Details

Time bar (total: 22.5s)

sample46.0ms

Algorithm
intervals
Results
8.0ms184×body80valid
8.0ms32×body2560valid
6.0ms30×body1280valid
4.0ms24×body640valid
3.0ms83×body80nan
1.0ms7×body320valid
0.0ms4×body160valid

simplify24.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01013
11813
23213
34113
44413
done4413

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize11.0ms

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)))

rewrite190.0ms

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:
107.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms
(- (* b_2 b_2) (* a c))
31.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
40.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series395.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
51.0ms
(- (* b_2 b_2) (* a c))
102.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
91.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts
103 → 103
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01561821
13661727
210051611
327731595
done50011593

prune426.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize14.0ms

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)))

rewrite238.0ms

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:
13.0ms
(- (* b_2 b_2) (* a c))
140.0ms
(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
65.0ms
(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series731.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(- (* b_2 b_2) (* a c))
307.0ms
(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
298.0ms
(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
87.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts
136 → 136
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02372999
15862794
219382466
done50012460

prune480.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ c (- (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)))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×add-exp-log associate-/r* add-cbrt-cube
5×pow1 distribute-lft-out--
4×flip3-- flip--
3×associate-/l*
2×sub-neg sqrt-div diff-log associate-/r/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
4 → 83
Calls
4 calls:
59.0ms
(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
47.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms
(- (* b_2 b_2) (* a c))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series596.0ms

Counts
4 → 12
Calls
4 calls:
315.0ms
(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
126.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
51.0ms
(- (* b_2 b_2) (* a c))
104.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify4.8s

Counts
95 → 95
Iterations

Useful iterations: 4 (2.6s)

IterNodesCost
01471588
13111491
27741393
318101389
445681375
done50011375

prune325.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.4b

localize21.0ms

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)))

rewrite262.0ms

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))
62.0ms
(/ c (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a))
119.0ms
(/ (/ c (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)) a)
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series669.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(- (* b_2 b_2) (* a c))
231.0ms
(/ c (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a))
281.0ms
(/ (/ c (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)) a)
92.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify3.3s

Counts
449 → 449
Iterations

Useful iterations: 2 (1.5s)

IterNodesCost
061813278
1147912697
2493911847
done500011847

prune1.9s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.4b

regimes203.0ms

Accuracy

95% (1.2b remaining)

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

bsearch213.0ms

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

simplify9.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
03153
13949
done3949

end0.0ms

sample3.0s

Algorithm
intervals
Results
773.0ms891×body1280valid
511.0ms1082×body2560valid
499.0ms5908×body80valid
226.0ms472×body640valid
214.0ms3009×body80nan
49.0ms107×body5120valid
47.0ms104×body160valid
38.0ms212×body320valid