Details

sample320.0ms

Algorithm

intervals

Results

90.0ms	83×	body	5120	valid
52.0ms	234×	body	80	valid
41.0ms	407×	body	80	nan
31.0ms	53×	body	2560	valid
19.0ms	24×	body	10240	exit
11.0ms	22×	body	1280	valid
6.0ms	14×	body	640	valid
1.0ms	5×	body	320	valid
1.0ms	3×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: done (2.0s)

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 59.8b

localize46.0ms

Local error

Found 4 expressions with local error:

16.2b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
16.2b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
16.2b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
28.9b	(+ (/ (* 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:

71.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
57.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
75.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
851.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series872.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
158.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
177.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
387.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify2.0s

Counts

155 → 155

Iterations

Useful iterations: done (2.0s)

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

prune486.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 34.3b

localize12.0ms

Local error

Found 1 expressions with local error:

5.4b	(* (/ c0 (* 2.0 w)) 0)

rewrite31.0ms

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:

30.0ms

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

series2.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

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

simplify3.3s

Counts

31 → 31

Iterations

Useful iterations: 2 (143.0ms)

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

prune91.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 32.7b

localize4.0ms

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

5 alts after pruning (4 fresh and 1 done)

Merged error: 32.7b

localize46.0ms

Local error

Found 4 expressions with local error:

27.7b	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
27.7b	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
27.7b	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
34.6b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (* (* (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))))) (* M M))))

rewrite1.6s

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:

44.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
40.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
43.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
1.4s	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (* (* (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))))) (* M M))))

series1.3s

Counts

4 → 12

Calls

4 calls:

271.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
253.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
306.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
468.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (* (* (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))))) (* M M))))

simplify1.3s

Counts

68 → 68

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	142	3353
1	359	3196
2	1600	2217
done	5001	1795

prune510.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 32.2b

regimes761.0ms

Accuracy

0% (2.6b remaining)

Error of 33.9b against oracle of 31.3b and baseline of 33.9b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	5
1	6	5
done	6	5

end0.0ms

sample13.7s

Algorithm

intervals

Results

3.1s	2332×	body	5120	valid
2.8s	12850×	body	80	nan
1.7s	539×	body	10240	exit
1.6s	6866×	body	80	valid
1.4s	1672×	body	2560	valid
670.0ms	894×	body	1280	valid
270.0ms	448×	body	640	valid
75.0ms	224×	body	320	valid
23.0ms	98×	body	160	valid