Details

sample222.0ms

Algorithm

intervals

Results

74.0ms	500×	body	80	nan
63.0ms	290×	body	80	valid

simplify2.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	21	28
1	49	28
2	154	27
3	642	27
4	3239	27
done	5000	27

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize26.0ms

Local error

Found 4 expressions with local error:

6.6b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.6b	(/ (* l l) Om)
9.8b	(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
19.3b	(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

rewrite256.0ms

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:

72.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
16.0ms	(/ (* l l) Om)
99.0ms	(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
62.0ms	(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

series4.1s

Counts

4 → 12

Calls

4 calls:

394.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
20.0ms	(/ (* l l) Om)
969.0ms	(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
2.8s	(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

simplify1.7s

Counts

127 → 127

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	281	3038
1	706	2772
2	2538	2368
done	5002	2339

prune556.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 21.7b

localize24.0ms

Local error

Found 4 expressions with local error:

5.7b	(* n (pow (/ l Om) 2.0))
6.6b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.8b	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
19.3b	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

rewrite267.0ms

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:

41.0ms	(* n (pow (/ l Om) 2.0))
60.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
82.0ms	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
76.0ms	(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:

188.0ms	(* n (pow (/ l Om) 2.0))
465.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
939.0ms	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
2.7s	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

simplify2.0s

Counts

143 → 143

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	314	3277
1	762	2989
2	2562	2595
done	5002	2566

prune822.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 20.7b

localize50.0ms

Local error

Found 4 expressions with local error:

5.0b	(* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( 2.0 n)) U)
5.7b	(* n (pow (/ l Om) 2.0))
6.6b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
19.3b	(sqrt (* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( 2.0 n)) U))

rewrite290.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
35×	`add-exp-log`
29×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`pow1` `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`
8×	`associate-*l/`
5×	`associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `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` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 129

Calls

4 calls:

70.0ms	(* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( 2.0 n)) U)
43.0ms	(* n (pow (/ l Om) 2.0))
74.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
97.0ms	(sqrt (* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( 2.0 n)) U))

series4.7s

Counts

4 → 12

Calls

4 calls:

1.2s	(* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( 2.0 n)) U)
213.0ms	(* n (pow (/ l Om) 2.0))
535.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
2.8s	(sqrt (* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( 2.0 n)) U))

simplify2.0s

Counts

141 → 141

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	311	3207
1	763	2915
2	2568	2523
done	5000	2494

prune723.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 16.6b

localize71.0ms

Local error

Found 4 expressions with local error:

19.3b	(sqrt (* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* (cbrt (* n (pow (/ l Om) 2.0))) (cbrt (* n (pow (/ l Om) 2.0)))) (cbrt (* n (pow (/ l Om) 2.0)))) (- U U)))) ( 2.0 n)) U))
28.8b	(cbrt (* n (pow (/ l Om) 2.0)))
28.8b	(cbrt (* n (pow (/ l Om) 2.0)))
28.8b	(cbrt (* n (pow (/ l Om) 2.0)))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1`
6×	`pow-prod-down`
4×	`add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `-un-lft-identity` `sqrt-pow1` `associate-l/` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
2×	`sqrt-div`
1×	`flip3--` `pow1/2` `sqrt-prod` `flip--`

Counts

4 → 50

Calls

4 calls:

117.0ms	(sqrt (* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* (cbrt (* n (pow (/ l Om) 2.0))) (cbrt (* n (pow (/ l Om) 2.0)))) (cbrt (* n (pow (/ l Om) 2.0)))) (- U U)))) ( 2.0 n)) U))
29.0ms	(cbrt (* n (pow (/ l Om) 2.0)))
15.0ms	(cbrt (* n (pow (/ l Om) 2.0)))
15.0ms	(cbrt (* n (pow (/ l Om) 2.0)))

series3.8s

Counts

4 → 12

Calls

4 calls:

2.9s	(sqrt (* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* (cbrt (* n (pow (/ l Om) 2.0))) (cbrt (* n (pow (/ l Om) 2.0)))) (cbrt (* n (pow (/ l Om) 2.0)))) (- U U)))) ( 2.0 n)) U))
275.0ms	(cbrt (* n (pow (/ l Om) 2.0)))
324.0ms	(cbrt (* n (pow (/ l Om) 2.0)))
315.0ms	(cbrt (* n (pow (/ l Om) 2.0)))

simplify1.2s

Counts

62 → 62

Iterations

Useful iterations: 3 (366.0ms)

Iter	Nodes	Cost
0	87	1412
1	179	1305
2	464	941
3	1881	878
done	5000	878

prune599.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 16.6b

regimes839.0ms

Accuracy

26.8% (9.7b remaining)

Error of 27.9b against oracle of 18.3b and baseline of 31.5b

bsearch184.0ms

Steps

Iters	Range		Point
9	-4.742058940934219e-307	2.4877524142008153e-302	9.7257945165455e-311

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	78
1	44	78
done	44	78

end0.0ms

sample7.2s

Algorithm

intervals

Results

3.4s	15066×	body	80	nan
1.8s	9216×	body	80	valid