Details

sample279.0ms

Algorithm

intervals

Results

107.0ms	428×	body	80	nan
93.0ms	304×	body	80	valid

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
4	2001
3	693
2	157
1	50
0	21

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.0b

localize80.0ms

Local error

Found 4 expressions with local error:

6.5b	(* (* n (pow (/ l Om) 2)) (- U U*))
9.3b	(/ (* l l) Om)
9.7b	(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
20.0b	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

rewrite283.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
30×	`prod-diff`
26×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`pow1`
24×	`add-cube-cbrt`
23×	`add-cbrt-cube`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
16×	`prod-exp`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`associate--l+` `cbrt-unprod`
8×	`associate-r` `frac-sub`
6×	`sub-neg` `sqrt-div`
4×	`expm1-log1p-u` `sqrt-pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `times-frac` `div-exp`
2×	`cbrt-undiv` `associate-l` `pow-exp` `*-commutative`
1×	`pow-to-exp` `clear-num` `frac-2neg` `pow1/2` `sqrt-prod` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 145

Calls

4 calls:

45.0ms	(* (* n (pow (/ l Om) 2)) (- U U*))
9.0ms	(/ (* l l) Om)
140.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
87.0ms	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

series2.1s

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (* n (pow (/ l Om) 2)) (- U U*))
20.0ms	(/ (* l l) Om)
513.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
1.5s	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

simplify1.2s

Counts

157 → 157

Iterations

Iter	Nodes
done	2002
2	2002
1	1165
0	376

prune2.8s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 22.3b

localize36.0ms

Local error

Found 4 expressions with local error:

6.2b	(* n (pow (/ l Om) 2))
6.5b	(* (* n (pow (/ l Om) 2)) (- U U*))
9.7b	(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*))))
20.0b	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

rewrite276.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
35×	`add-exp-log`
33×	`*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`prod-diff`
26×	`associate-r`
25×	`pow1`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
20×	`add-cbrt-cube`
19×	`prod-exp`
15×	`unpow-prod-down`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`times-frac` `associate--l+` `cbrt-unprod`
8×	`frac-sub`
6×	`sub-neg` `sqrt-div`
5×	`associate-l` `unswap-sqr`
4×	`expm1-log1p-u` `sqrt-pow1` `pow-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-to-exp` `div-exp` `unpow2` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 163

Calls

4 calls:

16.0ms	(* n (pow (/ l Om) 2))
33.0ms	(* (* n (pow (/ l Om) 2)) (- U U*))
121.0ms	(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*))))
102.0ms	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

series2.1s

Counts

4 → 12

Calls

4 calls:

52.0ms	(* n (pow (/ l Om) 2))
119.0ms	(* (* n (pow (/ l Om) 2)) (- U U*))
481.0ms	(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*))))
1.5s	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

simplify1.2s

Counts

175 → 175

Iterations

Iter	Nodes
done	2002
2	2002
1	1216
0	406

prune3.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 20.5b

localize53.0ms

Local error

Found 4 expressions with local error:

6.2b	(* (* (/ l Om) (/ l Om)) n)
6.5b	(* (* 2 n) (* U (- t (fma l (* (/ l Om) 2) (* (* (* (/ l Om) (/ l Om)) n) (- U U*))))))
6.5b	(* (* (* (/ l Om) (/ l Om)) n) (- U U*))
20.0b	(sqrt (* (* 2 n) (* U (- t (fma l (* (/ l Om) 2) (* (* (* (/ l Om) (/ l Om)) n) (- U U*)))))))

rewrite253.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-cbrt-cube` `add-exp-log`
55×	`distribute-rgt-in` `distribute-lft-in`
54×	`prod-diff`
45×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
43×	`pow1`
42×	`add-cube-cbrt`
32×	`prod-exp` `cbrt-unprod`
25×	`pow-prod-down`
19×	`associate-*l/`
14×	`associate-*r/`
10×	`frac-times`
9×	`associate-r`
8×	`cbrt-undiv` `div-exp`
6×	`sub-neg` `flip3--` `flip--`
5×	`sqrt-pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `*-commutative`
2×	`sqrt-div`
1×	`pow1/2` `sqrt-prod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 186

Calls

4 calls:

31.0ms	(* (* (/ l Om) (/ l Om)) n)
44.0ms	(* (* 2 n) (* U (- t (fma l (* (/ l Om) 2) (* (* (* (/ l Om) (/ l Om)) n) (- U U*))))))
133.0ms	(* (* (* (/ l Om) (/ l Om)) n) (- U U*))
41.0ms	(sqrt (* (* 2 n) (* U (- t (fma l (* (/ l Om) 2) (* (* (* (/ l Om) (/ l Om)) n) (- U U*)))))))

series2.0s

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (* (/ l Om) (/ l Om)) n)
465.0ms	(* (* 2 n) (* U (- t (fma l (* (/ l Om) 2) (* (* (* (/ l Om) (/ l Om)) n) (- U U*))))))
128.0ms	(* (* (* (/ l Om) (/ l Om)) n) (- U U*))
1.4s	(sqrt (* (* 2 n) (* U (- t (fma l (* (/ l Om) 2) (* (* (* (/ l Om) (/ l Om)) n) (- U U*)))))))

simplify1.4s

Counts

198 → 198

Iterations

Iter	Nodes
done	2005
2	2005
1	1283
0	431

prune3.9s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 16.2b

localize69.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (cbrt n) (/ l Om))
6.5b	(* (* 2 n) (* U (- t (fma l (* (/ l Om) 2) (* (* (* (* (cbrt n) (/ l Om)) (* (cbrt n) (/ l Om))) (cbrt n)) (- U U*))))))
6.5b	(* (* (* (* (cbrt n) (/ l Om)) (* (cbrt n) (/ l Om))) (cbrt n)) (- U U*))
20.0b	(sqrt (* (* 2 n) (* U (- t (fma l (* (/ l Om) 2) (* (* (* (* (cbrt n) (/ l Om)) (* (cbrt n) (/ l Om))) (cbrt n)) (- U U*)))))))

rewrite683.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-exp-log`
62×	`add-sqr-sqrt`
56×	`pow1` `add-cbrt-cube`
55×	`distribute-rgt-in` `distribute-lft-in`
54×	`prod-diff`
52×	`*-un-lft-identity` `prod-exp` `cbrt-unprod`
50×	`add-cube-cbrt`
36×	`pow-prod-down`
26×	`associate-*r/`
19×	`associate-r`
15×	`associate-*l/`
11×	`times-frac`
9×	`frac-times`
8×	`associate-l`
7×	`cbrt-undiv` `div-exp`
6×	`sub-neg` `flip3--` `flip--`
5×	`cbrt-prod` `sqrt-pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`sqrt-div`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 208

Calls

4 calls:

10.0ms	(* (cbrt n) (/ l Om))
40.0ms	(* (* 2 n) (* U (- t (fma l (* (/ l Om) 2) (* (* (* (* (cbrt n) (/ l Om)) (* (cbrt n) (/ l Om))) (cbrt n)) (- U U*))))))
567.0ms	(* (* (* (* (cbrt n) (/ l Om)) (* (cbrt n) (/ l Om))) (cbrt n)) (- U U*))
59.0ms	(sqrt (* (* 2 n) (* U (- t (fma l (* (/ l Om) 2) (* (* (* (* (cbrt n) (/ l Om)) (* (cbrt n) (/ l Om))) (cbrt n)) (- U U*)))))))

series2.3s

Counts

4 → 12

Calls

4 calls:

135.0ms	(* (cbrt n) (/ l Om))
503.0ms	(* (* 2 n) (* U (- t (fma l (* (/ l Om) 2) (* (* (* (* (cbrt n) (/ l Om)) (* (cbrt n) (/ l Om))) (cbrt n)) (- U U*))))))
201.0ms	(* (* (* (* (cbrt n) (/ l Om)) (* (cbrt n) (/ l Om))) (cbrt n)) (- U U*))
1.5s	(sqrt (* (* 2 n) (* U (- t (fma l (* (/ l Om) 2) (* (* (* (* (cbrt n) (/ l Om)) (* (cbrt n) (/ l Om))) (cbrt n)) (- U U*)))))))

simplify1.2s

Counts

220 → 220

Iterations

Iter	Nodes
done	2001
2	2001
1	1547
0	514

prune4.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 16.0b

regimes1.8s

Accuracy

30.6% (8.4b remaining)

Error of 25.5b against oracle of 17.1b and baseline of 29.2b

bsearch317.0ms

Steps

Iters	Range		Point
3	-1.4769956903761988e-301	-1.090236820459215e-301	-1.1144092498290265e-301
9	-1.9079485429944646e-68	-6.699710906253194e-75	-9.944037691838278e-75

simplify14.0ms

Iterations

Iter	Nodes
done	66
1	66
0	49

end0.0ms

sample8.5s

Algorithm

intervals

Results

4.3s	14975×	body	80	nan
2.5s	9155×	body	80	valid