Details

sample239.0ms

Algorithm

intervals

Results

82.0ms	70×	body	5120	valid
35.0ms	379×	body	80	nan
28.0ms	51×	body	2560	valid
18.0ms	201×	body	80	valid
18.0ms	41×	body	1280	valid
12.0ms	18×	body	10240	exit
3.0ms	9×	body	640	valid
2.0ms	7×	body	320	valid
1.0ms	4×	body	160	valid

simplify2.5s

Counts

1 → 1

Iterations

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

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 53.0b

localize56.0ms

Local error

Found 4 expressions with local error:

16.1b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
16.1b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
16.1b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
26.3b	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

rewrite2.3s

Algorithm

rewrite-expression-head

Rules

172×	`add-cbrt-cube` `add-exp-log`
72×	`cbrt-undiv` `div-exp`
63×	`add-sqr-sqrt`
60×	`prod-exp` `cbrt-unprod`
48×	`times-frac`
39×	`associate-l`
33×	`*-un-lft-identity` `add-cube-cbrt`
21×	`associate-r`
12×	`unswap-sqr`
10×	`pow1`
7×	`fma-def`
6×	`sqrt-div` `frac-add` `div-inv` `add-log-exp`
5×	`frac-times` `associate-l/` `associate-r/`
4×	`expm1-log1p-u` `sqrt-prod` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `pow-prod-down` `*-commutative` `flip--`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+` `difference-of-squares`

Counts

4 → 216

Calls

4 calls:

54.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
76.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
58.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
2.1s	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

series958.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
121.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
108.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
605.0ms	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

simplify2.1s

Counts

228 → 228

Iterations

Iter	Nodes
done	5007
2	3007
1	697
0	217

prune1.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 27.7b

localize9.0ms

Local error

Found 1 expressions with local error:

5.7b	(* (/ c0 w) (/ 0 2))

rewrite22.0ms

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:

21.0ms

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

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

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

simplify13.6s

Counts

56 → 56

Iterations

Iter	Nodes
done	5015
3	1300
2	492
1	278
0	112

prune289.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 26.8b

localize1.0ms

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

prune78.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 26.8b

localize77.0ms

Local error

Found 4 expressions with local error:

16.1b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
26.3b	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
26.3b	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
26.3b	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

rewrite6.9s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 144

Calls

4 calls:

65.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
2.5s	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
2.2s	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
2.1s	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

series2.0s

Counts

4 → 12

Calls

4 calls:

124.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
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)))
626.0ms	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
620.0ms	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

simplify2.2s

Counts

156 → 156

Iterations

Iter	Nodes
done	5007
2	3007
1	697
0	217

prune1.5s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 26.8b

regimes1.5s

Accuracy

-2.2% (8.8b remaining)

Error of 33.9b against oracle of 25.1b and baseline of 33.7b

bsearch4.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	27
1	27
0	24

end0.0ms

sample13.5s

Algorithm

intervals

Results

3.2s	2263×	body	5120	valid
2.8s	13010×	body	80	nan
1.9s	6718×	body	80	valid
1.8s	1817×	body	2560	valid
853.0ms	443×	body	640	valid
756.0ms	877×	body	1280	valid
732.0ms	616×	body	10240	exit
125.0ms	229×	body	320	valid
68.0ms	118×	body	160	valid