Details

sample511.0ms

Algorithm

intervals

Results

132.0ms	79×	body	5120	valid
109.0ms	434×	body	80	nan
61.0ms	28×	body	10240	exit
56.0ms	49×	body	2560	valid
46.0ms	229×	body	80	valid
24.0ms	25×	body	1280	valid
13.0ms	15×	body	640	valid
4.0ms	7×	body	320	valid
2.0ms	4×	body	160	valid

simplify985.0ms

Counts

1 → 1

Iterations

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

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 51.3b

localize60.0ms

Local error

Found 4 expressions with local error:

13.4b	(* (/ c0 h) (/ (* (/ d D) (/ d D)) w))
13.4b	(* (/ c0 h) (/ (* (/ d D) (/ d D)) w))
15.9b	(sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M)))
25.8b	(+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)))

rewrite2.5s

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:

54.0ms	(* (/ c0 h) (/ (* (/ d D) (/ d D)) w))
47.0ms	(* (/ c0 h) (/ (* (/ d D) (/ d D)) w))
399.0ms	(sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M)))
2.0s	(+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)))

series1.2s

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (/ c0 h) (/ (* (/ d D) (/ d D)) w))
120.0ms	(* (/ c0 h) (/ (* (/ d D) (/ d D)) w))
424.0ms	(sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M)))
559.0ms	(+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)))

simplify1.2s

Counts

184 → 184

Iterations

Iter	Nodes
done	2001
2	2001
1	719
0	236

prune1.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 23.9b

localize12.0ms

Local error

Found 1 expressions with local error:

6.9b	(* (/ 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))

simplify2.3s

Counts

56 → 56

Iterations

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

prune350.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 21.9b

localize0.0ms

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

prune114.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 21.9b

localize95.0ms

Local error

Found 4 expressions with local error:

13.4b	(* (/ c0 h) (/ (* (/ d D) (/ d D)) w))
15.9b	(sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M)))
27.2b	(log1p (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))))
38.6b	(+ (expm1 (log1p (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)))

rewrite435.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-cbrt-cube` `add-exp-log`
26×	`add-sqr-sqrt`
24×	`cbrt-undiv` `div-exp`
20×	`prod-exp` `cbrt-unprod`
16×	`times-frac`
15×	`*-un-lft-identity` `add-cube-cbrt`
13×	`associate-l`
7×	`pow1` `associate-r`
6×	`add-log-exp`
5×	`expm1-log1p-u`
4×	`sqrt-prod` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def`
2×	`sqrt-div` `div-inv`
1×	`frac-times` `+-commutative` `rem-sqrt-square` `log1p-udef` `sum-log` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `pow-prod-down` `associate-l/` `log1p-expm1` `associate-r/` `*-commutative` `associate-+l-` `flip-+` `flip--` `expm1-udef` `difference-of-squares`

Counts

4 → 112

Calls

4 calls:

27.0ms	(* (/ 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)))
1.0ms	(log1p (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))))
14.0ms	(+ (expm1 (log1p (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)))

series1.5s

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (/ 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)))
193.0ms	(log1p (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))))
766.0ms	(+ (expm1 (log1p (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

124 → 124

Iterations

Iter	Nodes
done	2001
2	2001
1	763
0	262

prune830.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 21.9b

regimes1.2s

Accuracy

-36.2% (9.9b remaining)

Error of 37.0b against oracle of 27.1b and baseline of 34.4b

bsearch613.0ms

Steps

Iters	Range		Point
8	1.4444572920035781e-34	1.2148806960765455e-31	1.535976817000598e-34
8	1.5461341164811597e-193	1.794753453507347e-190	1.7724222504113438e-190

simplify7.0ms

Iterations

Iter	Nodes
done	33
1	33
0	27

end0.0ms

sample19.7s

Algorithm

intervals

Results

5.0s	13246×	body	80	nan
4.6s	2289×	body	5120	valid
2.7s	1689×	body	2560	valid
2.2s	6836×	body	80	valid
1.7s	939×	body	1280	valid
1.2s	610×	body	10240	exit
902.0ms	444×	body	640	valid
176.0ms	224×	body	320	valid
48.0ms	112×	body	160	valid