Details

sample297.0ms

Algorithm

intervals

Results

96.0ms	503×	body	80	nan
36.0ms	279×	body	80	valid

simplify3.1s

Counts

1 → 1

Iterations

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

prune43.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.5b

localize47.0ms

Local error

Found 4 expressions with local error:

3.2b	(fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0)))
7.0b	(* n (pow (/ l Om) 2.0))
10.3b	(* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0))))
19.2b	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0)))))

rewrite208.0ms

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)))
39.0ms	(* n (pow (/ l Om) 2.0))
78.0ms	(* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0))))
87.0ms	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0)))))

series8.9s

Counts

4 → 12

Calls

4 calls:

1.9s	(fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0)))
249.0ms	(* n (pow (/ l Om) 2.0))
1.9s	(* (* (* 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)))))

simplify2.1s

Counts

101 → 101

Iterations

Iter	Nodes
done	5000
2	2103
1	444
0	187

prune1.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 21.4b

localize65.0ms

Local error

Found 4 expressions with local error:

3.2b	(fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))
3.7b	(* n (pow (/ l Om) (/ 2.0 2)))
10.3b	(* (* (* 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))))
19.2b	(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)))))

rewrite147.0ms

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)))
40.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
58.0ms	(* (* (* 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))))
42.0ms	(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)))))

series9.3s

Counts

4 → 12

Calls

4 calls:

1.7s	(fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))
262.0ms	(* 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))))
5.1s	(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)))))

simplify2.1s

Counts

101 → 101

Iterations

Iter	Nodes
done	5002
2	2210
1	465
0	194

prune971.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 20.2b

localize110.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2))))
3.2b	(fma (- U* U) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))
10.3b	(* (* (* 2.0 n) U) (fma (- U* U) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))
19.2b	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-exp-log`
29×	`prod-exp`
28×	`pow1`
19×	`add-cbrt-cube`
15×	`pow-prod-down`
14×	`cbrt-unprod`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-r` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef`
2×	`pow-to-exp` `div-exp` `associate-l` `*-commutative`
1×	`distribute-rgt-in` `distribute-lft-in` `pow1/2` `sqrt-prod`

Counts

4 → 78

Calls

4 calls:

43.0ms	(* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2))))
0.0ms	(fma (- U* U) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))
47.0ms	(* (* (* 2.0 n) U) (fma (- U* U) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))
66.0ms	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))))

series8.5s

Counts

4 → 12

Calls

4 calls:

245.0ms	(* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2))))
1.6s	(fma (- U* U) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))
1.8s	(* (* (* 2.0 n) U) (fma (- U* U) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))
4.8s	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))))

simplify1.8s

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
2	2063
1	415
0	158

prune716.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 20.2b

localize56.0ms

Local error

Found 4 expressions with local error:

3.7b	(* n (pow (/ l Om) (/ 2.0 2)))
4.5b	(* U (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))
7.1b	(* (* 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)))))
19.2b	(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))))))

rewrite78.0ms

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:

19.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
5.0ms	(* U (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))
26.0ms	(* (* 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)))))
25.0ms	(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))))))

series7.4s

Counts

4 → 12

Calls

4 calls:

182.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
1.4s	(* U (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))
1.6s	(* (* 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)))))
4.2s	(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))))))

simplify1.5s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
2	2141
1	522
0	213

prune667.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 17.4b

regimes892.0ms

Accuracy

21.2% (9.8b remaining)

Error of 28.4b against oracle of 18.6b and baseline of 31.0b

bsearch483.0ms

Steps

Iters	Range		Point
6	7.580377203180739e-276	9.871947728405373e-275	7.786798218553426e-276
8	-2.1805502857176623e-226	-2.8951376596890975e-229	-2.7761842636164956e-228

simplify10.0ms

Iterations

Iter	Nodes
done	55
1	55
0	42

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.3s	14889×	body	80	nan
1.2s	9174×	body	80	valid