Details

sample115.0ms

Algorithm

intervals

Results

40.0ms	39×	body	2560	valid
22.0ms	188×	body	80	valid
16.0ms	31×	body	1280	valid
9.0ms	87×	body	80	nan
5.0ms	13×	body	640	valid
3.0ms	3×	body	5120	valid
2.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify60.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	98
5	98
4	90
3	74
2	42
1	21
0	12

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
0.4b	(- (* b b) (* (* 3 a) c))
0.4b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
23.1b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`times-frac` `sqrt-prod` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `insert-posit16` `flip--`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 76

Calls

4 calls:

68.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
9.0ms	(- (* b b) (* (* 3 a) c))
40.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series487.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
61.0ms	(- (* b b) (* (* 3 a) c))
139.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
101.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.1s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1321
1	396
0	157

prune551.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.5b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3 a) c)
0.4b	(- (* b b) (* (* 3 a) c))
0.4b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
23.1b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod` `insert-posit16`
3×	`flip3--` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

15.0ms	(* (* 3 a) c)
7.0ms	(- (* b b) (* (* 3 a) c))
50.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
9.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series353.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (* 3 a) c)
63.0ms	(- (* b b) (* (* 3 a) c))
137.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
113.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify2.5s

Counts

76 → 76

Iterations

Iter	Nodes
done	5013
3	3910
2	944
1	297
0	123

prune449.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* 3 a) (- (sqrt (- (* b b) (* (* 3 a) c))) b))
0.4b	(- (* b b) (* (* 3 a) c))
0.4b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
23.1b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`associate-/r*` `times-frac` `sqrt-prod` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `insert-posit16` `flip--`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/r/`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 75

Calls

4 calls:

49.0ms	(/ (* 3 a) (- (sqrt (- (* b b) (* (* 3 a) c))) b))
15.0ms	(- (* b b) (* (* 3 a) c))
67.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
17.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series665.0ms

Counts

4 → 12

Calls

4 calls:

328.0ms	(/ (* 3 a) (- (sqrt (- (* b b) (* (* 3 a) c))) b))
65.0ms	(- (* b b) (* (* 3 a) c))
130.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
142.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.4s

Counts

87 → 87

Iterations

Iter	Nodes
done	5001
2	1290
1	390
0	150

prune490.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.4b

localize40.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
0.4b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
23.1b	(sqrt (- (* b b) (* (* 3 a) c)))
23.1b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

62.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
64.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
11.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
7.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series485.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
165.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
109.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
110.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify2.2s

Counts

76 → 76

Iterations

Iter	Nodes
done	5004
3	2645
2	612
1	191
0	82

prune480.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 6.4b

regimes708.0ms

Accuracy

83.3% (4.6b remaining)

Error of 10.5b against oracle of 5.9b and baseline of 33.7b

bsearch255.0ms

Steps

Iters	Range		Point
8	1.287554927770862e-68	8.304725640954512e-66	1.9030999523937384e-67
9	-5.599802959155633e+154	-4.186518194588193e+147	-2.874603183983119e+152

simplify9.0ms

Iterations

Iter	Nodes
done	32
1	32
0	27

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.5s	5889×	body	80	valid
978.0ms	1064×	body	2560	valid
731.0ms	903×	body	1280	valid
470.0ms	2854×	body	80	nan
227.0ms	446×	body	640	valid
117.0ms	206×	body	320	valid
100.0ms	95×	body	5120	valid
74.0ms	133×	body	160	valid