Details

sample242.0ms

Algorithm

intervals

Results

101.0ms	532×	body	80	nan
42.0ms	305×	body	80	valid

simplify5.5s

Counts

1 → 1

Iterations

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

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize119.0ms

Local error

Found 4 expressions with local error:

7.1b	(/ (* l l) Om)
8.0b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.1b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.1b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite525.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
25×	`pow1`
23×	`add-cbrt-cube`
22×	`associate-*r/`
16×	`prod-exp`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`add-sqr-sqrt` `*-un-lft-identity` `cbrt-unprod`
8×	`associate-r` `frac-sub` `add-cube-cbrt`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
4×	`sqrt-pow1` `associate--l+` `insert-posit16` `add-log-exp`
3×	`associate-/r*` `times-frac` `div-exp`
2×	`cbrt-undiv` `associate-l` `pow-exp` `*-commutative`
1×	`pow-to-exp` `clear-num` `frac-2neg` `pow1/2` `sqrt-prod` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 107

Calls

4 calls:

12.0ms	(/ (* l l) Om)
87.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
232.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
186.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series22.0s

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (* l l) Om)
1.2s	(* (* n (pow (/ l Om) 2.0)) (- U U*))
3.6s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
17.2s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify6.4s

Counts

119 → 119

Iterations

Iter	Nodes
done	5022
2	4278
1	988
0	322

prune2.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 25.1b

localize134.0ms

Local error

Found 4 expressions with local error:

6.2b	(* n (pow (/ l Om) 2.0))
8.0b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.1b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.1b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite589.0ms

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+` `insert-posit16` `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 → 123

Calls

4 calls:

48.0ms	(* n (pow (/ l Om) 2.0))
86.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
269.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
175.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series22.6s

Counts

4 → 12

Calls

4 calls:

554.0ms	(* n (pow (/ l Om) 2.0))
985.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
3.6s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
17.5s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify7.1s

Counts

135 → 135

Iterations

Iter	Nodes
done	5010
2	4067
1	1016
0	353

prune2.8s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 23.2b

localize119.0ms

Local error

Found 4 expressions with local error:

5.0b	(- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
8.0b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
9.1b	(* (* (* 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*))))
20.1b	(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*)))))

rewrite1.0s

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` `insert-posit16` `associate--r+`
3×	`diff-log`
2×	`associate-l` `*-commutative`
1×	`associate--l-` `pow1/2` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 127

Calls

4 calls:

103.0ms	(- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
315.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
362.0ms	(* (* (* 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*))))
243.0ms	(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*)))))

series24.1s

Counts

4 → 12

Calls

4 calls:

1.8s	(- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
1.0s	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
3.7s	(* (* (* 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*))))
17.5s	(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*)))))

simplify7.2s

Counts

139 → 139

Iterations

Iter	Nodes
done	5005
2	4331
1	1015
0	333

prune2.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 22.3b

localize89.0ms

Local error

Found 4 expressions with local error:

4.8b	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
5.0b	(- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))
9.1b	(* (* (* 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*)))))
20.1b	(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*))))))

rewrite715.0ms

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` `insert-posit16` `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 → 131

Calls

4 calls:

71.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
86.0ms	(- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))
330.0ms	(* (* (* 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*)))))
202.0ms	(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*))))))

series24.3s

Counts

4 → 12

Calls

4 calls:

979.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
2.0s	(- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))
3.6s	(* (* (* 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*)))))
17.7s	(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*))))))

simplify7.1s

Counts

143 → 143

Iterations

Iter	Nodes
done	5013
2	4356
1	1032
0	362

prune3.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 21.7b

regimes3.7s

Accuracy

16% (8.6b remaining)

Error of 29.0b against oracle of 20.4b and baseline of 30.7b

bsearch974.0ms

Steps

Iters	Range		Point
9	9.22710762468808e+283	1.2344502236012205e+291	1.2199917015699617e+291
4	3.562112880127445e-26	6.843023005463022e-26	3.638498443778453e-26
8	5.700086923092822e-71	1.4472394601144675e-67	1.4307548601344334e-67
8	-1.619269699894727e+64	-2.532481804488083e+59	-4.458146329554136e+62

simplify48.0ms

Iterations

Iter	Nodes
done	73
1	73
0	55

end0.0ms

sample6.4s

Algorithm

intervals

Results

3.0s	15197×	body	80	nan
1.7s	9217×	body	80	valid