Details

sample307.0ms

Algorithm

intervals

Results

108.0ms	449×	body	80	nan
38.0ms	309×	body	80	valid

simplify3.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	4135
3	665
2	154
1	49
0	21

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.4b

localize50.0ms

Local error

Found 4 expressions with local error:

5.1b	(fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0)))
5.8b	(* n (pow (/ l Om) 2.0))
12.0b	(* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0))))
17.6b	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0)))))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1`
22×	`add-sqr-sqrt`
21×	`add-exp-log`
20×	`associate-r`
15×	`unpow-prod-down` `add-cbrt-cube`
14×	`*-un-lft-identity` `add-cube-cbrt`
12×	`pow-prod-down`
10×	`times-frac` `prod-exp`
7×	`cbrt-unprod`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-l` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`fma-udef`
2×	`pow-exp` `*-commutative` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow1/2` `div-exp` `sqrt-prod` `div-inv`

Counts

4 → 89

Calls

4 calls:

0.0ms	(fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0)))
21.0ms	(* n (pow (/ l Om) 2.0))
53.0ms	(* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0))))
86.0ms	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0)))))

series8.5s

Counts

4 → 12

Calls

4 calls:

1.7s	(fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0)))
240.0ms	(* n (pow (/ l Om) 2.0))
1.8s	(* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0))))
4.8s	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0)))))

simplify1.9s

Counts

101 → 101

Iterations

Iter	Nodes
done	5000
2	2103
1	444
0	187

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 21.4b

localize76.0ms

Local error

Found 4 expressions with local error:

5.1b	(fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))
6.0b	(* n (pow (/ l Om) (/ 2.0 2)))
12.0b	(* (* (* 2.0 n) U) (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))
17.6b	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1`
22×	`add-sqr-sqrt`
21×	`add-exp-log`
20×	`associate-r`
15×	`unpow-prod-down` `add-cbrt-cube`
14×	`*-un-lft-identity` `add-cube-cbrt`
12×	`pow-prod-down`
10×	`times-frac` `prod-exp`
7×	`cbrt-unprod`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-l` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`fma-udef`
2×	`pow-exp` `*-commutative` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow1/2` `div-exp` `sqrt-prod` `div-inv`

Counts

4 → 89

Calls

4 calls:

1.0ms	(fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))
39.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
63.0ms	(* (* (* 2.0 n) U) (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))
46.0ms	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))))

series8.8s

Counts

4 → 12

Calls

4 calls:

1.8s	(fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))
228.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
2.2s	(* (* (* 2.0 n) U) (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))
4.6s	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))))

simplify2.4s

Counts

101 → 101

Iterations

Iter	Nodes
done	5002
2	2210
1	465
0	194

prune958.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 20.3b

localize69.0ms

Local error

Found 4 expressions with local error:

5.5b	(* U (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))
6.0b	(* n (pow (/ l Om) (/ 2.0 2)))
7.4b	(* (* 2.0 n) (* U (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))))
17.6b	(sqrt (* (* 2.0 n) (* U (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

31×	`pow1`
26×	`add-exp-log`
25×	`add-sqr-sqrt`
21×	`associate-r`
20×	`add-cbrt-cube`
17×	`pow-prod-down`
15×	`unpow-prod-down` `*-un-lft-identity` `add-cube-cbrt`
13×	`prod-exp`
10×	`times-frac` `cbrt-unprod`
7×	`associate-l`
6×	`fma-udef`
5×	`distribute-rgt-in` `distribute-lft-in` `sqrt-pow1` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-exp` `sqr-pow`
1×	`pow-to-exp` `pow1/2` `div-exp` `sqrt-prod` `div-inv`

Counts

4 → 105

Calls

4 calls:

9.0ms	(* U (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))
20.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
33.0ms	(* (* 2.0 n) (* U (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))))
22.0ms	(sqrt (* (* 2.0 n) (* U (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))))

series8.6s

Counts

4 → 12

Calls

4 calls:

1.6s	(* U (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))
218.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
1.9s	(* (* 2.0 n) (* U (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))))
4.9s	(sqrt (* (* 2.0 n) (* U (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))))

simplify2.6s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
2	2128
1	524
0	213

prune1.3s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 18.1b

localize84.0ms

Local error

Found 4 expressions with local error:

5.1b	(fma (- U* U) (* (* (pow (/ l Om) (/ 2.0 2)) n) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))
6.0b	(* (pow (/ l Om) (/ 2.0 2)) n)
12.0b	(* (* (* 2.0 n) U) (fma (- U* U) (* (* (pow (/ l Om) (/ 2.0 2)) n) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))
17.6b	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* (* (pow (/ l Om) (/ 2.0 2)) n) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1`
22×	`add-sqr-sqrt`
21×	`add-exp-log`
18×	`associate-l`
15×	`unpow-prod-down` `add-cbrt-cube`
14×	`*-un-lft-identity` `add-cube-cbrt`
12×	`pow-prod-down`
10×	`times-frac` `prod-exp`
7×	`cbrt-unprod`
6×	`associate-r`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`fma-udef`
2×	`pow-exp` `*-commutative` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow1/2` `div-exp` `sqrt-prod` `div-inv`

Counts

4 → 89

Calls

4 calls:

0.0ms	(fma (- U* U) (* (* (pow (/ l Om) (/ 2.0 2)) n) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))
21.0ms	(* (pow (/ l Om) (/ 2.0 2)) n)
51.0ms	(* (* (* 2.0 n) U) (fma (- U* U) (* (* (pow (/ l Om) (/ 2.0 2)) n) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))
75.0ms	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* (* (pow (/ l Om) (/ 2.0 2)) n) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))))

series7.1s

Counts

4 → 12

Calls

4 calls:

954.0ms	(fma (- U* U) (* (* (pow (/ l Om) (/ 2.0 2)) n) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))
259.0ms	(* (pow (/ l Om) (/ 2.0 2)) n)
1.4s	(* (* (* 2.0 n) U) (fma (- U* U) (* (* (pow (/ l Om) (/ 2.0 2)) n) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))
4.5s	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* (* (pow (/ l Om) (/ 2.0 2)) n) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))))

simplify1.6s

Counts

101 → 101

Iterations

Iter	Nodes
done	5001
2	2291
1	470
0	198

prune860.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 18.1b

regimes859.0ms

Accuracy

15.4% (10.7b remaining)

Error of 29.2b against oracle of 18.5b and baseline of 31.1b

bsearch308.0ms

Steps

Iters	Range		Point
10	4.481138192872432e-180	2.9877721031543767e-170	8.735191805518111e-172
9	-2.2840861367093013e+101	-3.4248176785688746e+96	-2.4843602301315434e+99

simplify14.0ms

Iterations

Iter	Nodes
done	51
3	51
2	49
1	46
0	34

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.9s	14813×	body	80	nan
1.3s	9174×	body	80	valid