Details

sample188.0ms

Algorithm

intervals

Results

81.0ms	483×	body	80	nan
32.0ms	278×	body	80	valid

simplify3.1s

Counts

1 → 1

Iterations

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

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.4b

localize47.0ms

Local error

Found 4 expressions with local error:

7.4b	(* n (pow (/ l Om) 2.0))
7.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.9b	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0))
18.3b	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0)))

rewrite217.0ms

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))
39.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
72.0ms	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0))
78.0ms	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0)))

series11.3s

Counts

4 → 12

Calls

4 calls:

242.0ms	(* n (pow (/ l Om) 2.0))
559.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.7s	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0))
8.7s	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0)))

simplify2.8s

Counts

141 → 141

Iterations

Iter	Nodes
done	5005
2	3241
1	968
0	353

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 21.3b

localize68.0ms

Local error

Found 4 expressions with local error:

3.6b	(* n (pow (/ l Om) (/ 2.0 2)))
7.7b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
7.9b	(* 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))
18.3b	(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)))

rewrite388.0ms

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:

21.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
199.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
83.0ms	(* 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))
77.0ms	(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)))

series11.9s

Counts

4 → 12

Calls

4 calls:

267.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
592.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.9s	(* 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))
9.2s	(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	5013
2	3679
1	1063
0	389

prune1.5s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 20.0b

localize92.0ms

Local error

Found 4 expressions with local error:

7.2b	(* (fma (- U) 1 ( U* 1)) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))))
7.9b	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (+ (* (pow (/ l Om) (/ 2.0 2)) (* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U))) ( (fma (- U) 1 ( U* 1)) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2)))))))) 2.0))
8.7b	(* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U*))
18.3b	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (+ (* (pow (/ l Om) (/ 2.0 2)) (* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U))) ( (fma (- U) 1 ( U* 1)) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2)))))))) 2.0)))

rewrite383.0ms

Algorithm

rewrite-expression-head

Rules

105×	`add-exp-log`
72×	`prod-exp`
27×	`pow1` `add-cbrt-cube`
21×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`pow-exp`
19×	`add-cube-cbrt`
18×	`prod-diff`
15×	`cbrt-unprod`
14×	`pow-prod-down`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`pow-to-exp` `div-exp` `associate-*r/`
7×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `*-commutative` `flip--`
2×	`sub-neg` `sqrt-div`
1×	`pow1/2` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 129

Calls

4 calls:

144.0ms	(* (fma (- U) 1 ( U* 1)) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))))
78.0ms	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (+ (* (pow (/ l Om) (/ 2.0 2)) (* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U))) ( (fma (- U) 1 ( U* 1)) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2)))))))) 2.0))
54.0ms	(* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U*))
96.0ms	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (+ (* (pow (/ l Om) (/ 2.0 2)) (* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U))) ( (fma (- U) 1 ( U* 1)) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2)))))))) 2.0)))

series18.6s

Counts

4 → 12

Calls

4 calls:

1.2s	(* (fma (- U) 1 ( U* 1)) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))))
4.9s	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (+ (* (pow (/ l Om) (/ 2.0 2)) (* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U))) ( (fma (- U) 1 ( U* 1)) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2)))))))) 2.0))
688.0ms	(* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U*))
11.8s	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (+ (* (pow (/ l Om) (/ 2.0 2)) (* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U))) ( (fma (- U) 1 ( U* 1)) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2)))))))) 2.0)))

simplify3.4s

Counts

141 → 141

Iterations

Iter	Nodes
done	5011
2	3699
1	1023
0	354

prune1.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 20.0b

localize179.0ms

Local error

Found 4 expressions with local error:

8.7b	(* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U*))
8.7b	(* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U*))
18.3b	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (+ (* (pow (/ l Om) (/ 2.0 2)) (* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U))) ( (fma (- U) 1 ( U* 1)) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2)))))))) 2.0)))
18.3b	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (+ (* (pow (/ l Om) (/ 2.0 2)) (* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U))) ( (fma (- U) 1 ( U* 1)) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2)))))))) 2.0)))

rewrite321.0ms

Algorithm

rewrite-expression-head

Rules

36×	`prod-diff`
34×	`add-sqr-sqrt` `*-un-lft-identity`
32×	`add-exp-log`
30×	`add-cube-cbrt`
28×	`pow1`
22×	`distribute-rgt-in` `distribute-lft-in`
18×	`prod-exp`
14×	`add-cbrt-cube` `pow-prod-down`
12×	`associate-*r/`
10×	`associate-r`
8×	`sqrt-pow1`
6×	`cbrt-unprod`
4×	`expm1-log1p-u` `sub-neg` `flip3--` `sqrt-div` `associate-*l/` `pow-exp` `log1p-expm1-u` `flip--` `add-log-exp`
2×	`pow-to-exp` `pow1/2` `div-exp` `associate-l` `*-commutative` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 130

Calls

4 calls:

57.0ms	(* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U*))
68.0ms	(* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U*))
87.0ms	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (+ (* (pow (/ l Om) (/ 2.0 2)) (* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U))) ( (fma (- U) 1 ( U* 1)) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2)))))))) 2.0)))
98.0ms	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (+ (* (pow (/ l Om) (/ 2.0 2)) (* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U))) ( (fma (- U) 1 ( U* 1)) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2)))))))) 2.0)))

series25.9s

Counts

4 → 12

Calls

4 calls:

583.0ms	(* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U*))
542.0ms	(* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U*))
12.0s	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (+ (* (pow (/ l Om) (/ 2.0 2)) (* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U))) ( (fma (- U) 1 ( U* 1)) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2)))))))) 2.0)))
12.8s	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (+ (* (pow (/ l Om) (/ 2.0 2)) (* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U))) ( (fma (- U) 1 ( U* 1)) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2)))))))) 2.0)))

simplify2.6s

Counts

142 → 142

Iterations

Iter	Nodes
done	5002
2	2232
1	670
0	241

prune1.9s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 20.0b

regimes1.7s

Accuracy

27% (7.3b remaining)

Error of 27.6b against oracle of 20.3b and baseline of 30.3b

bsearch8.0ms

simplify48.0ms

Iterations

Iter	Nodes
done	82
1	82
0	59

end0.0ms

sample7.1s

Algorithm

intervals

Results

2.6s	14839×	body	80	nan
2.4s	9163×	body	80	valid