Details

sample226.0ms

Algorithm

intervals

Results

39.0ms	403×	body	80	nan
27.0ms	295×	body	80	valid

simplify3.2s

Counts

1 → 1

Iterations

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

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.7b

localize70.0ms

Local error

Found 4 expressions with local error:

3.8b	(fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0)))
6.7b	(* n (pow (/ l Om) 2.0))
11.7b	(* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0))))
17.7b	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0)))))

rewrite160.0ms

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)) (- t (* (* (/ l Om) l) 2.0)))
40.0ms	(* n (pow (/ l Om) 2.0))
51.0ms	(* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0))))
62.0ms	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0)))))

series8.7s

Counts

4 → 12

Calls

4 calls:

1.7s	(fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0)))
232.0ms	(* 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))))
4.9s	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0)))))

simplify2.5s

Counts

101 → 101

Iterations

Iter	Nodes
done	5000
2	2103
1	444
0	187

prune874.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 20.1b

localize40.0ms

Local error

Found 4 expressions with local error:

3.8b	(fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))
4.0b	(* n (pow (/ l Om) (/ 2.0 2)))
11.7b	(* (* (* 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))))
17.7b	(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)))))

rewrite133.0ms

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 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))
26.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
61.0ms	(* (* (* 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))))
43.0ms	(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)))))

series7.9s

Counts

4 → 12

Calls

4 calls:

1.6s	(fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))
237.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
1.7s	(* (* (* 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))))
4.3s	(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)))))

simplify2.3s

Counts

101 → 101

Iterations

Iter	Nodes
done	5002
2	2210
1	465
0	194

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 19.8b

localize56.0ms

Local error

Found 4 expressions with local error:

4.0b	(* n (pow (/ l Om) (/ 2.0 2)))
5.2b	(* (* 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)))))
6.2b	(* U (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))
17.7b	(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))))))

rewrite114.0ms

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:

20.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
38.0ms	(* (* 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)))))
11.0ms	(* U (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))
41.0ms	(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))))))

series8.5s

Counts

4 → 12

Calls

4 calls:

290.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
1.8s	(* (* 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)))))
1.7s	(* U (fma (- U* U) (* (* 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) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))))

simplify2.4s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
2	2136
1	523
0	213

prune1.2s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 16.9b

localize137.0ms

Local error

Found 4 expressions with local error:

6.2b	(* U (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))
17.7b	(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))))))
17.7b	(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))))))
17.7b	(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))))))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

45×	`pow1`
25×	`pow-prod-down`
15×	`sqrt-pow1`
8×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2` `associate-r` `associate-l` `sqrt-prod`
2×	`fma-udef`
1×	`distribute-rgt-in` `distribute-lft-in` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 70

Calls

4 calls:

11.0ms	(* U (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))
36.0ms	(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))))))
36.0ms	(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))))))
20.0ms	(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))))))

series12.9s

Counts

4 → 12

Calls

4 calls:

1.1s	(* U (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))
3.5s	(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))))))
3.6s	(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))))))
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))))))

simplify1.8s

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
3	3436
2	568
1	156
0	74

prune480.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 16.9b

regimes892.0ms

Accuracy

27% (8.8b remaining)

Error of 27.2b against oracle of 18.3b and baseline of 30.4b

bsearch322.0ms

Steps

Iters	Range	Point
8	1.7912388976447322e-298	1.818133398613607e-295	1.8098734707949505e-298
8	-3.2305594868740995e-308	4.335369908492995e-306	1.3011407911573477e-306
7	-3.54818498077512e-278	-1.596422251113438e-279	-1.6117331823129693e-279

Iters

Range

Point

1.7912388976447322e-298

1.818133398613607e-295

1.8098734707949505e-298

-3.2305594868740995e-308

4.335369908492995e-306

1.3011407911573477e-306

-3.54818498077512e-278

-1.596422251113438e-279

-1.6117331823129693e-279

simplify17.0ms

Iterations

Iter	Nodes
done	69
1	69
0	53

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.7s	14786×	body	80	nan
1.3s	9202×	body	80	valid