Details

Time bar (total: 16.8s)

sample186.0ms

Algorithm
intervals
Results
16.0ms184×body80valid
13.0ms32×body2560valid
11.0ms30×body1280valid
6.0ms24×body640valid
5.0ms83×body80nan
1.0ms7×body320valid
1.0ms4×body160valid

simplify52.0ms

Counts
1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize84.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b
(- (* b_2 b_2) (* a c))
1.4b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite227.0ms

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:
136.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
10.0ms
(- (* b_2 b_2) (* a c))
50.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series384.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
43.0ms
(- (* b_2 b_2) (* a c))
103.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
111.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify657.0ms

Counts
103 → 103

prune422.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b_2 b_2) (* a c))
2.5b
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.2b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
19.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite266.0ms

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:
14.0ms
(- (* b_2 b_2) (* a c))
122.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
93.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
17.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series666.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b_2 b_2) (* a c))
247.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
277.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
94.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts
196 → 196

prune830.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b_2 b_2) (* a c))
2.5b
(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
3.4b
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
19.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite287.0ms

Algorithm
rewrite-expression-head
Rules
831×times-frac
545×add-sqr-sqrt
448×*-un-lft-identity
352×add-cube-cbrt
96×difference-of-squares
74×associate-/l*
51×sqrt-prod
48×distribute-lft-out--
25×associate-/r*
22×div-inv
18×add-exp-log add-cbrt-cube
9×cbrt-undiv div-exp
6×add-log-exp
5×pow1 associate-/r/
2×flip3-- frac-2neg sqrt-div clear-num flip--
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/l/
Counts
4 → 437
Calls
4 calls:
17.0ms
(- (* b_2 b_2) (* a c))
120.0ms
(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
77.0ms
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
21.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series637.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (* b_2 b_2) (* a c))
220.0ms
(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
243.0ms
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
100.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.0s

Counts
449 → 449

prune1.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.6b
(/ (/ 1 1) (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
0.6b
(- (* b_2 b_2) (* a c))
19.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite254.0ms

Algorithm
rewrite-expression-head
Rules
745×times-frac
479×add-sqr-sqrt
392×*-un-lft-identity
306×add-cube-cbrt
86×difference-of-squares
46×sqrt-prod
43×distribute-lft-out--
38×div-inv
37×add-exp-log
29×div-exp
22×associate-/r*
16×add-cbrt-cube
13×associate-/l*
10×1-exp
8×cbrt-undiv add-log-exp
5×pow1
4×rec-exp
3×flip3-- flip--
2×sub-neg sqrt-div diff-log
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/r/ associate-/l/
Counts
4 → 393
Calls
4 calls:
87.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
75.0ms
(/ (/ 1 1) (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
9.0ms
(- (* b_2 b_2) (* a c))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series374.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
143.0ms
(/ (/ 1 1) (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
46.0ms
(- (* b_2 b_2) (* a c))
90.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify901.0ms

Counts
405 → 405

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

regimes310.0ms

Accuracy

95.2% (1.2b remaining)

Error of 6.6b against oracle of 5.5b and baseline of 29.6b

bsearch198.0ms

Steps
ItersRangePoint
4
9.936283634246925e+77
1.8488019868481542e+78
1.7151811081882383e+78
9
3.6976431258031608e-267
1.8292500652683027e-260
7.061692521831336e-266
8
-6.990724105819741e+111
-2.6156774686163576e+108
-5.674469085146397e+110

simplify1.4s

end0.0ms

sample3.1s

Algorithm
intervals
Results
794.0ms3009×body80nan
545.0ms5908×body80valid
527.0ms1082×body2560valid
404.0ms891×body1280valid
122.0ms472×body640valid
58.0ms107×body5120valid
57.0ms104×body160valid
39.0ms212×body320valid