Details

sample201.0ms

Algorithm

intervals

Results

15.0ms	187×	body	80	valid
14.0ms	29×	body	2560	valid
10.0ms	25×	body	1280	valid
10.0ms	103×	body	80	nan
5.0ms	16×	body	640	valid
3.0ms	5×	body	5120	valid
1.0ms	7×	body	320	valid
1.0ms	4×	body	160	valid

simplify100.0ms

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

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize32.0ms

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))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite237.0ms

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)
16.0ms	(- (* b_2 b_2) (* a c))
107.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series442.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
37.0ms	(- (* b_2 b_2) (* a c))
133.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
131.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify825.0ms

Counts

96 → 96

Iterations

Useful iterations: done (821.0ms)

Iter	Nodes	Cost
0	154	1624
1	384	1534
2	1453	1428
done	5001	1420

prune537.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.8b	(- (* b_2 b_2) (* a c))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite160.0ms

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:

62.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
8.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series475.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
63.0ms	(- (* b_2 b_2) (* a c))
97.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
98.0ms	(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	640	3493
2	3061	3359
done	5000	3142

prune604.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.9b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.8b	(- (* b_2 b_2) (* a c))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite314.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

191.0ms	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
8.0ms	(- (* b_2 b_2) (* a c))
92.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
56.0ms	(- (* b_2 b_2) (* a c))
90.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
72.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.5s

Counts

100 → 100

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	162	1633
1	439	1514
2	2222	1292
done	5001	1288

prune579.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.9b

localize18.0ms

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))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite220.0ms

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:

134.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
10.0ms	(- (* b_2 b_2) (* a c))
60.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series435.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
58.0ms	(- (* b_2 b_2) (* a c))
107.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
100.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify958.0ms

Counts

96 → 96

Iterations

Useful iterations: done (953.0ms)

Iter	Nodes	Cost
0	154	1624
1	384	1534
2	1453	1428
done	5001	1420

prune457.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.9b

regimes468.0ms

Accuracy

83.7% (4.6b remaining)

Error of 9.9b against oracle of 5.3b and baseline of 33.6b

bsearch103.0ms

Steps

Iters	Range		Point
8	3.480389350692124e-86	1.1787098984122044e-83	5.010211019078224e-85
2	-3.2729874464247947e+146	-2.930804953841758e+146	-2.973577765414638e+146

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	36
1	28	36
done	28	36

end0.0ms

sample3.1s

Algorithm

intervals

Results

895.0ms	919×	body	1280	valid
543.0ms	1074×	body	2560	valid
522.0ms	5853×	body	80	valid
272.0ms	2888×	body	80	nan
143.0ms	458×	body	640	valid
59.0ms	112×	body	5120	valid
38.0ms	209×	body	320	valid
13.0ms	107×	body	160	valid