Details

Time bar (total: 5.4s)

sample40.0ms

Algorithm
intervals
Results
6.0ms179×body80valid
6.0ms38×body1280valid
5.0ms15×body640valid
4.0ms24×body2560valid
2.0ms73×body80nan
1.0ms4×body5120valid
1.0ms7×body320valid
0.0ms7×body160valid

simplify8.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0187
1327
2417
3447
4447
done447

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize9.0ms

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))))
22.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite106.0ms

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-exp-log add-cbrt-cube
5×pow1 distribute-rgt-neg-in
4×flip3-- flip--
3×diff-log associate-/r*
2×sub-neg sqrt-div associate-/l/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log clear-num div-inv
Counts
4 → 91
Calls
4 calls:
61.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
10.0ms
(- (* b_2 b_2) (* a c))
23.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series262.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms
(- (* b_2 b_2) (* a c))
75.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify41.0ms

Counts
103 → 103
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0368965
11241910
25001901
done5001901

prune242.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b_2 b_2) (* a c))
2.9b
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
8.2b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite175.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
146×add-sqr-sqrt
113×*-un-lft-identity
81×add-cube-cbrt
32×difference-of-squares
27×associate-/l*
19×sqrt-prod
16×distribute-lft-out--
11×add-exp-log add-cbrt-cube
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×frac-2neg sqrt-div clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 184
Calls
4 calls:
8.0ms
(- (* b_2 b_2) (* a c))
91.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
58.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series463.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (* b_2 b_2) (* a c))
164.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
199.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
66.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify101.0ms

Counts
196 → 196
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
07252897
132102743
250032723
done50032723

prune505.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b_2 b_2) (* a c))
1.8b
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
2.9b
(/ (* 1 (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))) a)
22.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
141×times-frac
119×add-sqr-sqrt
94×*-un-lft-identity
70×add-cube-cbrt
32×add-exp-log
25×associate-/r*
24×difference-of-squares
23×add-cbrt-cube
16×div-exp
15×sqrt-prod
12×distribute-lft-out--
10×cbrt-undiv
6×prod-exp div-inv add-log-exp
5×pow1
4×associate-/l*
3×1-exp cbrt-unprod
2×flip3-- frac-2neg sqrt-div clear-num flip--
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-*r/ associate-/r/ associate-/l/
Counts
4 → 162
Calls
4 calls:
8.0ms
(- (* b_2 b_2) (* a c))
42.0ms
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
35.0ms
(/ (* 1 (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))) a)
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series426.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (* b_2 b_2) (* a c))
179.0ms
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
144.0ms
(/ (* 1 (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))) a)
68.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify92.0ms

Counts
174 → 174
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
07732158
135911999
250021976
done50021976

prune413.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (/ (* 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c))
0.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b
(- (* b_2 b_2) (* a c))
22.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
33×times-frac
32×add-exp-log
26×add-sqr-sqrt
23×*-un-lft-identity
21×add-cube-cbrt
17×div-exp
13×add-cbrt-cube
8×add-log-exp
7×1-exp associate-/r*
6×pow1 prod-exp
5×cbrt-undiv div-inv
4×rec-exp sqrt-prod
3×flip3-- flip-- associate-/l*
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 clear-num associate-/r/ cbrt-unprod distribute-lft-out-- inv-pow
Counts
4 → 101
Calls
4 calls:
45.0ms
(/ 1 (/ (* 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c))
40.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms
(- (* b_2 b_2) (* a c))
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series283.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ 1 (/ (* 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c))
78.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
35.0ms
(- (* b_2 b_2) (* a c))
66.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify53.0ms

Counts
113 → 113
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
05041012
11989871
25001827
done5001827

prune191.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 3.7b

regimes492.0ms

Accuracy

95.5% (1.1b remaining)

Error of 6.6b against oracle of 5.5b and baseline of 29.9b

bsearch126.0ms

Steps
ItersRangePoint
9
1.4800420954007604e+99
2.6367850541344314e+108
4.3978336183962956e+103
6
1.0058798208127442e-173
1.0693689171863556e-172
1.0274168215380685e-173
10
-6.90058054258779e+154
-1.4735496756669211e+144
-6.483959257496842e+145

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03619
13819
23819
done3819

end0.0ms

sample1.1s

Algorithm
intervals
Results
195.0ms5915×body80valid
193.0ms1024×body2560valid
140.0ms899×body1280valid
85.0ms2902×body80nan
52.0ms449×body640valid
29.0ms117×body5120valid
21.0ms236×body320valid
8.0ms129×body160valid