Details

sample206.0ms

Algorithm

intervals

Results

80.0ms	126×	body	160	valid
65.0ms	306×	body	80	nan
29.0ms	130×	body	80	valid

simplify1.3s

Counts: 1 → 1

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize42.0ms

Local error

Found 4 expressions with local error:

11.3b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
0.6b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
0.3b	(* (/ Om Omc) (/ Om Omc))
0.2b	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-sqr-sqrt`
71×	`times-frac`
58×	`*-un-lft-identity`
51×	`add-cube-cbrt`
19×	`sqrt-prod`
18×	`add-cbrt-cube` `add-exp-log`
14×	`difference-of-squares`
13×	`swap-sqr` `associate-r` `associate-l`
12×	`pow1`
6×	`div-inv`
5×	`cbrt-undiv` `div-exp` `associate-/l*`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/r*`
2×	`rem-sqrt-square` `associate-/l/`
1×	`pow2` `frac-times` `asin-acos` `clear-num` `frac-2neg` `sqrt-pow1` `pow-plus` `flip3--` `pow1/2` `sqrt-div` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--`

Counts

4 → 156

Calls

4 calls:

Slowest

19.0ms	(* (/ Om Omc) (/ Om Omc))
19.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
8.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

series315.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

172.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
91.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
38.0ms	(* (/ Om Omc) (/ Om Omc))
14.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify772.0ms

Counts: 168 → 168

prune2.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 12.1b

localize37.0ms

Local error

Found 4 expressions with local error:

11.3b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
11.3b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
7.5b	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
7.5b	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

124×	`sqrt-prod`
68×	`add-sqr-sqrt`
64×	`times-frac`
54×	`*-un-lft-identity`
42×	`add-cube-cbrt`
24×	`difference-of-squares`
10×	`pow1` `rem-sqrt-square` `sqrt-pow1`
6×	`pow1/2` `sqrt-div`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

4 → 148

Calls

4 calls:

Slowest

11.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
8.0ms	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
8.0ms	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
5.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

series688.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

215.0ms	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
195.0ms	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
146.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
132.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

simplify794.0ms

Counts: 160 → 160

prune2.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 12.1b

localize54.0ms

Local error

Found 4 expressions with local error:

18.2b	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
18.2b	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
18.2b	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
11.3b	(sqrt (* (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

57×	`cbrt-prod`
45×	`times-frac`
40×	`add-sqr-sqrt` `*-un-lft-identity`
31×	`add-cube-cbrt`
24×	`pow1`
18×	`difference-of-squares`
15×	`cbrt-div` `sqrt-pow1`
12×	`pow1/3`
9×	`pow-prod-up`
7×	`sqrt-div`
6×	`pow-plus`
5×	`frac-times` `pow-prod-down` `associate-*l/`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-*r/` `pow-sqr` `div-inv`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 127

Calls

4 calls:

Slowest

36.0ms	(sqrt (* (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))))
3.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
3.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
3.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

series855.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

261.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
233.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
227.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
134.0ms	(sqrt (* (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))))

simplify841.0ms

Counts: 139 → 139

prune2.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 12.1b

localize89.0ms

Local error

Found 4 expressions with local error:

18.2b	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
18.2b	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
18.2b	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
11.9b	(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

57×	`cbrt-prod`
45×	`times-frac`
40×	`add-sqr-sqrt` `*-un-lft-identity`
31×	`add-cube-cbrt`
18×	`difference-of-squares`
12×	`pow1`
9×	`sqrt-pow1` `pow1/3`
7×	`cbrt-div`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-div` `div-inv`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `rem-sqrt-square` `pow-plus` `pow1/2` `associate-l/` `associate-r/` `sqrt-prod`

Counts

4 → 118

Calls

4 calls:

Slowest

12.0ms	(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))))
4.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
4.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
3.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

series977.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

268.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
262.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
225.0ms	(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))))
222.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

simplify805.0ms

Counts: 130 → 130

prune2.5s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 12.1b

regimes536.0ms

Accuracy

0% (0.0b remaining)

Error of 10.2b against oracle of 10.2b and baseline of 10.2b

bsearch3.0ms

end0.0ms

sample5.5s

Algorithm

intervals

Results

1.7s	7856×	body	80	nan
1.6s	3792×	body	160	valid
1.2s	4208×	body	80	valid