Details

sample334.0ms

Algorithm

intervals

Results

32.0ms	477×	body	80	nan
19.0ms	295×	body	80	valid

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	21	28
1	49	28
2	151	27
3	601	27
4	3101	27
done	5001	27

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.9b

localize28.0ms

Local error

Found 4 expressions with local error:

5.3b	(* (* 2.0 n) (* U (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
5.5b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
5.9b	(/ (* l l) Om)
18.3b	(sqrt (* (* 2.0 n) (* U (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

55×	`distribute-rgt-in` `distribute-lft-in`
54×	`prod-diff`
45×	`add-sqr-sqrt` `*-un-lft-identity`
43×	`add-cube-cbrt`
35×	`add-exp-log`
31×	`pow1`
26×	`add-cbrt-cube`
18×	`prod-exp`
17×	`pow-prod-down`
12×	`cbrt-unprod`
10×	`associate-*r/`
6×	`sub-neg` `associate-r`
5×	`sqrt-pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `times-frac` `div-exp` `associate-/r*` `flip--`
2×	`cbrt-undiv` `sqrt-div` `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 → 159

Calls

4 calls:

26.0ms	(* (* 2.0 n) (* U (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
25.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
3.0ms	(/ (* l l) Om)
33.0ms	(sqrt (* (* 2.0 n) (* U (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))

series5.9s

Counts

4 → 12

Calls

4 calls:

1.2s	(* (* 2.0 n) (* U (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
365.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
19.0ms	(/ (* l l) Om)
4.3s	(sqrt (* (* 2.0 n) (* U (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))

simplify1.5s

Counts

171 → 171

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	434	8380
1	1149	5945
2	4036	4660
done	5000	4642

prune489.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 21.8b

localize22.0ms

Local error

Found 4 expressions with local error:

5.3b	(* n (pow (/ l Om) 2.0))
5.3b	(* (* 2.0 n) (* U (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
5.5b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
18.3b	(sqrt (* (* 2.0 n) (* U (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
55×	`distribute-rgt-in` `distribute-lft-in`
54×	`prod-diff`
52×	`*-un-lft-identity`
50×	`add-cube-cbrt`
38×	`add-exp-log`
31×	`pow1`
23×	`associate-r` `add-cbrt-cube`
21×	`prod-exp`
17×	`pow-prod-down`
15×	`unpow-prod-down`
12×	`cbrt-unprod`
10×	`times-frac` `associate-*r/`
6×	`sub-neg`
5×	`sqrt-pow1` `associate-l`
4×	`expm1-log1p-u` `pow-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`flip3--` `*-commutative` `flip--`
2×	`pow-to-exp` `sqrt-div` `div-exp` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 175

Calls

4 calls:

15.0ms	(* n (pow (/ l Om) 2.0))
25.0ms	(* (* 2.0 n) (* U (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
25.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
31.0ms	(sqrt (* (* 2.0 n) (* U (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))

series6.1s

Counts

4 → 12

Calls

4 calls:

136.0ms	(* n (pow (/ l Om) 2.0))
1.3s	(* (* 2.0 n) (* U (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
366.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
4.3s	(sqrt (* (* 2.0 n) (* U (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))

simplify1.6s

Counts

187 → 187

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	465	8619
1	1203	6162
2	4021	4887
done	5000	4869

prune502.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 20.2b

localize19.0ms

Local error

Found 4 expressions with local error:

5.3b	(* (* 2.0 n) (* U (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))
5.5b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
6.4b	(* n (pow (/ l Om) (/ 2.0 2)))
18.3b	(sqrt (* (* 2.0 n) (* U (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-exp-log`
69×	`prod-exp`
60×	`add-sqr-sqrt`
55×	`distribute-rgt-in` `distribute-lft-in`
54×	`prod-diff`
52×	`*-un-lft-identity`
50×	`add-cube-cbrt`
31×	`pow1`
27×	`add-cbrt-cube`
23×	`associate-r`
20×	`pow-exp`
17×	`pow-prod-down`
15×	`unpow-prod-down` `cbrt-unprod`
10×	`pow-to-exp` `times-frac` `associate-*r/` `div-exp`
6×	`sub-neg`
5×	`sqrt-pow1` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`flip3--` `*-commutative` `flip--`
2×	`sqrt-div` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 192

Calls

4 calls:

22.0ms	(* (* 2.0 n) (* U (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))
86.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
15.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
33.0ms	(sqrt (* (* 2.0 n) (* U (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))))

series6.0s

Counts

4 → 12

Calls

4 calls:

1.2s	(* (* 2.0 n) (* U (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))
367.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
165.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
4.3s	(sqrt (* (* 2.0 n) (* U (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))))

simplify1.8s

Counts

204 → 204

Iterations

Useful iterations: 2 (939.0ms)

Iter	Nodes	Cost
0	501	12748
1	1329	7561
2	4515	6016
done	5000	6016

prune545.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 19.8b

localize23.0ms

Local error

Found 4 expressions with local error:

5.3b	(* (* 2.0 n) (* U (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2))))))))
6.4b	(* n (pow (/ l Om) (/ 2.0 2)))
6.4b	(* (- U U*) (pow (/ l Om) (/ 2.0 2)))
18.3b	(sqrt (* (* 2.0 n) (* U (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))))))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
48×	`*-un-lft-identity`
46×	`add-cube-cbrt`
44×	`distribute-rgt-in` `distribute-lft-in`
36×	`prod-diff`
35×	`associate-r`
32×	`add-exp-log`
30×	`unpow-prod-down`
29×	`pow1`
20×	`times-frac` `add-cbrt-cube`
16×	`pow-prod-down` `prod-exp`
10×	`cbrt-unprod`
9×	`associate-l`
8×	`associate-*r/` `unswap-sqr`
5×	`sqrt-pow1`
4×	`expm1-log1p-u` `sub-neg` `pow-exp` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`flip3--` `*-commutative` `flip--`
2×	`pow-to-exp` `sqrt-div` `div-exp` `associate-*l/` `div-inv`
1×	`pow1/2` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 170

Calls

4 calls:

22.0ms	(* (* 2.0 n) (* U (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2))))))))
18.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
23.0ms	(* (- U U*) (pow (/ l Om) (/ 2.0 2)))
30.0ms	(sqrt (* (* 2.0 n) (* U (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))))))

series6.2s

Counts

4 → 12

Calls

4 calls:

1.2s	(* (* 2.0 n) (* U (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2))))))))
159.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
517.0ms	(* (- U U*) (pow (/ l Om) (/ 2.0 2)))
4.4s	(sqrt (* (* 2.0 n) (* U (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))))))

simplify1.2s

Counts

182 → 182

Iterations

Useful iterations: 2 (571.0ms)

Iter	Nodes	Cost
0	439	10981
1	1106	7554
2	3649	5179
done	5001	5179

prune547.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 19.5b

regimes519.0ms

Accuracy

23.4% (7.5b remaining)

Error of 28.0b against oracle of 20.5b and baseline of 30.3b

bsearch104.0ms

Steps

Iters	Range		Point
8	9.142412603843217e-299	5.121089798437407e-296	2.050499822482108e-298

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	105
1	56	105
done	56	105

end0.0ms

sample2.4s

Algorithm

intervals

Results

969.0ms	14831×	body	80	nan
598.0ms	9205×	body	80	valid