Details

sample938.0ms

Algorithm

intervals

Results

517.0ms	298×	body	80	valid
67.0ms	419×	body	80	nan

simplify3.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	3869
3	632
2	152
1	49
0	21

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.6b

localize67.0ms

Local error

Found 4 expressions with local error:

5.8b	(* n (pow (/ l Om) 2.0))
6.6b	(* (* n (pow (/ l Om) 2.0)) (- U* U))
7.8b	(* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
18.3b	(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

rewrite929.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log`
25×	`add-sqr-sqrt` `pow1` `associate-r`
20×	`add-cbrt-cube`
19×	`prod-exp`
17×	`*-un-lft-identity`
15×	`unpow-prod-down` `add-cube-cbrt`
13×	`pow-prod-down`
10×	`times-frac` `cbrt-unprod`
6×	`associate-*r/`
5×	`associate-l`
4×	`sqrt-pow1` `associate-*l/` `pow-exp` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`distribute-rgt-in` `pow-to-exp` `sub-neg` `distribute-lft-in` `flip3-+` `sqrt-div` `div-exp` `flip-+` `sqr-pow`
1×	`flip3--` `pow1/2` `sqrt-prod` `div-inv` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 103

Calls

4 calls:

19.0ms	(* n (pow (/ l Om) 2.0))
57.0ms	(* (* n (pow (/ l Om) 2.0)) (- U* U))
424.0ms	(* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
421.0ms	(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

series17.5s

Counts

4 → 12

Calls

4 calls:

215.0ms	(* n (pow (/ l Om) 2.0))
594.0ms	(* (* n (pow (/ l Om) 2.0)) (- U* U))
1.6s	(* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
15.1s	(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

simplify3.3s

Counts

115 → 115

Iterations

Iter	Nodes
done	5002
2	4112
1	717
0	260

prune1.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 18.5b

localize51.0ms

Local error

Found 4 expressions with local error:

5.0b	(* (* 2.0 n) (* (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om)))) U))
5.8b	(* n (pow (/ l Om) 2.0))
6.6b	(* (* n (pow (/ l Om) 2.0)) (- U* U))
18.3b	(sqrt (* (* 2.0 n) (* (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om)))) U)))

rewrite707.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

320.0ms	(* (* 2.0 n) (* (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om)))) U))
22.0ms	(* n (pow (/ l Om) 2.0))
49.0ms	(* (* n (pow (/ l Om) 2.0)) (- U* U))
308.0ms	(sqrt (* (* 2.0 n) (* (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om)))) U)))

series15.8s

Counts

4 → 12

Calls

4 calls:

1.2s	(* (* 2.0 n) (* (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om)))) U))
159.0ms	(* n (pow (/ l Om) 2.0))
392.0ms	(* (* n (pow (/ l Om) 2.0)) (- U* U))
14.1s	(sqrt (* (* 2.0 n) (* (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om)))) U)))

simplify1.8s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
2	3642
1	699
0	257

prune736.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 15.9b

localize45.0ms

Local error

Found 4 expressions with local error:

5.0b	(* (* 2.0 n) (* (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om)))) U))
6.6b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
6.6b	(* n (pow (/ l Om) (/ 2.0 2)))
18.3b	(sqrt (* (* 2.0 n) (* (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om)))) U)))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 122

Calls

4 calls:

807.0ms	(* (* 2.0 n) (* (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om)))) U))
112.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
20.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
800.0ms	(sqrt (* (* 2.0 n) (* (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om)))) U)))

series11.8s

Counts

4 → 12

Calls

4 calls:

1.1s	(* (* 2.0 n) (* (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om)))) U))
364.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
164.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
10.2s	(sqrt (* (* 2.0 n) (* (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om)))) U)))

simplify1.9s

Counts

134 → 134

Iterations

Iter	Nodes
done	5000
2	4289
1	819
0	292

prune727.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.5b

localize39.0ms

Local error

Found 4 expressions with local error:

5.0b	(* (* 2.0 n) (* (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U))) (* (* 2.0 l) (/ l Om)))) U))
6.6b	(* n (pow (/ l Om) (/ 2.0 2)))
6.8b	(* (pow (/ l Om) (/ 2.0 2)) (- U* U))
18.3b	(sqrt (* (* 2.0 n) (* (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U))) (* (* 2.0 l) (/ l Om)))) U)))

rewrite754.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
32×	`add-exp-log`
30×	`unpow-prod-down`
29×	`pow1`
24×	`*-un-lft-identity`
23×	`associate-r`
22×	`add-cube-cbrt`
21×	`associate-l`
20×	`times-frac` `add-cbrt-cube`
16×	`pow-prod-down` `prod-exp`
10×	`cbrt-unprod`
8×	`unswap-sqr`
6×	`associate-*r/`
5×	`sqrt-pow1`
4×	`associate-*l/` `pow-exp` `add-log-exp` `sqr-pow`
3×	`*-commutative`
2×	`distribute-rgt-in` `pow-to-exp` `sub-neg` `distribute-lft-in` `flip3-+` `sqrt-div` `div-exp` `flip-+` `div-inv`
1×	`flip3--` `pow1/2` `sqrt-prod` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 122

Calls

4 calls:

352.0ms	(* (* 2.0 n) (* (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U))) (* (* 2.0 l) (/ l Om)))) U))
19.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
29.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U* U))
349.0ms	(sqrt (* (* 2.0 n) (* (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U))) (* (* 2.0 l) (/ l Om)))) U)))

series11.3s

Counts

4 → 12

Calls

4 calls:

1.1s	(* (* 2.0 n) (* (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U))) (* (* 2.0 l) (/ l Om)))) U))
168.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
341.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U* U))
9.7s	(sqrt (* (* 2.0 n) (* (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U))) (* (* 2.0 l) (/ l Om)))) U)))

simplify1.7s

Counts

134 → 134

Iterations

Iter	Nodes
done	5000
2	3605
1	766
0	299

prune832.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.5b

regimes988.0ms

Accuracy

25.8% (10.1b remaining)

Error of 27.1b against oracle of 17.0b and baseline of 30.6b

bsearch106.0ms

Steps

Iters	Range		Point
8	-5.352082936858468e-304	-1.6919138487008464e-307	-1.7120214689066866e-307

simplify27.0ms

Iterations

Iter	Nodes
done	52
1	52
0	37

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.5s	9147×	body	80	valid
1.5s	14935×	body	80	nan