Details

sample942.0ms

Algorithm

intervals

Results

706.0ms	503×	body	80	nan
47.0ms	279×	body	80	valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	4135
3	665
2	154
1	49
0	21

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.5b

localize59.0ms

Local error

Found 4 expressions with local error:

3.2b	(fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t))
7.0b	(* n (pow (/ l Om) 2.0))
10.3b	(* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t)))
19.2b	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t))))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1`
22×	`add-sqr-sqrt`
21×	`add-exp-log`
20×	`associate-r`
15×	`unpow-prod-down` `add-cbrt-cube`
14×	`*-un-lft-identity` `add-cube-cbrt`
12×	`pow-prod-down`
10×	`times-frac` `prod-exp`
7×	`cbrt-unprod`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-l` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`fma-udef`
2×	`pow-exp` `*-commutative` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow1/2` `div-exp` `sqrt-prod` `div-inv`

Counts

4 → 89

Calls

4 calls:

1.0ms	(fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t))
43.0ms	(* n (pow (/ l Om) 2.0))
83.0ms	(* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t)))
71.0ms	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t))))

series8.9s

Counts

4 → 12

Calls

4 calls:

1.9s	(fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t))
237.0ms	(* n (pow (/ l Om) 2.0))
1.9s	(* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t)))
4.9s	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t))))

simplify1.3s

Counts

101 → 101

Iterations

Iter	Nodes
done	5000
2	2103
1	442
0	187

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 21.6b

localize44.0ms

Local error

Found 4 expressions with local error:

3.2b	(fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t))
3.7b	(* n (pow (/ l Om) (/ 2.0 2)))
10.3b	(* (* (* 2.0 n) U) (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t)))
19.2b	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t))))

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1`
22×	`add-sqr-sqrt`
21×	`add-exp-log`
20×	`associate-r`
15×	`unpow-prod-down` `add-cbrt-cube`
14×	`*-un-lft-identity` `add-cube-cbrt`
12×	`pow-prod-down`
10×	`times-frac` `prod-exp`
7×	`cbrt-unprod`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-l` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`fma-udef`
2×	`pow-exp` `*-commutative` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow1/2` `div-exp` `sqrt-prod` `div-inv`

Counts

4 → 89

Calls

4 calls:

0.0ms	(fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t))
38.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
83.0ms	(* (* (* 2.0 n) U) (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t)))
73.0ms	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t))))

series8.8s

Counts

4 → 12

Calls

4 calls:

1.8s	(fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t))
202.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
1.9s	(* (* (* 2.0 n) U) (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t)))
4.9s	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t))))

simplify1.2s

Counts

101 → 101

Iterations

Iter	Nodes
done	5002
2	2211
1	463
0	194

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 20.4b

localize55.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (* (cbrt n) (cbrt n)) (* (pow (/ l Om) (/ 2.0 2)) (cbrt n)))
3.2b	(fma (- U* U) (* (* (* (cbrt n) (cbrt n)) (* (pow (/ l Om) (/ 2.0 2)) (cbrt n))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t))
10.3b	(* (* (* 2.0 n) U) (fma (- U* U) (* (* (* (cbrt n) (cbrt n)) (* (pow (/ l Om) (/ 2.0 2)) (cbrt n))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t)))
19.2b	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* (* (* (cbrt n) (cbrt n)) (* (pow (/ l Om) (/ 2.0 2)) (cbrt n))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t))))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-exp-log`
29×	`prod-exp`
28×	`pow1`
19×	`add-cbrt-cube`
15×	`pow-prod-down`
14×	`cbrt-unprod`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-r` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef`
2×	`pow-to-exp` `div-exp` `associate-l` `*-commutative`
1×	`distribute-rgt-in` `distribute-lft-in` `pow1/2` `sqrt-prod`

Counts

4 → 78

Calls

4 calls:

76.0ms	(* (* (cbrt n) (cbrt n)) (* (pow (/ l Om) (/ 2.0 2)) (cbrt n)))
0.0ms	(fma (- U* U) (* (* (* (cbrt n) (cbrt n)) (* (pow (/ l Om) (/ 2.0 2)) (cbrt n))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t))
60.0ms	(* (* (* 2.0 n) U) (fma (- U* U) (* (* (* (cbrt n) (cbrt n)) (* (pow (/ l Om) (/ 2.0 2)) (cbrt n))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t)))
47.0ms	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* (* (* (cbrt n) (cbrt n)) (* (pow (/ l Om) (/ 2.0 2)) (cbrt n))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t))))

series9.0s

Counts

4 → 12

Calls

4 calls:

211.0ms	(* (* (cbrt n) (cbrt n)) (* (pow (/ l Om) (/ 2.0 2)) (cbrt n)))
1.6s	(fma (- U* U) (* (* (* (cbrt n) (cbrt n)) (* (pow (/ l Om) (/ 2.0 2)) (cbrt n))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t))
2.2s	(* (* (* 2.0 n) U) (fma (- U* U) (* (* (* (cbrt n) (cbrt n)) (* (pow (/ l Om) (/ 2.0 2)) (cbrt n))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t)))
5.0s	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* (* (* (cbrt n) (cbrt n)) (* (pow (/ l Om) (/ 2.0 2)) (cbrt n))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t))))

simplify929.0ms

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
2	2095
1	418
0	158

prune642.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 19.5b

localize133.0ms

Local error

Found 4 expressions with local error:

12.8b	(cbrt (fma (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U)) (fma l (* (/ l Om) (- 2.0)) t)))
12.8b	(cbrt (fma (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U)) (fma l (* (/ l Om) (- 2.0)) t)))
12.8b	(cbrt (fma (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U)) (fma l (* (/ l Om) (- 2.0)) t)))
19.2b	(sqrt (* (* (* 2.0 n) U) (* (* (cbrt (fma (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U)) (fma l (* (/ l Om) (- 2.0)) t))) (cbrt (fma (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U)) (fma l (* (/ l Om) (- 2.0)) t)))) (cbrt (fma (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U)) (fma l (* (/ l Om) (- 2.0)) t))))))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

41×	`pow1`
27×	`pow-prod-down`
10×	`sqrt-pow1`
9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`pow1/2` `sqrt-prod`

Counts

4 → 60

Calls

4 calls:

1.0ms	(cbrt (fma (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U)) (fma l (* (/ l Om) (- 2.0)) t)))
2.0ms	(cbrt (fma (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U)) (fma l (* (/ l Om) (- 2.0)) t)))
3.0ms	(cbrt (fma (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U)) (fma l (* (/ l Om) (- 2.0)) t)))
104.0ms	(sqrt (* (* (* 2.0 n) U) (* (* (cbrt (fma (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U)) (fma l (* (/ l Om) (- 2.0)) t))) (cbrt (fma (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U)) (fma l (* (/ l Om) (- 2.0)) t)))) (cbrt (fma (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U)) (fma l (* (/ l Om) (- 2.0)) t))))))

series13.6s

Counts

4 → 12

Calls

4 calls:

2.5s	(cbrt (fma (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U)) (fma l (* (/ l Om) (- 2.0)) t)))
2.5s	(cbrt (fma (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U)) (fma l (* (/ l Om) (- 2.0)) t)))
2.6s	(cbrt (fma (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U)) (fma l (* (/ l Om) (- 2.0)) t)))
6.0s	(sqrt (* (* (* 2.0 n) U) (* (* (cbrt (fma (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U)) (fma l (* (/ l Om) (- 2.0)) t))) (cbrt (fma (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U)) (fma l (* (/ l Om) (- 2.0)) t)))) (cbrt (fma (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U)) (fma l (* (/ l Om) (- 2.0)) t))))))

simplify1.7s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
2	2774
1	1177
0	419

prune1.3s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 19.5b

regimes912.0ms

Accuracy

14.6% (9.4b remaining)

Error of 29.3b against oracle of 19.9b and baseline of 31.0b

bsearch631.0ms

Steps

Iters	Range		Point
9	5.988445812769684e+186	2.9041593993579594e+192	1.6282403628561025e+187
8	1.3892010829651123e+134	2.5545456556010434e+138	3.826937509623075e+134
9	4.96812581095375e+78	9.45571118856315e+83	1.055275531112388e+79
4	3.0623368313598077e-24	4.622330714825075e-24	4.114286479798258e-24
5	-5.557305086746166e-88	-1.6401870951494956e-88	-4.797165734624696e-88

simplify15.0ms

Iterations

Iter	Nodes
done	103
3	103
2	100
1	96
0	68

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.8s	14889×	body	80	nan
1.3s	9174×	body	80	valid