Details

sample347.0ms

Algorithm

intervals

Results

73.0ms	80×	body	5120	valid
64.0ms	363×	body	80	nan
63.0ms	33×	body	1280	valid
35.0ms	49×	body	2560	valid
22.0ms	190×	body	80	valid
15.0ms	16×	body	10240	exit
5.0ms	9×	body	640	valid
2.0ms	6×	body	320	valid
1.0ms	6×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

Useful iterations: done (1.8s)

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 58.6b

localize52.0ms

Local error

Found 4 expressions with local error:

15.6b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
15.6b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
15.6b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
27.9b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite1.1s

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)))
43.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
914.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series731.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
130.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
131.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
319.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify2.1s

Counts

155 → 155

Iterations

Useful iterations: done (2.1s)

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

prune399.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 32.2b

localize8.0ms

Local error

Found 1 expressions with local error:

6.9b	(* (/ c0 (* 2.0 w)) 0)

rewrite53.0ms

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:

50.0ms

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

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

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

simplify3.3s

Counts

31 → 31

Iterations

Useful iterations: 2 (120.0ms)

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

prune78.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 29.5b

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

prune23.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 29.5b

localize40.0ms

Local error

Found 4 expressions with local error:

15.6b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
15.6b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
15.7b	(* (* c0 (* d d)) (/ 1 (* (* w h) (* D D))))
31.5b	(+ (* (* c0 (* d d)) (/ 1 (* (* w h) (* D D)))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

373×	`add-exp-log`
246×	`prod-exp`
235×	`add-cbrt-cube`
138×	`cbrt-unprod`
60×	`div-exp`
45×	`cbrt-undiv`
15×	`rec-exp` `1-exp`
13×	`pow1`
7×	`associate-r`
6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `pow-prod-down` `add-log-exp`
5×	`times-frac`
4×	`sqrt-div` `frac-add`
3×	`associate-*r/` `un-div-inv` `div-inv`
2×	`flip3--` `frac-2neg` `clear-num` `associate-/r` `flip--` `associate-/l`
1×	`+-commutative` `flip3-+` `associate-l` `sum-log` `*-commutative` `flip-+`

Counts

4 → 188

Calls

4 calls:

58.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
61.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
211.0ms	(* (* c0 (* d d)) (/ 1 (* (* w h) (* D D))))
724.0ms	(+ (* (* c0 (* d d)) (/ 1 (* (* w h) (* D D)))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series801.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
134.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
147.0ms	(* (* c0 (* d d)) (/ 1 (* (* w h) (* D D))))
371.0ms	(+ (* (* c0 (* d d)) (/ 1 (* (* w h) (* D D)))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify3.4s

Counts

200 → 200

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	277	6099
1	720	5265
2	4256	3563
done	5000	3559

prune424.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 29.3b

regimes605.0ms

Accuracy

0% (2.3b remaining)

Error of 33.4b against oracle of 31.1b and baseline of 33.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: done (1.0ms)

Iter	Nodes	Cost
0	2	3
done	2	1

end0.0ms

sample14.2s

Algorithm

intervals

Results

3.0s	12757×	body	80	nan
2.9s	2362×	body	5120	valid
2.5s	1707×	body	2560	valid
1.8s	6848×	body	80	valid
830.0ms	871×	body	1280	valid
670.0ms	629×	body	10240	exit
227.0ms	448×	body	640	valid
105.0ms	200×	body	320	valid
24.0ms	104×	body	160	valid