Details

sample74.0ms

Algorithm

intervals

Results

14.0ms	516×	pre	80	true
13.0ms	148×	body	160	valid
12.0ms	260×	body	80	nan
6.0ms	42×	body	320	valid
3.0ms	66×	body	80	valid

simplify106.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	86	16
4	108	16
5	116	16
done	116	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.1b	(- (* b b) (* (* 4.0 a) c))
37.2b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`prod-diff`
18×	`sqrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg`
6×	`times-frac` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 106

Calls

4 calls:

22.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
137.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
13.0ms	(- (* b b) (* (* 4.0 a) c))
52.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series445.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
183.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
58.0ms	(- (* b b) (* (* 4.0 a) c))
112.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify1.4s

Counts

118 → 118

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	195	2476
1	480	2169
2	1446	1861
done	5000	1789

prune406.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 5.0b

localize4.0ms

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

prune70.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 5.0b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log` `add-cbrt-cube`
14×	`cbrt-undiv` `div-exp`
13×	`prod-exp` `cbrt-unprod`
4×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `times-frac` `associate-/r`
2×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
1×	`associate-*r/` `associate-/l/`

Counts

2 → 55

Calls

2 calls:

27.0ms	(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
22.0ms	(/ (* a c) b)

series76.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
37.0ms	(/ (* a c) b)

simplify916.0ms

Counts

61 → 61

Iterations

Useful iterations: 2 (307.0ms)

Iter	Nodes	Cost
0	111	818
1	314	787
2	1661	559
done	5001	559

prune207.0ms

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 5.0b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
44×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
39×	`add-exp-log` `add-cbrt-cube`
17×	`cbrt-undiv` `div-exp`
14×	`associate-/r*`
10×	`prod-exp` `cbrt-unprod`
6×	`div-inv`
4×	`associate-/l*`
2×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
1×	`associate-*r/` `associate-/r/` `associate-/l/`

Counts

2 → 104

Calls

2 calls:

43.0ms	(/ (* -2.0 (/ a (/ b c))) (* 2.0 a))
11.0ms	(/ a (/ b c))

series70.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(/ (* -2.0 (/ a (/ b c))) (* 2.0 a))
47.0ms	(/ a (/ b c))

simplify1.5s

Counts

110 → 110

Iterations

Useful iterations: 2 (532.0ms)

Iter	Nodes	Cost
0	214	1514
1	517	1423
2	2105	1185
done	5001	1185

prune250.0ms

Pruning

32 alts after pruning (31 fresh and 1 done)

Merged error: 5.0b

regimes557.0ms

Accuracy

13.5% (6.2b remaining)

Error of 11.4b against oracle of 5.2b and baseline of 12.3b

bsearch81.0ms

Steps

Iters	Range		Point
6	0.0015991185291722328	0.0064842211682737015	0.0016145486991948593

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	38
1	27	38
done	27	38

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.2s	16379×	pre	80	true
840.0ms	4832×	body	160	valid
771.0ms	8379×	body	80	nan
309.0ms	1311×	body	320	valid
164.0ms	1857×	body	80	valid