Details

sample457.0ms

Algorithm

intervals

Results

123.0ms	74×	body	5120	valid
78.0ms	455×	body	80	nan
62.0ms	60×	body	2560	valid
57.0ms	215×	body	80	valid
51.0ms	16×	body	10240	exit
28.0ms	31×	body	1280	valid
9.0ms	14×	body	640	valid
1.0ms	3×	body	320	valid
1.0ms	1×	body	160	valid

simplify2.4s

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: 52.9b

localize40.0ms

Local error

Found 4 expressions with local error:

10.5b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
10.5b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
13.6b	(sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M)))
28.2b	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

rewrite2.0s

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:

57.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
46.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
371.0ms	(sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M)))
1.5s	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

series1.2s

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
109.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
446.0ms	(sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M)))
589.0ms	(+ (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

184 → 184

Iterations

Iter	Nodes
done	5065
2	2978
1	718
0	235

prune1.5s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 22.0b

localize22.0ms

Local error

Found 1 expressions with local error:

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

rewrite27.0ms

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:

26.0ms

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

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

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

simplify14.5s

Counts

56 → 56

Iterations

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

prune358.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 20.6b

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

prune110.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 20.6b

localize88.0ms

Local error

Found 4 expressions with local error:

13.6b	(sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M)))
28.2b	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
28.2b	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
28.2b	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

rewrite5.1s

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` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`+-commutative` `sum-log` `flip3-+` `flip-+`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 100

Calls

4 calls:

425.0ms	(sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M)))
1.6s	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
1.5s	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
1.7s	(+ (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:

468.0ms	(sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M)))
559.0ms	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
490.0ms	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
515.0ms	(+ (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

112 → 112

Iterations

Iter	Nodes
done	5001
2	1092
1	295
0	107

prune1.2s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 20.6b

regimes1.2s

Accuracy

-0.4% (8.8b remaining)

Error of 33.8b against oracle of 25.0b and baseline of 33.8b

bsearch1.2s

Steps

Iters	Range		Point
10	3.0172524673861237e-272	7.22570326040676e-261	3.860215906667738e-266
7	-6.50572051550059e-142	-1.9403049553681466e-143	-1.960688023451719e-143

simplify10.0ms

Iterations

Iter	Nodes
done	32
1	32
0	26

end0.0ms

sample19.5s

Algorithm

intervals

Results

5.3s	2249×	body	5120	valid
3.7s	1814×	body	2560	valid
3.4s	12866×	body	80	nan
2.7s	6687×	body	80	valid
1.2s	570×	body	10240	exit
1.1s	912×	body	1280	valid
514.0ms	459×	body	640	valid
167.0ms	206×	body	320	valid
47.0ms	109×	body	160	valid