Details

Time bar (total: 12.2s)

sample244.0ms

Algorithm
intervals
Results
57.0ms85×body5120valid
38.0ms433×body80nan
28.0ms54×body2560valid
18.0ms206×body80valid
13.0ms19×body5120exit
11.0ms26×body1280valid
5.0ms14×body640valid
3.0ms10×body320valid
1.0ms6×body160valid

simplify833.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02152
15952
228552
3313852
done500052

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 59.2b

Counts
2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

17.0b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
17.0b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
17.0b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
30.9b
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
211×add-exp-log add-cbrt-cube
117×prod-exp cbrt-unprod
45×cbrt-undiv div-exp
6×*-un-lft-identity add-log-exp
4×pow1 add-sqr-sqrt add-cube-cbrt
3×frac-2neg times-frac clear-num associate-/r* div-inv associate-/l*
2×sqrt-div frac-add
1×+-commutative flip3-- flip3-+ sum-log flip-- flip-+ distribute-lft-out
Counts
4 → 143
Calls
4 calls:
14.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
15.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
15.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
40.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series215.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
36.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
34.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
112.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify867.0ms

Counts
155 → 155
Iterations

Useful iterations: 2 (224.0ms)

IterNodesCost
01574688
15624293
232692803
done50002803

prune175.0ms

Filtered
57 candidates to 155 candidates (-171.9%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1514155
Fresh000
Picked101
Done000
Total1524156

Merged error: 31.5b

Counts
156 → 4

localize5.0ms

Local error

Found 1 expressions with local error:

5.9b
(* (/ c0 (* 2.0 w)) 0)

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
10×add-exp-log add-cbrt-cube
7×associate-*l*
6×add-sqr-sqrt
4×add-cube-cbrt *-un-lft-identity prod-exp cbrt-unprod
3×pow1 times-frac associate-*r*
2×cbrt-undiv div-exp
1×mul0 pow-prod-down associate-*l/ *-commutative div-inv add-log-exp unswap-sqr
Counts
1 → 28
Calls
1 calls:
8.0ms
(* (/ c0 (* 2.0 w)) 0)

series1.0ms

Counts
1 → 3
Calls
1 calls:
1.0ms
(* (/ c0 (* 2.0 w)) 0)

simplify617.0ms

Counts
31 → 31
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
067283
1179104
262638
3258738
done500038

prune53.0ms

Filtered
19 candidates to 31 candidates (-63.2%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New30131
Fresh033
Picked101
Done000
Total31435

Merged error: 29.3b

Counts
35 → 4

localize0.0ms

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

prune16.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New000
Fresh033
Picked011
Done000
Total044

Merged error: 29.3b

Counts
4 → 4

localize25.0ms

Local error

Found 4 expressions with local error:

29.7b
(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
29.7b
(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
29.7b
(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
39.2b
(+ (* (* (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
27×cbrt-div
15×cbrt-prod
14×sqrt-div frac-add
10×frac-times associate-*l/
7×add-sqr-sqrt add-cube-cbrt flip3-- *-un-lft-identity flip--
6×associate-*r/ add-log-exp
4×pow1 add-exp-log add-cbrt-cube
3×times-frac pow1/3 div-inv
1×+-commutative flip3-+ sum-log flip-+
Counts
4 → 67
Calls
4 calls:
10.0ms
(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
12.0ms
(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
10.0ms
(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
41.0ms
(+ (* (* (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series335.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
71.0ms
(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
72.0ms
(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
121.0ms
(+ (* (* (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify501.0ms

Counts
79 → 79
Iterations

Useful iterations: 2 (137.0ms)

IterNodesCost
01905936
14685784
215794254
done50014254

prune120.0ms

Filtered
66 candidates to 79 candidates (-19.7%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New77279
Fresh022
Picked011
Done011
Total77683

Merged error: 29.3b

Counts
83 → 6

regimes753.0ms

Accuracy

0% (2.4b remaining)

Error of 34.0b against oracle of 31.6b and baseline of 34.0b

bsearch0.0ms

simplify0.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
011
done11

end0.0ms

sample7.2s

Algorithm
intervals
Results
1.5s2277×body5120valid
1.2s13433×body80nan
954.0ms1747×body2560valid
606.0ms6769×body80valid
428.0ms616×body5120exit
403.0ms923×body1280valid
146.0ms435×body640valid
59.0ms221×body320valid
19.0ms111×body160valid

Profiling

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