Details

sample173.0ms

Algorithm

intervals

Results

57.0ms	433×	body	80	nan
39.0ms	293×	body	80	valid

simplify3.4s

Counts

1 → 1

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	21	28
1	49	28
2	154	27
3	664	27
4	4143	27
done	5000	27

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize37.0ms

Local error

Found 4 expressions with local error:

6.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.1b	(/ (* l l) Om)
9.1b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
21.4b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite440.0ms

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` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `div-exp` `associate-/r*`
2×	`cbrt-undiv` `associate-l` `pow-exp` `*-commutative`
1×	`pow-to-exp` `frac-2neg` `pow1/2` `clear-num` `sqrt-prod` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 141

Calls

4 calls:

89.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
18.0ms	(/ (* l l) Om)
166.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
156.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series9.1s

Counts

4 → 12

Calls

4 calls:

456.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
29.0ms	(/ (* l l) Om)
1.8s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
6.8s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify774.0ms

Counts

153 → 153

Iterations

Useful iterations: done (765.0ms)

Iter	Nodes	Cost
0	411	4799
1	1278	4444
done	5000	3908

prune801.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 23.1b

localize32.0ms

Local error

Found 4 expressions with local error:

6.4b	(* n (pow (/ l Om) 2.0))
6.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.1b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
21.4b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite337.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
35×	`add-exp-log`
33×	`*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`prod-diff`
25×	`pow1` `associate-r`
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`
4×	`expm1-log1p-u` `sqrt-pow1` `pow-exp` `log1p-expm1-u` `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 → 157

Calls

4 calls:

26.0ms	(* n (pow (/ l Om) 2.0))
49.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
144.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
111.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series10.1s

Counts

4 → 12

Calls

4 calls:

237.0ms	(* n (pow (/ l Om) 2.0))
618.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
2.1s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.1s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify912.0ms

Counts

169 → 169

Iterations

Useful iterations: done (900.0ms)

Iter	Nodes	Cost
0	443	5038
1	1313	4661
done	5000	4111

prune1.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 22.0b

localize32.0ms

Local error

Found 4 expressions with local error:

6.1b	(* n (pow (/ l Om) (/ 2.0 2)))
6.7b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
9.1b	(* (* (* 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*))))
21.4b	(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*)))))

rewrite862.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
67×	`prod-exp`
41×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`prod-diff`
25×	`pow1` `associate-r`
24×	`add-cbrt-cube`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
20×	`pow-exp`
15×	`unpow-prod-down`
13×	`pow-prod-down` `cbrt-unprod`
11×	`flip3--` `flip--`
10×	`pow-to-exp` `times-frac` `div-exp` `associate--l+`
8×	`frac-sub`
6×	`sub-neg` `sqrt-div`
5×	`associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `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 → 174

Calls

4 calls:

48.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
277.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
295.0ms	(* (* (* 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*))))
226.0ms	(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*)))))

series10.6s

Counts

4 → 12

Calls

4 calls:

243.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
565.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.9s	(* (* (* 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*))))
7.9s	(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*)))))

simplify869.0ms

Counts

186 → 186

Iterations

Useful iterations: done (855.0ms)

Iter	Nodes	Cost
0	479	7307
1	1425	5736
done	5000	5068

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 21.5b

localize37.0ms

Local error

Found 4 expressions with local error:

6.1b	(* n (pow (/ l Om) (/ 2.0 2)))
7.5b	(* (- U U*) (pow (/ l Om) (/ 2.0 2)))
9.1b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2))))))
21.4b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))))

rewrite601.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
37×	`associate-r`
30×	`unpow-prod-down`
29×	`add-exp-log` `*-un-lft-identity`
27×	`add-cube-cbrt`
23×	`pow1`
20×	`times-frac` `associate-*r/`
17×	`add-cbrt-cube`
14×	`prod-exp`
12×	`prod-diff` `pow-prod-down`
11×	`flip3--` `flip--`
10×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `associate--l+`
9×	`associate-l`
8×	`frac-sub` `cbrt-unprod` `unswap-sqr`
6×	`sqrt-div`
4×	`expm1-log1p-u` `sub-neg` `sqrt-pow1` `pow-exp` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`*-commutative`
2×	`pow-to-exp` `div-exp` `div-inv`
1×	`pow1/2` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 152

Calls

4 calls:

45.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
52.0ms	(* (- U U*) (pow (/ l Om) (/ 2.0 2)))
278.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2))))))
213.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))))

series10.9s

Counts

4 → 12

Calls

4 calls:

220.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
973.0ms	(* (- U U*) (pow (/ l Om) (/ 2.0 2)))
2.1s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2))))))
7.6s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))))

simplify720.0ms

Counts

164 → 164

Iterations

Useful iterations: done (714.0ms)

Iter	Nodes	Cost
0	420	5540
1	1195	5261
done	5000	4287

prune1.2s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 21.2b

regimes882.0ms

Accuracy

8% (8.6b remaining)

Error of 30.0b against oracle of 21.4b and baseline of 30.7b

bsearch657.0ms

Steps

Iters	Range		Point
8	5.419790816469547e+125	1.8405755434187e+129	1.3217461293530347e+126
10	1.713202050375768e-106	8.437061114098603e-88	3.133024137349082e-104
8	1.110000930973235e-152	3.3367201306177223e-149	3.2926377278383827e-149

simplify12.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	62	155
1	84	155
done	84	155

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.9s	14858×	body	80	nan
2.1s	9220×	body	80	valid