Details

sample970.0ms

Algorithm

intervals

Results

492.0ms	63×	body	2560	valid
158.0ms	73×	body	5120	valid
91.0ms	389×	body	80	nan
70.0ms	217×	body	80	valid
56.0ms	29×	body	1280	valid
35.0ms	20×	body	10240	exit
13.0ms	13×	body	640	valid
4.0ms	6×	body	320	valid
2.0ms	4×	body	160	valid

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	2006
3	2006
2	280
1	59
0	21

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 52.6b

localize44.0ms

Local error

Found 4 expressions with local error:

14.0b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
14.0b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
14.0b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
28.5b	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

172×	`add-cbrt-cube` `add-exp-log`
72×	`cbrt-undiv` `div-exp`
61×	`add-sqr-sqrt`
60×	`prod-exp` `cbrt-unprod`
48×	`times-frac`
39×	`associate-l`
31×	`*-un-lft-identity` `add-cube-cbrt`
24×	`sqrt-div` `frac-add`
23×	`frac-times`
21×	`associate-r`
17×	`associate-l/` `associate-r/`
12×	`unswap-sqr`
10×	`pow1` `flip3-+` `flip-+`
9×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
4×	`insert-posit16`
3×	`pow-prod-down` `*-commutative`
1×	`+-commutative` `sum-log`

Counts

4 → 219

Calls

4 calls:

41.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
45.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
35.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
57.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

series1.3s

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
109.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
140.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
917.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

simplify1.5s

Counts

231 → 231

Iterations

Iter	Nodes
done	2008
2	2008
1	915
0	316

prune4.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 49.2b

localize122.0ms

Local error

Found 4 expressions with local error:

14.0b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
28.5b	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
28.5b	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
28.5b	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-div` `frac-add`
61×	`frac-times`
60×	`add-cbrt-cube` `add-exp-log`
43×	`associate-l/` `associate-r/`
30×	`flip3-+` `flip-+`
27×	`flip3--` `flip--`
24×	`cbrt-undiv` `div-exp`
23×	`add-sqr-sqrt`
20×	`prod-exp` `cbrt-unprod`
16×	`times-frac`
13×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
10×	`add-log-exp`
7×	`associate-r`
6×	`pow1`
4×	`insert-posit16` `unswap-sqr`
3×	`+-commutative` `sum-log`
2×	`div-inv`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 169

Calls

4 calls:

29.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
39.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
45.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
49.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

series3.0s

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
965.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
1.0s	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
909.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

simplify1.5s

Counts

181 → 181

Iterations

Iter	Nodes
done	2008
2	2008
1	915
0	316

prune4.5s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 49.2b

localize115.0ms

Local error

Found 4 expressions with local error:

16.6b	(cbrt (+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))))
28.5b	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
28.5b	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
36.1b	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)))

rewrite209.0ms

Algorithm

rewrite-expression-head

Rules

96×	`sqrt-div` `frac-add`
80×	`frac-times`
56×	`associate-l/` `associate-r/`
40×	`flip3-+` `flip-+`
36×	`flip3--` `flip--`
26×	`cbrt-div`
10×	`add-log-exp`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`cbrt-prod` `+-commutative` `sum-log`
1×	`pow1/3`

Counts

4 → 146

Calls

4 calls:

39.0ms	(cbrt (+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))))
57.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
37.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
71.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)))

series3.0s

Counts

4 → 12

Calls

4 calls:

529.0ms	(cbrt (+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))))
848.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
820.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
835.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)))

simplify1.5s

Counts

158 → 158

Iterations

Iter	Nodes
done	2006
2	2006
1	833
0	356

prune4.7s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 49.2b

localize167.0ms

Local error

Found 4 expressions with local error:

28.5b	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
36.1b	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)))
36.1b	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)))
36.1b	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)))

rewrite219.0ms

Algorithm

rewrite-expression-head

Rules

96×	`sqrt-div` `frac-add`
80×	`frac-times`
56×	`associate-l/` `associate-r/`
40×	`flip3-+` `flip-+`
36×	`flip3--` `flip--`
12×	`add-log-exp`
4×	`add-sqr-sqrt` `pow1` `+-commutative` `sum-log` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`

Counts

4 → 144

Calls

4 calls:

40.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
52.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)))
62.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)))
60.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)))

series3.3s

Counts

4 → 12

Calls

4 calls:

890.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
904.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)))
786.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)))
732.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)))

simplify1.9s

Counts

156 → 156

Iterations

Iter	Nodes
done	2000
2	2000
1	708
0	266

prune5.3s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 49.2b

regimes2.1s

Accuracy

-13% (5.0b remaining)

Error of 53.3b against oracle of 48.4b and baseline of 52.8b

bsearch877.0ms

Steps

Iters	Range		Point
8	7.528076764680937e-72	6.123061375347514e-69	1.1156496586195279e-69
10	-1.0028721268385378e-130	-1.3283169507921262e-143	-5.885464112857827e-142

simplify35.0ms

Iterations

Iter	Nodes
done	54
1	54
0	41

end0.0ms

sample20.3s

Algorithm

intervals

Results

5.7s	2275×	body	5120	valid
4.5s	1755×	body	2560	valid
3.6s	12832×	body	80	nan
1.7s	6755×	body	80	valid
1.6s	561×	body	10240	exit
1.2s	902×	body	1280	valid
463.0ms	476×	body	640	valid
143.0ms	220×	body	320	valid
49.0ms	112×	body	160	valid