Details

sample149.0ms

Algorithm

intervals

Results

56.0ms	43×	body	2560	valid
27.0ms	190×	body	80	valid
17.0ms	25×	body	1280	valid
12.0ms	85×	body	80	nan
8.0ms	13×	body	640	valid
4.0ms	11×	body	320	valid
3.0ms	3×	body	5120	valid
1.0ms	2×	body	160	valid

simplify84.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	93
7	93
6	92
5	90
4	82
3	66
2	40
1	21
0	12

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3 a) c)
0.5b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
1.0b	(- (* b b) (* (* 3 a) c))
24.5b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite80.0ms

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:

13.0ms	(* (* 3 a) c)
51.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
7.0ms	(- (* b b) (* (* 3 a) c))
7.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series306.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (* 3 a) c)
96.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
54.0ms	(- (* b b) (* (* 3 a) c))
124.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.2s

Counts

76 → 76

Iterations

Iter	Nodes
done	2032
3	2032
2	910
1	297
0	123

prune931.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 14.4b

localize45.0ms

Local error

Found 4 expressions with local error:

16.7b	(cbrt (* (* 3 a) c))
16.7b	(cbrt (* (* 3 a) c))
16.7b	(cbrt (* (* 3 a) c))
24.5b	(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c)))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`cbrt-prod` `pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--`

Counts

4 → 46

Calls

4 calls:

9.0ms	(cbrt (* (* 3 a) c))
12.0ms	(cbrt (* (* 3 a) c))
15.0ms	(cbrt (* (* 3 a) c))
7.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c)))))

series588.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(cbrt (* (* 3 a) c))
127.0ms	(cbrt (* (* 3 a) c))
115.0ms	(cbrt (* (* 3 a) c))
206.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c)))))

simplify1.8s

Counts

58 → 58

Iterations

Iter	Nodes
done	2002
4	2002
3	1652
2	491
1	205
0	89

prune736.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 14.4b

localize45.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (* (cbrt (* 3 a)) (cbrt c))))
16.7b	(cbrt (* (* 3 a) c))
16.7b	(cbrt (* (* 3 a) c))
24.5b	(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (* (cbrt (* 3 a)) (cbrt c)))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `add-log-exp`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`sqrt-prod`
2×	`cbrt-prod` `flip3--` `pow1/3` `sqrt-div` `flip--`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 49

Calls

4 calls:

12.0ms	(- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (* (cbrt (* 3 a)) (cbrt c))))
9.0ms	(cbrt (* (* 3 a) c))
18.0ms	(cbrt (* (* 3 a) c))
14.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (* (cbrt (* 3 a)) (cbrt c)))))

series849.0ms

Counts

4 → 12

Calls

4 calls:

222.0ms	(- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (* (cbrt (* 3 a)) (cbrt c))))
159.0ms	(cbrt (* (* 3 a) c))
122.0ms	(cbrt (* (* 3 a) c))
345.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (* (cbrt (* 3 a)) (cbrt c)))))

simplify1.1s

Counts

61 → 61

Iterations

Iter	Nodes
done	2011
3	2011
2	808
1	273
0	114

prune943.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 14.4b

localize34.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 3 a) c))
24.5b	(sqrt (- (* b b) (* (* 3 a) c)))
24.5b	(sqrt (- (* b b) (* (* 3 a) c)))
24.5b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
4×	`flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `diff-log`

Counts

4 → 61

Calls

4 calls:

7.0ms	(- (* b b) (* (* 3 a) c))
12.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
7.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
7.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series349.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (* b b) (* (* 3 a) c))
86.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
94.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
102.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify945.0ms

Counts

73 → 73

Iterations

Iter	Nodes
done	2013
3	2013
2	516
1	157
0	63

prune899.0ms

Pruning

12 alts after pruning (8 fresh and 4 done)

Merged error: 14.4b

regimes468.0ms

Accuracy

85.4% (3.1b remaining)

Error of 14.9b against oracle of 11.8b and baseline of 33.0b

bsearch204.0ms

Steps

Iters	Range		Point
10	4.030937871461662e-25	2.071699417983812e-14	6.399558563329366e-17
8	-4.336983712965787e+155	-6.488343844980391e+152	-1.3441037991607355e+154

simplify6.0ms

Iterations

Iter	Nodes
done	32
1	32
0	27

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.1s	1069×	body	2560	valid
952.0ms	5928×	body	80	valid
795.0ms	3004×	body	80	nan
530.0ms	874×	body	1280	valid
290.0ms	467×	body	640	valid
127.0ms	108×	body	5120	valid
85.0ms	219×	body	320	valid
29.0ms	109×	body	160	valid