Details

sample73.0ms

Algorithm

intervals

Results

13.0ms	35×	body	2560	valid
13.0ms	196×	body	80	valid
10.0ms	31×	body	1280	valid
6.0ms	89×	body	80	nan
3.0ms	11×	body	640	valid
2.0ms	3×	body	5120	valid
0.0ms	3×	body	160	valid
0.0ms	2×	body	320	valid

simplify34.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	44
4	44
3	41
2	32
1	18
0	10

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(- (* b_2 b_2) (* a c))
0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `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 → 91

Calls

4 calls:

61.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
11.0ms	(- (* b_2 b_2) (* a c))
19.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series362.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
38.0ms	(- (* b_2 b_2) (* a c))
109.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
104.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify676.0ms

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	1527
1	392
0	158

prune604.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.2b	(- (* b_2 b_2) (* a c))
0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

165×	`times-frac`
130×	`add-sqr-sqrt`
129×	`*-un-lft-identity`
77×	`add-cube-cbrt`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`add-cbrt-cube` `associate-/r/`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
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 → 177

Calls

4 calls:

66.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
12.0ms	(- (* 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)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
54.0ms	(- (* b_2 b_2) (* a c))
108.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
82.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts

189 → 189

Iterations

Iter	Nodes
done	5000
2	3515
1	665
0	266

prune748.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b_2 b_2) (* a c))
0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
13×	`associate-r` `add-exp-log` `add-cube-cbrt`
11×	`times-frac`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `distribute-rgt-neg-in` `sqrt-div` `div-exp` `associate-*l/` `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-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 89

Calls

4 calls:

13.0ms	(- (* b_2 b_2) (* a c))
115.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
44.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series403.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b_2 b_2) (* a c))
122.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
123.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
114.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.9s

Counts

101 → 101

Iterations

Iter	Nodes
done	5000
2	2879
1	462
0	177

prune512.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.8b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.6b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite219.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
150×	`add-sqr-sqrt`
115×	`*-un-lft-identity`
81×	`add-cube-cbrt`
34×	`difference-of-squares`
27×	`associate-/l*`
20×	`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×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-div`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 187

Calls

4 calls:

45.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
97.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
61.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series702.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
237.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
284.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
95.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts

199 → 199

Iterations

Iter	Nodes
done	5000
2	4138
1	765
0	304

prune1.1s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.4b

regimes400.0ms

Accuracy

86.9% (3.7b remaining)

Error of 9.1b against oracle of 5.4b and baseline of 33.9b

bsearch246.0ms

Steps

Iters	Range		Point
10	4.0721326822252617e+40	3.6590220876252264e+50	3.628799960716312e+50
9	-8.630995884000565e-306	7.211886341925621e-305	-4.76785797017381e-309
6	-1.278587798556269e+59	-1.7736353873113924e+58	-1.9700105655521088e+58

simplify5.0ms

Iterations

Iter	Nodes
done	38
2	38
1	37
0	32

end0.0ms

sample3.0s

Algorithm

intervals

Results

991.0ms	1136×	body	2560	valid
517.0ms	868×	body	1280	valid
445.0ms	5799×	body	80	valid
174.0ms	2815×	body	80	nan
119.0ms	109×	body	5120	valid
110.0ms	446×	body	640	valid
46.0ms	238×	body	320	valid
13.0ms	102×	body	160	valid