Details

sample309.0ms

Algorithm

intervals

Results

73.0ms	380×	body	80	nan
53.0ms	62×	body	5120	valid
51.0ms	212×	body	80	valid
36.0ms	55×	body	2560	valid
20.0ms	23×	body	10240	exit
16.0ms	32×	body	1280	valid
6.0ms	14×	body	640	valid
1.0ms	4×	body	320	valid
1.0ms	4×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5011
3	3014
2	286
1	60
0	21

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 53.9b

localize64.0ms

Local error

Found 4 expressions with local error:

15.9b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
15.9b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
16.2b	(sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M)))
25.9b	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

rewrite2.6s

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/` `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 → 168

Calls

4 calls:

63.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
71.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
512.0ms	(sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M)))
1.9s	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

series1.4s

Counts

4 → 12

Calls

4 calls:

130.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
115.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
533.0ms	(sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M)))
649.0ms	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

simplify2.3s

Counts

180 → 180

Iterations

Iter	Nodes
done	5042
2	3035
1	715
0	232

prune1.5s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 29.9b

localize12.0ms

Local error

Found 1 expressions with local error:

7.7b	(* (/ c0 w) (/ 0 2.0))

rewrite20.0ms

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` `log1p-expm1-u` `add-log-exp`

Counts

1 → 52

Calls

1 calls:

18.0ms

(* (/ c0 w) (/ 0 2.0))

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

(* (/ c0 w) (/ 0 2.0))

simplify7.7s

Counts

55 → 55

Iterations

Iter	Nodes
done	5002
3	1155
2	457
1	276
0	111

prune466.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 26.3b

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

prune129.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 26.3b

localize192.0ms

Local error

Found 4 expressions with local error:

16.2b	(sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M)))
25.9b	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
25.9b	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
25.9b	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

rewrite6.3s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

488.0ms	(sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M)))
1.9s	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
2.0s	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
1.9s	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

series2.7s

Counts

4 → 12

Calls

4 calls:

598.0ms	(sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M)))
653.0ms	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
743.0ms	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
693.0ms	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

simplify2.4s

Counts

108 → 108

Iterations

Iter	Nodes
done	5004
2	1090
1	293
0	105

prune1.3s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 26.3b

regimes2.3s

Accuracy

-1.7% (7.9b remaining)

Error of 33.9b against oracle of 26.0b and baseline of 33.8b

bsearch760.0ms

Steps

Iters	Range		Point
10	4.871993564851982e-155	1.002617522920487e-140	1.879814245604767e-151
8	-1.0472446387625169e-174	-3.945649583231356e-177	-6.236251574640033e-177

simplify16.0ms

Iterations

Iter	Nodes
done	39
1	39
0	30

end0.0ms

sample13.6s

Algorithm

intervals

Results

3.5s	2342×	body	5120	valid
3.2s	13230×	body	80	nan
2.0s	1660×	body	2560	valid
1.2s	6747×	body	80	valid
1.1s	908×	body	1280	valid
702.0ms	540×	body	10240	exit
329.0ms	450×	body	640	valid
152.0ms	211×	body	320	valid
29.0ms	127×	body	160	valid