Details

sample162.0ms

Algorithm

intervals

Results

35.0ms	73×	body	5120	valid
28.0ms	464×	body	80	nan
20.0ms	51×	body	2560	valid
17.0ms	225×	body	80	valid
9.0ms	27×	body	1280	valid
7.0ms	14×	body	10240	exit
5.0ms	21×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	3×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	52
1	59	52
2	285	52
3	3123	52
done	5001	52

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.2b

localize19.0ms

Local error

Found 4 expressions with local error:

18.4b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
18.4b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
18.4b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
24.4b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite367.0ms

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:

17.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
18.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
18.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
304.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series529.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
94.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
95.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
248.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify1.3s

Counts

155 → 155

Iterations

Useful iterations: 2 (366.0ms)

Iter	Nodes	Cost
0	157	4688
1	556	4293
2	3188	2803
done	5000	2803

prune312.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 33.8b

localize5.0ms

Local error

Found 1 expressions with local error:

7.9b	(* (/ c0 (* 2.0 w)) 0)

rewrite12.0ms

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:

11.0ms

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

series1.0ms

Counts

1 → 3

Calls

1 calls:

1.0ms

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

simplify2.0s

Counts

31 → 31

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	67	283
1	175	74
2	521	38
3	2123	38
done	5000	38

prune71.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 31.3b

localize3.0ms

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)

Iter	Nodes	Cost
0	0	0
done	0	0

prune17.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 31.3b

localize26.0ms

Local error

Found 4 expressions with local error:

23.1b	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
23.1b	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
23.1b	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
29.1b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (* (* (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite492.0ms

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:

14.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
15.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
14.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
447.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (* (* (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series874.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
188.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
190.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
311.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (* (* (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify626.0ms

Counts

68 → 68

Iterations

Useful iterations: 2 (135.0ms)

Iter	Nodes	Cost
0	142	3353
1	362	3196
2	1623	2217
done	5001	2217

prune390.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 31.3b

regimes523.0ms

Accuracy

69.5% (0.7b remaining)

Error of 32.4b against oracle of 31.8b and baseline of 33.9b

bsearch7.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	110
1	33	110
done	33	110

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.2s	2336×	body	5120	valid
832.0ms	13156×	body	80	nan
714.0ms	1777×	body	2560	valid
433.0ms	6637×	body	80	valid
295.0ms	542×	body	10240	exit
283.0ms	871×	body	1280	valid
104.0ms	416×	body	640	valid
42.0ms	215×	body	320	valid
12.0ms	101×	body	160	valid