Details

sample229.0ms

Algorithm

intervals

Results

53.0ms	31×	body	1280	valid
35.0ms	41×	body	2560	valid
29.0ms	183×	body	80	valid
10.0ms	84×	body	80	nan
7.0ms	12×	body	640	valid
4.0ms	4×	body	5120	valid
1.0ms	4×	body	320	valid
1.0ms	4×	body	160	valid

simplify46.0ms

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.8b

localize24.0ms

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))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite688.0ms

Algorithm

rewrite-expression-head

Rules

88×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
30×	`difference-of-squares`
22×	`sqrt-prod`
21×	`times-frac`
18×	`distribute-lft-out--`
17×	`add-cube-cbrt`
14×	`unswap-sqr`
10×	`add-log-exp`
8×	`associate-l`
7×	`associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `swap-sqr` `*-commutative` `insert-posit16` `flip--`
3×	`associate-/r*` `diff-log`
2×	`associate--l-` `neg-sub0` `sub-neg` `sqrt-div` `div-sub` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `neg-log` `div-inv`

Counts

4 → 124

Calls

4 calls:

344.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
81.0ms	(- (* b_2 b_2) (* a c))
130.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
127.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
46.0ms	(- (* b_2 b_2) (* a c))
91.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
112.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.8s

Counts

136 → 136

Iterations

Iter	Nodes
done	5000
3	4717
2	1287
1	454
0	195

prune651.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
4.9b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
8.7b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

303×	`*-un-lft-identity`
264×	`add-sqr-sqrt`
258×	`times-frac`
105×	`add-cube-cbrt`
74×	`difference-of-squares`
64×	`distribute-lft-out`
46×	`associate-/l*`
44×	`sqrt-prod`
40×	`associate-l`
35×	`distribute-lft-out--`
20×	`associate-/l/`
15×	`associate-/r*`
14×	`unswap-sqr`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `swap-sqr` `div-exp` `*-commutative` `insert-posit16`
3×	`clear-num` `frac-2neg`
2×	`flip3-+` `sqrt-div` `flip-+`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 293

Calls

4 calls:

68.0ms	(- (* b_2 b_2) (* a c))
770.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
431.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
72.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series700.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* b_2 b_2) (* a c))
209.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
293.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
158.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.2s

Counts

305 → 305

Iterations

Iter	Nodes
done	5010
2	2379
1	832
0	344

prune988.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
0.8b	(- (* b_2 b_2) (* c a))
13.5b	(/ (* c a) a)
20.7b	(sqrt (- (* b_2 b_2) (* c a)))

rewrite533.0ms

Algorithm

rewrite-expression-head

Rules

93×	`add-sqr-sqrt`
48×	`*-un-lft-identity`
36×	`times-frac`
30×	`add-cube-cbrt`
22×	`difference-of-squares`
20×	`associate-l`
18×	`sqrt-prod` `unswap-sqr`
12×	`associate-r` `associate-/l*`
9×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out--`
8×	`*-commutative` `add-log-exp`
5×	`pow1`
4×	`swap-sqr` `insert-posit16`
3×	`associate-/r*` `flip3--` `flip--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 139

Calls

4 calls:

371.0ms	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
69.0ms	(- (* b_2 b_2) (* c a))
19.0ms	(/ (* c a) a)
70.0ms	(sqrt (- (* b_2 b_2) (* c a)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
57.0ms	(- (* b_2 b_2) (* c a))
7.0ms	(/ (* c a) a)
81.0ms	(sqrt (- (* b_2 b_2) (* c a)))

simplify1.7s

Counts

151 → 151

Iterations

Iter	Nodes
done	5001
2	1829
1	530
0	224

prune594.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ c (- (sqrt (- (* b_2 b_2) (* c a))) b_2))
0.8b	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
0.8b	(- (* b_2 b_2) (* c a))
20.7b	(sqrt (- (* b_2 b_2) (* c a)))

rewrite932.0ms

Algorithm

rewrite-expression-head

Rules

87×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
30×	`difference-of-squares`
22×	`sqrt-prod`
18×	`times-frac`
16×	`add-cube-cbrt`
14×	`unswap-sqr`
13×	`distribute-lft-out--`
8×	`associate-l` `add-log-exp`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`flip3--` `swap-sqr` `*-commutative` `insert-posit16` `flip--`
3×	`associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 115

Calls

4 calls:

376.0ms	(/ c (- (sqrt (- (* b_2 b_2) (* c a))) b_2))
430.0ms	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
45.0ms	(- (* b_2 b_2) (* c a))
75.0ms	(sqrt (- (* b_2 b_2) (* c a)))

series502.0ms

Counts

4 → 12

Calls

4 calls:

228.0ms	(/ c (- (sqrt (- (* b_2 b_2) (* c a))) b_2))
126.0ms	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
62.0ms	(- (* b_2 b_2) (* c a))
87.0ms	(sqrt (- (* b_2 b_2) (* c a)))

simplify2.9s

Counts

127 → 127

Iterations

Iter	Nodes
done	5000
3	4727
2	1245
1	400
0	181

prune455.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.5b

regimes252.0ms

Accuracy

93.7% (1.5b remaining)

Error of 7.0b against oracle of 5.6b and baseline of 28.9b

bsearch283.0ms

Steps

Iters	Range		Point
7	5.455680955858941e+61	9.381769121995126e+63	9.19242293018462e+63
9	2.052878569093159e-301	1.4262517675988988e-296	1.8716662261062222e-300
8	-3.872027431050641e+50	-1.3801743424438113e+48	-3.812499047218918e+50

simplify13.0ms

Iterations

Iter	Nodes
done	43
1	43
0	36

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.3s	5893×	body	80	valid
986.0ms	1104×	body	2560	valid
933.0ms	854×	body	1280	valid
387.0ms	3005×	body	80	nan
216.0ms	463×	body	640	valid
109.0ms	98×	body	5120	valid
106.0ms	221×	body	320	valid
25.0ms	115×	body	160	valid