Details

sample107.0ms

Algorithm

intervals

Results

42.0ms	40×	body	2560	valid
19.0ms	186×	body	80	valid
15.0ms	28×	body	1280	valid
9.0ms	91×	body	80	nan
4.0ms	10×	body	640	valid
2.0ms	8×	body	320	valid
2.0ms	3×	body	5120	valid
1.0ms	4×	body	160	valid

simplify109.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	98
7	98
6	97
5	95
4	87
3	70
2	43
1	24
0	14

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
1.0b	(- (* b b) (* (* c a) 4))
1.3b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
21.9b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite154.0ms

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--` `insert-posit16` `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 → 88

Calls

4 calls:

63.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
16.0ms	(- (* b b) (* (* c a) 4))
67.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
7.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series347.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
60.0ms	(- (* b b) (* (* c a) 4))
97.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
90.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify1.7s

Counts

100 → 100

Iterations

Iter	Nodes
3	3565
2	1088
1	398
0	161

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b b) (* (* c a) 4))) b) (/ 1 a))
1.0b	(- (* b b) (* (* c a) 4))
1.3b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
21.9b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite236.0ms

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` `insert-posit16` `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 → 89

Calls

4 calls:

160.0ms	(* (- (sqrt (- (* b b) (* (* c a) 4))) b) (/ 1 a))
15.0ms	(- (* b b) (* (* c a) 4))
39.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
19.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series426.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (- (sqrt (- (* b b) (* (* c a) 4))) b) (/ 1 a))
52.0ms	(- (* b b) (* (* c a) 4))
134.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
137.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify3.4s

Counts

101 → 101

Iterations

Iter	Nodes
3	5062
2	1496
1	461
0	181

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.8b

localize17.0ms

Local error

Found 1 expressions with local error:

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

rewrite17.0ms

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` `insert-posit16` `div-inv` `add-log-exp`

Counts

1 → 33

Calls

1 calls:

16.0ms

(* -2 (/ c b))

series33.0ms

Counts

1 → 3

Calls

1 calls:

33.0ms

(* -2 (/ c b))

simplify7.0s

Counts

36 → 36

Iterations

Iter	Nodes
4	3714
3	1054
2	425
1	169
0	69

prune356.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 4.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt b) (cbrt b))
0.6b	(cbrt b)
0.6b	(cbrt b)
0.6b	(cbrt b)

rewrite10.0ms

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` `insert-posit16` `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 → 77

Calls

4 calls:

7.0ms	(* (cbrt b) (cbrt b))
1.0ms	(cbrt b)
1.0ms	(cbrt b)
1.0ms	(cbrt b)

series1.2s

Counts

4 → 12

Calls

4 calls:

336.0ms	(* (cbrt b) (cbrt b))
287.0ms	(cbrt b)
322.0ms	(cbrt b)
216.0ms	(cbrt b)

simplify1.2s

Counts

89 → 89

Iterations

Iter	Nodes
4	2788
3	812
2	309
1	132
0	63

prune935.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 4.7b

regimes490.0ms

Accuracy

84.7% (4.3b remaining)

Error of 9.7b against oracle of 5.4b and baseline of 33.6b

bsearch203.0ms

Steps

Iters	Range		Point
8	6.256891986679925e-86	3.543466061308676e-83	4.6659701943749105e-84
8	-6.435448379097954e+123	-1.4863434806956936e+121	-4.694684309811035e+121

simplify9.0ms

Iterations

Iter	Nodes
2	34
1	34
0	29

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.2s	1106×	body	2560	valid
1.0s	5845×	body	80	valid
818.0ms	2919×	body	80	nan
813.0ms	935×	body	1280	valid
278.0ms	453×	body	640	valid
146.0ms	111×	body	5120	valid
80.0ms	212×	body	320	valid
30.0ms	113×	body	160	valid