Details

sample57.0ms

Algorithm

intervals

Results

11.0ms	30×	body	1280	valid
10.0ms	36×	body	2560	valid
10.0ms	187×	body	80	valid
3.0ms	79×	body	80	nan
2.0ms	10×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify16.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	44
4	44
3	41
2	32
1	18
0	10

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 91

Calls

4 calls:

57.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
6.0ms	(- (* b_2 b_2) (* a c))
19.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series404.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
56.0ms	(- (* b_2 b_2) (* a c))
130.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
80.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify797.0ms

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	1527
1	392
0	158

prune439.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.4b	(- (* b_2 b_2) (* a c))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

165×	`times-frac`
130×	`add-sqr-sqrt`
129×	`*-un-lft-identity`
77×	`add-cube-cbrt`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`add-cbrt-cube` `associate-/r/`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`rec-exp` `sub-neg` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `pow-flip` `inv-pow`

Counts

4 → 177

Calls

4 calls:

43.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
12.0ms	(- (* b_2 b_2) (* a c))
43.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series420.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
43.0ms	(- (* b_2 b_2) (* a c))
118.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
95.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.5s

Counts

189 → 189

Iterations

Iter	Nodes
done	5000
2	3515
1	665
0	266

prune576.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.8b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.4b	(- (* b_2 b_2) (* a c))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

897×	`times-frac`
528×	`add-sqr-sqrt`
527×	`*-un-lft-identity`
355×	`add-cube-cbrt`
86×	`distribute-lft-out--` `difference-of-squares`
46×	`sqrt-prod`
44×	`add-exp-log`
43×	`distribute-rgt-neg-in` `div-inv`
32×	`div-exp`
29×	`associate-/r/`
27×	`associate-/r*`
17×	`flip3--` `flip--`
16×	`add-cbrt-cube`
13×	`associate-/l*`
10×	`add-log-exp`
8×	`cbrt-undiv` `rec-exp` `1-exp`
5×	`pow1`
3×	`diff-log`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 468

Calls

4 calls:

93.0ms	(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
20.0ms	(- (* b_2 b_2) (* a c))
23.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series380.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
55.0ms	(- (* b_2 b_2) (* a c))
99.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
83.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

480 → 480

Iterations

Iter	Nodes
done	5000
1	2051
0	595

prune854.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.8b

localize55.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt a)
0.5b	(* (cbrt a) (cbrt a))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
19×	`cbrt-prod`
18×	`*-un-lft-identity`
14×	`add-cube-cbrt`
12×	`pow1`
8×	`add-log-exp`
7×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `sqrt-prod` `unswap-sqr`
2×	`flip3--` `sqrt-div` `diff-log` `pow-prod-down` `pow-sqr` `pow-prod-up` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `pow2` `neg-sub0` `rem-sqrt-square` `sub-neg` `distribute-rgt-neg-in` `sqrt-pow1` `pow-plus` `pow1/2` `neg-log` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 84

Calls

4 calls:

1.0ms	(cbrt a)
17.0ms	(* (cbrt a) (cbrt a))
25.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series1.2s

Counts

4 → 12

Calls

4 calls:

639.0ms	(cbrt a)
338.0ms	(* (cbrt a) (cbrt a))
104.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
112.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.0s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
2	1595
1	342
0	142

prune520.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 4.8b

regimes472.0ms

Accuracy

85.1% (4.2b remaining)

Error of 10.0b against oracle of 5.8b and baseline of 34.2b

bsearch334.0ms

Steps

Iters	Range		Point
9	3.768382185355077e+69	1.107955803311012e+78	7.501979458872916e+77
6	-6.6625002027150184e-136	-1.2670716760605177e-136	-6.596302400897662e-136
9	-1.3974083100475422e-87	-7.780761669250176e-94	-7.877985662156599e-94
10	-4.6999773453873415e+54	-3.4259522644792056e+40	-5.84038254482515e+46

simplify9.0ms

Iterations

Iter	Nodes
done	41
2	41
1	40
0	35

end0.0ms

sample2.8s

Algorithm

intervals

Results

918.0ms	5896×	body	80	valid
630.0ms	1048×	body	2560	valid
246.0ms	877×	body	1280	valid
201.0ms	2811×	body	80	nan
124.0ms	446×	body	640	valid
97.0ms	121×	body	5120	valid
38.0ms	229×	body	320	valid
12.0ms	105×	body	160	valid