Details

Time bar (total: 22.9s)

sample222.0ms

Algorithm
intervals
Results
19.0ms174×body80valid
18.0ms30×body2560valid
13.0ms28×body1280valid
9.0ms97×body80nan
8.0ms23×body640valid
4.0ms6×body5120valid
2.0ms9×body320valid
1.0ms8×body160valid

simplify37.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
010283
118283
232283
341283
444283
done44283

prune37.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize40.0ms

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))
2.2b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite138.0ms

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-cbrt-cube add-exp-log
5×pow1 distribute-rgt-neg-in
4×flip3-- flip--
3×associate-/r* diff-log
2×sub-neg sqrt-div associate-/l/
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log div-inv
Counts
4 → 91
Calls
4 calls:
70.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
9.0ms
(- (* b_2 b_2) (* a c))
35.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series398.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
55.0ms
(- (* b_2 b_2) (* a c))
107.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
108.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify3.6s

Counts
103 → 103
Iterations

Useful iterations: done (3.6s)

IterNodesCost
015839129
138335913
2103935553
3360835393
done500135352

prune607.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.6b

localize45.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.5b
(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.2b
(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite213.0ms

Algorithm
rewrite-expression-head
Rules
66×times-frac
57×add-sqr-sqrt
42×*-un-lft-identity
28×add-cube-cbrt
18×add-cbrt-cube add-exp-log
14×difference-of-squares
13×associate-/l*
10×associate-/r/ sqrt-prod
9×associate-/r*
7×cbrt-undiv flip3-- div-exp flip-- distribute-lft-out--
6×div-inv add-log-exp
5×pow1
2×clear-num frac-2neg sqrt-div prod-exp cbrt-unprod
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log associate-/l/
Counts
4 → 127
Calls
4 calls:
44.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
96.0ms
(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
51.0ms
(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series746.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
217.0ms
(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
308.0ms
(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
113.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify3.1s

Counts
139 → 139
Iterations

Useful iterations: 2 (820.0ms)

IterNodesCost
023759212
160854042
2210653081
done500253081

prune614.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.6b

localize39.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.4b
(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
4.5b
(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
23.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite252.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
26×*-un-lft-identity
24×associate-*r*
22×times-frac
18×add-cbrt-cube add-exp-log add-cube-cbrt
8×difference-of-squares
7×pow1 sqrt-prod
6×add-log-exp
5×cbrt-undiv div-exp
4×prod-exp cbrt-unprod distribute-lft-out--
3×associate-/r* flip3-- associate-*l* flip--
2×sqrt-div associate-*r/ associate-/r/ div-inv unswap-sqr
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log pow-prod-down *-commutative associate-/l* associate-/l/
Counts
4 → 97
Calls
4 calls:
65.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
119.0ms
(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
48.0ms
(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series704.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
246.0ms
(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
260.0ms
(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
88.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.7s

Counts
109 → 109
Iterations

Useful iterations: done (2.7s)

IterNodesCost
020336308
153131960
2165931478
done500330760

prune647.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.5b
(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.2b
(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite229.0ms

Algorithm
rewrite-expression-head
Rules
66×times-frac
57×add-sqr-sqrt
42×*-un-lft-identity
28×add-cube-cbrt
18×add-cbrt-cube add-exp-log
14×difference-of-squares
13×associate-/l*
10×associate-/r/ sqrt-prod
9×associate-/r*
7×cbrt-undiv flip3-- div-exp flip-- distribute-lft-out--
6×div-inv add-log-exp
5×pow1
2×clear-num frac-2neg sqrt-div prod-exp cbrt-unprod
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log associate-/l/
Counts
4 → 127
Calls
4 calls:
45.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
94.0ms
(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
71.0ms
(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series663.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
235.0ms
(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
258.0ms
(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
70.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify3.3s

Counts
139 → 139
Iterations

Useful iterations: 2 (902.0ms)

IterNodesCost
023759212
160854042
2210653081
done500253081

prune696.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.6b

regimes515.0ms

Accuracy

89.7% (2.7b remaining)

Error of 8.5b against oracle of 5.8b and baseline of 32.0b

bsearch300.0ms

Steps
ItersRangePoint
10
7.868349732386487e+96
4.727011775790926e+114
1.0928779650362586e+104
10
-7.955104670113648e-283
-3.206335945357617e-294
-3.264171759716638e-294
9
-1.5616592422619596e-10
-4.8623869860036984e-17
-5.2605709473303605e-14

simplify11.0ms

Iterations

Useful iterations: 0 (6.0ms)

IterNodesCost
0321079
1371079
done371079

end0.0ms

sample3.0s

Algorithm
intervals
Results
966.0ms1040×body2560valid
546.0ms916×body1280valid
539.0ms5866×body80valid
240.0ms2929×body80nan
125.0ms462×body640valid
89.0ms110×body5120valid
48.0ms220×body320valid
16.0ms113×body160valid