Details

sample183.0ms

Algorithm

intervals

Results

79.0ms	464×	body	80	nan
44.0ms	291×	body	80	valid

simplify3.3s

Counts

1 → 1

Iterations

Useful iterations: 2 (74.0ms)

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

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize41.0ms

Local error

Found 4 expressions with local error:

6.5b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.8b	(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
11.4b	(/ (* l l) Om)
21.0b	(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

rewrite264.0ms

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:

71.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
83.0ms	(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
11.0ms	(/ (* l l) Om)
90.0ms	(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

series4.3s

Counts

4 → 12

Calls

4 calls:

480.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.1s	(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
33.0ms	(/ (* l l) Om)
2.6s	(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

simplify2.0s

Counts

127 → 127

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	281	3038
1	705	2772
2	2519	2368
done	5002	2339

prune781.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 23.3b

localize30.0ms

Local error

Found 4 expressions with local error:

6.4b	(* n (pow (/ l Om) 2.0))
6.5b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.8b	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
21.0b	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

rewrite251.0ms

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:

51.0ms	(* n (pow (/ l Om) 2.0))
66.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
65.0ms	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
59.0ms	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

series4.7s

Counts

4 → 12

Calls

4 calls:

233.0ms	(* n (pow (/ l Om) 2.0))
629.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.1s	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
2.8s	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

simplify2.0s

Counts

143 → 143

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	314	3277
1	762	2989
2	2562	2595
done	5002	2566

prune745.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 20.7b

localize30.0ms

Local error

Found 4 expressions with local error:

6.0b	(* n (pow (/ l Om) (/ 2.0 2)))
6.5b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
7.8b	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U))
21.0b	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U)))

rewrite428.0ms

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:

26.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
241.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
88.0ms	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U))
63.0ms	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U)))

series4.7s

Counts

4 → 12

Calls

4 calls:

250.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
515.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.2s	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U))
2.7s	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U)))

simplify2.3s

Counts

160 → 160

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	349	5166
1	853	3924
2	2944	3412
done	5000	3383

prune936.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 20.4b

localize48.0ms

Local error

Found 4 expressions with local error:

6.0b	(* n (pow (/ l Om) (/ 2.0 2)))
6.2b	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
7.8b	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U))))) ( (* 2.0 n) U))
21.0b	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U))))) ( (* 2.0 n) U)))

rewrite261.0ms

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:

40.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
44.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
114.0ms	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U))))) ( (* 2.0 n) U))
49.0ms	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U))))) ( (* 2.0 n) U)))

series4.8s

Counts

4 → 12

Calls

4 calls:

254.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
532.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
1.1s	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U))))) ( (* 2.0 n) U))
2.9s	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U))))) ( (* 2.0 n) U)))

simplify1.9s

Counts

160 → 160

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	357	4184
1	802	3860
2	2630	3116
done	5002	3087

prune971.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 20.4b

regimes599.0ms

Accuracy

12.8% (9.7b remaining)

Error of 30.6b against oracle of 21.0b and baseline of 32.0b

bsearch262.0ms

Steps

Iters	Range		Point
9	734804260553175.0	1.1371532249939426e+22	3.3220315693874754e+21

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	29	59
1	36	59
done	36	59

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.0s	15327×	body	80	nan
2.3s	9227×	body	80	valid