Details

sample161.0ms

Algorithm

intervals

Results

84.0ms	532×	body	80	nan
35.0ms	305×	body	80	valid

simplify2.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	3618
3	693
2	157
1	50
0	21

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.0b

localize40.0ms

Local error

Found 4 expressions with local error:

7.1b	(/ (* l l) Om)
8.0b	(* (* n (pow (/ l Om) 2)) (- U U*))
9.1b	(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
20.1b	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

rewrite328.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
30×	`prod-diff`
26×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`pow1`
24×	`add-cube-cbrt`
23×	`add-cbrt-cube`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
16×	`prod-exp`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`associate--l+` `cbrt-unprod`
8×	`associate-r` `frac-sub`
6×	`sub-neg` `sqrt-div`
4×	`expm1-log1p-u` `sqrt-pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `times-frac` `div-exp`
2×	`cbrt-undiv` `associate-l` `pow-exp` `*-commutative`
1×	`pow-to-exp` `clear-num` `frac-2neg` `pow1/2` `sqrt-prod` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 145

Calls

4 calls:

18.0ms	(/ (* l l) Om)
62.0ms	(* (* n (pow (/ l Om) 2)) (- U U*))
134.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
107.0ms	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

series2.2s

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (* l l) Om)
170.0ms	(* (* n (pow (/ l Om) 2)) (- U U*))
490.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
1.5s	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

simplify3.0s

Counts

157 → 157

Iterations

Iter	Nodes
done	5000
2	4706
1	1172
0	376

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 21.5b

localize59.0ms

Local error

Found 4 expressions with local error:

6.2b	(* n (pow (/ l Om) 2))
8.0b	(* (* n (pow (/ l Om) 2)) (- U U*))
9.1b	(* (* (* 2 n) U) (- (- t (* 2 (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)))) (* (* n (pow (/ l Om) 2)) (- U U*))))
20.1b	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

rewrite434.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
35×	`add-exp-log`
33×	`*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`prod-diff`
26×	`associate-r`
25×	`pow1`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
20×	`add-cbrt-cube`
19×	`prod-exp`
15×	`unpow-prod-down`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`times-frac` `associate--l+` `cbrt-unprod`
8×	`frac-sub`
6×	`sub-neg` `sqrt-div`
5×	`associate-l` `unswap-sqr`
4×	`expm1-log1p-u` `sqrt-pow1` `pow-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-to-exp` `div-exp` `unpow2` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 163

Calls

4 calls:

24.0ms	(* n (pow (/ l Om) 2))
62.0ms	(* (* n (pow (/ l Om) 2)) (- U U*))
211.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)))) (* (* n (pow (/ l Om) 2)) (- U U*))))
131.0ms	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

series2.7s

Counts

4 → 12

Calls

4 calls:

63.0ms	(* n (pow (/ l Om) 2))
161.0ms	(* (* n (pow (/ l Om) 2)) (- U U*))
696.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)))) (* (* n (pow (/ l Om) 2)) (- U U*))))
1.8s	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

simplify3.9s

Counts

175 → 175

Iterations

Iter	Nodes
done	5000
2	4395
1	1220
0	408

prune1.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 21.0b

localize60.0ms

Local error

Found 4 expressions with local error:

6.0b	(/ n (* (/ Om l) (/ Om l)))
8.0b	(* (/ n (* (/ Om l) (/ Om l))) (- U U*))
9.1b	(* (* (* 2 n) U) (- (- t (* 2 (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)))) (* (/ n (* (/ Om l) (/ Om l))) (- U U*))))
20.1b	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)))) (* (/ n (* (/ Om l) (/ Om l))) (- U U*)))))

rewrite432.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-cbrt-cube` `add-exp-log`
36×	`associate-*r/`
32×	`add-sqr-sqrt`
30×	`prod-diff`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
25×	`pow1`
22×	`flip3--` `flip--`
21×	`distribute-rgt-in` `distribute-lft-in`
20×	`prod-exp` `frac-sub` `cbrt-unprod`
18×	`cbrt-undiv` `div-exp`
13×	`pow-prod-down`
12×	`frac-times` `sqrt-div`
11×	`associate-l`
10×	`associate--l+`
8×	`associate-r`
7×	`times-frac` `associate-*l/`
6×	`sub-neg` `associate-/r/`
4×	`expm1-log1p-u` `sqrt-pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`*-commutative` `div-inv` `unswap-sqr`
1×	`clear-num` `associate-/r*` `frac-2neg` `pow1/2` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 185

Calls

4 calls:

23.0ms	(/ n (* (/ Om l) (/ Om l)))
68.0ms	(* (/ n (* (/ Om l) (/ Om l))) (- U U*))
194.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)))) (* (/ n (* (/ Om l) (/ Om l))) (- U U*))))
133.0ms	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)))) (* (/ n (* (/ Om l) (/ Om l))) (- U U*)))))

series2.9s

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ n (* (/ Om l) (/ Om l)))
166.0ms	(* (/ n (* (/ Om l) (/ Om l))) (- U U*))
601.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)))) (* (/ n (* (/ Om l) (/ Om l))) (- U U*))))
2.0s	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)))) (* (/ n (* (/ Om l) (/ Om l))) (- U U*)))))

simplify2.1s

Counts

197 → 197

Iterations

Iter	Nodes
done	5001
1	1368
0	447

prune1.8s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 20.3b

localize102.0ms

Local error

Found 4 expressions with local error:

6.2b	(* (* 2 n) (- (fma -2 (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) (* (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) 2)) (* (/ (- U U*) (/ Om l)) (/ n (/ Om l)))))
9.4b	(* U (* (* 2 n) (+ t (* (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) -2))))
10.1b	(fma -2 (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) (* (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) 2))
20.1b	(sqrt (+ (* U (* (* 2 n) (+ t (* (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) -2)))) (* U (* (* 2 n) (- (fma -2 (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) (* (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) 2)) (* (/ (- U U*) (/ Om l)) (/ n (/ Om l))))))))

rewrite273.0ms

Algorithm

rewrite-expression-head

Rules

22×	`associate-*r/`
19×	`pow1`
18×	`add-cbrt-cube` `add-exp-log`
10×	`distribute-rgt-in` `add-sqr-sqrt` `distribute-lft-in`
9×	`*-un-lft-identity` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
6×	`sqrt-div` `prod-diff`
4×	`expm1-log1p-u` `flip3-+` `associate-r` `associate-l` `frac-add` `sqrt-prod` `flip-+` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `fma-udef` `flip--`
2×	`sub-neg` `associate--l+` `*-commutative`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `distribute-lft-out`

Counts

4 → 99

Calls

4 calls:

47.0ms	(* (* 2 n) (- (fma -2 (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) (* (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) 2)) (* (/ (- U U*) (/ Om l)) (/ n (/ Om l)))))
79.0ms	(* U (* (* 2 n) (+ t (* (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) -2))))
0.0ms	(fma -2 (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) (* (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) 2))
141.0ms	(sqrt (+ (* U (* (* 2 n) (+ t (* (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) -2)))) (* U (* (* 2 n) (- (fma -2 (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) (* (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) 2)) (* (/ (- U U*) (/ Om l)) (/ n (/ Om l))))))))

series11.2s

Counts

4 → 12

Calls

4 calls:

402.0ms	(* (* 2 n) (- (fma -2 (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) (* (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) 2)) (* (/ (- U U*) (/ Om l)) (/ n (/ Om l)))))
246.0ms	(* U (* (* 2 n) (+ t (* (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) -2))))
99.0ms	(fma -2 (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) (* (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) 2))
10.5s	(sqrt (+ (* U (* (* 2 n) (+ t (* (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) -2)))) (* U (* (* 2 n) (- (fma -2 (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) (* (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) 2)) (* (/ (- U U*) (/ Om l)) (/ n (/ Om l))))))))

simplify3.4s

Counts

111 → 111

Iterations

Iter	Nodes
done	5000
2	4066
1	884
0	267

prune1.2s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 18.1b

regimes1.8s

Accuracy

23% (10.3b remaining)

Error of 27.5b against oracle of 17.2b and baseline of 30.6b

bsearch239.0ms

Steps

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

simplify24.0ms

Iterations

Iter	Nodes
done	52
1	52
0	43

end0.0ms

sample5.7s

Algorithm

intervals

Results

3.2s	15197×	body	80	nan
1.5s	9217×	body	80	valid