Details

sample1.2s

Algorithm

intervals

Results

858.0ms	1258×	body	80	nan
205.0ms	404×	body	80	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	1271
2	198
1	58
0	22

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.9b

localize63.0ms

Local error

Found 4 expressions with local error:

9.9b	(sqrt (/ d l))
10.5b	(sqrt (/ d h))
10.5b	(sqrt (/ d h))
11.4b	(* (/ M (/ (* 2 d) D)) (/ h l))

rewrite269.0ms

Algorithm

rewrite-expression-head

Rules

641×	`times-frac`
594×	`add-sqr-sqrt`
553×	`associate-/r*`
474×	`*-un-lft-identity`
473×	`add-cube-cbrt`
414×	`frac-times`
262×	`associate-l`
193×	`associate-/l*`
133×	`associate-r`
62×	`clear-num`
61×	`frac-2neg`
50×	`unswap-sqr`
46×	`associate-*l/`
41×	`*-commutative`
39×	`sqrt-prod`
36×	`add-cbrt-cube` `add-exp-log`
27×	`sqrt-div`
18×	`associate-/r/` `div-inv`
14×	`cbrt-undiv` `div-exp`
10×	`prod-exp` `cbrt-unprod`
9×	`pow1` `associate-*r/`
6×	`rem-sqrt-square`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1` `pow1/2`
2×	`un-div-inv`
1×	`pow-prod-down`

Counts

4 → 770

Calls

4 calls:

5.0ms	(sqrt (/ d l))
5.0ms	(sqrt (/ d h))
5.0ms	(sqrt (/ d h))
174.0ms	(* (/ M (/ (* 2 d) D)) (/ h l))

series308.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(sqrt (/ d l))
56.0ms	(sqrt (/ d h))
65.0ms	(sqrt (/ d h))
115.0ms	(* (/ M (/ (* 2 d) D)) (/ h l))

simplify3.1s

Counts

782 → 782

Iterations

Iter	Nodes
done	5001
1	4727
0	1272

prune7.0s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 16.1b

localize95.0ms

Local error

Found 4 expressions with local error:

9.9b	(sqrt (/ d l))
9.9b	(sqrt (/ d l))
10.5b	(sqrt (/ d h))
10.5b	(sqrt (/ d h))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt` `sqrt-prod`
40×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
36×	`sqrt-div`
12×	`associate-/r` `associate-/l`
8×	`pow1` `rem-sqrt-square`
4×	`expm1-log1p-u` `clear-num` `frac-2neg` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

4 → 144

Calls

4 calls:

10.0ms	(sqrt (/ d l))
10.0ms	(sqrt (/ d l))
10.0ms	(sqrt (/ d h))
10.0ms	(sqrt (/ d h))

series303.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(sqrt (/ d l))
89.0ms	(sqrt (/ d l))
82.0ms	(sqrt (/ d h))
75.0ms	(sqrt (/ d h))

simplify2.5s

Counts

156 → 156

Iterations

Iter	Nodes
done	5002
3	2168
2	692
1	292
0	173

prune1.9s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 15.2b

localize103.0ms

Local error

Found 4 expressions with local error:

7.4b	(* (* (/ M (/ (* 2 d) D)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))
9.9b	(sqrt (/ d l))
10.5b	(sqrt (/ d h))
10.5b	(sqrt (/ d h))

rewrite7.9s

Algorithm

rewrite-expression-head

Rules

38934×	`frac-times`
30607×	`add-sqr-sqrt`
27477×	`associate-/l*`
24328×	`associate-/r*`
21461×	`*-un-lft-identity`
21290×	`add-cube-cbrt`
17091×	`times-frac`
14905×	`cbrt-prod`
8155×	`associate-l`
7799×	`associate-r`
4531×	`unswap-sqr`
3748×	`swap-sqr`
2672×	`clear-num`
2658×	`frac-2neg`
2198×	`associate-*l/`
1984×	`*-commutative`
451×	`div-inv`
441×	`associate-*r/`
419×	`add-cbrt-cube`
241×	`add-exp-log`
213×	`cbrt-unprod`
200×	`cbrt-undiv`
108×	`prod-exp`
103×	`div-exp`
41×	`un-div-inv`
39×	`sqrt-prod`
27×	`sqrt-div`
18×	`associate-/r/`
16×	`1-exp`
12×	`pow1`
6×	`rem-sqrt-square`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1` `pow1/2` `pow-prod-down`

Counts

4 → 21613

Calls

4 calls:

2.7s	(* (* (/ M (/ (* 2 d) D)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))
5.0ms	(sqrt (/ d l))
5.0ms	(sqrt (/ d h))
11.0ms	(sqrt (/ d h))

series403.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(* (* (/ M (/ (* 2 d) D)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))
60.0ms	(sqrt (/ d l))
90.0ms	(sqrt (/ d h))
81.0ms	(sqrt (/ d h))

simplify41.6s

Counts

21625 → 21625

Iterations

Iter	Nodes
done	23187
0	23187

prune4.0m

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 13.4b

localize107.0ms

Local error

Found 4 expressions with local error:

6.9b	(fma (* (* (sqrt (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l)))) (sqrt (/ d h))) (* (* (* (* (/ M (/ (* 2 d) D)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l)) (/ M (/ (* 2 d) D))) -1/2) (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (sqrt (/ d h))))
7.4b	(* (* (/ M (/ (* 2 d) D)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))
10.5b	(sqrt (/ d h))
10.5b	(sqrt (/ d h))

rewrite5.3s

Algorithm

rewrite-expression-head

Rules

38934×	`frac-times`
30595×	`add-sqr-sqrt`
27474×	`associate-/l*`
24325×	`associate-/r*`
21452×	`*-un-lft-identity`
21281×	`add-cube-cbrt`
17081×	`times-frac`
14905×	`cbrt-prod`
8155×	`associate-l`
7799×	`associate-r`
4531×	`unswap-sqr`
3748×	`swap-sqr`
2671×	`clear-num`
2657×	`frac-2neg`
2198×	`associate-*l/`
1984×	`*-commutative`
450×	`div-inv`
441×	`associate-*r/`
419×	`add-cbrt-cube`
241×	`add-exp-log`
213×	`cbrt-unprod`
200×	`cbrt-undiv`
108×	`prod-exp`
103×	`div-exp`
41×	`un-div-inv`
26×	`sqrt-prod`
18×	`sqrt-div` `associate-/r/`
16×	`1-exp`
11×	`pow1`
4×	`expm1-log1p-u` `rem-sqrt-square` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down`
2×	`sqrt-pow1` `pow1/2`
1×	`fma-udef`

Counts

4 → 21588

Calls

4 calls:

0.0ms	(fma (* (* (sqrt (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l)))) (sqrt (/ d h))) (* (* (* (* (/ M (/ (* 2 d) D)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l)) (/ M (/ (* 2 d) D))) -1/2) (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (sqrt (/ d h))))
2.0s	(* (* (/ M (/ (* 2 d) D)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))
5.0ms	(sqrt (/ d h))
5.0ms	(sqrt (/ d h))

series1.6s

Counts

4 → 12

Calls

4 calls:

1.4s	(fma (* (* (sqrt (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l)))) (sqrt (/ d h))) (* (* (* (* (/ M (/ (* 2 d) D)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l)) (/ M (/ (* 2 d) D))) -1/2) (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (sqrt (/ d h))))
103.0ms	(* (* (/ M (/ (* 2 d) D)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))
50.0ms	(sqrt (/ d h))
61.0ms	(sqrt (/ d h))

simplify28.9s

Counts

21600 → 21600

Iterations

Iter	Nodes
done	23153
0	23153

prune3.4m

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 13.3b

regimes2.0s

Accuracy

0% (2.7b remaining)

Error of 17.5b against oracle of 14.9b and baseline of 17.5b

bsearch0.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	55
1	55
0	43

end0.0ms

sample15.0s

Algorithm

intervals

Results

10.2s	38867×	body	80	nan
3.3s	12785×	body	80	valid