Details

sample368.0ms

Algorithm

intervals

Results

74.0ms	213×	body	80	valid
66.0ms	67×	body	5120	valid
49.0ms	420×	body	80	nan
46.0ms	40×	body	1280	valid
46.0ms	57×	body	2560	valid
16.0ms	14×	body	10240	exit
7.0ms	14×	body	640	valid
2.0ms	7×	body	320	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5207
3	2972
2	280
1	59
0	21

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 53.1b

localize83.0ms

Local error

Found 4 expressions with local error:

13.3b	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
13.3b	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
14.6b	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
25.7b	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

134×	`add-cbrt-cube` `add-exp-log`
54×	`prod-exp` `cbrt-unprod`
48×	`cbrt-undiv` `div-exp`
16×	`sqrt-div`
10×	`frac-times` `associate-*r/`
8×	`frac-add`
7×	`pow1` `flip3-+` `flip-+`
6×	`-un-lft-identity` `flip3--` `associate-l/` `flip--` `add-log-exp` `associate-/l/`
4×	`add-sqr-sqrt` `add-cube-cbrt`
2×	`clear-num` `associate-/r` `frac-2neg` `sqrt-pow1` `times-frac` `div-inv` `associate-/l`
1×	`+-commutative` `sum-log` `pow1/2` `pow-prod-down` `sqrt-prod` `distribute-lft-out`

Counts

4 → 127

Calls

4 calls:

37.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
43.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
44.0ms	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
56.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

series2.0s

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
110.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
778.0ms	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
987.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

simplify2.9s

Counts

139 → 139

Iterations

Iter	Nodes
done	5025
2	3587
1	676
0	221

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 49.2b

localize142.0ms

Local error

Found 4 expressions with local error:

14.6b	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
14.6b	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
25.7b	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
25.7b	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

32×	`sqrt-div`
16×	`frac-times` `frac-add`
14×	`flip3-+` `flip-+`
12×	`flip3--` `flip--`
10×	`pow1`
8×	`-un-lft-identity` `associate-l/` `associate-*r/` `add-log-exp`
4×	`add-sqr-sqrt` `sqrt-pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
2×	`+-commutative` `sum-log` `pow1/2` `pow-prod-down` `sqrt-prod` `distribute-lft-out`

Counts

4 → 78

Calls

4 calls:

69.0ms	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
41.0ms	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
71.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
59.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

series4.0s

Counts

4 → 12

Calls

4 calls:

878.0ms	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
770.0ms	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
992.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
1.4s	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

simplify2.1s

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
2	1536
1	370
0	131

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 49.2b

localize343.0ms

Local error

Found 4 expressions with local error:

25.7b	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
25.7b	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
25.7b	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
25.7b	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

32×	`sqrt-div` `frac-add`
16×	`frac-times` `flip3-+` `flip-+`
12×	`*-un-lft-identity` `flip3--` `flip--` `add-log-exp`
8×	`associate-l/` `associate-r/`
4×	`add-sqr-sqrt` `pow1` `+-commutative` `sum-log` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `distribute-lft-out`

Counts

4 → 80

Calls

4 calls:

48.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
54.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
57.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
47.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

series3.6s

Counts

4 → 12

Calls

4 calls:

904.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
902.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
891.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
887.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

simplify1.9s

Counts

92 → 92

Iterations

Iter	Nodes
done	5001
2	1520
1	360
0	122

prune1.4s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 49.2b

localize79.0ms

Local error

Found 4 expressions with local error:

13.3b	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
13.3b	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
14.6b	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
30.8b	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* c0 (/ d D)) (/ (* w h) (/ d D))))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

134×	`add-cbrt-cube` `add-exp-log`
54×	`prod-exp` `cbrt-unprod`
48×	`cbrt-undiv` `div-exp`
16×	`sqrt-div`
10×	`frac-times` `associate-*r/`
8×	`frac-add`
7×	`pow1` `flip3-+` `flip-+`
6×	`-un-lft-identity` `flip3--` `associate-l/` `flip--` `add-log-exp` `associate-/l/`
4×	`add-sqr-sqrt` `add-cube-cbrt`
2×	`clear-num` `associate-/r` `frac-2neg` `sqrt-pow1` `times-frac` `div-inv` `associate-/l`
1×	`+-commutative` `sum-log` `pow1/2` `pow-prod-down` `sqrt-prod` `distribute-lft-out`

Counts

4 → 127

Calls

4 calls:

31.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
45.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
36.0ms	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
54.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* c0 (/ d D)) (/ (* w h) (/ d D))))

series1.9s

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
92.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
819.0ms	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
906.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* c0 (/ d D)) (/ (* w h) (/ d D))))

simplify2.6s

Counts

139 → 139

Iterations

Iter	Nodes
done	5009
2	3512
1	688
0	225

prune943.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 48.4b

regimes2.2s

Accuracy

-9.2% (4.0b remaining)

Error of 52.2b against oracle of 48.1b and baseline of 51.8b

bsearch576.0ms

Steps

Iters	Range		Point
9	2.7117127389286462e-11	2.8594212645294413e-05	2.740149334961432e-11
9	4.411523690724343e-174	3.1469958201313954e-167	3.109295687066295e-167

simplify12.0ms

Iterations

Iter	Nodes
done	55
1	55
0	39

end0.0ms

sample14.6s

Algorithm

intervals

Results

3.6s	2304×	body	5120	valid
3.1s	13349×	body	80	nan
2.4s	1786×	body	2560	valid
1.2s	6868×	body	80	valid
1.2s	602×	body	10240	exit
1.1s	967×	body	1280	valid
246.0ms	400×	body	640	valid
82.0ms	230×	body	320	valid
28.0ms	115×	body	160	valid