Details

sample218.0ms

Algorithm

intervals

Results

18.0ms	196×	body	80	valid
13.0ms	27×	body	2560	valid
13.0ms	32×	body	1280	valid
7.0ms	91×	body	80	nan
4.0ms	15×	body	640	valid
4.0ms	5×	body	5120	valid
1.0ms	4×	body	160	valid
1.0ms	3×	body	320	valid

simplify51.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (17.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b	(- (* b_2 b_2) (* a c))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite223.0ms

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:

112.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
83.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
88.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
50.0ms	(- (* b_2 b_2) (* a c))
126.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify886.0ms

Counts

96 → 96

Iterations

Useful iterations: done (879.0ms)

Iter	Nodes	Cost
0	154	1624
1	383	1534
2	1457	1428
done	5001	1420

prune384.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b	(- (* b_2 b_2) (* a c))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite227.0ms

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×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `inv-pow`

Counts

4 → 162

Calls

4 calls:

101.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
81.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series411.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
87.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
48.0ms	(- (* b_2 b_2) (* a c))
75.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

174 → 174

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	258	3976
1	641	3493
2	3068	3359
done	5001	3142

prune358.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b	(- (* b_2 b_2) (* a c))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite228.0ms

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:

127.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
70.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms	(- (* b_2 b_2) (* a c))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series406.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
128.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
55.0ms	(- (* b_2 b_2) (* a c))
79.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify975.0ms

Counts

96 → 96

Iterations

Useful iterations: done (970.0ms)

Iter	Nodes	Cost
0	154	1624
1	383	1534
2	1457	1428
done	5001	1420

prune300.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.6b

localize56.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

16.0ms	(- (* b_2 b_2) (* a c))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))
22.0ms	(sqrt (- (* b_2 b_2) (* a c)))
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (* b_2 b_2) (* a c))
111.0ms	(sqrt (- (* b_2 b_2) (* a c)))
96.0ms	(sqrt (- (* b_2 b_2) (* a c)))
96.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

69 → 69

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	58	891
1	155	805
2	554	727
3	2755	727
done	5002	727

prune402.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.6b

regimes335.0ms

Accuracy

85.2% (4.2b remaining)

Error of 10.0b against oracle of 5.7b and baseline of 34.4b

bsearch107.0ms

Steps

Iters	Range		Point
5	6.945766558749631e-52	1.7836275468166073e-51	8.70366778308292e-52
8	-1.5489453231745737e+155	-2.021963087226922e+151	-2.0907318212469142e+152

simplify5.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	26	38
1	33	36
2	34	36
done	34	36

end0.0ms

sample2.8s

Algorithm

intervals

Results

877.0ms	5751×	body	80	valid
487.0ms	1069×	body	2560	valid
327.0ms	918×	body	1280	valid
273.0ms	2906×	body	80	nan
151.0ms	494×	body	640	valid
81.0ms	239×	body	320	valid
47.0ms	111×	body	5120	valid
11.0ms	94×	body	160	valid