Details

Time bar (total: 6.2s)

sample55.0ms

Algorithm
intervals
Results
27.0ms289×body80valid
7.0ms79×body80nan

simplify88.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
02038
13838
27837
313637
415737
516637
616937
done16937

prune12.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 18.4b

Counts
2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
1.7b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
*-un-lft-identity add-log-exp
sqrt-prod
pow1 add-cube-cbrt
add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log difference-of-squares
distribute-lft-out--
Counts
4 → 57
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series71.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
29.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify745.0ms

Counts
69 → 69
Iterations

Useful iterations: 3 (209.0ms)

IterNodesCost
0911130
12051004
2681944
32362936
done5001936

prune178.0ms

Filtered
54 candidates to 69 candidates (-27.8%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New64569
Fresh000
Picked101
Done000
Total65570

Merged error: 8.7b

Counts
70 → 5

localize27.0ms

Local error

Found 4 expressions with local error:

21.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
pow1 add-cube-cbrt *-un-lft-identity sqrt-div
add-exp-log rem-sqrt-square flip3-- sqrt-pow1 pow1/2 add-cbrt-cube flip-- add-log-exp
Counts
4 → 60
Calls
4 calls:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series63.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify659.0ms

Counts
72 → 72
Iterations

Useful iterations: 3 (131.0ms)

IterNodesCost
0531140
11271012
2427940
31537932
done5000932

prune279.0ms

Filtered
60 candidates to 72 candidates (-20.0%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New72072
Fresh044
Picked011
Done000
Total72577

Merged error: 8.7b

Counts
77 → 5

localize28.0ms

Local error

Found 4 expressions with local error:

21.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
pow1 add-cube-cbrt *-un-lft-identity sqrt-div
add-exp-log rem-sqrt-square flip3-- sqrt-pow1 pow1/2 add-cbrt-cube flip-- add-log-exp
Counts
4 → 60
Calls
4 calls:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series65.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify633.0ms

Counts
72 → 72
Iterations

Useful iterations: 3 (125.0ms)

IterNodesCost
0531140
11271012
2427940
31537932
done5001932

prune281.0ms

Filtered
60 candidates to 72 candidates (-20.0%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New72072
Fresh033
Picked011
Done011
Total72577

Merged error: 8.7b

Counts
77 → 5

localize26.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.5b
(/ (- (neg b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
6.2b
(/ (* a c) b)
21.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
18×add-sqr-sqrt
14×add-exp-log add-cbrt-cube
add-cube-cbrt times-frac
associate-/l*
add-log-exp
pow1 distribute-lft-out--
cbrt-undiv div-exp associate-/r* sqrt-prod difference-of-squares
flip3-- flip--
distribute-rgt-neg-in frac-2neg sqrt-div prod-exp clear-num cbrt-unprod div-inv associate-/l/
sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-sub
Counts
4 → 81
Calls
4 calls:
10.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
11.0ms
(/ (- (neg b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
5.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series50.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
13.0ms
(/ (- (neg b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
5.0ms
(/ (* a c) b)
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify708.0ms

Counts
93 → 93
Iterations

Useful iterations: 2 (137.0ms)

IterNodesCost
01831537
14721434
218501280
done50011280

prune165.0ms

Filtered
67 candidates to 93 candidates (-38.8%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New91293
Fresh022
Picked101
Done022
Total92698

Merged error: 7.2b

Counts
98 → 6

regimes222.0ms

Accuracy

91.4% (1.2b remaining)

Error of 8.2b against oracle of 7.0b and baseline of 20.6b

bsearch84.0ms

Steps
ItersRangePoint
10
1.1487243557305423e+102
3.920821933018458e+112
1.3634580034127795e+109
10
-8.003596903883499e+165
-5.641302321031635e+152
-1.3279709836271267e+154

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
044135
152135
done52135

end0.0ms

sample1.6s

Algorithm
intervals
Results
841.0ms8785×body80valid
271.0ms2992×body80nan

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