Details

sample248.0ms

Algorithm

intervals

Results

89.0ms	483×	body	80	nan
28.0ms	278×	body	80	valid

simplify3.4s

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: 28.4b

localize77.0ms

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)))

rewrite336.0ms

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))
56.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
129.0ms	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0))
102.0ms	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0)))

series11.5s

Counts

4 → 12

Calls

4 calls:

186.0ms	(* n (pow (/ l Om) 2.0))
439.0ms	(* (* 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))
9.2s	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0)))

simplify2.6s

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)))

rewrite337.0ms

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:

20.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
149.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
81.0ms	(* 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))
82.0ms	(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)))

series11.7s

Counts

4 → 12

Calls

4 calls:

205.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
938.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
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))
8.8s	(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)))

simplify3.3s

Counts

158 → 158

Iterations

Iter	Nodes
done	5013
2	3679
1	1063
0	389

prune1.4s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 20.0b

localize67.0ms

Local error

Found 4 expressions with local error:

7.2b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (- U) 1 ( U* 1)))
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))) ( (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (- U) 1 ( U* 1))))))) 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))) ( (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (- U) 1 ( U* 1))))))) 2.0)))

rewrite401.0ms

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`
12×	`distribute-rgt-in` `distribute-lft-in`
10×	`pow-to-exp` `div-exp` `associate-*r/`
9×	`associate-r`
5×	`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` `fma-udef`
1×	`pow1/2` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 131

Calls

4 calls:

146.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (- U) 1 ( U* 1)))
85.0ms	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (+ (* (pow (/ l Om) (/ 2.0 2)) (* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U))) ( (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (- U) 1 ( U* 1))))))) 2.0))
68.0ms	(* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U*))
91.0ms	(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))) ( (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (- U) 1 ( U* 1))))))) 2.0)))

series16.5s

Counts

4 → 12

Calls

4 calls:

851.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (- U) 1 ( U* 1)))
3.8s	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (+ (* (pow (/ l Om) (/ 2.0 2)) (* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U))) ( (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (- U) 1 ( U* 1))))))) 2.0))
437.0ms	(* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U*))
11.5s	(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))) ( (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (- U) 1 ( U* 1))))))) 2.0)))

simplify2.0s

Counts

143 → 143

Iterations

Iter	Nodes
done	5001
2	3827
1	1049
0	361

prune931.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 19.5b

localize121.0ms

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))) ( (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (- U) 1 ( U* 1))))))) 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))) ( (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (- U) 1 ( U* 1))))))) 2.0)))

rewrite201.0ms

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:

37.0ms	(* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U*))
38.0ms	(* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U*))
60.0ms	(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))) ( (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (- U) 1 ( U* 1))))))) 2.0)))
61.0ms	(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))) ( (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (- U) 1 ( U* 1))))))) 2.0)))

series16.8s

Counts

4 → 12

Calls

4 calls:

411.0ms	(* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U*))
406.0ms	(* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U*))
7.9s	(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))) ( (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (- U) 1 ( U* 1))))))) 2.0)))
8.1s	(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))) ( (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (- U) 1 ( U* 1))))))) 2.0)))

simplify1.6s

Counts

142 → 142

Iterations

Iter	Nodes
done	5000
2	2226
1	670
0	241

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 19.5b

regimes886.0ms

Accuracy

-11.2% (11.5b remaining)

Error of 31.5b against oracle of 20.0b and baseline of 30.3b

bsearch589.0ms

Steps

Iters	Range		Point
3	2.7173325175205944e+109	3.3676137672993945e+109	3.2456860329658693e+109
8	4.627248042166408e-59	1.2062433354830887e-56	1.1902700963782319e-56
8	-2.0595590106923437e-147	-3.2396894233383667e-150	-1.9912237249324922e-147
6	-2.3225334145429813e-95	-1.6951765036931078e-96	-1.928586768576105e-95
7	-25664.776140390222	-113.2543634187002	-115.2035769670584

simplify25.0ms

Iterations

Iter	Nodes
done	104
1	104
0	79

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.8s	14839×	body	80	nan
1.5s	9163×	body	80	valid