Details

sample145.0ms

Algorithm

intervals

Results

51.0ms	298×	body	80	valid
45.0ms	419×	body	80	nan

simplify3.1s

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.6b

localize46.0ms

Local error

Found 4 expressions with local error:

5.8b	(* n (pow (/ l Om) 2.0))
6.6b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.8b	(* 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)))

rewrite289.0ms

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:

38.0ms	(* n (pow (/ l Om) 2.0))
50.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
108.0ms	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0))
88.0ms	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0)))

series11.1s

Counts

4 → 12

Calls

4 calls:

208.0ms	(* 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))
8.6s	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0)))

simplify2.5s

Counts

141 → 141

Iterations

Iter	Nodes
done	5005
2	3241
1	968
0	353

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 18.4b

localize66.0ms

Local error

Found 4 expressions with local error:

6.6b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
6.6b	(* n (pow (/ l Om) (/ 2.0 2)))
7.8b	(* 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)))

rewrite379.0ms

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:

166.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
32.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
85.0ms	(* 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))
88.0ms	(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)))

series12.0s

Counts

4 → 12

Calls

4 calls:

499.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
263.0ms	(* 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))
9.5s	(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)))

simplify3.4s

Counts

158 → 158

Iterations

Iter	Nodes
done	5002
2	3696
1	1066
0	389

prune1.6s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 17.4b

localize90.0ms

Local error

Found 4 expressions with local error:

6.6b	(* n (pow (/ l Om) (/ 2.0 2)))
6.8b	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
7.8b	(* 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)))

rewrite304.0ms

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:

42.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
59.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
112.0ms	(* 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))
84.0ms	(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)))

series11.4s

Counts

4 → 12

Calls

4 calls:

243.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
493.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
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))
9.0s	(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)))

simplify2.8s

Counts

158 → 158

Iterations

Iter	Nodes
done	5025
2	3403
1	1001
0	398

prune1.6s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 16.9b

localize144.0ms

Local error

Found 4 expressions with local error:

7.8b	(* 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))
7.8b	(* 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)))
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)))

rewrite395.0ms

Algorithm

rewrite-expression-head

Rules

42×	`pow1`
24×	`pow-prod-down`
22×	`add-cbrt-cube` `add-exp-log`
16×	`associate-*r/`
12×	`prod-exp` `cbrt-unprod`
8×	`sqrt-pow1` `associate-*l/`
6×	`add-sqr-sqrt` `-un-lft-identity` `associate-l*` `add-cube-cbrt`
4×	`expm1-log1p-u` `flip3--` `sqrt-div` `log1p-expm1-u` `flip--` `add-log-exp`
2×	`pow1/2` `associate-r` `*-commutative` `sqrt-prod`

Counts

4 → 84

Calls

4 calls:

104.0ms	(* 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))
101.0ms	(* 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))
102.0ms	(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)))
84.0ms	(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)))

series22.0s

Counts

4 → 12

Calls

4 calls:

2.1s	(* 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))
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))
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)))
9.3s	(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)))

simplify2.8s

Counts

96 → 96

Iterations

Iter	Nodes
done	5006
2	1934
1	493
0	175

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 16.9b

regimes2.2s

Accuracy

30.1% (8.0b remaining)

Error of 27.5b against oracle of 19.5b and baseline of 30.9b

bsearch7.0ms

simplify35.0ms

Iterations

Iter	Nodes
done	76
1	76
0	55

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.4s	14935×	body	80	nan
1.4s	9147×	body	80	valid