Details

sample289.0ms

Algorithm

intervals

Results

115.0ms	496×	body	80	nan
83.0ms	299×	body	80	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
4	2994
3	617
2	157
1	50
0	21

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.9b

localize39.0ms

Local error

Found 4 expressions with local error:

3.4b	(/ n (/ Om l))
3.5b	(* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma -2 (/ l (/ Om l)) t)))
6.9b	(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma -2 (/ l (/ Om l)) t))))
18.5b	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma -2 (/ l (/ Om l)) t)))))

rewrite79.0ms

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:

7.0ms	(/ n (/ Om l))
6.0ms	(* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma -2 (/ l (/ Om l)) t)))
36.0ms	(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma -2 (/ l (/ Om l)) t))))
28.0ms	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma -2 (/ l (/ Om l)) t)))))

series3.2s

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ n (/ Om l))
340.0ms	(* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma -2 (/ l (/ Om l)) t)))
436.0ms	(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma -2 (/ l (/ Om l)) t))))
2.4s	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma -2 (/ l (/ Om l)) t)))))

simplify933.0ms

Counts

154 → 154

Iterations

Iter	Nodes
2	2616
1	737
0	291

prune2.9s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 19.8b

localize52.0ms

Local error

Found 4 expressions with local error:

3.4b	(/ n (/ Om l))
6.1b	(* (- U* U) (* (/ n (/ Om l)) (/ n (/ Om l))))
6.9b	(* (* U 2) (+ (* (- U* U) (* (/ n (/ Om l)) (/ n (/ Om l)))) (* (fma -2 (/ l (/ Om l)) t) n)))
18.5b	(sqrt (* (* U 2) (+ (* (- U* U) (* (/ n (/ Om l)) (/ n (/ Om l)))) (* (fma -2 (/ l (/ Om l)) t) n))))

rewrite307.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
61×	`add-cbrt-cube` `add-exp-log`
51×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
48×	`add-cube-cbrt`
22×	`prod-exp` `cbrt-unprod`
21×	`cbrt-undiv` `div-exp`
20×	`pow1`
13×	`associate-/r*`
10×	`associate-*r/`
9×	`frac-times` `pow-prod-down`
6×	`associate-l`
5×	`associate-*l/` `div-inv`
4×	`expm1-log1p-u` `flip3--` `associate-r` `insert-posit16` `log1p-expm1-u` `flip--` `add-log-exp`
3×	`sqrt-pow1` `associate-/l*`
2×	`flip3-+` `sqrt-div` `*-commutative` `flip-+`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `pow1/2` `associate-/r/` `sqrt-prod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 166

Calls

4 calls:

6.0ms	(/ n (/ Om l))
75.0ms	(* (- U* U) (* (/ n (/ Om l)) (/ n (/ Om l))))
157.0ms	(* (* U 2) (+ (* (- U* U) (* (/ n (/ Om l)) (/ n (/ Om l)))) (* (fma -2 (/ l (/ Om l)) t) n)))
64.0ms	(sqrt (* (* U 2) (+ (* (- U* U) (* (/ n (/ Om l)) (/ n (/ Om l)))) (* (fma -2 (/ l (/ Om l)) t) n))))

series4.6s

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ n (/ Om l))
243.0ms	(* (- U* U) (* (/ n (/ Om l)) (/ n (/ Om l))))
569.0ms	(* (* U 2) (+ (* (- U* U) (* (/ n (/ Om l)) (/ n (/ Om l)))) (* (fma -2 (/ l (/ Om l)) t) n)))
3.8s	(sqrt (* (* U 2) (+ (* (- U* U) (* (/ n (/ Om l)) (/ n (/ Om l)))) (* (fma -2 (/ l (/ Om l)) t) n))))

simplify1.6s

Counts

178 → 178

Iterations

Iter	Nodes
2	4254
1	1081
0	378

prune4.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 19.6b

localize70.0ms

Local error

Found 4 expressions with local error:

3.4b	(/ n (/ Om l))
6.6b	(* (- U* U) (/ n (/ Om l)))
6.9b	(* (* U 2) (+ (* (* (- U* U) (/ n (/ Om l))) (/ n (/ Om l))) (* (fma -2 (/ l (/ Om l)) t) n)))
18.5b	(sqrt (* (* U 2) (+ (* (* (- U* U) (/ n (/ Om l))) (/ n (/ Om l))) (* (fma -2 (/ l (/ Om l)) t) n))))

rewrite365.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
94×	`add-sqr-sqrt`
85×	`*-un-lft-identity`
83×	`add-cube-cbrt`
47×	`associate-r`
23×	`add-cbrt-cube` `add-exp-log`
17×	`pow1`
13×	`associate-/r*`
9×	`div-inv`
7×	`pow-prod-down`
6×	`cbrt-undiv` `div-exp` `associate-l` `prod-exp` `cbrt-unprod`
5×	`associate-*r/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1` `associate-/l*` `unswap-sqr`
2×	`frac-times` `flip3-+` `flip3--` `sqrt-div` `associate-l/` `associate-/r/` `-commutative` `flip-+` `flip--`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `pow1/2` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 190

Calls

4 calls:

6.0ms	(/ n (/ Om l))
30.0ms	(* (- U* U) (/ n (/ Om l)))
229.0ms	(* (* U 2) (+ (* (* (- U* U) (/ n (/ Om l))) (/ n (/ Om l))) (* (fma -2 (/ l (/ Om l)) t) n)))
96.0ms	(sqrt (* (* U 2) (+ (* (* (- U* U) (/ n (/ Om l))) (/ n (/ Om l))) (* (fma -2 (/ l (/ Om l)) t) n))))

series4.6s

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ n (/ Om l))
106.0ms	(* (- U* U) (/ n (/ Om l)))
565.0ms	(* (* U 2) (+ (* (* (- U* U) (/ n (/ Om l))) (/ n (/ Om l))) (* (fma -2 (/ l (/ Om l)) t) n)))
3.9s	(sqrt (* (* U 2) (+ (* (* (- U* U) (/ n (/ Om l))) (/ n (/ Om l))) (* (fma -2 (/ l (/ Om l)) t) n))))

simplify1.8s

Counts

202 → 202

Iterations

Iter	Nodes
2	4552
1	1104
0	378

prune3.9s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 19.5b

localize61.0ms

Local error

Found 4 expressions with local error:

4.7b	(* (/ n Om) l)
6.6b	(* (- U* U) (/ n (/ Om l)))
6.9b	(* (* U 2) (+ (* (* (- U* U) (/ n (/ Om l))) (* (/ n Om) l)) (* (fma -2 (/ l (/ Om l)) t) n)))
18.5b	(sqrt (* (* U 2) (+ (* (* (- U* U) (/ n (/ Om l))) (* (/ n Om) l)) (* (fma -2 (/ l (/ Om l)) t) n))))

rewrite354.0ms

Algorithm

rewrite-expression-head

Rules

79×	`times-frac`
65×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
50×	`associate-r`
49×	`add-cube-cbrt`
23×	`add-cbrt-cube` `add-exp-log`
19×	`pow1` `associate-l`
8×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`associate-*r/` `div-inv` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1` `associate-l/` `-commutative`
2×	`frac-times` `flip3-+` `flip3--` `sqrt-div` `flip-+` `flip--`
1×	`distribute-rgt-in` `distribute-lft-in` `pow1/2` `associate-/r/` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 152

Calls

4 calls:

13.0ms	(* (/ n Om) l)
34.0ms	(* (- U* U) (/ n (/ Om l)))
203.0ms	(* (* U 2) (+ (* (* (- U* U) (/ n (/ Om l))) (* (/ n Om) l)) (* (fma -2 (/ l (/ Om l)) t) n)))
100.0ms	(sqrt (* (* U 2) (+ (* (* (- U* U) (/ n (/ Om l))) (* (/ n Om) l)) (* (fma -2 (/ l (/ Om l)) t) n))))

series4.7s

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (/ n Om) l)
124.0ms	(* (- U* U) (/ n (/ Om l)))
612.0ms	(* (* U 2) (+ (* (* (- U* U) (/ n (/ Om l))) (* (/ n Om) l)) (* (fma -2 (/ l (/ Om l)) t) n)))
4.0s	(sqrt (* (* U 2) (+ (* (* (- U* U) (/ n (/ Om l))) (* (/ n Om) l)) (* (fma -2 (/ l (/ Om l)) t) n))))

simplify1.7s

Counts

164 → 164

Iterations

Iter	Nodes
2	4837
1	1102
0	362

prune3.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 19.0b

regimes1.1s

Accuracy

32.7% (5.5b remaining)

Error of 24.9b against oracle of 19.5b and baseline of 27.6b

bsearch240.0ms

Steps

Iters	Range		Point
7	-7.910778363663916e-308	3.6341189872546634e-308	-8.0110620477323e-311

simplify14.0ms

Iterations

Iter	Nodes
2	42
1	42
0	32

end0.0ms

sample8.7s

Algorithm

intervals

Results

4.3s	14477×	body	80	nan
2.9s	9197×	body	80	valid