Details

sample125.0ms

Algorithm

intervals

Results

31.0ms	252×	body	80	nan
28.0ms	117×	body	160	valid
16.0ms	139×	body	80	valid

simplify6.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	2725
5	723
4	243
3	97
2	49
1	29
0	16

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.7b

localize71.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.3b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.5b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.8b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite315.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
65×	`times-frac`
51×	`*-un-lft-identity`
37×	`add-cube-cbrt`
30×	`sqrt-prod`
28×	`difference-of-squares`
27×	`unpow-prod-down`
9×	`add-exp-log`
8×	`associate-/l*` `sqr-pow`
7×	`distribute-lft-out--`
6×	`pow1` `add-cbrt-cube`
4×	`associate-/r/` `insert-posit16` `add-log-exp`
3×	`pow-unpow` `associate-/r*` `div-inv`
2×	`rem-sqrt-square` `flip3-+` `div-exp` `pow-exp` `flip-+` `associate-/l/`
1×	`pow-to-exp` `cbrt-undiv` `asin-acos` `clear-num` `pow-pow` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `sqrt-div` `div-sub` `flip--`

Counts

4 → 134

Calls

4 calls:

18.0ms	(pow (/ Om Omc) 2.0)
141.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
128.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series2.4s

Counts

4 → 12

Calls

4 calls:

181.0ms	(pow (/ Om Omc) 2.0)
903.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
109.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
1.2s	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify4.0s

Counts

146 → 146

Iterations

Iter	Nodes
done	5000
2	1760
1	727
0	312

prune2.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.6b

localize121.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.3b	(/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))
0.5b	(asin (sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))))
8.8b	(sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `times-frac`
16×	`*-un-lft-identity` `associate-/r/` `add-cube-cbrt` `sqrt-prod`
13×	`unpow-prod-down`
12×	`flip3-+` `add-exp-log` `flip-+`
9×	`add-cbrt-cube`
8×	`frac-times`
6×	`pow1`
4×	`associate-l/` `associate-r/` `insert-posit16` `associate-/l*` `add-log-exp`
3×	`pow-unpow` `div-exp` `div-inv` `difference-of-squares`
2×	`cbrt-undiv` `pow-exp` `associate-/l/`
1×	`pow-to-exp` `rem-sqrt-square` `asin-acos` `clear-num` `associate-/r*` `pow-pow` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `sqrt-div` `div-sub` `prod-exp` `cbrt-unprod` `flip--` `sqr-pow`

Counts

4 → 101

Calls

4 calls:

9.0ms	(pow (/ Om Omc) 2.0)
93.0ms	(/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))
3.0ms	(asin (sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))))
65.0ms	(sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))

series5.2s

Counts

4 → 12

Calls

4 calls:

180.0ms	(pow (/ Om Omc) 2.0)
2.2s	(/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))
114.0ms	(asin (sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))))
2.7s	(sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))

simplify6.7s

Counts

113 → 113

Iterations

Iter	Nodes
done	5014
2	3304
1	873
0	303

prune2.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.6b

localize157.0ms

Local error

Found 4 expressions with local error:

8.9b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.9b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
19.9b	(sqrt (pow (/ Om Omc) 2.0))
19.9b	(sqrt (pow (/ Om Omc) 2.0))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

40×	`sqrt-prod`
32×	`add-sqr-sqrt`
30×	`unpow-prod-down`
22×	`*-un-lft-identity` `add-cube-cbrt`
20×	`times-frac`
10×	`rem-sqrt-square`
6×	`pow1`
4×	`sqrt-pow1` `add-cbrt-cube` `pow1/2` `sqrt-div` `add-exp-log` `insert-posit16` `add-log-exp` `sqr-pow`
2×	`flip3-+` `flip-+` `div-inv`

Counts

4 → 94

Calls

4 calls:

15.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
22.0ms	(sqrt (pow (/ Om Omc) 2.0))
14.0ms	(sqrt (pow (/ Om Omc) 2.0))

series3.3s

Counts

4 → 12

Calls

4 calls:

496.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
506.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
1.1s	(sqrt (pow (/ Om Omc) 2.0))
1.2s	(sqrt (pow (/ Om Omc) 2.0))

simplify7.0s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
3	2549
2	860
1	368
0	177

prune2.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 9.6b

localize220.0ms

Local error

Found 4 expressions with local error:

15.3b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.3b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
19.9b	(sqrt (pow (/ Om Omc) 2.0))
19.9b	(sqrt (pow (/ Om Omc) 2.0))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

34×	`sqrt-prod`
30×	`add-sqr-sqrt` `unpow-prod-down`
22×	`*-un-lft-identity` `add-cube-cbrt`
20×	`times-frac`
8×	`rem-sqrt-square`
6×	`cbrt-prod`
4×	`pow1` `cbrt-div` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp` `sqr-pow`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `flip-+` `div-inv`

Counts

4 → 90

Calls

4 calls:

9.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
28.0ms	(sqrt (pow (/ Om Omc) 2.0))
27.0ms	(sqrt (pow (/ Om Omc) 2.0))

series3.9s

Counts

4 → 12

Calls

4 calls:

697.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
733.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
1.2s	(sqrt (pow (/ Om Omc) 2.0))
1.2s	(sqrt (pow (/ Om Omc) 2.0))

simplify7.6s

Counts

102 → 102

Iterations

Iter	Nodes
done	5009
3	2861
2	897
1	376
0	179

prune2.1s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 9.6b

regimes4.5s

Accuracy

0% (0.1b remaining)

Error of 10.1b against oracle of 10.0b and baseline of 10.1b

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	24
1	24
0	20

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.1s	4176×	body	80	valid
1.0s	7980×	body	80	nan
901.0ms	3824×	body	160	valid