Details

sample202.0ms

Algorithm

intervals

Results

74.0ms	129×	body	160	valid
60.0ms	267×	body	80	nan
29.0ms	127×	body	80	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2050
6	2050
5	1097
4	396
3	153
2	63
1	32
0	16

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.7b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (* (/ t l) 2) (/ t l) 1)
0.2b	(* (/ Om Omc) (/ Om Omc))
0.6b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))))
7.0b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
56×	`times-frac`
44×	`*-un-lft-identity`
41×	`add-cube-cbrt`
19×	`sqrt-prod`
16×	`add-cbrt-cube` `add-exp-log`
13×	`swap-sqr` `associate-r` `associate-l`
12×	`pow1`
6×	`difference-of-squares`
5×	`div-inv`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `frac-times` `asin-acos` `sqrt-pow1` `pow-plus` `pow1/2` `sqrt-div` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `fma-udef`

Counts

4 → 126

Calls

4 calls:

0.0ms	(fma (* (/ t l) 2) (/ t l) 1)
19.0ms	(* (/ Om Omc) (/ Om Omc))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))))
10.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(fma (* (/ t l) 2) (/ t l) 1)
35.0ms	(* (/ Om Omc) (/ Om Omc))
18.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))))
189.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))

simplify1.5s

Counts

138 → 138

Iterations

Iter	Nodes
done	2023
3	2023
2	1697
1	592
0	237

prune1.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.6b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.6b	(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) 2) (/ t l) 1))))
4.0b	(log (exp (* (/ Om Omc) (/ Om Omc))))
7.0b	(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) 2) (/ t l) 1)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
62×	`times-frac`
56×	`*-un-lft-identity`
44×	`add-cube-cbrt`
25×	`sqrt-prod`
16×	`pow1` `add-cbrt-cube` `add-exp-log`
13×	`swap-sqr` `associate-r` `associate-l`
6×	`log-pow` `distribute-lft-out--` `difference-of-squares`
5×	`div-inv` `add-log-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`log-prod`
2×	`rem-sqrt-square`
1×	`pow2` `frac-times` `asin-acos` `exp-prod` `sqrt-pow1` `pow-plus` `exp-to-pow` `pow1/2` `sqrt-div` `rem-log-exp` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 138

Calls

4 calls:

15.0ms	(* (/ Om Omc) (/ Om Omc))
1.0ms	(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) 2) (/ t l) 1))))
8.0ms	(log (exp (* (/ Om Omc) (/ Om Omc))))
16.0ms	(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) 2) (/ t l) 1)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (/ Om Omc) (/ Om Omc))
16.0ms	(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) 2) (/ t l) 1))))
48.0ms	(log (exp (* (/ Om Omc) (/ Om Omc))))
184.0ms	(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) 2) (/ t l) 1)))

simplify1.2s

Counts

150 → 150

Iterations

Iter	Nodes
done	2000
3	2000
2	1579
1	575
0	244

prune2.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.6b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (/ t l) (* 2 (/ t l)) 1)
0.2b	(* (/ Om Omc) (/ Om Omc))
0.6b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (/ t l) (* 2 (/ t l)) 1))))
7.0b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (/ t l) (* 2 (/ t l)) 1)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
56×	`times-frac`
44×	`*-un-lft-identity`
41×	`add-cube-cbrt`
19×	`sqrt-prod`
16×	`add-cbrt-cube` `add-exp-log`
13×	`swap-sqr` `associate-r` `associate-l`
12×	`pow1`
6×	`difference-of-squares`
5×	`div-inv`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `frac-times` `asin-acos` `sqrt-pow1` `pow-plus` `pow1/2` `sqrt-div` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `fma-udef`

Counts

4 → 126

Calls

4 calls:

0.0ms	(fma (/ t l) (* 2 (/ t l)) 1)
18.0ms	(* (/ Om Omc) (/ Om Omc))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (/ t l) (* 2 (/ t l)) 1))))
7.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (/ t l) (* 2 (/ t l)) 1)))

series283.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(fma (/ t l) (* 2 (/ t l)) 1)
38.0ms	(* (/ Om Omc) (/ Om Omc))
16.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (/ t l) (* 2 (/ t l)) 1))))
169.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (/ t l) (* 2 (/ t l)) 1)))

simplify1.2s

Counts

138 → 138

Iterations

Iter	Nodes
done	2010
3	2010
2	1669
1	584
0	235

prune2.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.6b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.2b	(* (/ Om Omc) (/ Om Omc))
0.6b	(asin (* (sqrt (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (fma (/ t l) (* 2 (/ t l)) 1)))))
7.0b	(sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (fma (/ t l) (* 2 (/ t l)) 1)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-sqr-sqrt`
106×	`times-frac`
78×	`*-un-lft-identity`
75×	`add-cube-cbrt`
44×	`sqrt-prod`
28×	`add-cbrt-cube` `add-exp-log`
26×	`swap-sqr` `associate-r` `associate-l`
19×	`pow1`
9×	`div-inv`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`difference-of-squares`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square`
2×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`asin-acos` `sqrt-pow1` `pow1/2` `sqrt-div`

Counts

4 → 195

Calls

4 calls:

21.0ms	(* (/ Om Omc) (/ Om Omc))
30.0ms	(* (/ Om Omc) (/ Om Omc))
2.0ms	(asin (* (sqrt (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (fma (/ t l) (* 2 (/ t l)) 1)))))
10.0ms	(sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (fma (/ t l) (* 2 (/ t l)) 1)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (/ Om Omc) (/ Om Omc))
28.0ms	(* (/ Om Omc) (/ Om Omc))
11.0ms	(asin (* (sqrt (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (fma (/ t l) (* 2 (/ t l)) 1)))))
310.0ms	(sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (fma (/ t l) (* 2 (/ t l)) 1)))

simplify1.4s

Counts

207 → 207

Iterations

Iter	Nodes
done	2001
3	2001
2	1531
1	557
0	250

prune4.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.6b

regimes507.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	20
1	20
0	17

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.0s	8206×	body	80	nan
1.5s	3807×	body	160	valid
955.0ms	4193×	body	80	valid