Details

sample165.0ms

Algorithm

intervals

Results

39.0ms	87×	body	5120	valid
25.0ms	430×	body	80	nan
21.0ms	51×	body	2560	valid
14.0ms	207×	body	80	valid
8.0ms	27×	body	1280	valid
7.0ms	15×	body	10240	exit
3.0ms	14×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	1×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	21	52
1	59	52
2	289	52
3	3227	52
done	5000	46

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 60.8b

localize19.0ms

Local error

Found 4 expressions with local error:

17.4b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
17.4b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
17.4b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
28.7b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite730.0ms

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:

41.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
41.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
41.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
597.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series555.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
98.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
99.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
261.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify1.4s

Counts

155 → 155

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	157	4688
1	468	4293
2	3049	2845
done	5001	2809

prune498.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 33.7b

localize5.0ms

Local error

Found 1 expressions with local error:

5.2b	(* (/ c0 (* 2.0 w)) 0)

rewrite26.0ms

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:

25.0ms

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

series2.0ms

Counts

1 → 3

Calls

1 calls:

1.0ms

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

simplify2.0s

Counts

31 → 31

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	67	283
1	158	74
2	472	38
3	2113	38
done	5000	38

prune68.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 30.9b

localize2.0ms

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)

Iter	Nodes	Cost
0	0	0
done	0	0

prune14.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 30.9b

localize26.0ms

Local error

Found 4 expressions with local error:

29.8b	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
29.8b	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
29.8b	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
33.8b	(+ (/ (* 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))))

rewrite1.2s

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:

28.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
29.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
28.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
1.1s	(+ (/ (* 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))))

series850.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
182.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
182.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
306.0ms	(+ (/ (* 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))))

simplify808.0ms

Counts

68 → 68

Iterations

Useful iterations: done (805.0ms)

Iter	Nodes	Cost
0	142	3353
1	359	3196
2	1603	2217
done	5001	1768

prune333.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 30.7b

regimes358.0ms

Accuracy

0% (2.6b remaining)

Error of 33.3b against oracle of 30.7b and baseline of 33.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 1 (0.0ms)

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

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.1s	2303×	body	5120	valid
775.0ms	12953×	body	80	nan
641.0ms	1726×	body	2560	valid
416.0ms	6843×	body	80	valid
301.0ms	588×	body	10240	exit
269.0ms	882×	body	1280	valid
103.0ms	421×	body	640	valid
42.0ms	245×	body	320	valid
11.0ms	92×	body	160	valid