Details

sample801.0ms

Algorithm

intervals

Results

516.0ms	1367×	body	80	nan
190.0ms	430×	body	80	valid

simplify5.0s

Counts

1 → 1

Iterations

Iter	Nodes
4	9507
3	1091
2	188
1	55
0	22

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.2b

localize55.0ms

Local error

Found 4 expressions with local error:

10.4b	(sqrt (/ d h))
12.0b	(* (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D))) (/ (* h -1/2) l))
12.7b	(sqrt (/ d l))
12.7b	(sqrt (/ d l))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

349×	`add-cbrt-cube` `add-exp-log`
154×	`cbrt-undiv` `div-exp`
140×	`prod-exp` `cbrt-unprod`
39×	`sqrt-prod`
37×	`add-sqr-sqrt`
33×	`times-frac`
27×	`*-un-lft-identity` `add-cube-cbrt`
12×	`pow1`
7×	`associate-r`
6×	`rem-sqrt-square`
5×	`frac-times` `associate-*l/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `associate-*r/`
1×	`associate-l` `*-commutative` `unswap-sqr`

Counts

4 → 215

Calls

4 calls:

2.0ms	(sqrt (/ d h))
112.0ms	(* (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D))) (/ (* h -1/2) l))
5.0ms	(sqrt (/ d l))
3.0ms	(sqrt (/ d l))

series304.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(sqrt (/ d h))
102.0ms	(* (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D))) (/ (* h -1/2) l))
58.0ms	(sqrt (/ d l))
87.0ms	(sqrt (/ d l))

simplify2.5s

Counts

227 → 227

Iterations

Iter	Nodes
2	4714
1	978
0	386

prune2.8s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 13.4b

localize116.0ms

Local error

Found 4 expressions with local error:

6.2b	(/ M (/ (* 2 d) D))
12.0b	(* (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D))) (/ (* h -1/2) l))
12.7b	(sqrt (/ d l))
12.7b	(sqrt (/ d l))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

358×	`add-cbrt-cube` `add-exp-log`
159×	`cbrt-undiv` `div-exp`
141×	`prod-exp` `cbrt-unprod`
56×	`times-frac`
43×	`add-sqr-sqrt`
36×	`*-un-lft-identity` `add-cube-cbrt`
26×	`sqrt-prod`
11×	`pow1`
8×	`div-inv`
7×	`associate-/r` `associate-r*`
5×	`frac-times` `associate-*l/`
4×	`expm1-log1p-u` `rem-sqrt-square` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `associate-r/` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div`
1×	`clear-num` `frac-2neg` `associate-l` `associate-/r/` `*-commutative` `unswap-sqr`

Counts

4 → 238

Calls

4 calls:

8.0ms	(/ M (/ (* 2 d) D))
159.0ms	(* (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D))) (/ (* h -1/2) l))
5.0ms	(sqrt (/ d l))
5.0ms	(sqrt (/ d l))

series294.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ M (/ (* 2 d) D))
109.0ms	(* (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D))) (/ (* h -1/2) l))
81.0ms	(sqrt (/ d l))
59.0ms	(sqrt (/ d l))

simplify2.1s

Counts

250 → 250

Iterations

Iter	Nodes
2	4867
1	1024
0	402

prune3.7s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 12.4b

localize60.0ms

Local error

Found 4 expressions with local error:

5.1b	(* (/ (* D M) (* d 2)) h)
5.7b	(* (* (/ (* D M) (* d 2)) (* (/ (* D M) (* d 2)) h)) (/ -1/2 l))
12.7b	(sqrt (/ d l))
12.7b	(sqrt (/ d l))

rewrite477.0ms

Algorithm

rewrite-expression-head

Rules

463×	`add-cbrt-cube` `add-exp-log`
269×	`prod-exp` `cbrt-unprod`
123×	`cbrt-undiv` `div-exp`
35×	`add-sqr-sqrt`
30×	`times-frac`
27×	`*-un-lft-identity` `add-cube-cbrt`
26×	`sqrt-prod`
17×	`pow1`
16×	`associate-r`
10×	`associate-*l/`
7×	`pow-prod-down`
6×	`associate-l`
5×	`frac-times`
4×	`expm1-log1p-u` `rem-sqrt-square` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-*r/`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `*-commutative`
1×	`unswap-sqr`

Counts

4 → 247

Calls

4 calls:

40.0ms	(* (/ (* D M) (* d 2)) h)
421.0ms	(* (* (/ (* D M) (* d 2)) (* (/ (* D M) (* d 2)) h)) (/ -1/2 l))
2.0ms	(sqrt (/ d l))
3.0ms	(sqrt (/ d l))

series302.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (/ (* D M) (* d 2)) h)
97.0ms	(* (* (/ (* D M) (* d 2)) (* (/ (* D M) (* d 2)) h)) (/ -1/2 l))
75.0ms	(sqrt (/ d l))
63.0ms	(sqrt (/ d l))

simplify3.6s

Counts

259 → 259

Iterations

Iter	Nodes
2	7080
1	1253
0	421

prune2.9s

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 11.1b

localize79.0ms

Local error

Found 4 expressions with local error:

4.5b	(* (fma (sqrt (/ d l)) (* (* (/ (* D M) (* d 2)) (* (/ (* D M) (* d 2)) h)) (/ -1/2 l)) (* (fabs (/ (cbrt d) (cbrt l))) (sqrt (/ (cbrt d) (cbrt l))))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))
5.1b	(* (/ (* D M) (* d 2)) h)
5.7b	(* (* (/ (* D M) (* d 2)) (* (/ (* D M) (* d 2)) h)) (/ -1/2 l))
12.7b	(sqrt (/ d l))

rewrite501.0ms

Algorithm

rewrite-expression-head

Rules

468×	`add-cbrt-cube` `add-exp-log`
272×	`prod-exp` `cbrt-unprod`
123×	`cbrt-undiv` `div-exp`
26×	`add-sqr-sqrt`
21×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
20×	`times-frac`
17×	`associate-r`
13×	`sqrt-prod`
10×	`pow-prod-down` `associate-*l/`
9×	`associate-l`
5×	`frac-times` `associate-*r/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `div-inv`
2×	`rem-sqrt-square` `sqrt-div`
1×	`sqrt-pow1` `pow1/2` `unswap-sqr`

Counts

4 → 241

Calls

4 calls:

24.0ms	(* (fma (sqrt (/ d l)) (* (* (/ (* D M) (* d 2)) (* (/ (* D M) (* d 2)) h)) (/ -1/2 l)) (* (fabs (/ (cbrt d) (cbrt l))) (sqrt (/ (cbrt d) (cbrt l))))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))
39.0ms	(* (/ (* D M) (* d 2)) h)
424.0ms	(* (* (/ (* D M) (* d 2)) (* (/ (* D M) (* d 2)) h)) (/ -1/2 l))
2.0ms	(sqrt (/ d l))

series1.2s

Counts

4 → 12

Calls

4 calls:

983.0ms	(* (fma (sqrt (/ d l)) (* (* (/ (* D M) (* d 2)) (* (/ (* D M) (* d 2)) h)) (/ -1/2 l)) (* (fabs (/ (cbrt d) (cbrt l))) (sqrt (/ (cbrt d) (cbrt l))))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))
75.0ms	(* (/ (* D M) (* d 2)) h)
99.0ms	(* (* (/ (* D M) (* d 2)) (* (/ (* D M) (* d 2)) h)) (/ -1/2 l))
78.0ms	(sqrt (/ d l))

simplify4.9s

Counts

253 → 253

Iterations

Iter	Nodes
2	8429
1	1536
0	526

prune3.0s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 8.0b

regimes2.8s

Accuracy

0% (3.7b remaining)

Error of 11.1b against oracle of 7.5b and baseline of 11.1b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
2	35
1	35
0	27

end0.0ms

sample24.7s

Algorithm

intervals

Results

16.0s	39000×	body	80	nan
5.9s	12829×	body	80	valid