Details

sample315.0ms

Algorithm

intervals

Results

123.0ms	449×	body	80	nan
57.0ms	282×	body	80	valid

simplify1.2s

Counts

1 → 1

Iterations

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

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.3b

localize57.0ms

Local error

Found 4 expressions with local error:

4.1b	(fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
4.9b	(/ n (/ Om l))
6.2b	(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
21.3b	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
46×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
29×	`pow1`
21×	`add-cbrt-cube` `add-exp-log`
16×	`pow-prod-down`
13×	`associate-/r*`
8×	`prod-exp` `cbrt-unprod`
5×	`sqrt-pow1` `fma-udef` `div-inv`
4×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
1×	`clear-num` `frac-2neg` `pow1/2` `associate-r` `associate-l` `associate-/r/` `*-commutative` `sqrt-prod`

Counts

4 → 130

Calls

4 calls:

0.0ms	(fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
6.0ms	(/ n (/ Om l))
32.0ms	(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
36.0ms	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

series3.7s

Counts

4 → 12

Calls

4 calls:

413.0ms	(fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
42.0ms	(/ n (/ Om l))
492.0ms	(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
2.8s	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

simplify1.0s

Counts

142 → 142

Iterations

Iter	Nodes
2	2590
1	740
0	284

prune2.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 21.9b

localize71.0ms

Local error

Found 4 expressions with local error:

6.2b	(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
6.2b	(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
21.3b	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
21.3b	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

54×	`pow1`
32×	`pow-prod-down`
28×	`add-cbrt-cube` `add-exp-log`
16×	`prod-exp` `cbrt-unprod`
10×	`sqrt-pow1`
8×	`distribute-rgt-in` `distribute-lft-in` `fma-udef`
4×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow1/2` `associate-r` `associate-l` `*-commutative` `sqrt-prod`

Counts

4 → 92

Calls

4 calls:

47.0ms	(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
50.0ms	(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
45.0ms	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
20.0ms	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

series5.3s

Counts

4 → 12

Calls

4 calls:

402.0ms	(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
414.0ms	(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
2.3s	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
2.2s	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

simplify3.4s

Counts

104 → 104

Iterations

Iter	Nodes
3	8854
2	1432
1	355
0	127

prune1.6s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 21.9b

localize75.0ms

Local error

Found 4 expressions with local error:

21.3b	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
21.3b	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
21.3b	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
21.3b	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

56×	`pow1`
32×	`pow-prod-down`
20×	`sqrt-pow1`
4×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cbrt-cube` `pow1/2` `add-exp-log` `add-cube-cbrt` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 68

Calls

4 calls:

20.0ms	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
20.0ms	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
21.0ms	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
20.0ms	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

series7.1s

Counts

4 → 12

Calls

4 calls:

1.8s	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
1.8s	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
1.8s	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
1.8s	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

simplify2.8s

Counts

80 → 80

Iterations

Iter	Nodes
4	7742
3	1746
2	426
1	125
0	55

prune1.3s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 21.9b

localize83.0ms

Local error

Found 4 expressions with local error:

21.3b	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
21.3b	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
21.3b	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
21.3b	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

56×	`pow1`
32×	`pow-prod-down`
20×	`sqrt-pow1`
4×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cbrt-cube` `pow1/2` `add-exp-log` `add-cube-cbrt` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 68

Calls

4 calls:

20.0ms	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
19.0ms	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
19.0ms	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
24.0ms	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

series7.0s

Counts

4 → 12

Calls

4 calls:

1.7s	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
1.8s	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
1.8s	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
1.7s	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

simplify2.6s

Counts

80 → 80

Iterations

Iter	Nodes
4	7742
3	1746
2	426
1	125
0	55

prune1.3s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 21.9b

regimes801.0ms

Accuracy

40.6% (5.1b remaining)

Error of 26.3b against oracle of 21.2b and baseline of 29.7b

bsearch149.0ms

Steps

Iters	Range		Point
9	-2.3871958361750157e-301	-1.1485916109250096e-307	-1.1668341231116616e-307

simplify6.0ms

Iterations

Iter	Nodes
2	31
1	31
0	27

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.7s	14542×	body	80	nan
1.7s	9217×	body	80	valid