Details

sample144.0ms

Algorithm

intervals

Results

47.0ms	481×	body	80	nan
27.0ms	298×	body	80	valid

simplify2.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (24.0ms)

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize27.0ms

Local error

Found 4 expressions with local error:

6.9b	(* n (pow (/ l Om) 2.0))
8.0b	(/ (* l l) Om)
10.6b	(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
19.2b	(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

rewrite242.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log` `add-sqr-sqrt`
23×	`pow1`
20×	`add-cbrt-cube`
18×	`-un-lft-identity` `associate-r*`
16×	`add-cube-cbrt`
15×	`unpow-prod-down`
13×	`times-frac`
12×	`pow-prod-down`
11×	`prod-exp`
8×	`associate-l` `cbrt-unprod`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-*l/` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`div-exp` `associate-/r*`
2×	`cbrt-undiv` `flip3--` `sqrt-div` `pow-exp` `*-commutative` `flip--` `div-inv` `sqr-pow`
1×	`pow-to-exp` `frac-2neg` `pow1/2` `clear-num` `sqrt-prod` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 106

Calls

4 calls:

31.0ms	(* n (pow (/ l Om) 2.0))
22.0ms	(/ (* l l) Om)
106.0ms	(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
80.0ms	(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

series3.8s

Counts

4 → 12

Calls

4 calls:

214.0ms	(* n (pow (/ l Om) 2.0))
27.0ms	(/ (* l l) Om)
1.0s	(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
2.6s	(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

simplify1.4s

Counts

118 → 118

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	251	2234
1	589	2131
2	1949	1847
done	5001	1842

prune657.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 23.4b

localize20.0ms

Local error

Found 4 expressions with local error:

6.4b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.9b	(* n (pow (/ l Om) 2.0))
10.6b	(* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
19.2b	(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

rewrite301.0ms

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:

91.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
35.0ms	(* n (pow (/ l Om) 2.0))
89.0ms	(* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
80.0ms	(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

series4.6s

Counts

4 → 12

Calls

4 calls:

538.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
197.0ms	(* n (pow (/ l Om) 2.0))
1.0s	(* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
2.9s	(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

simplify1.8s

Counts

143 → 143

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	313	3277
1	762	2989
2	2550	2595
done	5001	2566

prune767.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 21.0b

localize38.0ms

Local error

Found 4 expressions with local error:

5.4b	(fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
6.4b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
10.6b	(* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U))
19.2b	(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U)))

rewrite394.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 119

Calls

4 calls:

0.0ms	(fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
231.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
85.0ms	(* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U))
71.0ms	(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U)))

series5.0s

Counts

4 → 12

Calls

4 calls:

456.0ms	(fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
568.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.1s	(* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U))
2.8s	(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U)))

simplify2.0s

Counts

131 → 131

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	288	5065
1	729	3749
2	2724	3260
done	5000	3231

prune697.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 20.7b

localize45.0ms

Local error

Found 4 expressions with local error:

5.0b	(* n (pow (/ l Om) (/ 2.0 2)))
5.4b	(fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))
10.6b	(* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U))))) ( (* 2.0 n) U))
19.2b	(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U))))) ( (* 2.0 n) U)))

rewrite230.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
23×	`pow1`
21×	`add-exp-log`
18×	`associate-r`
16×	`*-un-lft-identity`
15×	`unpow-prod-down` `add-cbrt-cube`
14×	`add-cube-cbrt`
12×	`pow-prod-down`
10×	`times-frac` `prod-exp`
8×	`associate-l`
7×	`cbrt-unprod`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-*l/` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`flip3--` `sqrt-div` `pow-exp` `*-commutative` `flip--` `sqr-pow`
1×	`pow-to-exp` `pow1/2` `div-exp` `sqrt-prod` `fma-udef` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 93

Calls

4 calls:

39.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
1.0ms	(fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))
115.0ms	(* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U))))) ( (* 2.0 n) U))
72.0ms	(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U))))) ( (* 2.0 n) U)))

series4.6s

Counts

4 → 12

Calls

4 calls:

269.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
461.0ms	(fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))
1.1s	(* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U))))) ( (* 2.0 n) U))
2.8s	(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U))))) ( (* 2.0 n) U)))

simplify1.2s

Counts

105 → 105

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	242	3140
1	580	2953
2	1921	2274
done	5001	2249

prune698.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 20.6b

regimes786.0ms

Accuracy

17.8% (8.4b remaining)

Error of 29.5b against oracle of 21.1b and baseline of 31.4b

bsearch394.0ms

Steps

Iters	Range		Point
10	5.9142685482905006e+106	1.1318126295060305e+120	6.298121475305343e+116
10	-2.464175888512086e-85	-1.0964605146059926e-96	-7.152776844878304e-89

simplify13.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	39	100
1	51	100
done	51	100

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	14744×	body	80	nan
882.0ms	9169×	body	80	valid