Details

sample201.0ms

Algorithm

intervals

Results

65.0ms	476×	body	80	nan
57.0ms	293×	body	80	valid

simplify2.2s

Counts: 1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize42.0ms

Local error

Found 4 expressions with local error:

7.3b	(* n (pow (/ l Om) 2.0))
8.1b	(/ (* l l) Om)
10.9b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.5b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite367.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
24×	`add-sqr-sqrt`
23×	`pow1`
20×	`associate-r/` `associate-r*` `add-cbrt-cube`
16×	`add-cube-cbrt` `*-un-lft-identity`
15×	`unpow-prod-down`
13×	`times-frac`
12×	`pow-prod-down`
11×	`prod-exp`
10×	`flip3--` `flip--`
8×	`frac-sub` `cbrt-unprod`
6×	`sqrt-div`
4×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-pow1` `associate-l` `associate--l+` `add-log-exp` `unswap-sqr`
3×	`div-exp` `associate-/r*`
2×	`cbrt-undiv` `pow-exp` `*-commutative` `div-inv` `sqr-pow`
1×	`pow-to-exp` `frac-2neg` `pow1/2` `clear-num` `sqrt-prod` `associate-/l*`

Counts

4 → 112

Calls

4 calls:

51.0ms	(* n (pow (/ l Om) 2.0))
21.0ms	(/ (* l l) Om)
159.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
127.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series9.0s

Counts

4 → 12

Calls

4 calls:

273.0ms	(* n (pow (/ l Om) 2.0))
36.0ms	(/ (* l l) Om)
1.9s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
6.7s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify2.3s

Counts: 124 → 124

prune936.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 20.9b

localize35.0ms

Local error

Found 4 expressions with local error:

6.1b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.3b	(* n (pow (/ l Om) 2.0))
10.9b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.5b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite469.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 119

Calls

4 calls:

77.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
35.0ms	(* n (pow (/ l Om) 2.0))
224.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
128.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series10.5s

Counts

4 → 12

Calls

4 calls:

534.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
253.0ms	(* n (pow (/ l Om) 2.0))
1.9s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.8s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify593.0ms

Counts: 131 → 131

prune860.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 19.5b

localize34.0ms

Local error

Found 4 expressions with local error:

4.9b	(* n (pow (/ l Om) (/ 2.0 2)))
6.1b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
10.9b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
18.5b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite740.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
67×	`prod-exp`
25×	`pow1` `add-sqr-sqrt` `associate-r`
24×	`add-cbrt-cube`
22×	`associate-*r/`
20×	`pow-exp`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt` `unpow-prod-down`
13×	`pow-prod-down` `cbrt-unprod`
11×	`flip3--` `flip--`
10×	`pow-to-exp` `times-frac` `div-exp`
8×	`frac-sub`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
5×	`associate-l`
4×	`sqrt-pow1` `associate--l+` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 136

Calls

4 calls:

39.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
253.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
300.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
135.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series10.5s

Counts

4 → 12

Calls

4 calls:

307.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
535.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
2.0s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
7.7s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify691.0ms

Counts: 148 → 148

prune940.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 19.4b

localize43.0ms

Local error

Found 4 expressions with local error:

6.0b	(* (* (* 2.0 n) (- t (- (* 2.0 (/ l (/ Om l))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U)
6.1b	(* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))
7.3b	(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
18.5b	(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (/ l (/ Om l))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U) 1))

rewrite376.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
25×	`associate-r`
23×	`add-exp-log`
19×	`*-un-lft-identity`
17×	`add-cube-cbrt` `add-cbrt-cube`
16×	`unpow-prod-down`
15×	`pow1`
11×	`prod-exp`
10×	`times-frac` `associate-l`
8×	`cbrt-unprod`
7×	`pow-prod-down`
5×	`sqrt-prod` `unswap-sqr`
4×	`associate-*r/` `add-log-exp` `sqr-pow`
3×	`*-commutative`
2×	`distribute-rgt-in` `sub-neg` `rem-sqrt-square` `flip3--` `distribute-lft-in` `associate-*l/` `pow-exp` `flip--`
1×	`distribute-lft-neg-out` `distribute-lft-neg-in` `pow-to-exp` `neg-mul-1` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `div-exp` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 106

Calls

4 calls:

280.0ms	(* (* (* 2.0 n) (- t (- (* 2.0 (/ l (/ Om l))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U)
44.0ms	(* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))
36.0ms	(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
12.0ms	(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (/ l (/ Om l))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U) 1))

series17.9s

Counts

4 → 12

Calls

4 calls:

1.7s	(* (* (* 2.0 n) (- t (- (* 2.0 (/ l (/ Om l))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U)
440.0ms	(* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))
244.0ms	(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
15.6s	(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (/ l (/ Om l))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U) 1))

simplify1.9s

Counts: 118 → 118

prune877.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 16.9b

regimes973.0ms

Accuracy

8.1% (11.6b remaining)

Error of 30.2b against oracle of 18.6b and baseline of 31.2b

bsearch999.0ms

Steps

Iters	Range		Point
7	1.288531225676383e+262	3.6137232352492556e+263	1.976343330438959e+262
10	960649127616.5507	5.170311694882416e+21	4.361934755255584e+20
6	1.4341566573600888e-226	1.1818197341596392e-225	5.824775899044275e-226
8	-5.704069418746261e-199	-1.2080201743982823e-201	-6.212072691974284e-200
9	-2.3988152764038513e+205	-2.292627744121757e+200	-2.2140464730475112e+201

simplify1.1s

end0.0ms

sample6.8s

Algorithm

intervals

Results

3.6s	14796×	body	80	nan
1.4s	9256×	body	80	valid