Details

sample257.0ms

Algorithm

intervals

Results

52.0ms	16×	body	640	valid
27.0ms	32×	body	2560	valid
22.0ms	176×	body	80	valid
19.0ms	29×	body	1280	valid
14.0ms	85×	body	80	nan
6.0ms	6×	body	5120	valid
3.0ms	9×	body	320	valid
1.0ms	4×	body	160	valid

simplify58.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	49
4	49
3	46
2	33
1	19
0	10

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite166.0ms

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:

66.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
17.0ms	(- (* b_2 b_2) (* a c))
39.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
37.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
46.0ms	(- (* b_2 b_2) (* a c))
97.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
134.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.8s

Counts

187 → 187

Iterations

Iter	Nodes
3	4034
2	1423
1	576
0	248

prune743.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.7b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.8b	(- (* b_2 b_2) (* a c))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite109.0ms

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:

40.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
16.0ms	(- (* b_2 b_2) (* a c))
28.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
45.0ms	(- (* b_2 b_2) (* a c))
96.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
78.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

273 → 273

Iterations

Iter	Nodes
2	2075
1	834
0	355

prune890.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.7b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt 1) (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.8b	(- (* b_2 b_2) (* a c))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

309×	`times-frac`
268×	`add-sqr-sqrt`
267×	`*-un-lft-identity`
179×	`add-cube-cbrt`
139×	`sqrt-prod`
61×	`prod-diff`
44×	`distribute-lft-out--` `difference-of-squares`
43×	`distribute-rgt-neg-in`
27×	`associate-/r*`
21×	`distribute-lft-neg-in`
15×	`associate-/r/`
11×	`fma-neg`
10×	`flip3--` `flip--` `add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
8×	`div-inv`
7×	`neg-mul-1`
6×	`associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `diff-log` `div-exp`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 339

Calls

4 calls:

58.0ms	(/ (sqrt 1) (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
21.0ms	(- (* b_2 b_2) (* a c))
40.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series425.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(/ (sqrt 1) (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
63.0ms	(- (* b_2 b_2) (* a c))
110.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
95.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.2s

Counts

351 → 351

Iterations

Iter	Nodes
2	2219
1	971
0	411

prune844.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.7b

localize26.0ms

Local error

Found 4 expressions with local error:

3.7b	(/ (/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.4b	(/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
18.3b	(- (* b_2 b_2) (* b_2 b_2))
22.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite311.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
33×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
17×	`distribute-lft-out--`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-div` `associate-+l-`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `distribute-rgt-out--` `pow1/2` `+-inverses` `fma-neg` `diff-log` `prod-diff` `flip-+`

Counts

4 → 204

Calls

4 calls:

157.0ms	(/ (/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
128.0ms	(/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
14.0ms	(- (* b_2 b_2) (* b_2 b_2))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ (/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
236.0ms	(/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
1.0ms	(- (* b_2 b_2) (* b_2 b_2))
86.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify894.0ms

Counts

216 → 216

Iterations

Iter	Nodes
2	2029
1	786
0	327

prune970.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.7b

regimes325.0ms

Accuracy

88% (3.0b remaining)

Error of 8.6b against oracle of 5.6b and baseline of 30.9b

bsearch297.0ms

Steps

Iters	Range		Point
8	2.231296991249122e+66	2.5939819947174796e+69	2.559678284282607e+69
10	-1.9680749876012584e-137	-1.346954522507992e-154	-2.16299334697662e-148
7	-7.217464048007885e+64	-4.4034929414238996e+63	-3.213987834649125e+64

simplify6.0ms

Iterations

Iter	Nodes
2	38
1	38
0	35

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.1s	5788×	body	80	valid
1.0s	1053×	body	2560	valid
637.0ms	956×	body	1280	valid
368.0ms	2937×	body	80	nan
228.0ms	453×	body	640	valid
133.0ms	98×	body	5120	valid
71.0ms	216×	body	320	valid
23.0ms	108×	body	160	valid