Details

sample479.0ms

Algorithm

intervals

Results

115.0ms	62×	body	5120	valid
109.0ms	386×	body	80	nan
95.0ms	60×	body	2560	valid
44.0ms	228×	body	80	valid
29.0ms	19×	body	10240	exit
27.0ms	28×	body	1280	valid
8.0ms	13×	body	320	valid
7.0ms	9×	body	640	valid
1.0ms	2×	body	160	valid

simplify866.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2006
3	2006
2	280
1	59
0	21

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 50.3b

localize57.0ms

Local error

Found 4 expressions with local error:

13.7b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
13.7b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
13.7b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
26.4b	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

172×	`add-cbrt-cube` `add-exp-log`
72×	`cbrt-undiv` `div-exp`
61×	`add-sqr-sqrt`
60×	`prod-exp` `cbrt-unprod`
48×	`times-frac`
39×	`associate-l`
31×	`*-un-lft-identity` `add-cube-cbrt`
24×	`sqrt-div` `frac-add`
23×	`frac-times`
21×	`associate-r`
17×	`associate-l/` `associate-r/`
12×	`unswap-sqr`
10×	`pow1` `flip3-+` `flip-+`
9×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
4×	`insert-posit16`
3×	`pow-prod-down` `*-commutative`
1×	`+-commutative` `sum-log`

Counts

4 → 219

Calls

4 calls:

46.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
30.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
29.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
41.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

series1.3s

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
98.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
109.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
972.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

simplify1.5s

Counts

231 → 231

Iterations

Iter	Nodes
done	2008
2	2008
1	915
0	316

prune1.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 47.5b

localize117.0ms

Local error

Found 4 expressions with local error:

13.7b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
26.4b	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
26.4b	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
26.4b	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-div` `frac-add`
61×	`frac-times`
60×	`add-cbrt-cube` `add-exp-log`
43×	`associate-l/` `associate-r/`
30×	`flip3-+` `flip-+`
27×	`flip3--` `flip--`
24×	`cbrt-undiv` `div-exp`
23×	`add-sqr-sqrt`
20×	`prod-exp` `cbrt-unprod`
16×	`times-frac`
13×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
10×	`add-log-exp`
7×	`associate-r`
6×	`pow1`
4×	`insert-posit16` `unswap-sqr`
3×	`+-commutative` `sum-log`
2×	`div-inv`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 169

Calls

4 calls:

38.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
39.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
40.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
39.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

series2.5s

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
876.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
694.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
861.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

simplify1.5s

Counts

181 → 181

Iterations

Iter	Nodes
done	2008
2	2008
1	915
0	316

prune2.1s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 47.5b

localize48.0ms

Local error

Found 4 expressions with local error:

13.7b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
13.7b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
13.7b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
26.4b	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

172×	`add-cbrt-cube` `add-exp-log`
72×	`cbrt-undiv` `div-exp`
61×	`add-sqr-sqrt`
60×	`prod-exp` `cbrt-unprod`
48×	`times-frac`
39×	`associate-l`
31×	`*-un-lft-identity` `add-cube-cbrt`
24×	`sqrt-div` `frac-add`
23×	`frac-times`
21×	`associate-r`
17×	`associate-l/` `associate-r/`
12×	`unswap-sqr`
10×	`pow1` `flip3-+` `flip-+`
9×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
4×	`insert-posit16`
3×	`pow-prod-down` `*-commutative`
1×	`+-commutative` `sum-log`

Counts

4 → 219

Calls

4 calls:

46.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
45.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
46.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
39.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

series1.2s

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
122.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
103.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
877.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

simplify1.4s

Counts

231 → 231

Iterations

Iter	Nodes
done	2008
2	2008
1	915
0	316

prune1.9s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 47.5b

localize94.0ms

Local error

Found 4 expressions with local error:

13.3b	(sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M)))
13.7b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
13.7b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
34.9b	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

116×	`add-cbrt-cube` `add-exp-log`
48×	`cbrt-undiv` `div-exp`
42×	`add-sqr-sqrt`
40×	`prod-exp` `cbrt-unprod`
32×	`times-frac` `sqrt-div`
26×	`frac-times` `associate-l`
24×	`frac-add`
22×	`*-un-lft-identity` `add-cube-cbrt`
18×	`associate-l/` `associate-r/`
14×	`associate-r`
13×	`flip3-+` `flip-+`
12×	`flip3--` `flip--`
11×	`pow1`
8×	`unswap-sqr`
6×	`add-log-exp`
4×	`insert-posit16` `div-inv`
3×	`pow-prod-down`
2×	`sqrt-pow1` `*-commutative`
1×	`+-commutative` `sum-log` `pow1/2` `sqrt-prod`

Counts

4 → 178

Calls

4 calls:

59.0ms	(sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M)))
32.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
39.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
52.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)))

series1.9s

Counts

4 → 12

Calls

4 calls:

757.0ms	(sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M)))
107.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
123.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
957.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)))

simplify1.4s

Counts

190 → 190

Iterations

Iter	Nodes
done	2000
2	2000
1	995
0	335

prune1.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 45.5b

regimes2.5s

Accuracy

-4% (7.4b remaining)

Error of 54.8b against oracle of 47.4b and baseline of 54.5b

bsearch425.0ms

Steps

Iters	Range		Point
10	3.6696251092936084e-297	7.132814083827276e-286	5.43376491402612e-292

simplify27.0ms

Iterations

Iter	Nodes
done	46
1	46
0	35

end0.0ms

sample20.1s

Algorithm

intervals

Results

4.8s	2253×	body	5120	valid
4.6s	13145×	body	80	nan
4.4s	1764×	body	2560	valid
1.8s	6803×	body	80	valid
1.3s	903×	body	1280	valid
1.2s	577×	body	10240	exit
405.0ms	444×	body	640	valid
211.0ms	227×	body	320	valid
54.0ms	113×	body	160	valid