Details

sample160.0ms

Algorithm

intervals

Results

31.0ms	180×	body	80	valid
30.0ms	37×	body	1280	valid
25.0ms	24×	body	2560	valid
17.0ms	4×	body	5120	valid
14.0ms	93×	body	80	nan
12.0ms	18×	body	640	valid
3.0ms	6×	body	320	valid
1.0ms	4×	body	160	valid

simplify146.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	105
7	105
6	104
5	102
4	94
3	77
2	44
1	25
0	14

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* a -4) c)
0.5b	(fma b b (* (* a -4) c))
1.6b	(- (sqrt (fma b b (* (* a -4) c))) b)
21.3b	(sqrt (fma b b (* (* a -4) c)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`prod-diff`
16×	`sqrt-prod`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
6×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`difference-of-squares`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `associate-l` `*-commutative` `fma-udef` `flip--` `distribute-lft-out--`

Counts

4 → 90

Calls

4 calls:

15.0ms	(* (* a -4) c)
0.0ms	(fma b b (* (* a -4) c))
8.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
1.0ms	(sqrt (fma b b (* (* a -4) c)))

series319.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (* a -4) c)
71.0ms	(fma b b (* (* a -4) c))
114.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
101.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify1.2s

Counts

102 → 102

Iterations

Iter	Nodes
done	2002
3	2002
2	915
1	335
0	146

prune610.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* a (* -4 c))
0.5b	(fma b b (* a (* -4 c)))
1.6b	(- (sqrt (fma b b (* a (* -4 c)))) b)
21.3b	(sqrt (fma b b (* a (* -4 c))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`prod-diff`
16×	`sqrt-prod`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
6×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`difference-of-squares`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `associate-r` `*-commutative` `fma-udef` `flip--` `distribute-lft-out--`

Counts

4 → 90

Calls

4 calls:

24.0ms	(* a (* -4 c))
0.0ms	(fma b b (* a (* -4 c)))
19.0ms	(- (sqrt (fma b b (* a (* -4 c)))) b)
2.0ms	(sqrt (fma b b (* a (* -4 c))))

series338.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* a (* -4 c))
79.0ms	(fma b b (* a (* -4 c)))
122.0ms	(- (sqrt (fma b b (* a (* -4 c)))) b)
102.0ms	(sqrt (fma b b (* a (* -4 c))))

simplify1.2s

Counts

102 → 102

Iterations

Iter	Nodes
done	2032
3	2032
2	833
1	324
0	144

prune592.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.3b

localize68.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
0.6b	(cbrt a)
1.6b	(- (sqrt (fma b b (* (* (cbrt a) (cbrt a)) (* (cbrt a) (* -4 c))))) b)
21.3b	(sqrt (fma b b (* (* (cbrt a) (cbrt a)) (* (cbrt a) (* -4 c)))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`prod-diff`
16×	`sqrt-prod`
6×	`cbrt-prod` `fma-neg` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`pow1/3` `difference-of-squares`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 86

Calls

4 calls:

1.0ms	(cbrt a)
1.0ms	(cbrt a)
9.0ms	(- (sqrt (fma b b (* (* (cbrt a) (cbrt a)) (* (cbrt a) (* -4 c))))) b)
3.0ms	(sqrt (fma b b (* (* (cbrt a) (cbrt a)) (* (cbrt a) (* -4 c)))))

series944.0ms

Counts

4 → 12

Calls

4 calls:

349.0ms	(cbrt a)
315.0ms	(cbrt a)
135.0ms	(- (sqrt (fma b b (* (* (cbrt a) (cbrt a)) (* (cbrt a) (* -4 c))))) b)
145.0ms	(sqrt (fma b b (* (* (cbrt a) (cbrt a)) (* (cbrt a) (* -4 c)))))

simplify1.6s

Counts

98 → 98

Iterations

Iter	Nodes
done	2061
4	2061
3	1840
2	619
1	272
0	126

prune784.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 11.2b

localize65.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
0.6b	(cbrt a)
1.6b	(- (sqrt (fma b b (* (* (cbrt a) (cbrt a)) (* (* (* (cbrt (cbrt a)) (cbrt (cbrt a))) (cbrt (cbrt a))) (* -4 c))))) b)
21.3b	(sqrt (fma b b (* (* (cbrt a) (cbrt a)) (* (* (* (cbrt (cbrt a)) (cbrt (cbrt a))) (cbrt (cbrt a))) (* -4 c)))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`prod-diff`
16×	`sqrt-prod`
6×	`cbrt-prod` `fma-neg` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`pow1/3` `difference-of-squares`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 86

Calls

4 calls:

1.0ms	(cbrt a)
1.0ms	(cbrt a)
8.0ms	(- (sqrt (fma b b (* (* (cbrt a) (cbrt a)) (* (* (* (cbrt (cbrt a)) (cbrt (cbrt a))) (cbrt (cbrt a))) (* -4 c))))) b)
1.0ms	(sqrt (fma b b (* (* (cbrt a) (cbrt a)) (* (* (* (cbrt (cbrt a)) (cbrt (cbrt a))) (cbrt (cbrt a))) (* -4 c)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

326.0ms	(cbrt a)
272.0ms	(cbrt a)
170.0ms	(- (sqrt (fma b b (* (* (cbrt a) (cbrt a)) (* (* (* (cbrt (cbrt a)) (cbrt (cbrt a))) (cbrt (cbrt a))) (* -4 c))))) b)
572.0ms	(sqrt (fma b b (* (* (cbrt a) (cbrt a)) (* (* (* (cbrt (cbrt a)) (cbrt (cbrt a))) (cbrt (cbrt a))) (* -4 c)))))

simplify1.6s

Counts

98 → 98

Iterations

Iter	Nodes
done	2004
4	2004
3	1880
2	642
1	276
0	127

prune574.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 11.2b

regimes445.0ms

Accuracy

86.1% (3.1b remaining)

Error of 13.8b against oracle of 10.7b and baseline of 33.3b

bsearch238.0ms

Steps

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

simplify12.0ms

Iterations

Iter	Nodes
done	36
1	36
0	30

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.4s	1060×	body	2560	valid
1.0s	5860×	body	80	valid
810.0ms	910×	body	1280	valid
610.0ms	3006×	body	80	nan
308.0ms	471×	body	640	valid
180.0ms	108×	body	5120	valid
155.0ms	225×	body	320	valid
28.0ms	103×	body	160	valid