Details

Time bar (total: 20.7s)

sample116.0ms

Algorithm
intervals
Results
15.0ms32×body2560valid
13.0ms184×body80valid
9.0ms30×body1280valid
6.0ms24×body640valid
5.0ms83×body80nan
1.0ms7×body320valid
1.0ms4×body160valid

simplify77.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
01013
11813
23213
34113
44413
done4413

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize19.0ms

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)))

rewrite151.0ms

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:
84.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
10.0ms
(- (* b_2 b_2) (* a c))
40.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series450.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
69.0ms
(- (* b_2 b_2) (* a c))
122.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
117.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.2s

Counts
103 → 103
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01561821
13661727
210051611
327731595
done50011593

prune338.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
66×times-frac
53×add-sqr-sqrt
40×*-un-lft-identity
28×add-cube-cbrt
18×add-exp-log add-cbrt-cube
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
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/l/
Counts
4 → 124
Calls
4 calls:
9.0ms
(- (* b_2 b_2) (* a c))
99.0ms
(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
56.0ms
(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series721.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(- (* b_2 b_2) (* a c))
359.0ms
(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
230.0ms
(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
76.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts
136 → 136
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02372999
15862794
219382466
done50012460

prune546.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ c 1) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.5b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.6b
(- (* b_2 b_2) (* a c))
19.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
141×times-frac
129×add-sqr-sqrt
98×*-un-lft-identity
68×add-cube-cbrt
30×difference-of-squares
18×sqrt-prod
15×distribute-lft-out--
13×associate-/l*
11×add-exp-log
9×add-cbrt-cube
8×div-inv add-log-exp
6×associate-/r*
5×pow1 div-exp
4×flip3-- flip--
3×cbrt-undiv
2×sub-neg sqrt-div diff-log associate-/r/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 1-exp clear-num associate-/l/
Counts
4 → 157
Calls
4 calls:
63.0ms
(/ (/ c 1) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
46.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
25.0ms
(- (* b_2 b_2) (* a c))
19.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series585.0ms

Counts
4 → 12
Calls
4 calls:
316.0ms
(/ (/ c 1) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
108.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
56.0ms
(- (* b_2 b_2) (* a c))
105.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts
169 → 169
Iterations

Useful iterations: done (2.4s)

IterNodesCost
02623935
15913277
211393153
325163149
done50003137

prune445.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b_2 b_2) (* a c))
2.1b
(/ c (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a))
2.5b
(/ (/ c (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)) a)
19.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite251.0ms

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))
51.0ms
(/ c (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a))
114.0ms
(/ (/ c (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)) a)
18.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series645.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(- (* b_2 b_2) (* a c))
241.0ms
(/ c (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a))
256.0ms
(/ (/ c (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)) a)
86.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify3.6s

Counts
449 → 449
Iterations

Useful iterations: 2 (1.9s)

IterNodesCost
061813278
1147912697
2493911847
done500011847

prune1.7s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.4b

regimes163.0ms

Accuracy

95% (1.2b remaining)

Error of 6.7b against oracle of 5.5b and baseline of 29.6b

bsearch245.0ms

Steps
ItersRangePoint
4
9.936283634246925e+77
1.8488019868481542e+78
1.7151811081882383e+78
9
3.6976431258031608e-267
1.8292500652683027e-260
1.4099136946117732e-265
8
-6.990724105819741e+111
-2.6156774686163576e+108
-5.674469085146397e+110

simplify31.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
03051
13649
done3649

end0.0ms

sample3.6s

Algorithm
intervals
Results
997.0ms5908×body80valid
645.0ms472×body640valid
493.0ms1082×body2560valid
449.0ms891×body1280valid
256.0ms3009×body80nan
118.0ms107×body5120valid
39.0ms212×body320valid
13.0ms104×body160valid