Details

sample164.0ms

Algorithm

intervals

Results

72.0ms	503×	body	80	nan
27.0ms	288×	body	80	valid

simplify3.1s

Counts

1 → 1

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	21	28
1	49	28
2	154	27
3	664	27
4	4143	27
done	5000	27

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.4b

localize48.0ms

Local error

Found 4 expressions with local error:

6.9b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.3b	(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
11.1b	(/ (* l l) Om)
22.5b	(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

rewrite325.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
25×	`pow1`
24×	`add-sqr-sqrt` `*-un-lft-identity`
23×	`add-cbrt-cube`
20×	`add-cube-cbrt`
18×	`prod-diff`
16×	`prod-exp`
13×	`pow-prod-down`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`cbrt-unprod`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `times-frac` `div-exp` `associate-/r*` `flip--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `associate-r/` `pow-exp` `-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`pow-to-exp` `frac-2neg` `pow1/2` `clear-num` `sqrt-prod` `div-inv` `associate-/l*`

Counts

4 → 115

Calls

4 calls:

90.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
116.0ms	(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
18.0ms	(/ (* l l) Om)
93.0ms	(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

series4.2s

Counts

4 → 12

Calls

4 calls:

491.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
952.0ms	(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
25.0ms	(/ (* l l) Om)
2.7s	(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

simplify568.0ms

Counts

127 → 127

Iterations

Useful iterations: done (563.0ms)

Iter	Nodes	Cost
0	281	3038
1	799	2788
done	5000	2386

prune609.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 24.1b

localize39.0ms

Local error

Found 4 expressions with local error:

4.7b	(* n (pow (/ l Om) 2.0))
6.9b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.3b	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
22.5b	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

rewrite321.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
35×	`add-exp-log`
31×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`pow1`
23×	`associate-r`
20×	`add-cbrt-cube`
19×	`prod-exp`
18×	`prod-diff`
15×	`unpow-prod-down`
13×	`pow-prod-down`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`times-frac` `cbrt-unprod`
9×	`associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-*l/` `pow-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`flip3--` `*-commutative` `flip--`
2×	`pow-to-exp` `sub-neg` `sqrt-div` `associate-*r/` `div-exp` `distribute-lft-out--` `difference-of-squares` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv`

Counts

4 → 131

Calls

4 calls:

42.0ms	(* n (pow (/ l Om) 2.0))
78.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
104.0ms	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
89.0ms	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

series4.3s

Counts

4 → 12

Calls

4 calls:

185.0ms	(* n (pow (/ l Om) 2.0))
577.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.0s	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
2.5s	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

simplify3.0s

Counts

143 → 143

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	314	3277
1	841	3008
2	4509	2611
done	5000	2607

prune758.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 23.1b

localize42.0ms

Local error

Found 4 expressions with local error:

3.5b	(fma 2.0 (/ l (/ Om l)) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) 2.0))) (- U U*)))
6.9b	(* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) 2.0))) (- U U*))
8.3b	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) 2.0))) (- U U)))) ( (* 2.0 n) U))
22.5b	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) 2.0))) (- U U)))) ( (* 2.0 n) U)))

rewrite395.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-exp-log`
40×	`prod-exp`
32×	`pow1`
25×	`add-cbrt-cube`
22×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`cbrt-unprod`
18×	`add-cube-cbrt` `prod-diff` `pow-prod-down`
11×	`distribute-rgt-in` `distribute-lft-in`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-*l/` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `flip--`
2×	`pow-to-exp` `sub-neg` `sqrt-div` `associate-r/` `div-exp` `-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`pow1/2` `sqrt-prod` `fma-udef`

Counts

4 → 113

Calls

4 calls:

0.0ms	(fma 2.0 (/ l (/ Om l)) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) 2.0))) (- U U*)))
205.0ms	(* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) 2.0))) (- U U*))
101.0ms	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) 2.0))) (- U U)))) ( (* 2.0 n) U))
83.0ms	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) 2.0))) (- U U)))) ( (* 2.0 n) U)))

series5.1s

Counts

4 → 12

Calls

4 calls:

538.0ms	(fma 2.0 (/ l (/ Om l)) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) 2.0))) (- U U*)))
566.0ms	(* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) 2.0))) (- U U*))
1.1s	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) 2.0))) (- U U)))) ( (* 2.0 n) U))
2.9s	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) 2.0))) (- U U)))) ( (* 2.0 n) U)))

simplify3.3s

Counts

125 → 125

Iterations

Useful iterations: 2 (951.0ms)

Iter	Nodes	Cost
0	291	4466
1	836	4126
2	4946	3046
done	5000	3046

prune821.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 22.9b

localize76.0ms

Local error

Found 4 expressions with local error:

8.3b	(* (- t (fma 2.0 (/ l (/ Om l)) (+ (* (pow (/ l Om) 2.0) (* n (- U U))) ( n (* (pow (/ l Om) 2.0) (+ U* (- U))))))) ( (* 2.0 n) U))
8.9b	(* (pow (/ l Om) 2.0) (+ U* (- U*)))
11.0b	(* (pow (/ l Om) 2.0) (* n (- U U*)))
22.5b	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (+ (* (pow (/ l Om) 2.0) (* n (- U U))) ( n (* (pow (/ l Om) 2.0) (+ U* (- U))))))) ( (* 2.0 n) U)))

rewrite358.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
50×	`add-cube-cbrt`
45×	`distribute-rgt-in` `distribute-lft-in`
41×	`add-exp-log`
39×	`associate-l`
36×	`prod-diff`
28×	`unpow-prod-down`
23×	`pow1`
22×	`prod-exp`
20×	`add-cbrt-cube`
19×	`times-frac`
15×	`associate-r`
12×	`pow-prod-down`
10×	`cbrt-unprod`
6×	`associate-*r/` `pow-exp`
4×	`distribute-lft-neg-in` `expm1-log1p-u` `sub-neg` `distribute-rgt-out` `sqrt-pow1` `associate-*l/` `log1p-expm1-u` `distribute-lft-out` `add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `flip3--` `distribute-rgt-neg-in` `div-exp` `*-commutative` `flip--` `sqr-pow`
2×	`neg-mul-1` `sqrt-div` `distribute-rgt1-in` `div-inv`
1×	`flip3-+` `pow1/2` `sqrt-prod` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 181

Calls

4 calls:

88.0ms	(* (- t (fma 2.0 (/ l (/ Om l)) (+ (* (pow (/ l Om) 2.0) (* n (- U U))) ( n (* (pow (/ l Om) 2.0) (+ U* (- U))))))) ( (* 2.0 n) U))
88.0ms	(* (pow (/ l Om) 2.0) (+ U* (- U*)))
93.0ms	(* (pow (/ l Om) 2.0) (* n (- U U*)))
70.0ms	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (+ (* (pow (/ l Om) 2.0) (* n (- U U))) ( n (* (pow (/ l Om) 2.0) (+ U* (- U))))))) ( (* 2.0 n) U)))

series4.9s

Counts

4 → 12

Calls

4 calls:

1.4s	(* (- t (fma 2.0 (/ l (/ Om l)) (+ (* (pow (/ l Om) 2.0) (* n (- U U))) ( n (* (pow (/ l Om) 2.0) (+ U* (- U))))))) ( (* 2.0 n) U))
5.0ms	(* (pow (/ l Om) 2.0) (+ U* (- U*)))
689.0ms	(* (pow (/ l Om) 2.0) (* n (- U U*)))
2.8s	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (+ (* (pow (/ l Om) 2.0) (* n (- U U))) ( n (* (pow (/ l Om) 2.0) (+ U* (- U))))))) ( (* 2.0 n) U)))

simplify906.0ms

Counts

193 → 193

Iterations

Useful iterations: done (895.0ms)

Iter	Nodes	Cost
0	399	5204
1	1195	4596
done	5000	3226

prune1.4s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 22.6b

regimes1.0s

Accuracy

15.1% (9.0b remaining)

Error of 30.6b against oracle of 21.6b and baseline of 32.2b

bsearch230.0ms

Steps

Iters	Range		Point
8	8.888398750328554e-40	5.106000304326758e-36	1.0455162025778439e-37

simplify12.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	39	82
1	52	82
done	52	82

end0.0ms

sample7.0s

Algorithm

intervals

Results

2.5s	14686×	body	80	nan
2.5s	9214×	body	80	valid