Details

sample383.0ms

Algorithm

intervals

Results

113.0ms	72×	body	5120	valid
85.0ms	388×	body	80	nan
45.0ms	58×	body	2560	valid
26.0ms	206×	body	80	valid
24.0ms	38×	body	1280	valid
17.0ms	16×	body	10240	exit
6.0ms	12×	body	640	valid
2.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

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

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 53.7b

localize87.0ms

Local error

Found 4 expressions with local error:

11.1b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
11.1b	(* (/ 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)))
27.2b	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

rewrite2.5s

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/` `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:

69.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
64.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
529.0ms	(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:

117.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
145.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
542.0ms	(sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M)))
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)))

simplify2.3s

Counts

180 → 180

Iterations

Iter	Nodes
done	5042
2	3035
1	715
0	232

prune1.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 28.3b

localize15.0ms

Local error

Found 1 expressions with local error:

5.4b	(* (/ c0 w) (/ 0 2.0))

rewrite40.0ms

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:

36.0ms

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

series5.0ms

Counts

1 → 3

Calls

1 calls:

5.0ms

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

simplify6.6s

Counts

55 → 55

Iterations

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

prune379.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 24.9b

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

prune95.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 24.9b

localize138.0ms

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)))
27.2b	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
27.2b	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
27.2b	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

rewrite5.2s

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:

440.0ms	(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)))
1.6s	(+ (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)))

series2.3s

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)))
585.0ms	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
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)))
603.0ms	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

simplify2.0s

Counts

108 → 108

Iterations

Iter	Nodes
done	5004
2	1090
1	293
0	105

prune1.1s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 24.9b

regimes1.8s

Accuracy

10.4% (7.1b remaining)

Error of 32.9b against oracle of 25.8b and baseline of 33.8b

bsearch5.0ms

simplify14.0ms

Iterations

Iter	Nodes
done	49
1	49
0	39

end0.0ms

sample12.9s

Algorithm

intervals

Results

3.1s	13371×	body	80	nan
2.9s	2270×	body	5120	valid
2.0s	1749×	body	2560	valid
1.1s	6750×	body	80	valid
1.0s	970×	body	1280	valid
631.0ms	595×	body	10240	exit
389.0ms	110×	body	160	valid
257.0ms	480×	body	640	valid
80.0ms	227×	body	320	valid