Details

sample256.0ms

Algorithm

intervals

Results

25.0ms	39×	body	2560	valid
21.0ms	29×	body	1280	valid
21.0ms	180×	body	80	valid
10.0ms	21×	body	640	valid
8.0ms	70×	body	80	nan
2.0ms	7×	body	320	valid
0.0ms	1×	body	160	valid

simplify58.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	29
5	29
4	27
3	25
2	22
1	14
0	10

prune196.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b	(- (* b_2 b_2) (* a c))
19.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite445.0ms

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:

259.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
128.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
18.0ms	(- (* b_2 b_2) (* a c))
34.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series410.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
89.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
59.0ms	(- (* b_2 b_2) (* a c))
116.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
3	4048
2	1029
1	379
0	158

prune518.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.2b

localize50.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b	(- (* b_2 b_2) (* a c))
19.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

1.0ms	(cbrt a)
36.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series529.0ms

Counts

4 → 12

Calls

4 calls:

248.0ms	(cbrt a)
114.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
63.0ms	(- (* b_2 b_2) (* a c))
104.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts

69 → 69

Iterations

Iter	Nodes
done	5000
3	2154
2	678
1	250
0	113

prune554.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.2b

localize52.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
19.1b	(sqrt (- (* b_2 b_2) (* a c)))
19.1b	(sqrt (- (* b_2 b_2) (* a c)))
19.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite59.0ms

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:

15.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (* b_2 b_2) (* a c))
101.0ms	(sqrt (- (* b_2 b_2) (* a c)))
106.0ms	(sqrt (- (* b_2 b_2) (* a c)))
91.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.0s

Counts

73 → 73

Iterations

Iter	Nodes
done	5002
4	4845
3	1344
2	414
1	148
0	60

prune578.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 4.2b

localize53.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
19.1b	(sqrt (- (* b_2 b_2) (* a c)))
19.1b	(sqrt (- (* b_2 b_2) (* a c)))
19.1b	(sqrt (- (* b_2 b_2) (* 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:

8.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* b_2 b_2) (* a c))
78.0ms	(sqrt (- (* b_2 b_2) (* a c)))
94.0ms	(sqrt (- (* b_2 b_2) (* a c)))
88.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.1s

Counts

73 → 73

Iterations

Iter	Nodes
done	5002
4	4845
3	1344
2	414
1	148
0	60

prune584.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 4.2b

regimes569.0ms

Accuracy

84.4% (4.4b remaining)

Error of 10.1b against oracle of 5.7b and baseline of 33.7b

bsearch183.0ms

Steps

Iters	Range		Point
9	1.542649851819534e-86	4.188981380654902e-77	5.930445637544082e-86
10	-9.235597319251238e+162	-1.2115114540629089e+151	-4.600306435637794e+151

simplify11.0ms

Iterations

Iter	Nodes
done	29
1	29
0	26

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.2s	5901×	body	80	valid
954.0ms	895×	body	1280	valid
892.0ms	1060×	body	2560	valid
360.0ms	2936×	body	80	nan
244.0ms	454×	body	640	valid
103.0ms	106×	body	5120	valid
64.0ms	212×	body	320	valid
21.0ms	94×	body	160	valid