Details

Time bar (total: 6.4s)

sample81.0ms

Algorithm
intervals
Results
16.0ms542×pre80true
15.0ms286×body80nan
15.0ms146×body160valid
6.0ms110×body80valid

simplify45.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01417
12417
24416
37916
49216
510016
done10016

prune8.0ms

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: 29.8b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
0.3b
(- (* b b) (* (* 4.0 a) c))
29.7b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
121×add-sqr-sqrt
94×*-un-lft-identity
68×add-cube-cbrt
26×difference-of-squares
22×associate-/l*
16×sqrt-prod
13×distribute-lft-out--
9×add-exp-log add-cbrt-cube
8×add-log-exp
5×pow1 div-inv
3×cbrt-undiv flip3-- div-exp associate-/r* flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 149
Calls
4 calls:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
4.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series70.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
28.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
9.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify522.0ms

Counts
161 → 161
Iterations

Useful iterations: 2 (186.0ms)

IterNodesCost
02774079
16603908
221253756
done50013756

prune395.0ms

Filtered
115 candidates to 161 candidates (-40.0%)
Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New13922161
Fresh000
Picked101
Done000
Total14022162

Merged error: 8.6b

Counts
162 → 22

localize4.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000
done00

prune93.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

PrunedKeptTotal
New000
Fresh02121
Picked011
Done000
Total02222

Merged error: 8.6b

Counts
22 → 22

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
0.3b
(/ (* a c) b)

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
27×add-exp-log add-cbrt-cube
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
13×cbrt-undiv div-exp
8×associate-/l*
6×associate-/r* div-inv
5×prod-exp cbrt-unprod
2×pow1 frac-2neg clear-num add-log-exp
1×associate-/l/
Counts
2 → 73
Calls
2 calls:
11.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
5.0ms
(/ (* a c) b)

series11.0ms

Counts
2 → 6
Calls
2 calls:
5.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
5.0ms
(/ (* a c) b)

simplify448.0ms

Counts
79 → 79
Iterations

Useful iterations: 2 (147.0ms)

IterNodesCost
01671164
14551118
22056956
done5000956

prune226.0ms

Filtered
54 candidates to 79 candidates (-46.3%)
Pruning

34 alts after pruning (33 fresh and 1 done)

PrunedKeptTotal
New661379
Fresh02020
Picked101
Done011
Total6734101

Merged error: 8.5b

Counts
101 → 34

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (* -2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) 2.0) a)
0.2b
(/ a (sqrt b))
0.3b
(/ c (sqrt b))
0.3b
(* (/ a (sqrt b)) (/ c (sqrt b)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
117×times-frac
106×add-sqr-sqrt
76×add-cube-cbrt *-un-lft-identity
53×add-exp-log add-cbrt-cube
48×sqrt-prod
23×cbrt-undiv div-exp
22×associate-*r* associate-*l*
15×associate-/r*
13×prod-exp cbrt-unprod associate-/l*
9×div-inv unswap-sqr
6×pow1
4×add-log-exp
3×frac-2neg clear-num
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative associate-/l/
Counts
4 → 207
Calls
4 calls:
16.0ms
(/ (/ (* -2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) 2.0) a)
5.0ms
(/ a (sqrt b))
5.0ms
(/ c (sqrt b))
18.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))

series43.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(/ (/ (* -2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) 2.0) a)
8.0ms
(/ a (sqrt b))
8.0ms
(/ c (sqrt b))
16.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))

simplify1.1s

Counts
219 → 219
Iterations

Useful iterations: 2 (532.0ms)

IterNodesCost
03513284
19823096
243472488
done50002488

prune218.0ms

Filtered
153 candidates to 219 candidates (-43.1%)
Pruning

41 alts after pruning (40 fresh and 1 done)

PrunedKeptTotal
New20613219
Fresh52732
Picked101
Done011
Total21241253

Merged error: 8.4b

Counts
253 → 41

regimes758.0ms

Accuracy

43.5% (7.6b remaining)

Error of 16.6b against oracle of 8.9b and baseline of 22.5b

bsearch3.0ms

Steps
ItersRangePoint
0
7489.35264549372
7494.567155557807
7491.959900525763

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02639
13239
done3239

end0.0ms

sample2.2s

Algorithm
intervals
Results
486.0ms16605×pre80true
473.0ms8605×body80nan
470.0ms4527×body160valid
183.0ms3473×body80valid

Profiling

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