Details

sample507.0ms

Algorithm

intervals

Results

137.0ms	73×	body	5120	valid
100.0ms	63×	body	2560	valid
76.0ms	389×	body	80	nan
72.0ms	217×	body	80	valid
34.0ms	20×	body	10240	exit
30.0ms	29×	body	1280	valid
10.0ms	13×	body	640	valid
4.0ms	6×	body	320	valid
1.0ms	4×	body	160	valid

simplify829.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2004
3	2004
2	286
1	60
0	21

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 52.3b

localize69.0ms

Local error

Found 4 expressions with local error:

12.2b	(* (/ c0 h) (/ (* (/ d D) (/ d D)) w))
12.2b	(* (/ c0 h) (/ (* (/ d D) (/ d D)) w))
13.6b	(sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M)))
28.5b	(+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)))

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

116×	`add-cbrt-cube` `add-exp-log`
48×	`cbrt-undiv` `div-exp`
46×	`add-sqr-sqrt`
40×	`prod-exp` `cbrt-unprod`
32×	`times-frac`
26×	`associate-l`
25×	`*-un-lft-identity` `add-cube-cbrt`
14×	`associate-r`
9×	`pow1`
8×	`sqrt-div` `sqrt-prod` `unswap-sqr`
7×	`fma-def`
6×	`frac-add` `add-log-exp`
4×	`expm1-log1p-u` `frac-times` `flip3--` `associate-l/` `associate-r/` `insert-posit16` `log1p-expm1-u` `div-inv` `flip--`
2×	`pow-prod-down` `*-commutative` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 172

Calls

4 calls:

40.0ms	(* (/ c0 h) (/ (* (/ d D) (/ d D)) w))
36.0ms	(* (/ c0 h) (/ (* (/ d D) (/ d D)) w))
390.0ms	(sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M)))
1.6s	(+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)))

series1.3s

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (/ c0 h) (/ (* (/ d D) (/ d D)) w))
109.0ms	(* (/ c0 h) (/ (* (/ d D) (/ d D)) w))
458.0ms	(sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M)))
578.0ms	(+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)))

simplify1.1s

Counts

184 → 184

Iterations

Iter	Nodes
done	2001
2	2001
1	719
0	236

prune3.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 28.6b

localize11.0ms

Local error

Found 1 expressions with local error:

4.9b	(* (/ c0 w) (/ 0 2))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
22×	`times-frac`
15×	`*-un-lft-identity` `add-cube-cbrt`
13×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
3×	`pow1`
2×	`div-inv`
1×	`expm1-log1p-u` `frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

1 → 53

Calls

1 calls:

12.0ms

(* (/ c0 w) (/ 0 2))

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

(* (/ c0 w) (/ 0 2))

simplify2.4s

Counts

56 → 56

Iterations

Iter	Nodes
done	2129
4	2129
3	1300
2	492
1	278
0	112

prune616.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 27.7b

localize20.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune111.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 27.7b

localize112.0ms

Local error

Found 4 expressions with local error:

13.6b	(sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M)))
13.6b	(sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M)))
28.5b	(+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)))
28.5b	(+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)))

rewrite3.8s

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-div` `sqrt-prod`
14×	`fma-def`
12×	`add-sqr-sqrt` `frac-add`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`flip3--` `flip--` `add-log-exp`
6×	`pow1`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `associate-l/` `associate-r/` `add-exp-log` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
2×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 92

Calls

4 calls:

370.0ms	(sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M)))
456.0ms	(sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M)))
1.6s	(+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)))
1.4s	(+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)))

series2.0s

Counts

4 → 12

Calls

4 calls:

478.0ms	(sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M)))
430.0ms	(sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M)))
555.0ms	(+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)))
496.0ms	(+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)))

simplify1.4s

Counts

104 → 104

Iterations

Iter	Nodes
done	2000
3	2000
2	1099
1	295
0	108

prune2.2s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 27.7b

regimes1.8s

Accuracy

21.7% (6.1b remaining)

Error of 32.4b against oracle of 26.3b and baseline of 34.0b

bsearch4.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	33
1	33
0	27

end0.0ms

sample20.2s

Algorithm

intervals

Results

5.7s	2275×	body	5120	valid
4.0s	12832×	body	80	nan
3.4s	1755×	body	2560	valid
1.9s	6755×	body	80	valid
1.8s	902×	body	1280	valid
1.5s	561×	body	10240	exit
553.0ms	476×	body	640	valid
154.0ms	220×	body	320	valid
50.0ms	112×	body	160	valid