Details

sample132.0ms

Algorithm

intervals

Results

18.0ms	36×	body	2560	valid
16.0ms	179×	body	80	valid
12.0ms	29×	body	1280	valid
6.0ms	79×	body	80	nan
5.0ms	14×	body	640	valid
2.0ms	8×	body	320	valid
2.0ms	3×	body	5120	valid
0.0ms	2×	body	160	valid

simplify86.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	10	13
1	14	13
2	22	12
3	25	12
4	27	12
5	29	12
done	29	12

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.6b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.6b	(- (* b_2 b_2) (* a c))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite231.0ms

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-exp-log` `add-cbrt-cube` `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` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 84

Calls

4 calls:

133.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
58.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms	(- (* b_2 b_2) (* a c))
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
95.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
47.0ms	(- (* b_2 b_2) (* a c))
80.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

96 → 96

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	154	1624
1	361	1526
2	928	1426
3	2333	1418
done	5000	1410

prune324.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.6b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.6b	(- (* b_2 b_2) (* a c))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite185.0ms

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-exp-log` `add-cbrt-cube` `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` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 84

Calls

4 calls:

87.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
72.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
10.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series358.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
88.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
43.0ms	(- (* b_2 b_2) (* a c))
110.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts

96 → 96

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	154	1624
1	361	1526
2	928	1426
3	2333	1418
done	5000	1410

prune380.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
0.6b	(- (* b_2 b_2) (* a c))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

17.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (* b_2 b_2) (* a c))
54.0ms	(- (* b_2 b_2) (* a c))
74.0ms	(sqrt (- (* b_2 b_2) (* a c)))
106.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts

66 → 66

Iterations

Useful iterations: 4 (1.2s)

Iter	Nodes	Cost
0	58	826
1	139	762
2	382	678
3	1046	678
4	2569	676
done	5001	676

prune348.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
0.6b	(cbrt a)
0.6b	(cbrt a)
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`

Counts

4 → 48

Calls

4 calls:

1.0ms	(cbrt a)
1.0ms	(cbrt a)
1.0ms	(cbrt a)
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series1.1s

Counts

4 → 12

Calls

4 calls:

363.0ms	(cbrt a)
348.0ms	(cbrt a)
273.0ms	(cbrt a)
74.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.9s

Counts

60 → 60

Iterations

Useful iterations: 4 (1.2s)

Iter	Nodes	Cost
0	71	434
1	159	395
2	411	359
3	988	350
4	2193	349
done	5001	349

prune263.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.2b

regimes352.0ms

Accuracy

84.2% (4.5b remaining)

Error of 10.3b against oracle of 5.8b and baseline of 34.3b

bsearch113.0ms

Steps

Iters	Range		Point
5	1.8656011488683937e-53	5.89324344694736e-53	1.8920981354719558e-53
8	-3.0008378519073826e+120	-1.7813274366303991e+117	-1.0062396840173395e+118

simplify8.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	27	40
1	35	36
done	35	36

end0.0ms

sample3.1s

Algorithm

intervals

Results

909.0ms	1024×	body	2560	valid
517.0ms	5910×	body	80	valid
376.0ms	872×	body	1280	valid
337.0ms	2916×	body	80	nan
228.0ms	467×	body	640	valid
60.0ms	125×	body	5120	valid
44.0ms	239×	body	320	valid
13.0ms	107×	body	160	valid