Details

sample178.0ms

Algorithm

intervals

Results

14.0ms	184×	body	80	valid
12.0ms	32×	body	2560	valid
9.0ms	32×	body	1280	valid
5.0ms	84×	body	80	nan
4.0ms	16×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify107.0ms

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.4b	(- (* b_2 b_2) (* a c))
24.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite578.0ms

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-cbrt-cube` `add-exp-log` `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` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 84

Calls

4 calls:

94.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
457.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
6.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
132.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
53.0ms	(- (* b_2 b_2) (* a c))
101.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.8s

Counts

96 → 96

Iterations

Iter	Nodes
done	5008
3	4099
2	1023
1	374
0	154

prune600.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.8b

localize57.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b_2 b_2) (* a c))
1.4b	(- (* b_2 b_2) (* a c))
24.6b	(sqrt (- (* b_2 b_2) (* a c)))
24.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

6.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* b_2 b_2) (* a c))
67.0ms	(- (* b_2 b_2) (* a c))
89.0ms	(sqrt (- (* b_2 b_2) (* a c)))
69.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.3s

Counts

66 → 66

Iterations

Iter	Nodes
done	5000
4	4824
3	1339
2	413
1	147
0	58

prune480.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.8b

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 32

Calls

1 calls:

12.0ms

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

series26.0ms

Counts

1 → 3

Calls

1 calls:

26.0ms

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

simplify1.8s

Counts

35 → 35

Iterations

Iter	Nodes
done	5000
3	1422
2	508
1	172
0	68

prune257.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 4.8b

localize36.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt b_2) (cbrt b_2))
0.6b	(cbrt b_2)
0.6b	(cbrt b_2)
0.6b	(cbrt b_2)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

17.0ms	(* (cbrt b_2) (cbrt b_2))
1.0ms	(cbrt b_2)
1.0ms	(cbrt b_2)
1.0ms	(cbrt b_2)

series1.1s

Counts

4 → 12

Calls

4 calls:

337.0ms	(* (cbrt b_2) (cbrt b_2))
248.0ms	(cbrt b_2)
302.0ms	(cbrt b_2)
245.0ms	(cbrt b_2)

simplify3.0s

Counts

85 → 85

Iterations

Iter	Nodes
done	5028
4	3114
3	971
2	377
1	136
0	61

prune428.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 4.8b

regimes411.0ms

Accuracy

84.4% (4.4b remaining)

Error of 10.5b against oracle of 6.1b and baseline of 34.4b

bsearch114.0ms

Steps

Iters	Range		Point
8	2.8373581988670566e-35	2.2677514638291856e-31	3.1423118580081215e-35
8	-2.748004767191833e+152	-7.260401024913698e+147	-2.221067196710922e+149

simplify4.0ms

Iterations

Iter	Nodes
done	26
1	26
0	23

end0.0ms

sample2.7s

Algorithm

intervals

Results

941.0ms	5833×	body	80	valid
491.0ms	1043×	body	2560	valid
302.0ms	911×	body	1280	valid
228.0ms	449×	body	640	valid
211.0ms	2878×	body	80	nan
55.0ms	102×	body	5120	valid
39.0ms	232×	body	320	valid
16.0ms	119×	body	160	valid