Details

sample195.0ms

Algorithm

intervals

Results

17.0ms	30×	body	2560	valid
15.0ms	186×	body	80	valid
10.0ms	102×	body	80	nan
9.0ms	23×	body	1280	valid
4.0ms	14×	body	640	valid
3.0ms	5×	body	5120	valid
2.0ms	9×	body	320	valid
1.0ms	4×	body	160	valid

simplify22.0ms

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.6b	(- (* b_2 b_2) (* a c))
1.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite150.0ms

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:

82.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
6.0ms	(- (* b_2 b_2) (* a c))
45.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series456.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
68.0ms	(- (* b_2 b_2) (* a c))
115.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
102.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify695.0ms

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
2	1459
1	384
0	154

prune566.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (pow b_2 2) (* a c))) b_2)))
0.6b	(- (pow b_2 2) (* a c))
1.3b	(- (sqrt (- (pow b_2 2) (* a c))) b_2)
22.9b	(sqrt (- (pow b_2 2) (* a c)))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `sub-neg` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-flip` `inv-pow`

Counts

4 → 162

Calls

4 calls:

67.0ms	(/ 1 (/ a (- (sqrt (- (pow b_2 2) (* a c))) b_2)))
12.0ms	(- (pow b_2 2) (* a c))
54.0ms	(- (sqrt (- (pow b_2 2) (* a c))) b_2)
14.0ms	(sqrt (- (pow b_2 2) (* a c)))

series432.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(/ 1 (/ a (- (sqrt (- (pow b_2 2) (* a c))) b_2)))
65.0ms	(- (pow b_2 2) (* a c))
99.0ms	(- (sqrt (- (pow b_2 2) (* a c))) b_2)
71.0ms	(sqrt (- (pow b_2 2) (* a c)))

simplify1.3s

Counts

174 → 174

Iterations

Iter	Nodes
done	5000
2	3515
1	621
0	257

prune702.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (pow b_2 2) (* a c))) a)
0.6b	(- (pow b_2 2) (* a c))
5.5b	(- (/ (sqrt (- (pow b_2 2) (* a c))) a) (/ b_2 a))
22.9b	(sqrt (- (pow b_2 2) (* a c)))

rewrite156.0ms

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:

19.0ms	(/ (sqrt (- (pow b_2 2) (* a c))) a)
13.0ms	(- (pow b_2 2) (* a c))
110.0ms	(- (/ (sqrt (- (pow b_2 2) (* a c))) a) (/ b_2 a))
11.0ms	(sqrt (- (pow b_2 2) (* a c)))

series442.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (sqrt (- (pow b_2 2) (* a c))) a)
59.0ms	(- (pow b_2 2) (* a c))
149.0ms	(- (/ (sqrt (- (pow b_2 2) (* a c))) a) (/ b_2 a))
93.0ms	(sqrt (- (pow b_2 2) (* a c)))

simplify646.0ms

Counts

105 → 105

Iterations

Iter	Nodes
done	5001
2	1243
1	385
0	173

prune606.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.7b

localize42.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* c a))
13.1b	(- (* (sqrt (sqrt (- (* b_2 b_2) (* c a)))) (/ (sqrt (sqrt (- (* b_2 b_2) (* c a)))) a)) (/ b_2 a))
22.9b	(sqrt (- (* b_2 b_2) (* c a)))
22.9b	(sqrt (- (* b_2 b_2) (* c a)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

12×	`sqrt-div`
8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `flip3--` `add-cube-cbrt` `sqrt-prod` `flip--`
5×	`frac-sub`
4×	`add-cbrt-cube` `add-exp-log`
2×	`frac-times` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-l/` `associate-r/`
1×	`sub-div`

Counts

4 → 60

Calls

4 calls:

11.0ms	(- (* b_2 b_2) (* c a))
42.0ms	(- (* (sqrt (sqrt (- (* b_2 b_2) (* c a)))) (/ (sqrt (sqrt (- (* b_2 b_2) (* c a)))) a)) (/ b_2 a))
7.0ms	(sqrt (- (* b_2 b_2) (* c a)))
12.0ms	(sqrt (- (* b_2 b_2) (* c a)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (* b_2 b_2) (* c a))
122.0ms	(- (* (sqrt (sqrt (- (* b_2 b_2) (* c a)))) (/ (sqrt (sqrt (- (* b_2 b_2) (* c a)))) a)) (/ b_2 a))
80.0ms	(sqrt (- (* b_2 b_2) (* c a)))
83.0ms	(sqrt (- (* b_2 b_2) (* c a)))

simplify668.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
2	1322
1	338
0	128

prune449.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.7b

regimes486.0ms

Accuracy

84.2% (4.5b remaining)

Error of 10.0b against oracle of 5.5b and baseline of 34.1b

bsearch191.0ms

Steps

Iters	Range		Point
9	7.013128997607284e-77	5.714800893424793e-72	4.425266767149826e-76
8	-9.061058506829192e+105	-7.154008779742083e+102	-5.062954969806706e+105

simplify5.0ms

Iterations

Iter	Nodes
done	27
1	27
0	25

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.0s	1055×	body	2560	valid
421.0ms	5961×	body	80	valid
316.0ms	880×	body	1280	valid
248.0ms	2944×	body	80	nan
209.0ms	451×	body	640	valid
91.0ms	218×	body	320	valid
49.0ms	97×	body	5120	valid
14.0ms	109×	body	160	valid