Details

sample219.0ms

Algorithm

intervals

Results

84.0ms	532×	body	80	nan
28.0ms	305×	body	80	valid

simplify6.6s

Counts

1 → 1

Iterations

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

prune98.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.6b

localize126.0ms

Local error

Found 4 expressions with local error:

6.2b	(* n (pow (/ l Om) 2.0))
7.3b	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0))
8.0b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
20.1b	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0)))

rewrite584.0ms

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` `insert-posit16` `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 → 133

Calls

4 calls:

68.0ms	(* n (pow (/ l Om) 2.0))
224.0ms	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0))
80.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
199.0ms	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0)))

series28.4s

Counts

4 → 12

Calls

4 calls:

633.0ms	(* n (pow (/ l Om) 2.0))
3.3s	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0))
1.1s	(* (* n (pow (/ l Om) 2.0)) (- U U*))
23.3s	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0)))

simplify6.0s

Counts

145 → 145

Iterations

Iter	Nodes
done	5005
2	3310
1	978
0	357

prune2.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 22.6b

localize130.0ms

Local error

Found 4 expressions with local error:

4.1b	(fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
7.3b	(* 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))
8.0b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
20.1b	(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)))

rewrite719.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-exp-log`
63×	`prod-exp`
25×	`pow1`
22×	`add-cbrt-cube`
20×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`prod-diff` `pow-exp` `add-cube-cbrt`
13×	`pow-prod-down`
12×	`cbrt-unprod`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`associate-*r/`
9×	`pow-to-exp` `div-exp`
6×	`associate-r`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-l` `associate-*l/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `flip--`
2×	`sub-neg` `sqrt-div` `*-commutative`
1×	`pow1/2` `sqrt-prod` `fma-udef` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 121

Calls

4 calls:

2.0ms	(fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
150.0ms	(* 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))
345.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
209.0ms	(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)))

series25.8s

Counts

4 → 12

Calls

4 calls:

660.0ms	(fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
2.7s	(* 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))
907.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
21.5s	(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)))

simplify4.1s

Counts

133 → 133

Iterations

Iter	Nodes
done	5004
2	3584
1	954
0	335

prune1.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 21.9b

localize78.0ms

Local error

Found 4 expressions with local error:

4.1b	(fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))
4.8b	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
7.3b	(* 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))
20.1b	(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)))

rewrite295.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
23×	`pow1`
21×	`add-exp-log`
20×	`associate-l`
18×	`prod-diff`
15×	`unpow-prod-down` `add-cbrt-cube`
12×	`pow-prod-down`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`times-frac` `prod-exp` `associate-*r/`
7×	`cbrt-unprod`
6×	`associate-r`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-*l/` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`flip3--` `flip--`
2×	`sub-neg` `sqrt-div` `pow-exp` `*-commutative` `sqr-pow`
1×	`pow-to-exp` `pow1/2` `div-exp` `sqrt-prod` `fma-udef` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 121

Calls

4 calls:

1.0ms	(fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))
60.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
117.0ms	(* 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))
108.0ms	(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)))

series18.4s

Counts

4 → 12

Calls

4 calls:

612.0ms	(fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))
645.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
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))
15.0s	(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)))

simplify3.3s

Counts

133 → 133

Iterations

Iter	Nodes
done	5008
2	3167
1	899
0	354

prune1.7s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 21.1b

localize171.0ms

Local error

Found 4 expressions with local error:

4.0b	(* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) (* (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2)) (- U U*)))))))
4.1b	(fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) (* (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2)) (- U U*)))))
7.3b	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) (* (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2)) (- U U*))))))) 2.0))
20.1b	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) (* (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2)) (- U U*))))))) 2.0)))

rewrite252.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1`
23×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`prod-diff`
15×	`add-cbrt-cube` `add-exp-log`
13×	`pow-prod-down`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`associate-*r/`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-*l/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `flip--`
2×	`sub-neg` `sqrt-div` `*-commutative`
1×	`pow1/2` `sqrt-prod` `fma-udef` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

31.0ms	(* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) (* (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2)) (- U U*)))))))
1.0ms	(fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) (* (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2)) (- U U*)))))
111.0ms	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) (* (pow (/ (cbrt l) (cbrt 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 (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) (* (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2)) (- U U*))))))) 2.0)))

series19.3s

Counts

4 → 12

Calls

4 calls:

1.6s	(* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) (* (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2)) (- U U*)))))))
619.0ms	(fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) (* (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2)) (- U U*)))))
2.1s	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) (* (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2)) (- U U*))))))) 2.0))
15.0s	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) (* (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2)) (- U U*))))))) 2.0)))

simplify3.3s

Counts

114 → 114

Iterations

Iter	Nodes
done	5006
2	2655
1	748
0	286

prune1.6s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 20.7b

regimes2.6s

Accuracy

30.3% (7.4b remaining)

Error of 27.3b against oracle of 19.9b and baseline of 30.6b

bsearch149.0ms

Steps

Iters	Range		Point
9	-1.8258581717670128e-306	1.8155718285527778e-305	-5.889660218949e-311

simplify24.0ms

Iterations

Iter	Nodes
done	61
1	61
0	44

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.8s	15197×	body	80	nan
1.2s	9217×	body	80	valid