Details

sample181.0ms

Algorithm

intervals

Results

57.0ms	453×	body	80	nan
37.0ms	291×	body	80	valid

simplify3.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
4	2913
3	614
2	150
1	49
0	21

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.7b

localize58.0ms

Local error

Found 4 expressions with local error:

5.4b	(* n (pow (/ l Om) 2.0))
6.6b	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0))
7.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
20.4b	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0)))

rewrite285.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
35×	`add-exp-log`
29×	`*-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` `associate-*r/` `cbrt-unprod`
7×	`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` `div-exp` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 129

Calls

4 calls:

20.0ms	(* n (pow (/ l Om) 2.0))
114.0ms	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0))
46.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
101.0ms	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0)))

series10.7s

Counts

4 → 12

Calls

4 calls:

211.0ms	(* n (pow (/ l Om) 2.0))
1.6s	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0))
488.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.4s	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0)))

simplify2.2s

Counts

141 → 141

Iterations

Iter	Nodes
done	5009
2	3230
1	967
0	353

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 22.7b

localize81.0ms

Local error

Found 4 expressions with local error:

5.2b	(* n (pow (/ l Om) (/ 2.0 2)))
6.6b	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))
7.7b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
20.4b	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0)))

rewrite417.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
67×	`prod-exp`
37×	`add-sqr-sqrt`
29×	`*-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` `associate-*r/`
7×	`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` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 146

Calls

4 calls:

25.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
108.0ms	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))
176.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
99.0ms	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0)))

series11.5s

Counts

4 → 12

Calls

4 calls:

257.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
1.7s	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))
536.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
8.9s	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0)))

simplify3.5s

Counts

158 → 158

Iterations

Iter	Nodes
done	5018
2	3717
1	1070
0	389

prune1.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 22.2b

localize74.0ms

Local error

Found 4 expressions with local error:

5.2b	(* n (pow (/ l Om) (/ 2.0 2)))
6.6b	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))) 2.0))
7.6b	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
20.4b	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))) 2.0)))

rewrite291.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
35×	`add-cube-cbrt`
30×	`unpow-prod-down`
29×	`add-exp-log`
23×	`pow1` `associate-r` `associate-l`
20×	`times-frac`
18×	`prod-diff`
17×	`add-cbrt-cube`
14×	`prod-exp`
12×	`pow-prod-down`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`associate-*r/`
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` `div-exp` `div-inv`
1×	`pow1/2` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 146

Calls

4 calls:

37.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
108.0ms	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))) 2.0))
48.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
92.0ms	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))) 2.0)))

series12.7s

Counts

4 → 12

Calls

4 calls:

247.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
1.8s	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))) 2.0))
557.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
10.0s	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))) 2.0)))

simplify3.0s

Counts

158 → 158

Iterations

Iter	Nodes
done	5003
2	3346
1	1001
0	398

prune1.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 22.0b

localize136.0ms

Local error

Found 4 expressions with local error:

15.8b	(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
15.8b	(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
15.8b	(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
20.4b	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* (cbrt (* n (pow (/ l Om) (/ 2.0 2)))) (cbrt (* n (pow (/ l Om) (/ 2.0 2))))) (cbrt (* n (pow (/ l Om) (/ 2.0 2))))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))) 2.0)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 50

Calls

4 calls:

13.0ms	(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
14.0ms	(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
13.0ms	(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
107.0ms	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* (cbrt (* n (pow (/ l Om) (/ 2.0 2)))) (cbrt (* n (pow (/ l Om) (/ 2.0 2))))) (cbrt (* n (pow (/ l Om) (/ 2.0 2))))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))) 2.0)))

series10.4s

Counts

4 → 12

Calls

4 calls:

324.0ms	(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
316.0ms	(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
292.0ms	(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
9.5s	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* (cbrt (* n (pow (/ l Om) (/ 2.0 2)))) (cbrt (* n (pow (/ l Om) (/ 2.0 2))))) (cbrt (* n (pow (/ l Om) (/ 2.0 2))))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))) 2.0)))

simplify2.1s

Counts

62 → 62

Iterations

Iter	Nodes
done	5000
2	1189
1	352
0	140

prune781.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 22.0b

regimes2.2s

Accuracy

34.9% (6.7b remaining)

Error of 28.1b against oracle of 21.3b and baseline of 31.7b

bsearch7.0ms

simplify26.0ms

Iterations

Iter	Nodes
done	79
1	79
0	56

end0.0ms

sample6.0s

Algorithm

intervals

Results

3.3s	15070×	body	80	nan
1.4s	9237×	body	80	valid