Details

sample140.0ms

Algorithm

intervals

Results

11.0ms	43×	body	2560	valid
9.0ms	176×	body	80	valid
6.0ms	31×	body	1280	valid
4.0ms	106×	body	80	nan
3.0ms	19×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	4×	body	160	valid

simplify33.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (11.0ms)

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize12.0ms

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))
1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite233.0ms

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:

133.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
9.0ms	(- (* b_2 b_2) (* a c))
68.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
46.0ms	(- (* b_2 b_2) (* a c))
110.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
129.0ms	(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

prune478.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.3b

localize9.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify1.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune31.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize24.0ms

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))
1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite204.0ms

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:

79.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
9.0ms	(- (* b_2 b_2) (* a c))
90.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series464.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
65.0ms	(- (* b_2 b_2) (* a c))
88.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
103.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.1s

Counts

208 → 208

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	299	4764
1	641	4074
2	1433	3649
3	4208	3500
done	5000	3500

prune506.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.2b

localize11.0ms

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))
1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite325.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
55×	`prod-diff`
51×	`add-cube-cbrt`
35×	`sqrt-prod`
20×	`distribute-rgt-in` `distribute-lft-in`
13×	`add-exp-log` `associate-l`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1` `fma-neg`
6×	`associate-r`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `sub-neg` `prod-exp` `log1p-expm1-u` `difference-of-squares`
3×	`unswap-sqr`
2×	`frac-times` `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 → 158

Calls

4 calls:

205.0ms	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
15.0ms	(- (* b_2 b_2) (* a c))
80.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
50.0ms	(- (* b_2 b_2) (* a c))
107.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
90.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.2s

Counts

170 → 170

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	239	4053
1	566	3273
2	1412	2573
3	4335	2352
done	5000	2352

prune448.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.2b

regimes232.0ms

Accuracy

82.7% (5.9b remaining)

Error of 11.8b against oracle of 5.9b and baseline of 39.8b

bsearch122.0ms

Steps

Iters	Range		Point
6	1.6855676195581707e-170	7.565529323099765e-170	7.455592343308264e-170
10	-1.4318549199647532e+71	-1.1598944120121166e+59	-2.007820467288354e+70

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	37
1	31	37
done	31	37

end0.0ms

sample2.9s

Algorithm

intervals

Results

895.0ms	1075×	body	2560	valid
522.0ms	5874×	body	80	valid
309.0ms	885×	body	1280	valid
301.0ms	3008×	body	80	nan
164.0ms	496×	body	640	valid
71.0ms	216×	body	320	valid
47.0ms	107×	body	5120	valid
11.0ms	93×	body	160	valid