Details

sample103.0ms

Algorithm

intervals

Results

30.0ms	41×	body	2560	valid
20.0ms	183×	body	80	valid
17.0ms	31×	body	1280	valid
9.0ms	84×	body	80	nan
5.0ms	12×	body	640	valid
4.0ms	4×	body	5120	valid
2.0ms	4×	body	320	valid
1.0ms	4×	body	160	valid

simplify39.0ms

Counts

1 → 1

Iterations

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.8b

localize19.0ms

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)))

rewrite72.0ms

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--` `insert-posit16` `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 → 95

Calls

4 calls:

42.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series357.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
45.0ms	(- (* b_2 b_2) (* a c))
97.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
67.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.9s

Counts

107 → 107

Iterations

Iter	Nodes
done	5005
3	3743
2	1046
1	388
0	162

prune525.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
53×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
28×	`add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
13×	`associate-/l*`
12×	`difference-of-squares`
10×	`associate-/r/`
9×	`associate-/r*` `sqrt-prod`
7×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
6×	`div-inv` `distribute-lft-out--` `add-log-exp`
5×	`pow1`
4×	`insert-posit16`
2×	`clear-num` `frac-2neg` `sqrt-div` `prod-exp` `cbrt-unprod`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 128

Calls

4 calls:

9.0ms	(- (* b_2 b_2) (* a c))
102.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
75.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series588.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (* b_2 b_2) (* a c))
208.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
231.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
93.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

140 → 140

Iterations

Iter	Nodes
done	5000
2	2144
1	614
0	238

prune656.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize54.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (/ (/ a (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (* (cbrt a) (cbrt a))) (/ (/ c (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (cbrt a)))
2.9b	(/ (/ a (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (* (cbrt a) (cbrt a)))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite382.0ms

Algorithm

rewrite-expression-head

Rules

582×	`times-frac`
438×	`add-sqr-sqrt`
272×	`*-un-lft-identity`
218×	`add-cube-cbrt`
210×	`sqrt-prod`
202×	`associate-r`
111×	`cbrt-prod`
85×	`add-exp-log`
59×	`add-cbrt-cube`
54×	`difference-of-squares`
39×	`cbrt-undiv` `div-exp`
37×	`associate-l`
33×	`associate-/l*`
28×	`unswap-sqr`
27×	`distribute-lft-out--`
23×	`prod-exp` `cbrt-unprod`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`div-inv`
11×	`flip3--` `flip--`
8×	`pow1`
4×	`insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `clear-num` `associate-/r` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `-commutative` `associate-/l/`

Counts

4 → 429

Calls

4 calls:

251.0ms	(* (/ (/ a (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (* (cbrt a) (cbrt a))) (/ (/ c (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (cbrt a)))
88.0ms	(/ (/ a (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (* (cbrt a) (cbrt a)))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series1.3s

Counts

4 → 12

Calls

4 calls:

288.0ms	(* (/ (/ a (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (* (cbrt a) (cbrt a))) (/ (/ c (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (cbrt a)))
805.0ms	(/ (/ a (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (* (cbrt a) (cbrt a)))
71.0ms	(sqrt (- (* b_2 b_2) (* a c)))
91.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.3s

Counts

441 → 441

Iterations

Iter	Nodes
done	5000
1	2454
0	700

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize88.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (* (* (/ (cbrt a) (cbrt a)) (/ (cbrt a) (fabs (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))) (/ (/ (cbrt a) (sqrt (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))) (cbrt a))) (/ (/ c (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (cbrt a)))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite468.0ms

Algorithm

rewrite-expression-head

Rules

360×	`times-frac`
310×	`add-exp-log`
245×	`add-sqr-sqrt`
206×	`*-un-lft-identity`
202×	`associate-r`
179×	`add-cbrt-cube`
170×	`add-cube-cbrt`
135×	`sqrt-prod`
129×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
99×	`cbrt-prod`
36×	`difference-of-squares`
18×	`sqrt-div` `distribute-lft-out--`
17×	`frac-times` `associate-*l/`
16×	`pow1`
12×	`associate-/r/`
9×	`flip3--` `flip--`
7×	`associate-*r/` `div-inv`
6×	`pow-prod-down`
4×	`insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`associate-l` `*-commutative`

Counts

4 → 374

Calls

4 calls:

400.0ms	(* (* (* (/ (cbrt a) (cbrt a)) (/ (cbrt a) (fabs (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))) (/ (/ (cbrt a) (sqrt (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))) (cbrt a))) (/ (/ c (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (cbrt a)))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series10.3s

Counts

4 → 12

Calls

4 calls:

10.0s	(* (* (* (/ (cbrt a) (cbrt a)) (/ (cbrt a) (fabs (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))) (/ (/ (cbrt a) (sqrt (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))) (cbrt a))) (/ (/ c (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (cbrt a)))
97.0ms	(sqrt (- (* b_2 b_2) (* a c)))
85.0ms	(sqrt (- (* b_2 b_2) (* a c)))
90.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.8s

Counts

386 → 386

Iterations

Iter	Nodes
done	5002
1	2320
0	656

prune1.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.5b

regimes224.0ms

Accuracy

90.7% (2.4b remaining)

Error of 7.9b against oracle of 5.6b and baseline of 31.1b

bsearch332.0ms

Steps

Iters	Range		Point
7	5.455680955858941e+61	9.381769121995126e+63	9.19242293018462e+63
8	-1.062177424076527e-128	-2.2311151369229123e-133	-4.475531474079766e-133
9	-1.3801743424438113e+48	-5.488676459076893e+41	-1.3041251107393795e+48

simplify17.0ms

Iterations

Iter	Nodes
done	54
1	54
0	45

end0.0ms

sample3.6s

Algorithm

intervals

Results

823.0ms	1104×	body	2560	valid
711.0ms	5893×	body	80	valid
614.0ms	854×	body	1280	valid
374.0ms	3005×	body	80	nan
360.0ms	115×	body	160	valid
196.0ms	463×	body	640	valid
98.0ms	221×	body	320	valid
76.0ms	98×	body	5120	valid