Details

sample162.0ms

Algorithm

intervals

Results

40.0ms	73×	body	5120	valid
28.0ms	464×	body	80	nan
19.0ms	51×	body	2560	valid
14.0ms	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

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	21	52
1	60	52
2	291	50
3	3205	50
done	5000	50

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.2b

localize20.0ms

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))))

rewrite334.0ms

Algorithm

rewrite-expression-head

Rules

211×	`add-exp-log` `add-cbrt-cube`
117×	`prod-exp` `cbrt-unprod`
45×	`cbrt-undiv` `div-exp`
7×	`*-un-lft-identity`
6×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def`
4×	`pow1` `expm1-log1p-u` `times-frac` `log1p-expm1-u` `div-inv`
3×	`frac-2neg` `clear-num` `associate-/r` `associate-/l`
2×	`sqrt-div` `frac-add`
1×	`+-commutative` `flip3--` `flip3-+` `sum-log` `flip--` `flip-+` `distribute-lft-out`

Counts

4 → 156

Calls

4 calls:

16.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
16.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
16.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
277.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series517.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
91.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
92.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
242.0ms	(+ (/ (* 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

168 → 168

Iterations

Useful iterations: 2 (372.0ms)

Iter	Nodes	Cost
0	161	4866
1	572	4432
2	3262	2929
done	5000	2929

prune377.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 33.8b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite11.0ms

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×	`expm1-log1p-u` `mul0` `pow-prod-down` `associate-l/` `-commutative` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`

Counts

1 → 30

Calls

1 calls:

10.0ms

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

series1.0ms

Counts

1 → 3

Calls

1 calls:

1.0ms

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

simplify2.0s

Counts

33 → 33

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	69	299
1	177	78
2	523	42
3	2123	42
done	5000	42

prune72.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 31.3b

localize2.0ms

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

prune16.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 31.3b

localize21.0ms

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)))
19.3b	(/ (/ (* c0 (* d d)) (* w h)) (* D D))
27.3b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (/ (* c0 (* d d)) (* w h)) (* D D)) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite262.0ms

Algorithm

rewrite-expression-head

Rules

207×	`add-exp-log` `add-cbrt-cube`
103×	`prod-exp` `cbrt-unprod`
56×	`cbrt-undiv` `div-exp`
10×	`times-frac`
9×	`*-un-lft-identity`
7×	`add-sqr-sqrt` `add-cube-cbrt` `associate-/l*`
6×	`div-inv` `add-log-exp`
5×	`fma-def`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num` `associate-/r*`
2×	`sqrt-div` `frac-add`
1×	`+-commutative` `flip3--` `flip3-+` `sum-log` `flip--` `flip-+` `associate-/l/` `distribute-lft-out`

Counts

4 → 163

Calls

4 calls:

16.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
16.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
11.0ms	(/ (/ (* c0 (* d d)) (* w h)) (* D D))
210.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (/ (* c0 (* d d)) (* w h)) (* D D)) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series521.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
93.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
97.0ms	(/ (/ (* c0 (* d d)) (* w h)) (* D D))
240.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (/ (* c0 (* d d)) (* w h)) (* D D)) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify1.6s

Counts

175 → 175

Iterations

Useful iterations: 2 (535.0ms)

Iter	Nodes	Cost
0	239	4948
1	772	4549
2	4420	3038
done	5000	3038

prune340.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 31.2b

regimes249.0ms

Accuracy

0% (2.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	4	4
done	4	4

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.2s	2336×	body	5120	valid
806.0ms	13156×	body	80	nan
695.0ms	1777×	body	2560	valid
410.0ms	6637×	body	80	valid
291.0ms	542×	body	10240	exit
275.0ms	871×	body	1280	valid
102.0ms	416×	body	640	valid
43.0ms	215×	body	320	valid
13.0ms	101×	body	160	valid