Details

sample215.0ms

Algorithm

intervals

Results

75.0ms	287×	body	80	valid
37.0ms	382×	body	80	nan

simplify2.5s

Counts

1 → 1

Iterations

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

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.9b

localize54.0ms

Local error

Found 4 expressions with local error:

5.2b	(fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t))
7.4b	(* n (pow (/ l Om) 2.0))
10.0b	(* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t)))
19.9b	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t))))

rewrite149.0ms

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)) (fma (* (/ l Om) l) (- 2.0) t))
24.0ms	(* n (pow (/ l Om) 2.0))
53.0ms	(* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t)))
64.0ms	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t))))

series8.4s

Counts

4 → 12

Calls

4 calls:

1.6s	(fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t))
234.0ms	(* n (pow (/ l Om) 2.0))
2.0s	(* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t)))
4.6s	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t))))

simplify1.4s

Counts

101 → 101

Iterations

Iter	Nodes
done	5000
2	2103
1	442
0	187

prune965.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 23.4b

localize68.0ms

Local error

Found 4 expressions with local error:

3.4b	(* n (pow (/ l Om) (/ 2.0 2)))
5.2b	(fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t))
10.0b	(* (* (* 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)))
19.9b	(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))))

rewrite138.0ms

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:

29.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
1.0ms	(fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t))
55.0ms	(* (* (* 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)))
51.0ms	(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))))

series8.9s

Counts

4 → 12

Calls

4 calls:

238.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
1.7s	(fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t))
2.2s	(* (* (* 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)))
4.8s	(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	5000
2	2212
1	466
0	194

prune965.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 22.7b

localize75.0ms

Local error

Found 4 expressions with local error:

19.9b	(sqrt (* (* (cbrt (* (* 2.0 (* n U)) (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma (/ l Om) (* l (- 2.0)) t)))) (cbrt (* (* 2.0 (* n U)) (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma (/ l Om) (* l (- 2.0)) t))))) (cbrt (* (* 2.0 (* n U)) (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma (/ l Om) (* l (- 2.0)) t))))))
21.4b	(cbrt (* (* 2.0 (* n U)) (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma (/ l Om) (* l (- 2.0)) t))))
21.4b	(cbrt (* (* 2.0 (* n U)) (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma (/ l Om) (* l (- 2.0)) t))))
21.4b	(cbrt (* (* 2.0 (* n U)) (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma (/ l Om) (* l (- 2.0)) t))))

rewrite316.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1`
15×	`sqrt-pow1`
12×	`pow1/3`
9×	`pow-prod-up`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 59

Calls

4 calls:

129.0ms	(sqrt (* (* (cbrt (* (* 2.0 (* n U)) (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma (/ l Om) (* l (- 2.0)) t)))) (cbrt (* (* 2.0 (* n U)) (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma (/ l Om) (* l (- 2.0)) t))))) (cbrt (* (* 2.0 (* n U)) (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma (/ l Om) (* l (- 2.0)) t))))))
62.0ms	(cbrt (* (* 2.0 (* n U)) (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma (/ l Om) (* l (- 2.0)) t))))
56.0ms	(cbrt (* (* 2.0 (* n U)) (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma (/ l Om) (* l (- 2.0)) t))))
66.0ms	(cbrt (* (* 2.0 (* n U)) (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma (/ l Om) (* l (- 2.0)) t))))

series10.0s

Counts

4 → 12

Calls

4 calls:

6.0s	(sqrt (* (* (cbrt (* (* 2.0 (* n U)) (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma (/ l Om) (* l (- 2.0)) t)))) (cbrt (* (* 2.0 (* n U)) (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma (/ l Om) (* l (- 2.0)) t))))) (cbrt (* (* 2.0 (* n U)) (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma (/ l Om) (* l (- 2.0)) t))))))
1.2s	(cbrt (* (* 2.0 (* n U)) (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma (/ l Om) (* l (- 2.0)) t))))
1.4s	(cbrt (* (* 2.0 (* n U)) (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma (/ l Om) (* l (- 2.0)) t))))
1.4s	(cbrt (* (* 2.0 (* n U)) (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma (/ l Om) (* l (- 2.0)) t))))

simplify431.0ms

Counts

71 → 71

Iterations

Iter	Nodes
done	5001
2	1149
1	373
0	161

prune612.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 22.7b

localize39.0ms

Local error

Found 4 expressions with local error:

5.2b	(fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma (/ l Om) (* l (- 2.0)) t))
7.4b	(* (pow (/ l Om) (* 2 (/ 2.0 2))) n)
10.0b	(* (* 2.0 (* n U)) (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma (/ l Om) (* l (- 2.0)) t)))
21.4b	(cbrt (* (* 2.0 (* n U)) (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma (/ l Om) (* l (- 2.0)) t))))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

0.0ms	(fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma (/ l Om) (* l (- 2.0)) t))
23.0ms	(* (pow (/ l Om) (* 2 (/ 2.0 2))) n)
35.0ms	(* (* 2.0 (* n U)) (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma (/ l Om) (* l (- 2.0)) t)))
36.0ms	(cbrt (* (* 2.0 (* n U)) (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma (/ l Om) (* l (- 2.0)) t))))

series3.0s

Counts

4 → 12

Calls

4 calls:

593.0ms	(fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma (/ l Om) (* l (- 2.0)) t))
260.0ms	(* (pow (/ l Om) (* 2 (/ 2.0 2))) n)
1.1s	(* (* 2.0 (* n U)) (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma (/ l Om) (* l (- 2.0)) t)))
1.0s	(cbrt (* (* 2.0 (* n U)) (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma (/ l Om) (* l (- 2.0)) t))))

simplify1.1s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
2	2947
1	624
0	251

prune599.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 19.6b

regimes898.0ms

Accuracy

-13.5% (11.7b remaining)

Error of 28.7b against oracle of 17.0b and baseline of 27.3b

bsearch730.0ms

Steps

Iters	Range		Point
6	1.583250720483607e-07	8.0506939258486e-07	7.962768658598781e-07
8	3.856101644728124e-108	9.568801019347765e-104	1.407519843109884e-104
10	1.0581842782042033e-203	4.1393533541678516e-187	3.3349011025921906e-187
4	2.4319967872361378e-273	4.711546405212307e-273	2.5981494862601002e-273
4	-1.556985101396922e-259	-8.919580631633139e-260	-9.422947167583052e-260

simplify31.0ms

Iterations

Iter	Nodes
done	95
5	95
4	93
3	87
2	83
1	75
0	60

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.0s	14653×	body	80	nan
1.0s	9155×	body	80	valid