Details

sample129.0ms

Algorithm

intervals

Results

16.0ms	190×	body	80	valid
14.0ms	36×	body	2560	valid
8.0ms	28×	body	1280	valid
6.0ms	92×	body	80	nan
4.0ms	16×	body	640	valid
2.0ms	7×	body	320	valid
1.0ms	1×	body	5120	valid
0.0ms	3×	body	160	valid

simplify101.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	10	13
1	15	13
2	23	12
3	30	12
4	32	12
5	34	12
done	34	12

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.2b	(- (* b_2 b_2) (* a c))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`fma-neg`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
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 → 118

Calls

4 calls:

131.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
9.0ms	(- (* b_2 b_2) (* a c))
76.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series396.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
47.0ms	(- (* b_2 b_2) (* a c))
109.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
103.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.3s

Counts

130 → 130

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	195	2408
1	453	2113
2	1107	1874
3	3402	1795
done	5000	1785

prune543.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b_2 b_2) (* a c))
0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
137×	`add-sqr-sqrt`
110×	`*-un-lft-identity`
84×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
24×	`associate-/r*`
19×	`prod-diff`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `fma-neg` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
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 → 196

Calls

4 calls:

9.0ms	(- (* b_2 b_2) (* a c))
112.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
68.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (* b_2 b_2) (* a c))
177.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
98.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
104.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.9s

Counts

208 → 208

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	299	4764
1	641	4074
2	1436	3649
3	4234	3500
done	5000	3500

prune450.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
0.2b	(- (* b_2 b_2) (* a c))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite296.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
27×	`add-cube-cbrt`
19×	`prod-diff`
17×	`sqrt-prod`
13×	`add-exp-log` `associate-r`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1` `fma-neg`
6×	`associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `difference-of-squares`
3×	`unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-*l/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 119

Calls

4 calls:

175.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
12.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
32.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series399.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
61.0ms	(- (* b_2 b_2) (* a c))
98.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
98.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.9s

Counts

131 → 131

Iterations

Useful iterations: done (3.9s)

Iter	Nodes	Cost
0	215	2391
1	507	1990
2	1333	1701
3	4586	1622
done	5000	1621

prune417.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
0.2b	(- (* b_2 b_2) (* a c))
6.1b	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

481×	`times-frac`
378×	`add-sqr-sqrt`
366×	`*-un-lft-identity`
358×	`add-cube-cbrt`
287×	`prod-diff`
143×	`sqrt-prod`
39×	`div-inv`
23×	`fma-neg`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `sqrt-div` `flip--` `log1p-expm1-u` `distribute-lft-out--`
3×	`associate-/r*`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `distribute-rgt-out--` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 411

Calls

4 calls:

29.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
9.0ms	(- (* b_2 b_2) (* a c))
111.0ms	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
23.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
63.0ms	(- (* b_2 b_2) (* a c))
114.0ms	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
101.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts

423 → 423

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	497	18768
1	1098	16536
2	2352	13182
done	5001	10638

prune715.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.6b

regimes308.0ms

Accuracy

84.4% (4.5b remaining)

Error of 9.8b against oracle of 5.3b and baseline of 34.2b

bsearch206.0ms

Steps

Iters	Range		Point
11	1.5906747666251227e-34	6.100620313640196e-08	1.611450844781215e-34
9	-6.354265220965125e+156	-1.769171722317776e+149	-1.0084023741576003e+154

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	37
1	27	37
done	27	37

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.0s	5880×	body	80	valid
556.0ms	1077×	body	2560	valid
392.0ms	850×	body	1280	valid
204.0ms	466×	body	640	valid
192.0ms	2914×	body	80	nan
78.0ms	212×	body	320	valid
54.0ms	107×	body	5120	valid
16.0ms	123×	body	160	valid