Details

sample290.0ms

Algorithm

intervals

Results

56.0ms	465×	body	80	nan
36.0ms	286×	body	80	valid

simplify2.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	3618
3	693
2	157
1	50
0	21

prune38.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.2b

localize102.0ms

Local error

Found 4 expressions with local error:

6.7b	(* (* n (pow (/ l Om) 2)) (- U U*))
8.7b	(/ (* l l) Om)
10.0b	(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
21.3b	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

rewrite387.0ms

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:

55.0ms	(* (* n (pow (/ l Om) 2)) (- U U*))
11.0ms	(/ (* l l) Om)
159.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
148.0ms	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

series2.7s

Counts

4 → 12

Calls

4 calls:

151.0ms	(* (* n (pow (/ l Om) 2)) (- U U*))
35.0ms	(/ (* l l) Om)
561.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
2.0s	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

simplify3.0s

Counts

157 → 157

Iterations

Iter	Nodes
done	5000
2	4654
1	1165
0	376

prune1.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 22.5b

localize80.0ms

Local error

Found 4 expressions with local error:

4.8b	(* n (pow (/ l Om) 2))
6.7b	(* (* n (pow (/ l Om) 2)) (- U U*))
10.0b	(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*))))
21.3b	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

rewrite503.0ms

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:

30.0ms	(* n (pow (/ l Om) 2))
71.0ms	(* (* n (pow (/ l Om) 2)) (- U U*))
214.0ms	(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*))))
177.0ms	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

series2.7s

Counts

4 → 12

Calls

4 calls:

96.0ms	(* n (pow (/ l Om) 2))
159.0ms	(* (* n (pow (/ l Om) 2)) (- U U*))
607.0ms	(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*))))
1.9s	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

simplify3.0s

Counts

175 → 175

Iterations

Iter	Nodes
done	5000
2	4367
1	1216
0	406

prune1.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 20.4b

localize73.0ms

Local error

Found 4 expressions with local error:

5.2b	(* n (/ l Om))
6.7b	(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
10.0b	(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))
21.3b	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))

rewrite676.0ms

Algorithm

rewrite-expression-head

Rules

104×	`associate-*r/`
47×	`add-cbrt-cube` `add-exp-log`
45×	`frac-times`
44×	`flip3--` `frac-sub` `flip--`
37×	`add-sqr-sqrt`
34×	`pow1`
32×	`*-un-lft-identity`
30×	`prod-diff` `associate-*l/` `add-cube-cbrt`
25×	`prod-exp` `cbrt-unprod`
24×	`sqrt-div`
21×	`distribute-rgt-in` `distribute-lft-in` `associate-r`
19×	`pow-prod-down`
10×	`times-frac` `associate--l+`
6×	`cbrt-undiv` `sub-neg` `div-exp`
5×	`associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`unswap-sqr`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 210

Calls

4 calls:

26.0ms	(* n (/ l Om))
205.0ms	(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
262.0ms	(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))
167.0ms	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))

series2.7s

Counts

4 → 12

Calls

4 calls:

32.0ms	(* n (/ l Om))
155.0ms	(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
623.0ms	(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))
1.9s	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))

simplify2.3s

Counts

222 → 222

Iterations

Iter	Nodes
done	5003
1	1637
0	530

prune2.4s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 19.2b

localize73.0ms

Local error

Found 4 expressions with local error:

5.2b	(* (/ l Om) n)
6.7b	(* (* (* (/ l Om) n) (/ l Om)) (- U U*))
10.0b	(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* (/ l Om) n) (/ l Om)) (- U U*))))
21.3b	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* (/ l Om) n) (/ l Om)) (- U U*)))))

rewrite684.0ms

Algorithm

rewrite-expression-head

Rules

73×	`associate-*r/`
61×	`associate-*l/`
47×	`add-cbrt-cube` `add-exp-log`
45×	`frac-times`
44×	`flip3--` `frac-sub` `flip--`
37×	`add-sqr-sqrt`
34×	`pow1`
32×	`*-un-lft-identity`
30×	`prod-diff` `add-cube-cbrt`
25×	`prod-exp` `cbrt-unprod`
24×	`sqrt-div`
21×	`distribute-rgt-in` `distribute-lft-in`
19×	`pow-prod-down`
15×	`associate-l`
11×	`associate-r`
10×	`times-frac` `associate--l+`
6×	`cbrt-undiv` `sub-neg` `div-exp`
4×	`expm1-log1p-u` `sqrt-pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`unswap-sqr`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 210

Calls

4 calls:

15.0ms	(* (/ l Om) n)
156.0ms	(* (* (* (/ l Om) n) (/ l Om)) (- U U*))
275.0ms	(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* (/ l Om) n) (/ l Om)) (- U U*))))
224.0ms	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* (/ l Om) n) (/ l Om)) (- U U*)))))

series2.6s

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (/ l Om) n)
149.0ms	(* (* (* (/ l Om) n) (/ l Om)) (- U U*))
565.0ms	(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* (/ l Om) n) (/ l Om)) (- U U*))))
1.8s	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* (/ l Om) n) (/ l Om)) (- U U*)))))

simplify2.1s

Counts

222 → 222

Iterations

Iter	Nodes
done	5000
1	1648
0	529

prune1.8s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 18.9b

regimes1.6s

Accuracy

15.6% (9.0b remaining)

Error of 28.4b against oracle of 19.4b and baseline of 30.1b

bsearch665.0ms

Steps

Iters	Range		Point
10	3.9529156979092325e+59	5.5443182457697264e+76	8.755812112715264e+71
7	7.876630513652142e-27	1.336367624547666e-25	7.97946278428516e-27
8	2.9218556913198843e-307	1.8743607621913695e-302	9.930109553502569e-303

simplify12.0ms

Iterations

Iter	Nodes
done	62
1	62
0	46

end0.0ms

sample6.0s

Algorithm

intervals

Results

3.1s	14647×	body	80	nan
1.8s	9145×	body	80	valid