Details

sample311.0ms

Algorithm

intervals

Results

59.0ms	180×	body	80	valid
38.0ms	39×	body	2560	valid
33.0ms	7×	body	320	valid
25.0ms	29×	body	1280	valid
13.0ms	21×	body	640	valid
10.0ms	70×	body	80	nan
0.0ms	1×	body	160	valid

simplify147.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	34
5	34
4	32
3	30
2	23
1	15
0	10

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize38.0ms

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)))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`fma-neg`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `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 → 122

Calls

4 calls:

76.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
74.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
18.0ms	(- (* b_2 b_2) (* a c))
22.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series404.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
102.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
65.0ms	(- (* b_2 b_2) (* a c))
132.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.9s

Counts

134 → 134

Iterations

Iter	Nodes
done	5000
3	4672
2	1291
1	494
0	199

prune723.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.2b

localize41.0ms

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)))

rewrite55.0ms

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×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 71

Calls

4 calls:

17.0ms	(- (* b_2 b_2) (* a c))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b_2 b_2) (* a c))
82.0ms	(sqrt (- (* b_2 b_2) (* a c)))
106.0ms	(sqrt (- (* b_2 b_2) (* a c)))
79.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

83 → 83

Iterations

Iter	Nodes
done	5001
3	1558
2	467
1	166
0	69

prune635.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.2b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 70

Calls

4 calls:

16.0ms	(- (* b_2 b_2) (* a c))
22.0ms	(- (* b_2 b_2) (* a c))
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))
22.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* b_2 b_2) (* a c))
43.0ms	(- (* b_2 b_2) (* a c))
92.0ms	(sqrt (- (* b_2 b_2) (* a c)))
79.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

82 → 82

Iterations

Iter	Nodes
done	5001
3	1558
2	467
1	166
0	69

prune942.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.2b

localize47.0ms

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)))

rewrite67.0ms

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×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 71

Calls

4 calls:

18.0ms	(- (* b_2 b_2) (* a c))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* b_2 b_2) (* a c))
69.0ms	(sqrt (- (* b_2 b_2) (* a c)))
79.0ms	(sqrt (- (* b_2 b_2) (* a c)))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

83 → 83

Iterations

Iter	Nodes
done	5001
3	1558
2	467
1	166
0	69

prune576.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 4.2b

regimes426.0ms

Accuracy

84.4% (4.4b remaining)

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

bsearch257.0ms

Steps

Iters	Range		Point
9	1.542649851819534e-86	4.188981380654902e-77	5.930445637544082e-86
10	-9.235597319251238e+162	-1.2115114540629089e+151	-4.499464302465673e+151

simplify10.0ms

Iterations

Iter	Nodes
done	31
1	31
0	28

end0.0ms

sample3.9s

Algorithm

intervals

Results

819.0ms	1060×	body	2560	valid
771.0ms	5901×	body	80	valid
741.0ms	454×	body	640	valid
614.0ms	895×	body	1280	valid
395.0ms	2936×	body	80	nan
89.0ms	106×	body	5120	valid
71.0ms	212×	body	320	valid
42.0ms	94×	body	160	valid