Details

sample54.0ms

Algorithm

intervals

Results

10.0ms	184×	body	80	valid
10.0ms	32×	body	2560	valid
8.0ms	31×	body	1280	valid
4.0ms	84×	body	80	nan
4.0ms	17×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify68.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0) a)
0.2b	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
1.4b	(- (* b b) (* (* c a) 4.0))
24.6b	(sqrt (- (* b b) (* (* c a) 4.0)))

rewrite196.0ms

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:

109.0ms	(/ (/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0) a)
61.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
7.0ms	(- (* b b) (* (* c a) 4.0))
11.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

series406.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ (/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0) a)
121.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
65.0ms	(- (* b b) (* (* c a) 4.0))
86.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

simplify1.9s

Counts

161 → 161

Iterations

Iter	Nodes
done	5001
2	3061
1	692
0	280

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize71.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* (* c a) 4.0))
1.4b	(- (* b b) (* (* c a) 4.0))
24.6b	(sqrt (- (* b b) (* (* c a) 4.0)))
24.6b	(sqrt (- (* b b) (* (* c a) 4.0)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 54

Calls

4 calls:

12.0ms	(- (* b b) (* (* c a) 4.0))
8.0ms	(- (* b b) (* (* c a) 4.0))
7.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
7.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- (* b b) (* (* c a) 4.0))
79.0ms	(- (* b b) (* (* c a) 4.0))
104.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
86.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

simplify3.0s

Counts

66 → 66

Iterations

Iter	Nodes
done	5001
3	4732
2	725
1	165
0	62

prune542.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.8b

localize86.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* (* c a) 4.0))
24.6b	(sqrt (- (* b b) (* (* c a) 4.0)))
24.6b	(sqrt (- (* b b) (* (* c a) 4.0)))
24.6b	(sqrt (- (* b b) (* (* c a) 4.0)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
4×	`flip3--` `add-cbrt-cube` `add-exp-log` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `diff-log`

Counts

4 → 57

Calls

4 calls:

6.0ms	(- (* b b) (* (* c a) 4.0))
7.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
11.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
23.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

series349.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* b b) (* (* c a) 4.0))
105.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
93.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
99.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

simplify3.0s

Counts

69 → 69

Iterations

Iter	Nodes
done	5001
3	4732
2	725
1	165
0	62

prune555.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.8b

localize85.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* (* c a) 4.0))
24.6b	(sqrt (- (* b b) (* (* c a) 4.0)))
24.6b	(sqrt (- (* b b) (* (* c a) 4.0)))
24.6b	(sqrt (- (* b b) (* (* c a) 4.0)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
4×	`flip3--` `add-cbrt-cube` `add-exp-log` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `diff-log`

Counts

4 → 57

Calls

4 calls:

6.0ms	(- (* b b) (* (* c a) 4.0))
7.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
7.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
7.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

series726.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (* b b) (* (* c a) 4.0))
124.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
123.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
422.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

simplify2.6s

Counts

69 → 69

Iterations

Iter	Nodes
done	5001
3	4732
2	725
1	165
0	62

prune503.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 4.8b

regimes333.0ms

Accuracy

84.1% (4.6b remaining)

Error of 10.7b against oracle of 6.2b and baseline of 34.7b

bsearch158.0ms

Steps

Iters	Range		Point
8	2.8373581988670566e-35	2.2677514638291856e-31	2.8983489306952693e-35
10	-2.0003538938970096e+122	-1.6569790030408257e+112	-5.6179139475653e+116

simplify6.0ms

Iterations

Iter	Nodes
done	32
1	32
0	28

end0.0ms

sample2.6s

Algorithm

intervals

Results

568.0ms	2881×	body	80	nan
554.0ms	5835×	body	80	valid
426.0ms	1040×	body	2560	valid
406.0ms	906×	body	1280	valid
112.0ms	456×	body	640	valid
107.0ms	102×	body	5120	valid
80.0ms	232×	body	320	valid
17.0ms	116×	body	160	valid