Details

sample99.0ms

Algorithm

intervals

Results

33.0ms	455×	body	80	nan
19.0ms	293×	body	80	valid

simplify1.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (16.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize23.0ms

Local error

Found 4 expressions with local error:

6.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.0b	(/ (* l l) Om)
8.0b	(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
20.2b	(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

46.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.0ms	(/ (* l l) Om)
61.0ms	(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
48.0ms	(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

series3.3s

Counts

4 → 12

Calls

4 calls:

385.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
20.0ms	(/ (* l l) Om)
957.0ms	(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
1.9s	(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

simplify1.2s

Counts

127 → 127

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	281	3038
1	706	2772
2	2538	2368
done	5002	2339

prune429.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 24.1b

localize18.0ms

Local error

Found 4 expressions with local error:

5.6b	(* n (pow (/ l Om) 2.0))
6.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.0b	(* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
20.2b	(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
35×	`add-exp-log`
31×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`pow1`
23×	`associate-r`
20×	`add-cbrt-cube`
19×	`prod-exp`
18×	`prod-diff`
15×	`unpow-prod-down`
13×	`pow-prod-down`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`times-frac` `cbrt-unprod`
9×	`associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-*l/` `pow-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`flip3--` `*-commutative` `flip--`
2×	`pow-to-exp` `sub-neg` `sqrt-div` `associate-*r/` `div-exp` `distribute-lft-out--` `difference-of-squares` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv`

Counts

4 → 131

Calls

4 calls:

25.0ms	(* n (pow (/ l Om) 2.0))
46.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
61.0ms	(* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
46.0ms	(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

series3.2s

Counts

4 → 12

Calls

4 calls:

156.0ms	(* n (pow (/ l Om) 2.0))
390.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
763.0ms	(* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
1.9s	(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

simplify1.2s

Counts

143 → 143

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	313	3277
1	762	2989
2	2561	2595
done	5001	2566

prune469.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 21.8b

localize20.0ms

Local error

Found 4 expressions with local error:

5.0b	(* n (pow (/ l Om) (/ 2.0 2)))
6.7b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
8.0b	(* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U))
20.2b	(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U)))

rewrite287.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
67×	`prod-exp`
39×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`pow1`
24×	`add-cbrt-cube`
23×	`associate-r`
20×	`pow-exp`
18×	`prod-diff`
15×	`unpow-prod-down`
13×	`pow-prod-down` `cbrt-unprod`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`pow-to-exp` `times-frac` `div-exp`
9×	`associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-*l/` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`flip3--` `*-commutative` `flip--`
2×	`sub-neg` `sqrt-div` `associate-*r/` `distribute-lft-out--` `difference-of-squares` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv`

Counts

4 → 148

Calls

4 calls:

24.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
147.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
60.0ms	(* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U))
48.0ms	(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U)))

series3.3s

Counts

4 → 12

Calls

4 calls:

180.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
399.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
777.0ms	(* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U))
1.9s	(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U)))

simplify1.4s

Counts

160 → 160

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	348	5166
1	853	3924
2	2947	3412
done	5000	3383

prune533.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 21.8b

localize20.0ms

Local error

Found 4 expressions with local error:

5.0b	(* n (pow (/ l Om) (/ 2.0 2)))
6.3b	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
8.0b	(* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U))))) ( (* 2.0 n) U))
20.2b	(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U))))) ( (* 2.0 n) U)))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 148

Calls

4 calls:

26.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
41.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
60.0ms	(* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U))))) ( (* 2.0 n) U))
47.0ms	(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U))))) ( (* 2.0 n) U)))

series3.3s

Counts

4 → 12

Calls

4 calls:

180.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
365.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
789.0ms	(* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U))))) ( (* 2.0 n) U))
2.0s	(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U))))) ( (* 2.0 n) U)))

simplify1.2s

Counts

160 → 160

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	356	4184
1	803	3860
2	2621	3116
done	5000	3087

prune827.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 20.1b

regimes491.0ms

Accuracy

13.6% (9.5b remaining)

Error of 30.0b against oracle of 20.5b and baseline of 31.5b

bsearch163.0ms

Steps

Iters	Range		Point
5	3.9577902924876285e-153	8.504070466052334e-153	8.420291904348501e-153
7	-6.685941971687323e-133	-7.369303412132716e-135	-2.0370585079861942e-134

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	52	151
1	69	151
done	69	151

end0.0ms

sample2.9s

Algorithm

intervals

Results

996.0ms	15080×	body	80	nan
615.0ms	9188×	body	80	valid