Details

sample200.0ms

Algorithm

intervals

Results

86.0ms	483×	body	80	nan
33.0ms	278×	body	80	valid

simplify2.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5006
4	2710
3	599
2	148
1	49
0	21

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.6b

localize47.0ms

Local error

Found 4 expressions with local error:

7.4b	(* n (pow (/ l Om) 2.0))
7.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
11.2b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.3b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite341.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log`
25×	`add-sqr-sqrt` `pow1` `associate-r`
22×	`associate-*r/`
20×	`add-cbrt-cube`
19×	`prod-exp`
17×	`*-un-lft-identity`
15×	`unpow-prod-down` `add-cube-cbrt`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`times-frac` `cbrt-unprod`
8×	`frac-sub`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
5×	`associate-l`
4×	`sqrt-pow1` `pow-exp` `associate--l+` `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 → 119

Calls

4 calls:

20.0ms	(* n (pow (/ l Om) 2.0))
66.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
122.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
129.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series9.8s

Counts

4 → 12

Calls

4 calls:

237.0ms	(* n (pow (/ l Om) 2.0))
516.0ms	(* (* 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*))))
7.2s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify2.9s

Counts

131 → 131

Iterations

Iter	Nodes
done	5001
2	3945
1	1015
0	350

prune1.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 23.7b

localize82.0ms

Local error

Found 4 expressions with local error:

5.2b	(/ (* l l) Om)
7.7b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
11.2b	(* (* (* 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*))))
18.3b	(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*)))))

rewrite573.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-exp-log`
64×	`prod-exp`
27×	`add-cbrt-cube`
25×	`pow1`
22×	`associate-*r/`
18×	`pow-exp`
13×	`pow-prod-down` `cbrt-unprod`
11×	`flip3--` `div-exp` `flip--`
10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`pow-to-exp`
8×	`associate-r` `frac-sub` `add-cube-cbrt`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
4×	`sqrt-pow1` `associate--l+` `add-log-exp`
3×	`associate-/r*` `times-frac`
2×	`cbrt-undiv` `associate-l` `*-commutative`
1×	`clear-num` `frac-2neg` `pow1/2` `sqrt-prod` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 120

Calls

4 calls:

15.0ms	(/ (* l l) Om)
233.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
165.0ms	(* (* (* 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*))))
150.0ms	(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*)))))

series10.1s

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (* l l) Om)
498.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
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*)))))

simplify3.5s

Counts

132 → 132

Iterations

Iter	Nodes
done	5001
2	4688
1	1066
0	347

prune1.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 21.5b

localize53.0ms

Local error

Found 4 expressions with local error:

3.7b	(- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
7.7b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
11.2b	(* (* (* 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*))))
18.3b	(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*)))))

rewrite608.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-exp-log`
63×	`prod-exp`
26×	`associate-*r/`
25×	`pow1`
22×	`add-cbrt-cube`
18×	`pow-exp`
16×	`flip3--` `flip--`
13×	`pow-prod-down`
12×	`frac-sub` `cbrt-unprod`
10×	`sub-neg`
9×	`pow-to-exp` `div-exp` `add-log-exp`
8×	`distribute-rgt-in` `add-sqr-sqrt` `-un-lft-identity` `distribute-lft-in` `associate-r*`
6×	`sqrt-div` `associate--l+` `add-cube-cbrt`
4×	`sqrt-pow1` `associate--r+`
3×	`diff-log`
2×	`associate-l` `*-commutative`
1×	`associate--l-` `pow1/2` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 123

Calls

4 calls:

52.0ms	(- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
160.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
222.0ms	(* (* (* 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*))))
167.0ms	(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*)))))

series10.6s

Counts

4 → 12

Calls

4 calls:

1.0s	(- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
546.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.8s	(* (* (* 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*))))
7.2s	(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*)))))

simplify3.3s

Counts

135 → 135

Iterations

Iter	Nodes
done	5012
2	4285
1	1008
0	329

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 18.9b

localize62.0ms

Local error

Found 4 expressions with local error:

3.7b	(- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))
6.9b	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
11.2b	(* (* (* 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*)))))
18.3b	(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*))))))

rewrite503.0ms

Algorithm

rewrite-expression-head

Rules

38×	`associate-*r/`
24×	`add-sqr-sqrt`
23×	`pow1`
21×	`add-exp-log`
18×	`associate-l`
16×	`*-un-lft-identity` `flip3--` `flip--`
15×	`unpow-prod-down` `add-cbrt-cube`
14×	`distribute-rgt-in` `distribute-lft-in` `add-cube-cbrt`
12×	`sub-neg` `pow-prod-down` `frac-sub`
10×	`times-frac` `prod-exp`
9×	`add-log-exp`
8×	`associate-r` `associate--r+`
7×	`cbrt-unprod`
6×	`sqrt-div` `associate--l+`
4×	`sqrt-pow1` `unswap-sqr`
3×	`diff-log`
2×	`pow-exp` `*-commutative` `sqr-pow`
1×	`associate--l-` `pow-to-exp` `pow1/2` `div-exp` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 127

Calls

4 calls:

77.0ms	(- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))
64.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
194.0ms	(* (* (* 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*)))))
158.0ms	(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*))))))

series11.1s

Counts

4 → 12

Calls

4 calls:

1.0s	(- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))
526.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
2.3s	(* (* (* 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*)))))
7.3s	(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*))))))

simplify3.3s

Counts

139 → 139

Iterations

Iter	Nodes
done	5004
2	4353
1	1032
0	358

prune1.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 18.6b

regimes1.6s

Accuracy

11.2% (10.8b remaining)

Error of 29.2b against oracle of 18.4b and baseline of 30.6b

bsearch742.0ms

Steps

Iters	Range	Point
7	1.8858956155785848e-06	0.00019283035021077605	0.00013931170067333777
10	-1.7030146629720901e-171	-2.2611338748487402e-181	-3.7722456661959136e-180
8	-2.018885558656855e+244	-4.881717160484606e+240	-9.37971981582653e+241

Iters

Range

Point

1.8858956155785848e-06

0.00019283035021077605

0.00013931170067333777

-1.7030146629720901e-171

-2.2611338748487402e-181

-3.7722456661959136e-180

-2.018885558656855e+244

-4.881717160484606e+240

-9.37971981582653e+241

simplify49.0ms

Iterations

Iter	Nodes
done	76
3	76
2	75
1	67
0	47

end0.0ms

sample7.0s

Algorithm

intervals

Results

3.0s	14839×	body	80	nan
1.9s	9163×	body	80	valid