Details

sample218.0ms

Algorithm

intervals

Results

97.0ms	459×	body	80	nan
78.0ms	293×	body	80	valid

simplify528.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
3	642
2	155
1	50
0	21

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.5b

localize49.0ms

Local error

Found 4 expressions with local error:

4.6b	(* n (/ l Om))
5.9b	(* (* U 2) (* n (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U)) ( (* (/ l Om) 2) l)))))
7.2b	(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
21.6b	(sqrt (* (* U 2) (* n (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U)) ( (* (/ l Om) 2) l))))))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

50×	`add-cbrt-cube` `add-exp-log`
40×	`pow1`
27×	`prod-exp` `cbrt-unprod`
23×	`pow-prod-down`
20×	`add-sqr-sqrt` `associate-*r/`
19×	`associate-r`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
10×	`distribute-rgt-in` `distribute-lft-in` `times-frac`
9×	`frac-times`
6×	`cbrt-undiv` `sub-neg` `flip3--` `div-exp` `associate-*l/` `flip--`
5×	`sqrt-pow1` `associate-l`
4×	`insert-posit16` `add-log-exp`
3×	`*-commutative`
2×	`sqrt-div` `unswap-sqr`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 130

Calls

4 calls:

9.0ms	(* n (/ l Om))
590.0ms	(* (* U 2) (* n (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U)) ( (* (/ l Om) 2) l)))))
106.0ms	(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
746.0ms	(sqrt (* (* U 2) (* n (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U)) ( (* (/ l Om) 2) l))))))

series2.6s

Counts

4 → 12

Calls

4 calls:

34.0ms	(* n (/ l Om))
523.0ms	(* (* U 2) (* n (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U)) ( (* (/ l Om) 2) l)))))
144.0ms	(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
1.9s	(sqrt (* (* U 2) (* n (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U)) ( (* (/ l Om) 2) l))))))

simplify657.0ms

Counts

142 → 142

Iterations

Iter	Nodes
done	2001
1	905
0	292

prune894.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 21.2b

localize60.0ms

Local error

Found 4 expressions with local error:

5.4b	(/ (* (* (* n (/ l Om)) l) (- U U*)) Om)
5.9b	(* (* U 2) (* n (- t (+ (/ (* (* (* n (/ l Om)) l) (- U U)) Om) ( (* (/ l Om) 2) l)))))
8.0b	(* (* (* n (/ l Om)) l) (- U U*))
21.6b	(sqrt (* (* U 2) (* n (- t (+ (/ (* (* (* n (/ l Om)) l) (- U U)) Om) ( (* (/ l Om) 2) l))))))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

50×	`add-cbrt-cube` `add-exp-log`
38×	`pow1`
26×	`prod-exp` `cbrt-unprod`
22×	`pow-prod-down`
18×	`associate-*r/`
10×	`distribute-rgt-in` `distribute-lft-in`
9×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`associate-*l/`
7×	`cbrt-undiv` `div-exp` `add-cube-cbrt`
6×	`sub-neg` `flip3--` `associate-r` `flip--`
5×	`sqrt-pow1` `associate-/l/`
4×	`frac-times` `insert-posit16` `add-log-exp`
3×	`associate-/r*` `times-frac`
2×	`sqrt-div` `associate-l` `*-commutative`
1×	`clear-num` `frac-2neg` `pow1/2` `sqrt-prod` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 118

Calls

4 calls:

97.0ms	(/ (* (* (* n (/ l Om)) l) (- U U*)) Om)
673.0ms	(* (* U 2) (* n (- t (+ (/ (* (* (* n (/ l Om)) l) (- U U)) Om) ( (* (/ l Om) 2) l)))))
93.0ms	(* (* (* n (/ l Om)) l) (- U U*))
613.0ms	(sqrt (* (* U 2) (* n (- t (+ (/ (* (* (* n (/ l Om)) l) (- U U)) Om) ( (* (/ l Om) 2) l))))))

series2.5s

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (* (* (* n (/ l Om)) l) (- U U*)) Om)
510.0ms	(* (* U 2) (* n (- t (+ (/ (* (* (* n (/ l Om)) l) (- U U)) Om) ( (* (/ l Om) 2) l)))))
119.0ms	(* (* (* n (/ l Om)) l) (- U U*))
1.7s	(sqrt (* (* U 2) (* n (- t (+ (/ (* (* (* n (/ l Om)) l) (- U U)) Om) ( (* (/ l Om) 2) l))))))

simplify660.0ms

Counts

130 → 130

Iterations

Iter	Nodes
done	2000
1	825
0	269

prune855.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 21.2b

localize42.0ms

Local error

Found 4 expressions with local error:

4.6b	(* n (/ l Om))
5.9b	(* (* U 2) (* n (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U)) ( (* (/ l Om) 2) l)))))
7.2b	(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
21.6b	(pow (* (* U 2) (* n (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U)) ( (* (/ l Om) 2) l))))) 1/2)

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

63×	`add-exp-log`
50×	`add-cbrt-cube`
40×	`pow1`
35×	`prod-exp`
27×	`cbrt-unprod`
23×	`pow-prod-down`
21×	`add-sqr-sqrt`
19×	`associate-r`
16×	`-un-lft-identity` `associate-r/`
14×	`add-cube-cbrt`
10×	`distribute-rgt-in` `distribute-lft-in` `times-frac`
9×	`frac-times`
6×	`cbrt-undiv` `sub-neg` `div-exp` `associate-*l/`
5×	`pow-pow` `flip3--` `associate-l` `pow-exp` `flip--`
4×	`insert-posit16` `add-log-exp`
3×	`pow-unpow` `*-commutative`
2×	`unswap-sqr`
1×	`pow-to-exp` `unpow-prod-down` `div-inv` `distribute-lft-out--` `unpow1/2` `difference-of-squares` `sqr-pow`

Counts

4 → 138

Calls

4 calls:

9.0ms	(* n (/ l Om))
659.0ms	(* (* U 2) (* n (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U)) ( (* (/ l Om) 2) l)))))
97.0ms	(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
683.0ms	(pow (* (* U 2) (* n (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U)) ( (* (/ l Om) 2) l))))) 1/2)

series1.2s

Counts

4 → 12

Calls

4 calls:

33.0ms	(* n (/ l Om))
483.0ms	(* (* U 2) (* n (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U)) ( (* (/ l Om) 2) l)))))
140.0ms	(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
499.0ms	(pow (* (* U 2) (* n (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U)) ( (* (/ l Om) 2) l))))) 1/2)

simplify1.3s

Counts

150 → 150

Iterations

Iter	Nodes
done	2003
1	999
0	327

prune1.0s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 21.2b

localize70.0ms

Local error

Found 4 expressions with local error:

4.6b	(* n (/ l Om))
7.2b	(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
7.4b	(* (* (* U 2) n) (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U)) ( (* (/ l Om) 2) l))))
21.6b	(pow (* (* (* U 2) n) (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U)) ( (* (/ l Om) 2) l)))) 1/2)

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

57×	`add-exp-log`
47×	`add-cbrt-cube`
34×	`pow1`
31×	`prod-exp`
25×	`cbrt-unprod`
24×	`add-sqr-sqrt`
23×	`associate-r`
19×	`*-un-lft-identity` `pow-prod-down`
15×	`add-cube-cbrt`
14×	`associate-*r/`
10×	`times-frac`
9×	`frac-times`
6×	`cbrt-undiv` `div-exp` `associate-*l/`
5×	`flip3--` `associate-l` `flip--`
4×	`distribute-rgt-in` `sub-neg` `pow-pow` `distribute-lft-in` `pow-exp` `insert-posit16` `add-log-exp`
3×	`pow-unpow` `*-commutative`
2×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`pow-to-exp` `unpow-prod-down` `div-inv` `unpow1/2` `sqr-pow`

Counts

4 → 133

Calls

4 calls:

15.0ms	(* n (/ l Om))
126.0ms	(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
768.0ms	(* (* (* U 2) n) (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U)) ( (* (/ l Om) 2) l))))
313.0ms	(pow (* (* (* U 2) n) (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U)) ( (* (/ l Om) 2) l)))) 1/2)

series1.2s

Counts

4 → 12

Calls

4 calls:

30.0ms	(* n (/ l Om))
120.0ms	(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
509.0ms	(* (* (* U 2) n) (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U)) ( (* (/ l Om) 2) l))))
512.0ms	(pow (* (* (* U 2) n) (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U)) ( (* (/ l Om) 2) l)))) 1/2)

simplify885.0ms

Counts

145 → 145

Iterations

Iter	Nodes
done	2000
1	996
0	325

prune935.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 17.0b

regimes1.1s

Accuracy

12.5% (10.0b remaining)

Error of 28.0b against oracle of 18.0b and baseline of 29.4b

bsearch826.0ms

Steps

Iters	Range		Point
7	8.375985039493173e+95	1.5022059380756963e+97	2.539192710887033e+96
9	1.327246488227529e-157	1.2812697067031588e-149	6.552094729632033e-157
10	7.769412597450992e-263	5.455613985372002e-251	4.583682591988209e-251

simplify28.0ms

Iterations

Iter	Nodes
done	65
1	65
0	45

end0.0ms

sample8.9s

Algorithm

intervals

Results

5.1s	14841×	body	80	nan
2.4s	9156×	body	80	valid