Details

Time bar (total: 29.3s)

sample263.0ms

Algorithm
intervals
Results
46.0ms66×body5120valid
39.0ms416×body80nan
32.0ms57×body2560valid
25.0ms229×body80valid
21.0ms28×body10240exit
14.0ms31×body1280valid
5.0ms15×body640valid
1.0ms6×body320valid
1.0ms4×body160valid

simplify2.0s

Counts
1 → 1
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02152
15952
228952
3322752
done500046

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 58.4b

localize42.0ms

Local error

Found 4 expressions with local error:

19.0b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
19.0b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
19.0b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
25.2b
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite1.0s

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:
47.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
62.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
53.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
851.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series744.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
150.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
152.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
301.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify2.2s

Counts
155 → 155
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01574688
14684293
230492845
done50012809

prune453.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 32.7b

localize6.0ms

Local error

Found 1 expressions with local error:

6.2b
(* (/ c0 (* 2.0 w)) 0)

rewrite40.0ms

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:
38.0ms
(* (/ c0 (* 2.0 w)) 0)

series2.0ms

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

simplify3.0s

Counts
31 → 31
Iterations

Useful iterations: 2 (115.0ms)

IterNodesCost
067283
115874
247238
3211338
done500038

prune113.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 31.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.5b
(* (cbrt c0) (cbrt c0))
0.6b
(cbrt c0)
0.6b
(cbrt c0)

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
22×cbrt-prod
21×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
10×pow1
8×pow1/3
6×swap-sqr associate-*r* associate-*l*
5×add-exp-log
4×unswap-sqr
3×add-cbrt-cube add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
3 → 62
Calls
3 calls:
23.0ms
(* (cbrt c0) (cbrt c0))
2.0ms
(cbrt c0)
2.0ms
(cbrt c0)

series988.0ms

Counts
3 → 9
Calls
3 calls:
332.0ms
(* (cbrt c0) (cbrt c0))
322.0ms
(cbrt c0)
333.0ms
(cbrt c0)

simplify5.7s

Counts
71 → 71
Iterations

Useful iterations: done (5.7s)

IterNodesCost
061459
1115360
2319342
31092327
44427322
done5001314

prune317.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 31.0b

localize28.0ms

Local error

Found 4 expressions with local error:

19.0b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
19.0b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
22.6b
(cbrt (pow (/ (* c0 (* d d)) (* (* w h) (* D D))) 3))
25.2b
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (cbrt (pow (/ (* c0 (* d d)) (* (* w h) (* D D))) 3)) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite651.0ms

Algorithm
rewrite-expression-head
Rules
142×add-exp-log add-cbrt-cube
78×prod-exp cbrt-unprod
30×cbrt-undiv div-exp
16×cbrt-prod
9×*-un-lft-identity
7×add-sqr-sqrt add-cube-cbrt
6×add-log-exp
5×unpow-prod-down cube-prod
4×pow1 times-frac div-inv
2×frac-2neg sqrt-div frac-add clear-num associate-/r* associate-/l*
1×+-commutative cube-div cube-mult cbrt-div flip3-- flip3-+ pow1/3 unpow3 sum-log flip-- rem-cbrt-cube flip-+ distribute-lft-out sqr-pow
Counts
4 → 126
Calls
4 calls:
46.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
48.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
18.0ms
(cbrt (pow (/ (* c0 (* d d)) (* (* w h) (* D D))) 3))
530.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (cbrt (pow (/ (* c0 (* d d)) (* (* w h) (* D D))) 3)) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series852.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
117.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
182.0ms
(cbrt (pow (/ (* c0 (* d d)) (* (* w h) (* D D))) 3))
445.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (cbrt (pow (/ (* c0 (* d d)) (* (* w h) (* D D))) 3)) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify2.7s

Counts
138 → 138
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01984389
15683651
235532600
done50022594

prune403.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 30.3b

regimes627.0ms

Accuracy

0% (2.6b remaining)

Error of 33.2b against oracle of 30.6b and baseline of 33.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
189
done89

end0.0ms

sample7.1s

Algorithm
intervals
Results
1.5s2317×body5120valid
1.1s12746×body80nan
912.0ms1704×body2560valid
567.0ms6570×body80valid
432.0ms961×body1280valid
400.0ms577×body10240exit
145.0ms411×body640valid
61.0ms233×body320valid
21.0ms124×body160valid