Details

sample267.0ms

Algorithm

intervals

Results

86.0ms	84×	body	5120	valid
32.0ms	386×	body	80	nan
31.0ms	12×	body	640	valid
22.0ms	44×	body	2560	valid
18.0ms	198×	body	80	valid
11.0ms	26×	body	1280	valid
10.0ms	15×	body	10240	exit
2.0ms	9×	body	320	valid
1.0ms	5×	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

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 59.1b

localize39.0ms

Local error

Found 4 expressions with local error:

15.9b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
15.9b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
15.9b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
29.9b	(+ (/ (* 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:

46.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
68.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
65.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
933.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series768.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
131.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
139.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
356.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify1.9s

Counts

155 → 155

Iterations

Useful iterations: done (1.9s)

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

prune472.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 30.8b

localize5.0ms

Local error

Found 1 expressions with local error:

5.7b	(* (/ c0 (* 2.0 w)) 0)

rewrite40.0ms

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:

38.0ms

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

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

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

simplify2.7s

Counts

31 → 31

Iterations

Useful iterations: 2 (108.0ms)

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

prune97.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 29.5b

localize6.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify6.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune33.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 29.5b

localize49.0ms

Local error

Found 4 expressions with local error:

15.9b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
15.9b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
18.2b	(cbrt (pow (/ (* c0 (* d d)) (* (* w h) (* D D))) 3))
29.9b	(+ (cbrt (pow (/ (* c0 (* d d)) (* (* w h) (* D D))) 3)) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

142×	`add-exp-log` `add-cbrt-cube`
78×	`prod-exp` `cbrt-unprod`
30×	`cbrt-undiv` `div-exp`
16×	`cbrt-prod`
9×	`*-un-lft-identity`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`add-log-exp`
5×	`unpow-prod-down` `cube-prod`
4×	`pow1` `times-frac` `div-inv`
3×	`cube-div` `cbrt-div`
2×	`frac-2neg` `sqrt-div` `frac-add` `clear-num` `associate-/r` `associate-/l`
1×	`+-commutative` `cube-mult` `flip3--` `flip3-+` `pow1/3` `unpow3` `sum-log` `flip--` `rem-cbrt-cube` `flip-+` `distribute-lft-out` `sqr-pow`

Counts

4 → 126

Calls

4 calls:

66.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
61.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
19.0ms	(cbrt (pow (/ (* c0 (* d d)) (* (* w h) (* D D))) 3))
1.0s	(+ (cbrt (pow (/ (* c0 (* d d)) (* (* w h) (* D D))) 3)) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series968.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
163.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
206.0ms	(cbrt (pow (/ (* c0 (* d d)) (* (* w h) (* D D))) 3))
425.0ms	(+ (cbrt (pow (/ (* c0 (* d d)) (* (* w h) (* D D))) 3)) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify2.8s

Counts

138 → 138

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	198	4374
1	559	3651
2	3549	2600
done	5001	2594

prune449.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 29.5b

regimes818.0ms

Accuracy

65.2% (0.8b remaining)

Error of 32.2b against oracle of 31.3b and baseline of 33.7b

bsearch6.0ms

simplify13.0ms

Iterations

Useful iterations: done (13.0ms)

Iter	Nodes	Cost
0	27	111
1	34	110
done	34	108

end0.0ms

sample14.1s

Algorithm

intervals

Results

3.6s	12983×	body	80	nan
2.8s	1758×	body	2560	valid
2.6s	2315×	body	5120	valid
1.1s	6655×	body	80	valid
681.0ms	876×	body	1280	valid
654.0ms	575×	body	10240	exit
271.0ms	427×	body	640	valid
82.0ms	229×	body	320	valid
76.0ms	128×	body	160	valid