Details

sample140.0ms

Algorithm

intervals

Results

12.0ms	36×	body	2560	valid
11.0ms	187×	body	80	valid
7.0ms	30×	body	1280	valid
4.0ms	79×	body	80	nan
2.0ms	10×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify98.0ms

Counts

1 → 1

Iterations

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

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
0.4b	(- (* b_2 b_2) (* a c))
0.9b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity`
36×	`times-frac`
31×	`add-sqr-sqrt`
30×	`add-cube-cbrt`
16×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`associate-/l*`
9×	`distribute-lft-out`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`neg-mul-1`
3×	`associate-/r*` `sqrt-prod`
2×	`flip3-+` `flip3--` `sqrt-div` `flip-+` `flip--` `distribute-neg-frac` `associate-/l/`
1×	`neg-sub0` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `distribute-frac-neg` `div-inv`

Counts

4 → 106

Calls

4 calls:

104.0ms	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
10.0ms	(- (* b_2 b_2) (* a c))
25.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series404.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
40.0ms	(- (* b_2 b_2) (* a c))
114.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
123.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify958.0ms

Counts

118 → 118

Iterations

Iter	Nodes
done	5001
2	1823
1	448
0	186

prune625.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.4b	(- (* b_2 b_2) (* a c))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite123.0ms

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:

57.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
11.0ms	(- (* b_2 b_2) (* a c))
32.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
54.0ms	(- (* b_2 b_2) (* a c))
105.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
97.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts

189 → 189

Iterations

Iter	Nodes
done	5000
2	3515
1	665
0	266

prune715.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.8b

localize42.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt a)
0.5b	(* (cbrt a) (cbrt a))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
19×	`cbrt-prod`
18×	`*-un-lft-identity`
14×	`add-cube-cbrt`
12×	`pow1`
8×	`add-log-exp`
7×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `sqrt-prod` `unswap-sqr`
2×	`flip3--` `sqrt-div` `diff-log` `pow-prod-down` `pow-sqr` `pow-prod-up` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `pow2` `neg-sub0` `rem-sqrt-square` `sub-neg` `distribute-rgt-neg-in` `sqrt-pow1` `pow-plus` `pow1/2` `neg-log` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 84

Calls

4 calls:

1.0ms	(cbrt a)
16.0ms	(* (cbrt a) (cbrt a))
31.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series770.0ms

Counts

4 → 12

Calls

4 calls:

262.0ms	(cbrt a)
310.0ms	(* (cbrt a) (cbrt a))
103.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
95.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
2	1595
1	342
0	142

prune538.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
10×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt`
6×	`sqrt-div`
4×	`flip3--` `add-cbrt-cube` `add-exp-log` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `distribute-rgt-neg-in` `neg-log`

Counts

4 → 63

Calls

4 calls:

34.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
68.0ms	(sqrt (- (* b_2 b_2) (* a c)))
80.0ms	(sqrt (- (* b_2 b_2) (* a c)))
89.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify503.0ms

Counts

75 → 75

Iterations

Iter	Nodes
done	5000
2	829
1	208
0	84

prune478.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.8b

regimes450.0ms

Accuracy

85.1% (4.2b remaining)

Error of 10.0b against oracle of 5.8b and baseline of 34.2b

bsearch350.0ms

Steps

Iters	Range		Point
9	3.768382185355077e+69	1.107955803311012e+78	7.501979458872916e+77
6	-6.6625002027150184e-136	-1.2670716760605177e-136	-6.596302400897662e-136
9	-1.3974083100475422e-87	-7.780761669250176e-94	-7.877985662156599e-94
10	-4.6999773453873415e+54	-3.4259522644792056e+40	-5.84038254482515e+46

simplify9.0ms

Iterations

Iter	Nodes
done	59
3	59
2	57
1	45
0	36

end0.0ms

sample3.1s

Algorithm

intervals

Results

962.0ms	5896×	body	80	valid
732.0ms	1048×	body	2560	valid
308.0ms	877×	body	1280	valid
192.0ms	446×	body	640	valid
183.0ms	2811×	body	80	nan
63.0ms	121×	body	5120	valid
44.0ms	229×	body	320	valid
13.0ms	105×	body	160	valid