Details

sample190.0ms

Algorithm

intervals

Results

17.0ms	39×	body	2560	valid
13.0ms	29×	body	1280	valid
12.0ms	180×	body	80	valid
5.0ms	21×	body	640	valid
5.0ms	70×	body	80	nan
2.0ms	7×	body	320	valid
0.0ms	1×	body	160	valid

simplify52.0ms

Counts

1 → 1

Iterations

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

prune51.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize40.0ms

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)))

rewrite204.0ms

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:

104.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
55.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
16.0ms	(- (* b_2 b_2) (* a c))
24.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series343.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
90.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
49.0ms	(- (* b_2 b_2) (* a c))
89.0ms	(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

prune543.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.2b

localize68.0ms

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)))

rewrite72.0ms

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:

8.0ms	(- (* b_2 b_2) (* a c))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))
25.0ms	(sqrt (- (* b_2 b_2) (* a c)))
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series271.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* b_2 b_2) (* a c))
78.0ms	(sqrt (- (* b_2 b_2) (* a c)))
68.0ms	(sqrt (- (* b_2 b_2) (* a c)))
87.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Counts

83 → 83

Iterations

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

prune575.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.2b

localize53.0ms

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)))

rewrite39.0ms

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:

8.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* b_2 b_2) (* a c))
58.0ms	(- (* b_2 b_2) (* a c))
75.0ms	(sqrt (- (* b_2 b_2) (* a c)))
91.0ms	(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

prune486.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.2b

localize66.0ms

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)))

rewrite79.0ms

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))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))
24.0ms	(sqrt (- (* b_2 b_2) (* a c)))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series317.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b_2 b_2) (* a c))
97.0ms	(sqrt (- (* b_2 b_2) (* a c)))
75.0ms	(sqrt (- (* b_2 b_2) (* a c)))
96.0ms	(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

prune597.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 4.2b

regimes417.0ms

Accuracy

84.4% (4.4b remaining)

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

bsearch179.0ms

Steps

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

simplify7.0ms

Iterations

Iter	Nodes
done	31
1	31
0	28

end0.0ms

sample2.9s

Algorithm

intervals

Results

935.0ms	5901×	body	80	valid
681.0ms	1060×	body	2560	valid
422.0ms	895×	body	1280	valid
235.0ms	2936×	body	80	nan
149.0ms	454×	body	640	valid
80.0ms	212×	body	320	valid
56.0ms	106×	body	5120	valid
13.0ms	94×	body	160	valid