Details

sample210.0ms

Algorithm

intervals

Results

96.0ms	503×	body	80	nan
44.0ms	279×	body	80	valid

simplify2.9s

Counts

1 → 1

Iterations

Useful iterations: 4 (1.4s)

Iter	Nodes	Cost
0	21	737
1	49	737
2	154	712
3	665	712
4	4135	672
done	5000	672

prune38.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.2b

localize78.0ms

Local error

Found 4 expressions with local error:

6.4b	(* n (* (pow (/ l Om) 2.0) (- U U*)))
7.1b	(* (pow (/ l Om) 2.0) (- U U*))
10.7b	(* (* n U) (- t (fma (/ l Om) (* 2.0 l) (* n (* (pow (/ l Om) 2.0) (- U U*))))))
19.2b	(sqrt (* 2.0 (* (* n U) (- t (fma (/ l Om) (* 2.0 l) (* n (* (pow (/ l Om) 2.0) (- U U*))))))))

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
72×	`prod-diff`
67×	`*-un-lft-identity`
66×	`distribute-rgt-in` `distribute-lft-in`
63×	`add-cube-cbrt`
31×	`add-exp-log`
21×	`pow1` `associate-l`
16×	`add-cbrt-cube` `prod-exp`
15×	`unpow-prod-down`
12×	`associate-*r/`
11×	`associate-r`
10×	`times-frac` `pow-prod-down`
8×	`sub-neg`
7×	`cbrt-unprod`
4×	`expm1-log1p-u` `sqrt-pow1` `flip3--` `pow-exp` `log1p-expm1-u` `flip--` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`pow-to-exp` `sqrt-div` `div-exp` `distribute-lft-out--` `difference-of-squares` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv`

Counts

4 → 196

Calls

4 calls:

66.0ms	(* n (* (pow (/ l Om) 2.0) (- U U*)))
46.0ms	(* (pow (/ l Om) 2.0) (- U U*))
26.0ms	(* (* n U) (- t (fma (/ l Om) (* 2.0 l) (* n (* (pow (/ l Om) 2.0) (- U U*))))))
97.0ms	(sqrt (* 2.0 (* (* n U) (- t (fma (/ l Om) (* 2.0 l) (* n (* (pow (/ l Om) 2.0) (- U U*))))))))

series8.6s

Counts

4 → 12

Calls

4 calls:

474.0ms	(* n (* (pow (/ l Om) 2.0) (- U U*)))
507.0ms	(* (pow (/ l Om) 2.0) (- U U*))
1.7s	(* (* n U) (- t (fma (/ l Om) (* 2.0 l) (* n (* (pow (/ l Om) 2.0) (- U U*))))))
5.9s	(sqrt (* 2.0 (* (* n U) (- t (fma (/ l Om) (* 2.0 l) (* n (* (pow (/ l Om) 2.0) (- U U*))))))))

simplify1.8s

Counts

208 → 208

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	455	165062
1	1208	152596
done	5000	139111

prune1.8s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 26.4b

localize55.0ms

Local error

Found 4 expressions with local error:

4.4b	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
6.4b	(* n (* (pow (/ l Om) (/ 2.0 2)) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))
10.7b	(* (* n U) (- t (fma (/ l Om) (* 2.0 l) (* n (* (pow (/ l Om) (/ 2.0 2)) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))))
19.2b	(sqrt (* 2.0 (* (* n U) (- t (fma (/ l Om) (* 2.0 l) (* n (* (pow (/ l Om) (/ 2.0 2)) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))))))

rewrite378.0ms

Algorithm

rewrite-expression-head

Rules

154×	`distribute-rgt-in` `distribute-lft-in`
108×	`prod-diff`
99×	`add-sqr-sqrt`
95×	`add-exp-log`
91×	`*-un-lft-identity`
87×	`add-cube-cbrt`
64×	`prod-exp`
21×	`pow1` `associate-l`
20×	`add-cbrt-cube` `pow-exp`
15×	`unpow-prod-down`
14×	`associate-*r/`
12×	`sub-neg`
11×	`associate-r`
10×	`pow-to-exp` `times-frac` `div-exp` `pow-prod-down` `cbrt-unprod`
4×	`expm1-log1p-u` `sqrt-pow1` `flip3--` `log1p-expm1-u` `flip--` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`sqrt-div` `distribute-lft-out--` `difference-of-squares` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv`

Counts

4 → 257

Calls

4 calls:

56.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
188.0ms	(* n (* (pow (/ l Om) (/ 2.0 2)) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))
46.0ms	(* (* n U) (- t (fma (/ l Om) (* 2.0 l) (* n (* (pow (/ l Om) (/ 2.0 2)) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))))
61.0ms	(sqrt (* 2.0 (* (* n U) (- t (fma (/ l Om) (* 2.0 l) (* n (* (pow (/ l Om) (/ 2.0 2)) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))))))

series8.6s

Counts

4 → 12

Calls

4 calls:

491.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
538.0ms	(* n (* (pow (/ l Om) (/ 2.0 2)) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))
1.6s	(* (* n U) (- t (fma (/ l Om) (* 2.0 l) (* n (* (pow (/ l Om) (/ 2.0 2)) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))))
6.0s	(sqrt (* 2.0 (* (* n U) (- t (fma (/ l Om) (* 2.0 l) (* n (* (pow (/ l Om) (/ 2.0 2)) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))))))

simplify2.9s

Counts

269 → 269

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	605	247534
1	1746	228643
done	5001	208535

prune2.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 25.3b

localize77.0ms

Local error

Found 4 expressions with local error:

3.7b	(* n (pow (/ l Om) (/ 2.0 2)))
4.4b	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
10.7b	(* (* n U) (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
19.2b	(sqrt (* 2.0 (* (* n U) (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))))

rewrite242.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
47×	`add-cube-cbrt`
36×	`prod-diff`
30×	`unpow-prod-down`
27×	`associate-r`
25×	`add-exp-log`
22×	`distribute-rgt-in` `distribute-lft-in`
21×	`associate-l`
20×	`times-frac`
19×	`pow1`
13×	`add-cbrt-cube`
11×	`prod-exp`
9×	`pow-prod-down`
8×	`associate-*r/` `unswap-sqr`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `sub-neg` `sqrt-pow1` `pow-exp` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`flip3--` `*-commutative` `flip--`
2×	`pow-to-exp` `sqrt-div` `div-exp` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`pow1/2` `sqrt-prod`

Counts

4 → 167

Calls

4 calls:

42.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
43.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
43.0ms	(* (* n U) (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
100.0ms	(sqrt (* 2.0 (* (* n U) (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))))

series9.1s

Counts

4 → 12

Calls

4 calls:

234.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
490.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
1.8s	(* (* n U) (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
6.6s	(sqrt (* 2.0 (* (* n U) (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))))

simplify2.2s

Counts

179 → 179

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	445	133560
1	1143	125235
done	5000	118610

prune1.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 25.1b

localize84.0ms

Local error

Found 4 expressions with local error:

3.7b	(* n (pow (/ l Om) (/ 2.0 2)))
4.4b	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
10.7b	(* (* n U) (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
19.0b	(sqrt (* (* n U) (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
47×	`add-cube-cbrt`
36×	`prod-diff`
30×	`unpow-prod-down`
27×	`associate-r`
25×	`add-exp-log`
22×	`distribute-rgt-in` `distribute-lft-in`
21×	`associate-l`
20×	`times-frac`
15×	`pow1`
13×	`add-cbrt-cube`
11×	`prod-exp`
8×	`unswap-sqr`
6×	`pow-prod-down` `associate-*r/`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `sub-neg` `pow-exp` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`sqrt-pow1` `flip3--` `*-commutative` `flip--`
2×	`pow-to-exp` `sqrt-div` `div-exp` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`pow1/2` `sqrt-prod`

Counts

4 → 166

Calls

4 calls:

22.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
51.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
28.0ms	(* (* n U) (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
54.0ms	(sqrt (* (* n U) (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))))

series8.1s

Counts

4 → 12

Calls

4 calls:

254.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
521.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
1.7s	(* (* n U) (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
5.7s	(sqrt (* (* n U) (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))))

simplify2.0s

Counts

178 → 178

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	436	132880
1	1112	124646
done	5000	117723

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 20.2b

regimes1.9s

Accuracy

39.4% (5.8b remaining)

Error of 27.0b against oracle of 21.2b and baseline of 30.8b

bsearch6.0ms

simplify34.0ms

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	46	1905
1	62	1905
done	62	1905

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.8s	14889×	body	80	nan
1.9s	9174×	body	80	valid