Details

sample574.0ms

Algorithm

intervals

Results

173.0ms	71×	body	5120	valid
152.0ms	461×	body	80	nan
74.0ms	55×	body	2560	valid
47.0ms	223×	body	80	valid
30.0ms	18×	body	10240	exit
27.0ms	25×	body	1280	valid
12.0ms	16×	body	640	valid
3.0ms	5×	body	320	valid
3.0ms	7×	body	160	valid

simplify670.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	2972
2	280
1	59
0	21

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 50.2b

localize45.0ms

Local error

Found 4 expressions with local error:

14.5b	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
14.5b	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
14.5b	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
29.1b	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

199×	`add-cbrt-cube` `add-exp-log`
81×	`prod-exp` `cbrt-unprod`
72×	`cbrt-undiv` `div-exp`
11×	`associate-*r/`
9×	`associate-/l/`
8×	`sqrt-div` `frac-add`
7×	`frac-times`
6×	`*-un-lft-identity` `add-log-exp`
5×	`associate-*l/`
4×	`add-sqr-sqrt` `pow1` `flip3-+` `add-cube-cbrt` `flip-+`
3×	`clear-num` `associate-/r` `frac-2neg` `times-frac` `flip3--` `div-inv` `flip--` `associate-/l`
1×	`+-commutative` `sum-log` `distribute-lft-out`

Counts

4 → 152

Calls

4 calls:

24.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
40.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
30.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
40.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

series1.5s

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
93.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
108.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
1.2s	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

simplify1.2s

Counts

164 → 164

Iterations

Iter	Nodes
2	3529
1	662
0	213

prune2.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 48.7b

localize98.0ms

Local error

Found 4 expressions with local error:

14.5b	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
29.1b	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
29.1b	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
29.1b	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-cbrt-cube` `add-exp-log`
27×	`prod-exp` `cbrt-unprod`
24×	`cbrt-undiv` `sqrt-div` `div-exp` `frac-add`
13×	`frac-times`
12×	`flip3-+` `flip-+`
10×	`*-un-lft-identity` `add-log-exp`
9×	`flip3--` `associate-*r/` `flip--`
7×	`associate-*l/`
4×	`add-sqr-sqrt` `pow1` `add-cube-cbrt`
3×	`+-commutative` `sum-log` `distribute-lft-out` `associate-/l/`
1×	`clear-num` `associate-/r` `frac-2neg` `times-frac` `div-inv` `associate-/l`

Counts

4 → 104

Calls

4 calls:

33.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
72.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
38.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
76.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

series2.8s

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
916.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
896.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
896.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

simplify1.5s

Counts

116 → 116

Iterations

Iter	Nodes
2	3529
1	662
0	213

prune2.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 48.7b

localize100.0ms

Local error

Found 4 expressions with local error:

27.8b	(cbrt (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
27.8b	(cbrt (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
27.8b	(cbrt (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
33.8b	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (* (* (cbrt (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (cbrt (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))) (cbrt (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
9×	`*-un-lft-identity`
8×	`sqrt-div` `frac-add`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`add-log-exp`
4×	`frac-times` `pow1` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+`
3×	`cbrt-div` `times-frac` `flip3--` `pow1/3` `div-inv` `flip--`
2×	`associate-l/` `associate-r/`
1×	`+-commutative` `sum-log` `distribute-lft-out`

Counts

4 → 62

Calls

4 calls:

28.0ms	(cbrt (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
17.0ms	(cbrt (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
14.0ms	(cbrt (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
76.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (* (* (cbrt (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (cbrt (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))) (cbrt (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

series1.7s

Counts

4 → 12

Calls

4 calls:

235.0ms	(cbrt (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
243.0ms	(cbrt (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
241.0ms	(cbrt (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
976.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (* (* (cbrt (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (cbrt (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))) (cbrt (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

simplify6.2s

Counts

74 → 74

Iterations

Iter	Nodes
3	11328
2	1834
1	521
0	197

prune1.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 46.7b

localize58.0ms

Local error

Found 4 expressions with local error:

7.5b	(/ (/ d D) w)
8.6b	(- (* (* (/ (* c0 (/ d D)) h) (/ (/ d D) w)) (* (/ (* c0 (/ d D)) h) (/ (/ d D) w))) (* M M))
13.2b	(sqrt (- (* (* (/ (* c0 (/ d D)) h) (/ (/ d D) w)) (* (/ (* c0 (/ d D)) h) (/ (/ d D) w))) (* M M)))
29.1b	(+ (sqrt (- (* (* (/ (* c0 (/ d D)) h) (/ (/ d D) w)) (* (/ (* c0 (/ d D)) h) (/ (/ d D) w))) (* M M))) (* (/ (* c0 (/ d D)) h) (/ (/ d D) w)))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
48×	`add-sqr-sqrt`
47×	`*-un-lft-identity` `add-cube-cbrt`
13×	`associate-/l*`
9×	`add-cbrt-cube` `add-exp-log`
8×	`sqrt-div` `add-log-exp`
6×	`frac-add`
5×	`pow1` `flip3--` `div-inv` `flip--`
4×	`sqrt-prod`
3×	`cbrt-undiv` `associate-/r*` `div-exp`
2×	`frac-times` `associate-l/` `associate-r/` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+` `associate-/l/`

Counts

4 → 116

Calls

4 calls:

6.0ms	(/ (/ d D) w)
179.0ms	(- (* (* (/ (* c0 (/ d D)) h) (/ (/ d D) w)) (* (/ (* c0 (/ d D)) h) (/ (/ d D) w))) (* M M))
330.0ms	(sqrt (- (* (* (/ (* c0 (/ d D)) h) (/ (/ d D) w)) (* (/ (* c0 (/ d D)) h) (/ (/ d D) w))) (* M M)))
1.1s	(+ (sqrt (- (* (* (/ (* c0 (/ d D)) h) (/ (/ d D) w)) (* (/ (* c0 (/ d D)) h) (/ (/ d D) w))) (* M M))) (* (/ (* c0 (/ d D)) h) (/ (/ d D) w)))

series1.1s

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ (/ d D) w)
456.0ms	(- (* (* (/ (* c0 (/ d D)) h) (/ (/ d D) w)) (* (/ (* c0 (/ d D)) h) (/ (/ d D) w))) (* M M))
305.0ms	(sqrt (- (* (* (/ (* c0 (/ d D)) h) (/ (/ d D) w)) (* (/ (* c0 (/ d D)) h) (/ (/ d D) w))) (* M M)))
338.0ms	(+ (sqrt (- (* (* (/ (* c0 (/ d D)) h) (/ (/ d D) w)) (* (/ (* c0 (/ d D)) h) (/ (/ d D) w))) (* M M))) (* (/ (* c0 (/ d D)) h) (/ (/ d D) w)))

simplify822.0ms

Counts

128 → 128

Iterations

Iter	Nodes
2	2134
1	653
0	267

prune2.3s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 26.7b

regimes1.9s

Accuracy

-1.3% (10.3b remaining)

Error of 34.0b against oracle of 23.7b and baseline of 33.9b

bsearch1.5s

Steps

Iters	Range		Point
11	-6.531884415335687e-299	6.641716713765292e-297	-5.1398908857458564e-300
10	-5.0314696167851455e-107	-1.3652868418827533e-124	-2.3788084210232337e-114

simplify10.0ms

Iterations

Iter	Nodes
2	34
1	34
0	26

end0.0ms

sample19.8s

Algorithm

intervals

Results

4.8s	2272×	body	5120	valid
3.9s	12974×	body	80	nan
3.3s	1747×	body	2560	valid
2.6s	6840×	body	80	valid
1.6s	577×	body	10240	exit
1.6s	925×	body	1280	valid
514.0ms	440×	body	640	valid
131.0ms	208×	body	320	valid
82.0ms	119×	body	160	valid