Details

Time bar (total: 36.6s)

sample410.0ms

Algorithm
intervals
Results
100.0ms399×body80nan
70.0ms67×body5120valid
42.0ms19×body10240exit
36.0ms43×body2560valid
32.0ms213×body80valid
24.0ms36×body1280valid
9.0ms16×body640valid
4.0ms9×body320valid
1.0ms3×body160valid

simplify2.7s

Counts
1 → 1
Iterations

Useful iterations: done (2.7s)

IterNodesCost
02152
15952
228952
3333452
done500146

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 56.7b

localize80.0ms

Local error

Found 4 expressions with local error:

17.7b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
17.7b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
17.7b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
25.3b
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite1.3s

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:
80.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
71.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
74.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
1.0s
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series916.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
166.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
157.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
425.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify613.0ms

Counts
155 → 155
Iterations

Useful iterations: done (605.0ms)

IterNodesCost
01574688
16024293
done50003059

prune731.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 34.9b

localize11.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ c0 (* 2.0 w))
5.4b
(* (/ c0 (* 2.0 w)) 0)

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
16×add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity associate-*l*
6×times-frac
5×prod-exp cbrt-unprod
4×pow1 cbrt-undiv div-exp
3×associate-*r* associate-/l*
2×div-inv add-log-exp
1×frac-2neg mul0 pow-prod-down associate-*l/ clear-num associate-/r* *-commutative unswap-sqr
Counts
2 → 49
Calls
2 calls:
12.0ms
(/ c0 (* 2.0 w))
36.0ms
(* (/ c0 (* 2.0 w)) 0)

series35.0ms

Counts
2 → 6
Calls
2 calls:
33.0ms
(/ c0 (* 2.0 w))
2.0ms
(* (/ c0 (* 2.0 w)) 0)

simplify1.8s

Counts
55 → 55
Iterations

Useful iterations: 2 (188.0ms)

IterNodesCost
081468
1209268
2915190
done5001190

prune404.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 33.0b

localize8.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune81.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 33.0b

localize104.0ms

Local error

Found 4 expressions with local error:

23.0b
(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
23.0b
(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
23.0b
(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
33.7b
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (* (* (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))))) (* M M))))

rewrite2.1s

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
9×*-un-lft-identity
7×add-sqr-sqrt add-cube-cbrt
6×add-log-exp
4×pow1 add-exp-log add-cbrt-cube
3×cbrt-div times-frac pow1/3 div-inv
2×sqrt-div frac-add
1×+-commutative flip3-- flip3-+ sum-log flip-- flip-+ distribute-lft-out
Counts
4 → 56
Calls
4 calls:
61.0ms
(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
60.0ms
(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
62.0ms
(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
2.0s
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (* (* (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))))) (* M M))))

series1.6s

Counts
4 → 12
Calls
4 calls:
359.0ms
(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
348.0ms
(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
331.0ms
(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
591.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (* (* (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))))) (* M M))))

simplify1.8s

Counts
68 → 68
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01423353
13613196
219042217
done50022043

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 33.0b

regimes1.8s

Accuracy

0% (2.4b remaining)

Error of 34.4b against oracle of 32.0b and baseline of 34.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: done (1.0ms)

IterNodesCost
023
done21

end0.0ms

sample18.9s

Algorithm
intervals
Results
5.4s2335×body5120valid
2.8s13180×body80nan
2.7s6867×body80valid
2.2s1619×body2560valid
1.0s964×body1280valid
808.0ms566×body10240exit
748.0ms257×body320valid
374.0ms441×body640valid
37.0ms120×body160valid