	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 84

Calls

4 calls:

13.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
9.0ms	(- (* b b) (* (* c a) 4.0))
96.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) a)
59.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)

series410.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
59.0ms	(- (* b b) (* (* c a) 4.0))
148.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) a)
129.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)

simplify1.2s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
2	1179
1	391
0	158

prune658.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.1b

localize14.0ms

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

prune109.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.1b

localize27.0ms

Local error

Found 2 expressions with local error:

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

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 47

Calls

2 calls:

21.0ms	(/ (* a c) b)
30.0ms	(/ (* -2.0 (/ (* a c) b)) a)

series51.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(/ (* a c) b)
28.0ms	(/ (* -2.0 (/ (* a c) b)) a)

simplify1.3s

Counts

53 → 53

Iterations

Iter	Nodes
done	5005
2	1483
1	273
0	97

prune531.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 6.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

8.0ms	(/ (* a c) b)
9.0ms	(/ (* a c) b)
135.0ms	(/ (* -2.0 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) a)
58.0ms	(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))

series203.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (* a c) b)
36.0ms	(/ (* a c) b)
66.0ms	(/ (* -2.0 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) a)
70.0ms	(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))

simplify1.5s

Counts

144 → 144

Iterations

Iter	Nodes
done	5012
2	1616
1	398
0	164

prune767.0ms

Pruning

25 alts after pruning (23 fresh and 2 done)

Merged error: 6.0b

regimes777.0ms

Accuracy

10.7% (6.0b remaining)

Error of 11.1b against oracle of 5.1b and baseline of 11.8b

bsearch44.0ms

Steps

Iters	Range		Point
3	0.03179800884184028	0.046932425441303355	0.03274390987930672

simplify7.0ms

Iterations

Iter	Nodes
done	34
1	34
0	26

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.0s	4857×	body	160	valid
935.0ms	16410×	pre	80	true
800.0ms	8410×	body	80	nan
399.0ms	1385×	body	320	valid
208.0ms	1758×	body	80	valid