Details

sample78.0ms

Algorithm

intervals

Results

15.0ms	32×	body	2560	valid
14.0ms	184×	body	80	valid
12.0ms	31×	body	1280	valid
6.0ms	84×	body	80	nan
5.0ms	17×	body	640	valid
2.0ms	3×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify87.0ms

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

localize29.0ms

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)))

rewrite199.0ms

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:

115.0ms	(/ (/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0) a)
63.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
6.0ms	(- (* b b) (* (* c a) 4.0))
7.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

series428.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(/ (/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0) a)
111.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
65.0ms	(- (* b b) (* (* c a) 4.0))
99.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

simplify1.9s

Counts

161 → 161

Iterations

Iter	Nodes
done	5001
2	3061
1	692
0	280

prune918.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize37.0ms

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)))

rewrite35.0ms

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:

6.0ms	(- (* b b) (* (* c a) 4.0))
14.0ms	(- (* b b) (* (* c a) 4.0))
7.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
7.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

series303.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* b b) (* (* c a) 4.0))
51.0ms	(- (* b b) (* (* c a) 4.0))
103.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
97.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

simplify2.6s

Counts

66 → 66

Iterations

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

prune622.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.8b

localize62.0ms

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)))

rewrite28.0ms

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)))

series341.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (* b b) (* (* c a) 4.0))
76.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
94.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
96.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

simplify2.9s

Counts

69 → 69

Iterations

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

prune602.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.8b

localize107.0ms

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)))

rewrite33.0ms

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:

10.0ms	(- (* 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)))

series427.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (* b b) (* (* c a) 4.0))
124.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
107.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
125.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

simplify3.2s

Counts

69 → 69

Iterations

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

prune609.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 4.8b

regimes476.0ms

Accuracy

84.1% (4.6b remaining)

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

bsearch239.0ms

Steps

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

simplify12.0ms

Iterations

Iter	Nodes
done	32
1	32
0	28

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.3s	1040×	body	2560	valid
566.0ms	5835×	body	80	valid
439.0ms	906×	body	1280	valid
281.0ms	2881×	body	80	nan
217.0ms	456×	body	640	valid
95.0ms	102×	body	5120	valid
79.0ms	232×	body	320	valid
17.0ms	116×	body	160	valid