Details

sample185.0ms

Algorithm

intervals

Results

36.0ms	78×	body	5120	valid
30.0ms	493×	body	80	nan
20.0ms	48×	body	2560	valid
15.0ms	251×	body	80	valid
14.0ms	22×	body	10240	exit
11.0ms	36×	body	1280	valid
4.0ms	16×	body	640	valid
1.0ms	5×	body	320	valid
1.0ms	5×	body	160	valid

simplify105.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	59	26
1	298	26
2	3398	26
3	5002	26
done	5002	26

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 57.4b

localize24.0ms

Local error

Found 4 expressions with local error:

16.6b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
16.6b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
16.6b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
27.8b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite746.0ms

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:

43.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
43.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
42.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
608.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series575.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
107.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
100.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
265.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify124.0ms

Counts

155 → 155

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	579	2159
1	3786	1523
2	5001	1523
done	5001	1523

prune312.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 31.6b

localize5.0ms

Local error

Found 1 expressions with local error:

3.7b	(* (/ c0 (* 2.0 w)) 0)

rewrite25.0ms

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:

24.0ms

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

series2.0ms

Counts

1 → 3

Calls

1 calls:

1.0ms

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

simplify279.0ms

Counts

31 → 31

Iterations

Useful iterations: 2 (276.0ms)

Iter	Nodes	Cost
0	176	32
1	1859	16
2	5001	6
done	5001	6

prune76.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 30.3b

localize2.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify2.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune21.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 30.3b

localize34.0ms

Local error

Found 4 expressions with local error:

16.6b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
27.8b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
27.8b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
27.8b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

73×	`add-exp-log` `add-cbrt-cube`
39×	`prod-exp` `cbrt-unprod`
15×	`cbrt-undiv` `div-exp`
10×	`*-un-lft-identity` `add-log-exp`
6×	`sqrt-div` `frac-add`
4×	`pow1` `add-sqr-sqrt` `add-cube-cbrt`
3×	`+-commutative` `flip3--` `flip3-+` `sum-log` `flip--` `flip-+` `distribute-lft-out`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 85

Calls

4 calls:

44.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
632.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
607.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
610.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series900.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
264.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
266.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
266.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify120.0ms

Counts

97 → 97

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	579	2389
1	3786	2041
2	5001	2041
done	5001	2041

prune360.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 30.2b

regimes435.0ms

Accuracy

0% (2.4b remaining)

Error of 33.9b against oracle of 31.5b and baseline of 33.9b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	0
1	8	0
2	8	0
done	8	0

end0.0ms

sample5.0s

Algorithm

intervals

Results

1.1s	2260×	body	5120	valid
806.0ms	13155×	body	80	nan
657.0ms	1715×	body	2560	valid
430.0ms	6957×	body	80	valid
294.0ms	950×	body	1280	valid
287.0ms	563×	body	10240	exit
114.0ms	466×	body	640	valid
39.0ms	218×	body	320	valid
14.0ms	113×	body	160	valid