Details

sample205.0ms

Algorithm

intervals

Results

24.0ms	43×	body	2560	valid
15.0ms	164×	body	80	valid
13.0ms	32×	body	1280	valid
6.0ms	80×	body	80	nan
6.0ms	8×	body	5120	valid
5.0ms	16×	body	640	valid
2.0ms	7×	body	320	valid
1.0ms	6×	body	160	valid

simplify93.0ms

Counts

1 → 1

Iterations

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

prune22.0ms

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)))

rewrite205.0ms

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:

12.0ms	(- (* b_2 b_2) (* a c))
111.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
57.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series404.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (* b_2 b_2) (* a c))
141.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
100.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
101.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
2	1463
1	384
0	154

prune617.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.6b

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

prune45.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.6b

localize25.0ms

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)))

rewrite217.0ms

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))
135.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
62.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series411.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b_2 b_2) (* a c))
153.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
119.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
93.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.7s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
2	2716
1	453
0	174

prune496.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.6b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite89.0ms

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:

6.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
54.0ms	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series433.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b_2 b_2) (* a c))
154.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
130.0ms	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
102.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.0s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
2	1415
1	405
0	175

prune580.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 3.6b

regimes328.0ms

Accuracy

87.9% (4.1b remaining)

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

bsearch64.0ms

Steps

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

simplify6.0ms

Iterations

Iter	Nodes
done	26
1	26
0	23

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.0s	1095×	body	2560	valid
497.0ms	5788×	body	80	valid
286.0ms	885×	body	1280	valid
264.0ms	470×	body	640	valid
221.0ms	2874×	body	80	nan
77.0ms	244×	body	320	valid
49.0ms	110×	body	5120	valid
14.0ms	116×	body	160	valid