Details

sample209.0ms

Algorithm

intervals

Results

66.0ms	521×	body	80	nan
64.0ms	299×	body	80	valid

simplify2.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	21	28
1	49	28
2	154	27
3	642	27
4	3239	27
done	5000	27

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.8b

localize41.0ms

Local error

Found 4 expressions with local error:

7.3b	(/ (* l l) Om)
7.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
12.4b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.8b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite417.0ms

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:

10.0ms	(/ (* l l) Om)
50.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
169.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
182.0ms	(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:

34.0ms	(/ (* l l) Om)
512.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.8s	(* (* (* 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*)))))

simplify3.2s

Counts

153 → 153

Iterations

Useful iterations: 2 (1.7s)

Iter	Nodes	Cost
0	411	4799
1	1141	4430
2	4681	3850
done	5000	3850

prune756.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 26.9b

localize35.0ms

Local error

Found 4 expressions with local error:

5.7b	(* n (pow (/ l Om) 2.0))
7.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
12.4b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.8b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite411.0ms

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:

25.0ms	(* n (pow (/ l Om) 2.0))
47.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
219.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
112.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series10.2s

Counts

4 → 12

Calls

4 calls:

225.0ms	(* n (pow (/ l Om) 2.0))
540.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
2.1s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.3s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify3.3s

Counts

169 → 169

Iterations

Useful iterations: 2 (1.5s)

Iter	Nodes	Cost
0	442	5038
1	1199	4647
2	4730	4089
done	5000	4089

prune1.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 25.8b

localize38.0ms

Local error

Found 4 expressions with local error:

7.7b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
8.0b	(* n (pow (/ l Om) (/ 2.0 2)))
12.4b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
20.8b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite818.0ms

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:

224.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
28.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
305.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
239.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series10.4s

Counts

4 → 12

Calls

4 calls:

600.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
274.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
2.0s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
7.6s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify1.1s

Counts

186 → 186

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	478	7307
1	1292	5730
done	5000	5038

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 25.7b

localize31.0ms

Local error

Found 4 expressions with local error:

8.0b	(* n (pow (/ l Om) (/ 2.0 2)))
8.7b	(* (- U U*) (pow (/ l Om) (/ 2.0 2)))
12.4b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2))))))
20.8b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))))

rewrite505.0ms

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:

29.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
47.0ms	(* (- U U*) (pow (/ l Om) (/ 2.0 2)))
245.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2))))))
178.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))))

series10.7s

Counts

4 → 12

Calls

4 calls:

305.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
889.0ms	(* (- U U*) (pow (/ l Om) (/ 2.0 2)))
1.9s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* 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 (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))))

simplify3.1s

Counts

164 → 164

Iterations

Useful iterations: 2 (1.2s)

Iter	Nodes	Cost
0	419	5540
1	1141	5261
2	4774	4273
done	5000	4273

prune1.2s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 25.7b

regimes666.0ms

Accuracy

18.4% (7.9b remaining)

Error of 29.7b against oracle of 21.8b and baseline of 31.5b

bsearch731.0ms

Steps

Iters	Range		Point
7	3.9531903612801053e+83	5.7320075067165725e+85	3.193896812984259e+84
6	-1.8074549885472418e-147	-1.327451324818211e-148	-1.7708242025566493e-147

simplify17.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	54	165
1	74	165
done	74	165

end0.0ms

sample7.3s

Algorithm

intervals

Results

3.2s	14816×	body	80	nan
2.0s	9208×	body	80	valid