Details

sample342.0ms

Algorithm

intervals

Results

86.0ms	491×	body	80	nan
86.0ms	301×	body	80	valid

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
4	3017
3	618
2	155
1	50
0	21

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.2b

localize42.0ms

Local error

Found 4 expressions with local error:

4.8b	(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
5.0b	(* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
6.0b	(/ n (/ Om l))
18.0b	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
50×	`add-sqr-sqrt`
48×	`*-un-lft-identity` `add-cube-cbrt`
31×	`pow1`
23×	`add-cbrt-cube` `add-exp-log`
17×	`pow-prod-down`
13×	`associate-/r*`
9×	`prod-exp` `cbrt-unprod`
6×	`fma-udef`
5×	`distribute-rgt-in` `distribute-lft-in` `sqrt-pow1` `div-inv`
4×	`expm1-log1p-u` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`*-commutative`
1×	`clear-num` `frac-2neg` `pow1/2` `associate-/r/` `sqrt-prod` `unswap-sqr`

Counts

4 → 142

Calls

4 calls:

23.0ms	(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
6.0ms	(* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
10.0ms	(/ n (/ Om l))
51.0ms	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

series3.3s

Counts

4 → 12

Calls

4 calls:

436.0ms	(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
368.0ms	(* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
24.0ms	(/ n (/ Om l))
2.5s	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

simplify1.2s

Counts

154 → 154

Iterations

Iter	Nodes
2	2611
1	750
0	291

prune2.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 20.2b

localize91.0ms

Local error

Found 4 expressions with local error:

3.7b	(fma (- U* U) (/ (/ (/ n (* (/ (cbrt Om) (cbrt l)) (/ (cbrt Om) (cbrt l)))) (/ (cbrt Om) (cbrt l))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
4.8b	(* (* U 2) (* n (fma (- U* U) (/ (/ (/ n (* (/ (cbrt Om) (cbrt l)) (/ (cbrt Om) (cbrt l)))) (/ (cbrt Om) (cbrt l))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
5.0b	(* n (fma (- U* U) (/ (/ (/ n (* (/ (cbrt Om) (cbrt l)) (/ (cbrt Om) (cbrt l)))) (/ (cbrt Om) (cbrt l))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
18.0b	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ (/ n (* (/ (cbrt Om) (cbrt l)) (/ (cbrt Om) (cbrt l)))) (/ (cbrt Om) (cbrt l))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

31×	`pow1`
18×	`add-cbrt-cube` `add-exp-log`
17×	`pow-prod-down`
9×	`prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
7×	`fma-udef`
6×	`*-un-lft-identity` `add-cube-cbrt`
5×	`distribute-rgt-in` `distribute-lft-in` `sqrt-pow1`
4×	`expm1-log1p-u` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative`
1×	`pow1/2` `sqrt-prod` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

0.0ms	(fma (- U* U) (/ (/ (/ n (* (/ (cbrt Om) (cbrt l)) (/ (cbrt Om) (cbrt l)))) (/ (cbrt Om) (cbrt l))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
22.0ms	(* (* U 2) (* n (fma (- U* U) (/ (/ (/ n (* (/ (cbrt Om) (cbrt l)) (/ (cbrt Om) (cbrt l)))) (/ (cbrt Om) (cbrt l))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
14.0ms	(* n (fma (- U* U) (/ (/ (/ n (* (/ (cbrt Om) (cbrt l)) (/ (cbrt Om) (cbrt l)))) (/ (cbrt Om) (cbrt l))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
38.0ms	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ (/ n (* (/ (cbrt Om) (cbrt l)) (/ (cbrt Om) (cbrt l)))) (/ (cbrt Om) (cbrt l))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

series3.6s

Counts

4 → 12

Calls

4 calls:

345.0ms	(fma (- U* U) (/ (/ (/ n (* (/ (cbrt Om) (cbrt l)) (/ (cbrt Om) (cbrt l)))) (/ (cbrt Om) (cbrt l))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
543.0ms	(* (* U 2) (* n (fma (- U* U) (/ (/ (/ n (* (/ (cbrt Om) (cbrt l)) (/ (cbrt Om) (cbrt l)))) (/ (cbrt Om) (cbrt l))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
382.0ms	(* n (fma (- U* U) (/ (/ (/ n (* (/ (cbrt Om) (cbrt l)) (/ (cbrt Om) (cbrt l)))) (/ (cbrt Om) (cbrt l))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
2.3s	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ (/ n (* (/ (cbrt Om) (cbrt l)) (/ (cbrt Om) (cbrt l)))) (/ (cbrt Om) (cbrt l))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

simplify5.5s

Counts

92 → 92

Iterations

Iter	Nodes
3	10130
2	1675
1	438
0	166

prune2.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 18.9b

localize62.0ms

Local error

Found 4 expressions with local error:

6.0b	(/ n (/ Om l))
6.0b	(/ n (/ Om l))
18.0b	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
18.0b	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
88×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
30×	`pow1`
26×	`associate-/r*`
16×	`pow-prod-down`
14×	`add-cbrt-cube` `add-exp-log`
10×	`sqrt-pow1` `div-inv`
6×	`cbrt-undiv` `div-exp` `associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `pow1/2` `associate-/r/` `sqrt-prod`

Counts

4 → 180

Calls

4 calls:

12.0ms	(/ n (/ Om l))
12.0ms	(/ n (/ Om l))
37.0ms	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
48.0ms	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

series4.9s

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ n (/ Om l))
27.0ms	(/ n (/ Om l))
2.5s	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
2.4s	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

simplify2.2s

Counts

192 → 192

Iterations

Iter	Nodes
3	5072
2	1445
1	473
0	201

prune4.7s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 18.9b

localize88.0ms

Local error

Found 4 expressions with local error:

18.0b	(sqrt (* (* (cbrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))) (cbrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))) (cbrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))))
19.2b	(cbrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
19.2b	(cbrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
19.2b	(cbrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1`
15×	`sqrt-pow1`
12×	`pow1/3`
9×	`pow-prod-up`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 63

Calls

4 calls:

82.0ms	(sqrt (* (* (cbrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))) (cbrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))) (cbrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))))
22.0ms	(cbrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
25.0ms	(cbrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
16.0ms	(cbrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

series5.2s

Counts

4 → 12

Calls

4 calls:

2.8s	(sqrt (* (* (cbrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))) (cbrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))) (cbrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))))
850.0ms	(cbrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
834.0ms	(cbrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
794.0ms	(cbrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

simplify947.0ms

Counts

75 → 75

Iterations

Iter	Nodes
3	2478
2	746
1	285
0	133

prune1.4s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 18.9b

regimes1.6s

Accuracy

37.7% (5.8b remaining)

Error of 26.7b against oracle of 20.9b and baseline of 30.2b

bsearch181.0ms

Steps

Iters	Range		Point
7	1.5310892420243093e-289	2.3774339382540392e-287	1.5604221343075467e-289

simplify10.0ms

Iterations

Iter	Nodes
2	31
1	31
0	27

end0.0ms

sample8.9s

Algorithm

intervals

Results

5.0s	14839×	body	80	nan
2.5s	9128×	body	80	valid