Details

sample105.0ms

Algorithm

intervals

Results

23.0ms	180×	body	80	valid
21.0ms	37×	body	1280	valid
18.0ms	24×	body	2560	valid
10.0ms	93×	body	80	nan
9.0ms	18×	body	640	valid
3.0ms	4×	body	5120	valid
2.0ms	6×	body	320	valid
1.0ms	4×	body	160	valid

simplify104.0ms

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* (* 3 a) c))
0.4b	(* (* 3 a) c)
1.7b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
21.3b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite97.0ms

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	(- (* b b) (* (* 3 a) c))
26.0ms	(* (* 3 a) c)
42.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
13.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (* b b) (* (* 3 a) c))
21.0ms	(* (* 3 a) c)
116.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
120.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.1s

Counts

76 → 76

Iterations

Iter	Nodes
done	2004
3	2004
2	911
1	298
0	123

prune407.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 12.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt c)
0.6b	(cbrt c)
1.7b	(- (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
21.3b	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

1.0ms	(cbrt c)
1.0ms	(cbrt c)
49.0ms	(- (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
11.0ms	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))

series723.0ms

Counts

4 → 12

Calls

4 calls:

234.0ms	(cbrt c)
251.0ms	(cbrt c)
125.0ms	(- (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
113.0ms	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))

simplify1.1s

Counts

68 → 68

Iterations

Iter	Nodes
done	2046
3	2046
2	736
1	238
0	106

prune506.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 12.1b

localize67.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt c)
0.7b	(cbrt (cbrt c))
1.7b	(- (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c)))))) b)
21.3b	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c))))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`cbrt-prod`
10×	`*-un-lft-identity`
8×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `sqrt-prod` `insert-posit16`
2×	`flip3--` `pow1/3` `sqrt-div` `flip--` `difference-of-squares`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 59

Calls

4 calls:

1.0ms	(cbrt c)
1.0ms	(cbrt (cbrt c))
38.0ms	(- (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c)))))) b)
12.0ms	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c))))))

series969.0ms

Counts

4 → 12

Calls

4 calls:

273.0ms	(cbrt c)
409.0ms	(cbrt (cbrt c))
153.0ms	(- (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c)))))) b)
133.0ms	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c))))))

simplify1.1s

Counts

71 → 71

Iterations

Iter	Nodes
done	2000
3	2000
2	887
1	276
0	126

prune550.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 12.0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (cbrt c))
0.7b	(cbrt (cbrt c))
1.7b	(- (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c)))))))) b)
21.3b	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c))))))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod`
14×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
9×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `sqrt-prod` `insert-posit16`
2×	`flip3--` `pow1/3` `sqrt-div` `flip--` `difference-of-squares`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 62

Calls

4 calls:

1.0ms	(cbrt (cbrt c))
1.0ms	(cbrt (cbrt c))
52.0ms	(- (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c)))))))) b)
10.0ms	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c))))))))

series1.0s

Counts

4 → 12

Calls

4 calls:

387.0ms	(cbrt (cbrt c))
390.0ms	(cbrt (cbrt c))
123.0ms	(- (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c)))))))) b)
119.0ms	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c))))))))

simplify1.2s

Counts

74 → 74

Iterations

Iter	Nodes
done	2045
3	2045
2	816
1	254
0	118

prune561.0ms

Pruning

17 alts after pruning (14 fresh and 3 done)

Merged error: 12.0b

regimes707.0ms

Accuracy

85.9% (3.0b remaining)

Error of 14.8b against oracle of 11.7b and baseline of 33.3b

bsearch255.0ms

Steps

Iters	Range		Point
9	1.9857735944483347e-57	1.377205241174095e-49	1.502588793204478e-55
9	-9.632418191944025e+160	-8.091671749741088e+152	-1.3307746224770355e+154

simplify10.0ms

Iterations

Iter	Nodes
done	32
1	32
0	27

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.7s	5859×	body	80	valid
1.1s	1061×	body	2560	valid
649.0ms	909×	body	1280	valid
372.0ms	3001×	body	80	nan
276.0ms	471×	body	640	valid
126.0ms	108×	body	5120	valid
109.0ms	225×	body	320	valid
26.0ms	104×	body	160	valid