Details

Time bar (total: 6.5s)

sample26.0ms

Algorithm
intervals
Results
12.0ms256×body80valid

simplify9.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01114
11514
22114
32214
done2214

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 38.0b

Counts
2 → 1

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.2b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×times-frac
18×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
add-exp-log add-cbrt-cube add-log-exp
pow1
associate-/r* associate-/l*
rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
cbrt-undiv +-commutative frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num sum-log
Counts
3 → 65
Calls
3 calls:
4.0ms
(+ (* x x) (* y y))
10.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
6.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series49.0ms

Counts
3 → 9
Calls
3 calls:
6.0ms
(+ (* x x) (* y y))
14.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
29.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify860.0ms

Counts
74 → 74
Iterations

Useful iterations: 3 (348.0ms)

IterNodesCost
01281436
12921370
210991243
332001233
done50001233

prune145.0ms

Filtered
61 candidates to 74 candidates (-21.3%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New68674
Fresh000
Picked101
Done000
Total69675

Merged error: 18.1b

Counts
75 → 6

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.1b
(* 0.3333333333333333 (+ (* z z) (+ (* x x) (* y y))))
35.2b
(sqrt (* 0.3333333333333333 (+ (* z z) (+ (* x x) (* y y)))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
pow1
add-sqr-sqrt
add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
associate-*r/
flip3-+ associate-*r* associate-*l* flip-+
sqrt-pow1 sqrt-div pow-prod-down
+-commutative distribute-rgt-in distribute-lft-in pow1/2 prod-exp sum-log sqrt-prod *-commutative cbrt-unprod unswap-sqr
Counts
3 → 46
Calls
3 calls:
4.0ms
(+ (* x x) (* y y))
8.0ms
(* 0.3333333333333333 (+ (* z z) (+ (* x x) (* y y))))
7.0ms
(sqrt (* 0.3333333333333333 (+ (* z z) (+ (* x x) (* y y)))))

series49.0ms

Counts
3 → 9
Calls
3 calls:
6.0ms
(+ (* x x) (* y y))
14.0ms
(* 0.3333333333333333 (+ (* z z) (+ (* x x) (* y y))))
30.0ms
(sqrt (* 0.3333333333333333 (+ (* z z) (+ (* x x) (* y y)))))

simplify1.4s

Counts
55 → 55
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
099887
1300831
21309728
34313728
done5000728

prune89.0ms

Filtered
41 candidates to 55 candidates (-34.1%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New53255
Fresh145
Picked011
Done000
Total54761

Merged error: 4.5b

Counts
61 → 7

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.4b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
35.1b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×times-frac
33×add-sqr-sqrt
32×add-cube-cbrt *-un-lft-identity
associate-/r* associate-/l*
add-exp-log add-cbrt-cube add-log-exp
pow1 sqrt-div
flip3-+ flip-+
associate-/l/
cbrt-undiv +-commutative rem-sqrt-square sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log div-inv
Counts
3 → 89
Calls
3 calls:
5.0ms
(+ (* x x) (* y y))
10.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
6.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series63.0ms

Counts
3 → 9
Calls
3 calls:
6.0ms
(+ (* x x) (* y y))
37.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
21.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify664.0ms

Counts
98 → 98
Iterations

Useful iterations: 3 (263.0ms)

IterNodesCost
01412253
12972048
29391966
323121945
done50011945

prune140.0ms

Filtered
64 candidates to 98 candidates (-53.1%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New95398
Fresh055
Picked011
Done011
Total9510105

Merged error: 4.3b

Counts
105 → 10

localize4.0ms

Local error

Found 1 expressions with local error:

0.2b
(* (sqrt 0.3333333333333333) z)

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt
associate-*l*
add-cube-cbrt *-un-lft-identity sqrt-prod
pow1 add-exp-log associate-*r* add-cbrt-cube
unswap-sqr
pow-prod-down prod-exp *-commutative cbrt-unprod add-log-exp
Counts
1 → 22
Calls
1 calls:
5.0ms
(* (sqrt 0.3333333333333333) z)

series4.0ms

Counts
1 → 3
Calls
1 calls:
4.0ms
(* (sqrt 0.3333333333333333) z)

simplify979.0ms

Counts
25 → 25
Iterations

Useful iterations: 3 (64.0ms)

IterNodesCost
034155
166145
2195139
3438136
4867136
51464136
63412136
done5000136

prune36.0ms

Filtered
15 candidates to 25 candidates (-66.7%)
Pruning

13 alts after pruning (10 fresh and 3 done)

PrunedKeptTotal
New22325
Fresh077
Picked011
Done022
Total221335

Merged error: 4.3b

Counts
35 → 13

regimes1.0s

Accuracy

36.4% (20.6b remaining)

Error of 26.9b against oracle of 6.2b and baseline of 38.6b

bsearch117.0ms

Steps
ItersRangePoint
10
1.0482406110855033e+106
6.160386974937138e+120
6.481855260996897e+118
10
3.2142997492552143e-84
2.790193438186946e-67
3.2709223867076652e-84
9
2.4583554313162875e-147
4.580889086208214e-142
4.52504895847286e-142
7
-3.011586157659086e-72
-5.237432825475734e-74
-2.7529309278232526e-72
7
-1.0522886606322474e-36
-6.600072493270754e-39
-6.767116379781297e-39
8
-6.855350646076268e+109
-6.181221441465999e+106
-6.4832562982794285e+109

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04089
15089
25789
done5789

end0.0ms

sample716.0ms

Algorithm
intervals
Results
397.0ms8000×body80valid

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