Details

sample216.0ms

Algorithm

intervals

Results

75.0ms	31×	body	2560	valid
26.0ms	190×	body	80	valid
18.0ms	31×	body	1280	valid
9.0ms	84×	body	80	nan
5.0ms	13×	body	640	valid
3.0ms	4×	body	5120	valid
3.0ms	8×	body	320	valid
1.0ms	4×	body	160	valid

simplify37.0ms

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b	(- (* b_2 b_2) (* a c))
1.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite112.0ms

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:

59.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
12.0ms	(- (* b_2 b_2) (* a c))
26.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series358.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
36.0ms	(- (* b_2 b_2) (* a c))
126.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
82.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify834.0ms

Counts

187 → 187

Iterations

Iter	Nodes
done	2004
2	1521
1	578
0	248

prune720.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
1.0b	(- (* b_2 b_2) (* a c))
1.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite85.0ms

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:

31.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
17.0ms	(- (* b_2 b_2) (* a c))
19.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
57.0ms	(- (* b_2 b_2) (* a c))
101.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
92.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify692.0ms

Counts

273 → 273

Iterations

Iter	Nodes
done	2001
1	837
0	355

prune913.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
1.0b	(- (* b_2 b_2) (* a c))
1.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

897×	`times-frac`
569×	`add-sqr-sqrt`
568×	`*-un-lft-identity`
396×	`add-cube-cbrt`
86×	`distribute-lft-out--` `difference-of-squares`
76×	`sqrt-prod`
64×	`distribute-rgt-neg-in`
61×	`prod-diff`
44×	`add-exp-log`
43×	`div-inv`
32×	`div-exp`
29×	`associate-/r/`
27×	`associate-/r*`
21×	`distribute-lft-neg-in`
17×	`flip3--` `flip--`
16×	`add-cbrt-cube`
13×	`associate-/l*`
11×	`fma-neg`
10×	`add-log-exp`
8×	`cbrt-undiv` `rec-exp` `1-exp`
7×	`neg-mul-1`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`diff-log`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 552

Calls

4 calls:

32.0ms	(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
14.0ms	(- (* b_2 b_2) (* a c))
20.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series358.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
36.0ms	(- (* b_2 b_2) (* a c))
78.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
87.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify741.0ms

Counts

564 → 564

Iterations

Iter	Nodes
done	2000
0	685

prune2.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

localize75.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
1.0b	(- (* b_2 b_2) (* a c))
1.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
52×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
47×	`add-cube-cbrt`
34×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-prod` `flip3--` `diff-log` `flip--`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `neg-log`

Counts

4 → 140

Calls

4 calls:

1.0ms	(cbrt a)
8.0ms	(- (* b_2 b_2) (* a c))
27.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series538.0ms

Counts

4 → 12

Calls

4 calls:

290.0ms	(cbrt a)
39.0ms	(- (* b_2 b_2) (* a c))
112.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
96.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify851.0ms

Counts

152 → 152

Iterations

Iter	Nodes
done	2000
2	1145
1	453
0	204

prune600.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.1b

regimes405.0ms

Accuracy

83.9% (4.5b remaining)

Error of 9.8b against oracle of 5.3b and baseline of 33.3b

bsearch123.0ms

Steps

Iters	Range		Point
7	1.9723660647371773e+81	3.4101289177416236e+83	1.7665622931893247e+83
7	-8.865960730997555e-39	-3.628908962658003e-41	-5.7874989996849275e-40

simplify5.0ms

Iterations

Iter	Nodes
done	31
1	31
0	27

end0.0ms

sample4.1s

Algorithm

intervals

Results

815.0ms	1054×	body	2560	valid
663.0ms	5925×	body	80	valid
658.0ms	921×	body	1280	valid
652.0ms	420×	body	640	valid
514.0ms	222×	body	320	valid
305.0ms	2980×	body	80	nan
181.0ms	116×	body	5120	valid
25.0ms	123×	body	160	valid