Details

sample145.0ms

Algorithm

intervals

Results

47.0ms	195×	body	80	valid
8.0ms	28×	body	2560	valid
7.0ms	34×	body	1280	valid
4.0ms	97×	body	80	nan
3.0ms	19×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify30.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	10	283
1	14	283
2	22	243
3	25	243
4	27	243
5	29	243
done	29	243

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.8b	(- (* b_2 b_2) (* a c))
0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite327.0ms

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

Counts

4 → 84

Calls

4 calls:

246.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
15.0ms	(- (* b_2 b_2) (* a c))
45.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series397.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
41.0ms	(- (* b_2 b_2) (* a c))
124.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
133.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.3s

Counts

96 → 96

Iterations

Useful iterations: 2 (303.0ms)

Iter	Nodes	Cost
0	154	33768
1	375	30653
2	1027	30453
3	4108	30453
done	5019	30453

prune567.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
0.8b	(- (* b_2 b_2) (* a c))
6.5b	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
21.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

13.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
6.0ms	(- (* b_2 b_2) (* a c))
89.0ms	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series328.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
37.0ms	(- (* b_2 b_2) (* a c))
90.0ms	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
67.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.9s

Counts

105 → 105

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	175	38088
1	395	34772
2	1004	34612
3	3156	34572
done	5014	34533

prune510.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))
0.8b	(- (* b_2 b_2) (* a c))
11.2b	(- (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)) (/ b_2 a))
21.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt`
13×	`times-frac` `associate-r` `add-exp-log`
10×	`sqrt-div`
9×	`add-cbrt-cube` `sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `flip3--` `flip--`
6×	`associate-l` `frac-sub` `unswap-sqr`
4×	`frac-times` `associate-*l/` `prod-exp`
3×	`associate-*r/` `un-div-inv`
2×	`sub-neg` `diff-log` `div-exp` `cbrt-unprod` `div-inv` `sub-div`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `distribute-rgt-out--` `pow1/2` `1-exp` `pow-prod-down` `*-commutative`

Counts

4 → 94

Calls

4 calls:

28.0ms	(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))
6.0ms	(- (* b_2 b_2) (* a c))
27.0ms	(- (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)) (/ b_2 a))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series414.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))
48.0ms	(- (* b_2 b_2) (* a c))
145.0ms	(- (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)) (/ b_2 a))
87.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify4.1s

Counts

106 → 106

Iterations

Useful iterations: 3 (2.3s)

Iter	Nodes	Cost
0	195	39334
1	511	33648
2	1448	31398
3	4567	31358
done	5049	31358

prune605.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.9b

localize36.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
16.5b	(- (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ a (sqrt (sqrt (- (* b_2 b_2) (* a c)))))) (/ b_2 a))
21.7b	(sqrt (- (* b_2 b_2) (* a c)))
21.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite514.0ms

Algorithm

rewrite-expression-head

Rules

115×	`add-sqr-sqrt`
57×	`times-frac`
48×	`sqrt-prod`
26×	`difference-of-squares`
12×	`*-un-lft-identity`
8×	`add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`
1×	`frac-sub`

Counts

4 → 83

Calls

4 calls:

12.0ms	(- (* b_2 b_2) (* a c))
469.0ms	(- (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ a (sqrt (sqrt (- (* b_2 b_2) (* a c)))))) (/ b_2 a))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series331.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (* b_2 b_2) (* a c))
109.0ms	(- (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ a (sqrt (sqrt (- (* b_2 b_2) (* a c)))))) (/ b_2 a))
89.0ms	(sqrt (- (* b_2 b_2) (* a c)))
79.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.7s

Counts

95 → 95

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	123	46985
1	302	44133
2	791	44013
3	2839	39693
done	5001	39693

prune449.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.9b

regimes504.0ms

Accuracy

80.2% (5.7b remaining)

Error of 11.6b against oracle of 5.9b and baseline of 34.4b

bsearch117.0ms

Steps

Iters	Range		Point
6	0.023031155523784402	0.1909160003853501	0.04537546925850253
7	-1.0039977798506215e+37	-1.0916525231587234e+35	-8.811095525294671e+36

simplify10.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	26	789
1	33	789
done	33	789

end0.0ms

sample2.7s

Algorithm

intervals

Results

881.0ms	5864×	body	80	valid
516.0ms	1041×	body	2560	valid
388.0ms	919×	body	1280	valid
235.0ms	2928×	body	80	nan
147.0ms	465×	body	640	valid
70.0ms	207×	body	320	valid
49.0ms	109×	body	5120	valid
13.0ms	118×	body	160	valid