Details

sample249.0ms

Algorithm

intervals

Results

75.0ms	28×	body	1280	valid
28.0ms	198×	body	80	valid
27.0ms	31×	body	2560	valid
14.0ms	87×	body	80	nan
10.0ms	18×	body	640	valid
4.0ms	4×	body	5120	valid
2.0ms	6×	body	320	valid
1.0ms	4×	body	160	valid

simplify84.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	49
4	49
3	46
2	33
1	19
0	10

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 175

Calls

4 calls:

55.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
23.0ms	(- (* b_2 b_2) (* a c))
38.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
63.0ms	(- (* b_2 b_2) (* a c))
118.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
105.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts

187 → 187

Iterations

Iter	Nodes
done	5000
2	1582
1	578
0	248

prune769.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.4b	(- (* b_2 b_2) (* a c))
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-sqr-sqrt`
170×	`*-un-lft-identity`
165×	`times-frac`
118×	`add-cube-cbrt`
61×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
15×	`add-exp-log`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube` `associate-/r/`
7×	`neg-mul-1` `flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`rec-exp` `sub-neg` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `pow-flip` `inv-pow`

Counts

4 → 261

Calls

4 calls:

32.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
8.0ms	(- (* b_2 b_2) (* a c))
35.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
45.0ms	(- (* b_2 b_2) (* a c))
98.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
111.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

273 → 273

Iterations

Iter	Nodes
done	5002
2	2419
1	837
0	355

prune842.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.6b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.4b	(- (* b_2 b_2) (* a c))
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

181×	`prod-diff`
146×	`add-sqr-sqrt`
139×	`*-un-lft-identity`
130×	`add-cube-cbrt`
95×	`sqrt-prod`
62×	`distribute-rgt-in` `distribute-lft-in`
59×	`distribute-rgt-neg-in`
57×	`distribute-lft-neg-in`
19×	`neg-mul-1`
13×	`associate-l` `add-exp-log`
11×	`times-frac` `fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `associate-r`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `sub-neg` `prod-exp` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sqrt-div` `div-exp` `associate-*r/` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `neg-log` `associate-l/` `-commutative` `div-inv`

Counts

4 → 296

Calls

4 calls:

90.0ms	(* (/ 1 a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
8.0ms	(- (* b_2 b_2) (* a c))
20.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series403.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (/ 1 a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
61.0ms	(- (* b_2 b_2) (* a c))
126.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
90.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

308 → 308

Iterations

Iter	Nodes
done	5001
2	2155
1	1004
0	360

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 175

Calls

4 calls:

68.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
16.0ms	(- (* b_2 b_2) (* a c))
38.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series322.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
50.0ms	(- (* b_2 b_2) (* a c))
82.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
81.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

187 → 187

Iterations

Iter	Nodes
done	5000
2	1582
1	578
0	248

prune660.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.6b

regimes514.0ms

Accuracy

82.7% (4.8b remaining)

Error of 10.6b against oracle of 5.8b and baseline of 33.6b

bsearch388.0ms

Steps

Iters	Range		Point
9	6.2301214455520334e+75	1.9082112581546424e+85	1.6691257204922504e+85
4	-2.3602019652593256e-123	-1.5355849018748885e-123	-2.3344326820285623e-123
9	-2.9300981025422624e-27	-1.2024011261401705e-33	-1.823572975982288e-27
8	-1.0943378505721803e-12	-1.4409381956716427e-15	-7.363255598823911e-15

simplify13.0ms

Iterations

Iter	Nodes
done	38
1	38
0	34

end0.0ms

sample3.9s

Algorithm

intervals

Results

916.0ms	1060×	body	2560	valid
829.0ms	5839×	body	80	valid
749.0ms	2843×	body	80	nan
638.0ms	889×	body	1280	valid
235.0ms	456×	body	640	valid
116.0ms	114×	body	5120	valid
76.0ms	228×	body	320	valid
27.0ms	121×	body	160	valid