Details

sample197.0ms

Algorithm

intervals

Results

82.0ms	490×	body	80	nan
31.0ms	290×	body	80	valid

simplify2.8s

Counts

1 → 1

Iterations

Useful iterations: 2 (39.0ms)

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize44.0ms

Local error

Found 4 expressions with local error:

6.9b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.3b	(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
10.7b	(/ (* l l) Om)
20.3b	(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

rewrite267.0ms

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:

61.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
90.0ms	(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
11.0ms	(/ (* l l) Om)
98.0ms	(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

series4.4s

Counts

4 → 12

Calls

4 calls:

568.0ms	(* (* 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))
34.0ms	(/ (* 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)))

simplify1.9s

Counts

127 → 127

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	281	3038
1	705	2772
2	2519	2368
done	5002	2339

prune668.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 23.2b

localize51.0ms

Local error

Found 4 expressions with local error:

6.0b	(* n (pow (/ l Om) 2.0))
6.9b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.3b	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
20.3b	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

rewrite322.0ms

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:

48.0ms	(* n (pow (/ l Om) 2.0))
65.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
128.0ms	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
73.0ms	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

series4.6s

Counts

4 → 12

Calls

4 calls:

220.0ms	(* n (pow (/ l Om) 2.0))
603.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.1s	(* (- 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)))

simplify1.8s

Counts

143 → 143

Iterations

Useful iterations: done (1.8s)

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

prune838.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 21.3b

localize27.0ms

Local error

Found 4 expressions with local error:

5.4b	(* n (pow (/ l Om) (/ 2.0 2)))
6.9b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
9.3b	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U))
20.3b	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U)))

rewrite470.0ms

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:

54.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
229.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
106.0ms	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U))
67.0ms	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U)))

series4.9s

Counts

4 → 12

Calls

4 calls:

249.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
430.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.5s	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U))
2.7s	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U)))

simplify2.0s

Counts

160 → 160

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	349	5166
1	853	3924
2	2944	3412
done	5000	3383

prune927.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 21.3b

localize49.0ms

Local error

Found 4 expressions with local error:

3.4b	(fma 2.0 (/ l (/ Om l)) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
6.9b	(* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
9.3b	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U))
20.3b	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

239×	`add-exp-log`
187×	`prod-exp`
38×	`pow-exp`
32×	`add-cbrt-cube`
25×	`pow1` `cbrt-unprod`
22×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`pow-to-exp` `div-exp`
18×	`add-cube-cbrt` `prod-diff`
13×	`pow-prod-down`
11×	`distribute-rgt-in` `distribute-lft-in`
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 → 146

Calls

4 calls:

0.0ms	(fma 2.0 (/ l (/ Om l)) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
975.0ms	(* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
71.0ms	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U))
68.0ms	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U)))

series5.1s

Counts

4 → 12

Calls

4 calls:

597.0ms	(fma 2.0 (/ l (/ Om l)) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
629.0ms	(* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.1s	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U))
2.7s	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U)))

simplify2.4s

Counts

158 → 158

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	348	7245
1	864	6619
2	3441	4235
done	5000	3666

prune615.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 21.3b

regimes773.0ms

Accuracy

15.2% (9.2b remaining)

Error of 29.3b against oracle of 20.1b and baseline of 31.0b

bsearch212.0ms

Steps

Iters	Range		Point
9	2.6088771481949757e+132	2.800602496479033e+140	3.683386903089246e+135

simplify20.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	80
1	51	80
done	51	80

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.5s	9173×	body	80	valid
2.4s	14522×	body	80	nan