Details

sample309.0ms

Algorithm

intervals

Results

86.0ms	82×	body	5120	valid
57.0ms	235×	body	80	valid
44.0ms	480×	body	80	nan
24.0ms	46×	body	2560	valid
17.0ms	21×	body	10240	exit
13.0ms	30×	body	1280	valid
5.0ms	15×	body	640	valid
2.0ms	10×	body	320	valid
0.0ms	2×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

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

prune38.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 51.3b

localize72.0ms

Local error

Found 4 expressions with local error:

11.6b	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
11.6b	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
11.8b	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
26.7b	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

rewrite206.0ms

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:

30.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
59.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
52.0ms	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
58.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

series1.9s

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
126.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
790.0ms	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
925.0ms	(+ (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

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 48.6b

localize238.0ms

Local error

Found 4 expressions with local error:

11.8b	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
26.7b	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
26.7b	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
26.7b	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

rewrite250.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

60.0ms	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
61.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
60.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
63.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

series4.2s

Counts

4 → 12

Calls

4 calls:

816.0ms	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
971.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
977.0ms	(+ (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)))

simplify2.3s

Counts

91 → 91

Iterations

Iter	Nodes
done	5001
2	1536
1	370
0	131

prune1.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 48.6b

localize77.0ms

Local error

Found 4 expressions with local error:

11.6b	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
11.8b	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
12.1b	(/ (* w h) (* (* c0 (/ d D)) (/ d D)))
32.1b	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ 1 (/ (* w h) (* (* c0 (/ d D)) (/ d D)))))

rewrite192.0ms

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

Counts

4 → 128

Calls

4 calls:

35.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
50.0ms	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
30.0ms	(/ (* w h) (* (* c0 (/ d D)) (/ d D)))
61.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ 1 (/ (* w h) (* (* c0 (/ d D)) (/ d D)))))

series2.2s

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
842.0ms	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
174.0ms	(/ (* w h) (* (* c0 (/ d D)) (/ d D)))
1.1s	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ 1 (/ (* w h) (* (* c0 (/ d D)) (/ d D)))))

simplify2.0s

Counts

140 → 140

Iterations

Iter	Nodes
done	5000
1	850
0	275

prune1.2s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 48.6b

localize138.0ms

Local error

Found 4 expressions with local error:

11.8b	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
11.8b	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
26.7b	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
26.7b	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

rewrite258.0ms

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:

54.0ms	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
45.0ms	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
66.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
90.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

series3.4s

Counts

4 → 12

Calls

4 calls:

826.0ms	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
791.0ms	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
937.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
881.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

simplify2.6s

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
2	1536
1	370
0	131

prune1.4s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 48.6b

regimes2.4s

Accuracy

-2.4% (4.3b remaining)

Error of 52.4b against oracle of 48.1b and baseline of 52.3b

bsearch585.0ms

Steps

Iters	Range		Point
7	7.090332893506187e+143	7.766814504083789e+145	7.635350550318418e+145
9	4.233320258344602e-109	1.7590015622742258e-101	1.2944989080373868e-101

simplify51.0ms

Iterations

Iter	Nodes
done	64
1	64
0	47

end0.0ms

sample14.5s

Algorithm

intervals

Results

3.5s	2316×	body	5120	valid
3.1s	13093×	body	80	nan
1.7s	6883×	body	80	valid
1.7s	1727×	body	2560	valid
1.2s	955×	body	1280	valid
869.0ms	582×	body	10240	exit
727.0ms	465×	body	640	valid
118.0ms	225×	body	320	valid
56.0ms	111×	body	160	valid