Details

sample186.0ms

Algorithm

intervals

Results

16.0ms	43×	body	2560	valid
12.0ms	164×	body	80	valid
9.0ms	32×	body	1280	valid
4.0ms	80×	body	80	nan
4.0ms	16×	body	640	valid
4.0ms	8×	body	5120	valid
1.0ms	7×	body	320	valid
1.0ms	6×	body	160	valid

simplify40.0ms

Counts

1 → 1

Iterations

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b_2 b_2) (* a c))
0.4b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite243.0ms

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:

6.0ms	(- (* b_2 b_2) (* a c))
122.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
91.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* b_2 b_2) (* a c))
134.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
98.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
118.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify618.0ms

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
2	1463
1	384
0	154

prune699.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.8b

localize6.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune64.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.8b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b_2 b_2) (* a c))
0.4b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`associate-r` `add-exp-log` `add-cube-cbrt`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`prod-exp` `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` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 85

Calls

4 calls:

6.0ms	(- (* b_2 b_2) (* a c))
149.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
53.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series330.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* b_2 b_2) (* a c))
117.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
88.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
85.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.7s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
2	2716
1	453
0	174

prune586.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (pow b_2 2) (* c a))
0.1b	(/ (sqrt (- (pow b_2 2) (* c a))) a)
9.9b	(- (/ (sqrt (- (pow b_2 2) (* c a))) a) (/ b_2 a))
21.2b	(sqrt (- (pow b_2 2) (* c a)))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
31×	`times-frac`
30×	`*-un-lft-identity`
22×	`add-cube-cbrt`
17×	`sqrt-prod`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `sqrt-div` `flip--` `distribute-lft-out--`
3×	`associate-/r*` `div-inv`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `distribute-rgt-out--` `pow1/2` `div-exp` `frac-sub` `sub-div`

Counts

4 → 93

Calls

4 calls:

11.0ms	(- (pow b_2 2) (* c a))
33.0ms	(/ (sqrt (- (pow b_2 2) (* c a))) a)
126.0ms	(- (/ (sqrt (- (pow b_2 2) (* c a))) a) (/ b_2 a))
11.0ms	(sqrt (- (pow b_2 2) (* c a)))

series817.0ms

Counts

4 → 12

Calls

4 calls:

468.0ms	(- (pow b_2 2) (* c a))
136.0ms	(/ (sqrt (- (pow b_2 2) (* c a))) a)
113.0ms	(- (/ (sqrt (- (pow b_2 2) (* c a))) a) (/ b_2 a))
100.0ms	(sqrt (- (pow b_2 2) (* c a)))

simplify659.0ms

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
2	1265
1	388
0	175

prune675.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 3.6b

regimes297.0ms

Accuracy

87.9% (4.1b remaining)

Error of 9.4b against oracle of 5.3b and baseline of 39.5b

bsearch53.0ms

Steps

Iters	Range		Point
2	3.964947473899983e-62	4.720485511979589e-62	4.626043257219638e-62
7	-5.856362438573669e+138	-1.280729871585891e+137	-3.7108875578650606e+138

simplify3.0ms

Iterations

Iter	Nodes
done	28
1	28
0	25

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.1s	5788×	body	80	valid
469.0ms	1095×	body	2560	valid
372.0ms	885×	body	1280	valid
228.0ms	2874×	body	80	nan
116.0ms	470×	body	640	valid
87.0ms	244×	body	320	valid
55.0ms	110×	body	5120	valid
14.0ms	116×	body	160	valid