Details

Time bar (total: 10.6s)

sample326.0ms

Algorithm
intervals
Results
6.0ms30×body1280valid
6.0ms186×body80valid
5.0ms28×body2560valid
2.0ms85×body80nan
2.0ms16×body640valid
1.0ms3×body5120valid
0.0ms4×body320valid
0.0ms2×body160valid

simplify50.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01013
11813
23213
34113
44413
done4413

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize12.0ms

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))
1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite111.0ms

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:
60.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms
(- (* b_2 b_2) (* a c))
27.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series272.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
36.0ms
(- (* b_2 b_2) (* a c))
75.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
73.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.5s

Counts
103 → 103
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01561821
13661727
210051611
327731595
done50011593

prune247.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.0b

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.1b
(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
8.6b
(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
25.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
66×times-frac
57×add-sqr-sqrt
42×*-un-lft-identity
28×add-cube-cbrt
18×add-exp-log add-cbrt-cube
14×difference-of-squares
13×associate-/l*
10×sqrt-prod associate-/r/
9×associate-/r*
7×cbrt-undiv flip3-- div-exp flip-- distribute-lft-out--
6×div-inv 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 → 127
Calls
4 calls:
40.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
79.0ms
(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
49.0ms
(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series532.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
201.0ms
(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
190.0ms
(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
65.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts
139 → 139
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02393118
15932899
219412569
done50002563

prune335.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ c 1) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.6b
(- (* b_2 b_2) (* a c))
1.2b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
25.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite117.0ms

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:
49.0ms
(/ (/ c 1) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
8.0ms
(- (* b_2 b_2) (* a c))
43.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series372.0ms

Counts
4 → 12
Calls
4 calls:
195.0ms
(/ (/ c 1) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
36.0ms
(- (* b_2 b_2) (* a c))
78.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
63.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.5s

Counts
169 → 169
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02623935
15913277
211393153
325143149
done50013137

prune246.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.9b

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
25.0b
(sqrt (- (* b_2 b_2) (* a c)))
25.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×*-un-lft-identity
8×sqrt-prod add-log-exp
6×pow1 add-cube-cbrt
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip-- difference-of-squares
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
41.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
43.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series278.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
76.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
61.0ms
(sqrt (- (* b_2 b_2) (* a c)))
65.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Counts
72 → 72
Iterations

Useful iterations: done (1.7s)

IterNodesCost
0781064
1182944
2496884
31172876
42461864
done5000862

prune197.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.9b

regimes177.0ms

Accuracy

96.2% (0.9b remaining)

Error of 6.9b against oracle of 6.0b and baseline of 29.9b

bsearch123.0ms

Steps
ItersRangePoint
9
8.777746745010686e+110
1.2290467223415774e+117
1.1912031425131646e+117
9
-5.951265309377375e-290
-1.5896185090842948e-298
-1.916322353859377e-297
7
-1.6239005782062206e+154
-7.680972122048022e+152
-1.457738542065717e+153

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
03249
13647
done3647

end0.0ms

sample1.0s

Algorithm
intervals
Results
207.0ms1108×body2560valid
189.0ms5896×body80valid
134.0ms886×body1280valid
82.0ms2950×body80nan
51.0ms446×body640valid
27.0ms110×body5120valid
22.0ms229×body320valid
6.0ms106×body160valid