Details

sample220.0ms

Algorithm

intervals

Results

20.0ms	38×	body	2560	valid
17.0ms	178×	body	80	valid
12.0ms	29×	body	1280	valid
6.0ms	79×	body	80	nan
4.0ms	11×	body	640	valid
2.0ms	3×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify42.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (18.0ms)

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.6b	(- (* b_2 b_2) (* a c))
20.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite270.0ms

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:

155.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
84.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
10.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series361.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
94.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
51.0ms	(- (* b_2 b_2) (* a c))
108.0ms	(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	1109	1874
3	3404	1795
done	5000	1785

prune586.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
0.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.6b	(- (* b_2 b_2) (* a c))
20.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite356.0ms

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:

230.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
82.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
11.0ms	(- (* b_2 b_2) (* a c))
23.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series419.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
97.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
68.0ms	(- (* b_2 b_2) (* a c))
107.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify4.0s

Counts

131 → 131

Iterations

Useful iterations: done (4.0s)

Iter	Nodes	Cost
0	215	2391
1	507	1990
2	1335	1701
3	4588	1622
done	5000	1621

prune345.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.1b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(* -1/2 (/ c b_2))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`associate-r`
10×	`times-frac`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `expm1-log1p-u` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 34

Calls

1 calls:

15.0ms

(* -1/2 (/ c b_2))

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

(* -1/2 (/ c b_2))

simplify6.0s

Counts

37 → 37

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	70	289
1	163	266
2	437	242
3	1135	242
4	2710	242
done	5000	242

prune139.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.1b

localize6.0ms

Local error

Found 1 expressions with local error:

0.1b	(* (* -1/2 c) (/ 1 b_2))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
13×	`associate-r` `add-cbrt-cube`
12×	`prod-exp`
9×	`times-frac`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-unprod`
4×	`div-exp`
3×	`pow-prod-down`
2×	`cbrt-undiv` `rec-exp` `1-exp`
1×	`expm1-log1p-u` `associate-r/` `associate-l` `un-div-inv` `-commutative` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 40

Calls

1 calls:

24.0ms

(* (* -1/2 c) (/ 1 b_2))

series36.0ms

Counts

1 → 3

Calls

1 calls:

36.0ms

(* (* -1/2 c) (/ 1 b_2))

simplify4.4s

Counts

43 → 43

Iterations

Useful iterations: 2 (215.0ms)

Iter	Nodes	Cost
0	86	427
1	222	310
2	719	250
3	2489	250
done	5001	250

prune76.0ms

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 5.1b

regimes323.0ms

Accuracy

83.6% (4.7b remaining)

Error of 10.3b against oracle of 5.6b and baseline of 34.3b

bsearch114.0ms

Steps

Iters	Range		Point
8	1.2806837237363044e-130	1.5764294416549136e-127	2.4821897765563124e-128
8	-6.990724105819741e+111	-2.6156774686163576e+108	-1.569310777886352e+111

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	35
1	26	35
done	26	35

end0.0ms

sample3.1s

Algorithm

intervals

Results

982.0ms	5805×	body	80	valid
621.0ms	1087×	body	2560	valid
324.0ms	936×	body	1280	valid
299.0ms	2994×	body	80	nan
113.0ms	443×	body	640	valid
59.0ms	117×	body	5120	valid
44.0ms	113×	body	160	valid
39.0ms	211×	body	320	valid