Details

sample289.0ms

Algorithm

intervals

Results

92.0ms	475×	body	80	nan
36.0ms	298×	body	80	valid

simplify3.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (76.0ms)

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: 34.9b

localize80.0ms

Local error

Found 4 expressions with local error:

7.8b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.0b	(/ (* l l) Om)
10.3b	(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
18.7b	(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

rewrite253.0ms

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:

78.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
21.0ms	(/ (* l l) Om)
80.0ms	(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
67.0ms	(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

series4.7s

Counts

4 → 12

Calls

4 calls:

593.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
20.0ms	(/ (* l l) Om)
1.2s	(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
3.0s	(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

simplify573.0ms

Counts

127 → 127

Iterations

Useful iterations: done (564.0ms)

Iter	Nodes	Cost
0	281	3038
1	798	2788
done	5000	2386

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 22.7b

localize40.0ms

Local error

Found 4 expressions with local error:

6.0b	(* n (pow (/ l Om) 2.0))
7.8b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.3b	(* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
18.7b	(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

rewrite287.0ms

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:

31.0ms	(* n (pow (/ l Om) 2.0))
70.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
98.0ms	(* (- 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)))

series4.7s

Counts

4 → 12

Calls

4 calls:

199.0ms	(* n (pow (/ l Om) 2.0))
546.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.1s	(* (- 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)))

simplify3.0s

Counts

143 → 143

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	313	3277
1	839	3008
2	4515	2607
done	5000	2603

prune969.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 21.8b

localize71.0ms

Local error

Found 4 expressions with local error:

4.8b	(* n (pow (/ l Om) (/ 2.0 2)))
7.8b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
10.3b	(* (- 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))
18.7b	(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)))

rewrite454.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 148

Calls

4 calls:

35.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
219.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
100.0ms	(* (- 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))
90.0ms	(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)))

series4.7s

Counts

4 → 12

Calls

4 calls:

279.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
574.0ms	(* (* (* 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)))

simplify637.0ms

Counts

160 → 160

Iterations

Useful iterations: done (628.0ms)

Iter	Nodes	Cost
0	348	5166
1	947	4089
done	5000	3432

prune1.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 21.5b

localize37.0ms

Local error

Found 4 expressions with local error:

4.8b	(* n (pow (/ l Om) (/ 2.0 2)))
5.0b	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
10.3b	(* (- 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))
18.7b	(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)))

rewrite238.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 148

Calls

4 calls:

29.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
58.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
87.0ms	(* (- 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))
57.0ms	(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:

275.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
472.0ms	(* (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)))

simplify2.8s

Counts

160 → 160

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	356	4184
1	868	3881
2	4105	3396
done	5000	3391

prune1.3s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 20.8b

regimes1.0s

Accuracy

13.4% (8.4b remaining)

Error of 29.7b against oracle of 21.3b and baseline of 31.0b

bsearch471.0ms

Steps

Iters	Range		Point
10	3.162679020012342e-117	2.9274069048778817e-107	9.344552933751734e-110
9	-1.5257359659462448e+74	-9.93160793826635e+68	-3.754223553154647e+71

simplify12.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	34	120
1	44	120
done	44	120

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.0s	14815×	body	80	nan
1.8s	9208×	body	80	valid